> **Comprehensive Reference for Mechanical Design, Power Transmission, and Machine Element Selection** --- ## Table of Contents ### PART I — PRIME MOVERS - **Chapter 1:** Electric Motors — Three-Phase - **Chapter 2:** Electric Motors — Gears, Motors & Geared Motor Units - **Chapter 3:** Electric Motors — Single-Phase Performance & Dimensions ### PART II — POWER TRANSMISSION: GEARS & GEARBOXES - **Chapter 4:** Worm Gearboxes & Geared Motor Units - **Chapter 5:** Couplings & Worm Gearbox Selection ### PART III — POWER TRANSMISSION: BELTS & CHAINS - **Chapter 6:** Chain Drives & Couplings - **Chapter 7:** Belt Drives — Power Ratings & Pulleys ### PART IV — SHAFTS, KEYS, BEARINGS & SEALS - **Chapter 8:** Shafts, Keys, Circlips, Seals & Rolled Steel Sections - **Chapter 9:** Rolling Element Bearings - **Chapter 10:** Journal Bearings, Belt Drives & Bearings Reference ### PART V — JOINTS, SPRINGS & MACHINE ELEMENTS - **Chapter 11:** Springs, Bolted Joints, Welded Joints, Power Screws & Machine Elements --- --- # PART I — PRIME MOVERS --- ## Chapter 1: Electric Motors — Three-Phase --- --- ### Overview This chapter covers the selection, specification, and application of **electric motors** used in mechanical design. It addresses both **three-phase** and **single-phase** motor types, focusing on enclosure protection ratings, mounting configurations, wiring connections, shaft load capacities, and combined load analysis. Understanding these parameters is essential for correctly specifying motors in industrial and commercial applications. --- ### Key Concepts - **Enclosure Protection (IP Ratings)** — Standardised codes indicating the degree of protection a motor enclosure provides against solid objects and water ingress - **Mounting Arrangements** — The physical orientation and method by which a motor is secured to equipment or a base structure - **Connection Diagrams** — Wiring schematics showing how motor terminals are connected for different configurations (e.g., star, delta, multi-speed) - **Maximum Shaft Loads** — The permissible radial and axial forces that can be applied to a motor shaft without causing premature bearing failure - **Combined Load Capacity** — The relationship between simultaneous radial and axial loading, where increasing one reduces the allowable proportion of the other - **Single-Phase Motor Types** — Different capacitor configurations used to achieve varying starting torque and running efficiency characteristics --- ### Detailed Notes #### Totally Enclosed Fan Cooled (TEFC) Three-Phase Motors - **Enclosure type**: Totally Enclosed Fan Cooled (TEFC) - **Protection rating**: Designed to achieve a high-level dust and water ingress protection rating - **Insulation class**: Class 'F' insulation standard - **Power range**: Typically available from fractional kilowatt ratings up to several hundred kilowatts - **Frame sizes**: Standardised frame designations enabling interchangeability between manufacturers #### Degrees of Protection (IP Rating System) - The **IP (Ingress Protection) code** uses two numerals to describe protection levels - **First numeral** — Protection against contact with live/moving parts and ingress of solid foreign bodies - **Second numeral** — Protection against water ingress ##### IP Rating Breakdown - **IP44** — Protected against solid objects greater than 1 mm and water splashed from any direction - **IP54** — Complete protection against contact with live or moving parts inside the enclosure; water splashed from any direction shall have no harmful effect - **IP55** — Protected against harmful dust deposits; protected against water jets projected by a nozzle from any direction - **IP56** — Dust cannot enter in sufficient quantity to interfere with operation; protected against heavy seas or powerful water jets - **IP65** — Complete protection against dust ingress; protected against water jets from any direction - **IP6X** — Dust-excluding, ignition-proof rating #### Mounting Arrangements - **Foot Mounting (Horizontal)** — Motor secured via feet on the base; most common arrangement - **Flange Mounting** — Motor attached via a flange on the drive end for direct coupling - **Face Mounting** — Motor secured via a face plate, typically for close-coupled applications - **Foot/Flange Combination** — Provides flexibility for both base-mounted and direct-coupled installations - **Foot/Face Combination** — Allows either foot or face mounting depending on the application - **Foot Mounting (Vertical)** — Used where vertical shaft orientation is required (e.g., pumps) - Standard designation codes (e.g., B3, B5, B14, V1, V3, V5, V6) identify the specific mounting configuration #### Connection Diagrams — Three-Phase Motors - **Star (Y) Connection** — Used for standard voltage applications; provides lower starting current - **Delta (Δ) Connection** — Used for lower voltage applications; provides higher starting torque - **Star-Delta Starting** — A switching method that starts in star (reduced voltage) then transitions to delta (full voltage) to limit inrush current - **Multi-Speed Motors (Dahlander Connection)** — Use tapped windings to achieve two operating speeds from a single winding - **Multi-Speed Motors (Separate Windings)** — Use two independent windings for two distinct operating speeds with greater flexibility #### Maximum Shaft Loads - Motor bearings are rated for specific **maximum radial** and **maximum axial** loads - Loads are specified per **frame size** and **number of poles** - As frame size increases, both radial and axial load capacities increase proportionally - Larger pole counts (lower speed motors) within the same frame generally have similar load ratings #### Combined Radial and Axial Load Capacity - When **both radial and axial loads** are applied simultaneously, neither can reach its individual maximum - The relationship follows a **curved reduction line** — as the proportion of one load type increases, the allowable proportion of the other decreases - **Smaller frame sizes** have steeper reduction curves (less tolerance for combined loading) - **Larger frame sizes** show more gradual curves (greater tolerance for combined loading) - The combined load chart is used to verify that the actual operating loads fall within the safe operating envelope #### Single-Phase Motor Designs - Manufactured to comply with relevant international standards - Standard enclosure provides high-level protection against dust and water ingress ##### Construction - Stator frames are typically die-cast with integral end-shields and flanges - **Bearings**: Ball-type bearings, fitted as standard and packed with grease for life ##### Insulation and Temperature Rise - **Insulation**: Class F rating as standard - **Temperature rise**: Class B temperature rise standard - Operates satisfactorily at ambient temperatures from approximately −30°C to +45°C - Rated for altitudes up to 1000 metres above sea level ##### Protection - **Thermal overloads**: Manual-reset type, fitted as standard - Located conveniently in the top-mounted terminal box - **Important**: Capacitor-type motors must not be run under no-load conditions (risk of capacitor or winding damage) ##### Single-Phase Motor Types - **(1) Permanent Capacitor (4APC)** - Suitable for fans, blowers, and centrifugal pumps - Starting torque: 30–50% of full load torque (depending on frame size) - Motor started by a permanently connected capacitor - **(2) Capacitor Start / Induction Run (4APJC)** - Suitable for industrial and agricultural applications requiring higher starting torque - Starting torque: 160–230% of full load torque (depending on frame size) - Uses a start capacitor with an auxiliary winding - Auxiliary winding disconnected by centrifugal switch after start-up - **(3) Capacitor Start / Capacitor Run (4APCC)** - Offers the highest starting performance, efficiency, and power factor - Uses both start and run capacitors permanently connected - Allows higher output within a given frame size ##### Mounting Arrangements (Single-Phase) - Standard: Foot mounting (B3) - Optional: "C" type face mounting (B14) at the drive end - Can be supplied with or without feet --- ### Tables #### IP Protection Rating Summary | IP Code | First Numeral (Solid Object Protection) | Second Numeral (Water Protection) | |---------|----------------------------------------|----------------------------------| | IP44 | Objects > 1 mm; wires and small foreign bodies | Water splashed from any direction | | IP54 | Complete contact protection | Water splashed — no harmful effect | | IP55 | Harmful dust deposits prevented | Water jets from any direction — no harmful effect | | IP56 | Dust cannot interfere with operation | Heavy seas / powerful water jets — no harmful quantity | | IP65 | Complete dust protection | Water jets from any direction — no harmful effect | | IP6X | Dust-excluding, ignition-proof | — | #### Maximum Shaft Loads (Selected Frame Sizes) | Frame–Poles | Max Radial Load (N) | Max Axial Load (N) | |-------------|---------------------|---------------------| | 63-2 | 185 | 120 | | 80-2 | 330 | 200 | | 100-2 | 650 | 390 | | 132-2 | 1350 | 800 | | 160-2 | 2250 | 1570 | | 200-2 | 4200 | 3000 | | 225-2 | 5200 | 3650 | | 250-2 | 6600 | 4600 | | 280-2 | 8400 | 5900 | #### Single-Phase Motor Type Comparison | Feature | Permanent Capacitor (4APC) | Capacitor Start / Induction Run (4APJC) | Capacitor Start / Capacitor Run (4APCC) | |---------|---------------------------|----------------------------------------|----------------------------------------| | **Starting Torque** | Low (30–50% FLT) | High (160–230% FLT) | High | | **Running Efficiency** | Moderate | Moderate | High | | **Power Factor** | Moderate | Moderate | High | | **Typical Applications** | Fans, blowers, centrifugal pumps | Industrial, agricultural, demanding start loads | High-performance applications requiring efficiency | | **Capacitor Arrangement** | Permanent run capacitor | Start capacitor + centrifugal switch | Start + run capacitors (both permanent) | | **No-Load Operation** | Not permitted | Not permitted | Not permitted | --- ### Mermaid Diagrams #### IP Rating Selection Flowchart ```mermaid flowchart TD A[Identify Operating Environment] --> B{Dust Exposure?} B -->|Minimal| C{Water Exposure?} B -->|Moderate - not harmful| D[IP5X First Numeral] B -->|Heavy - must exclude| E[IP6X First Numeral] C -->|Splashing only| F[IPX4 Second Numeral] C -->|Water jets| G[IPX5 Second Numeral] C -->|Heavy seas / powerful jets| H[IPX6 Second Numeral] D --> I[Combine First + Second Numeral] E --> I F --> I G --> I H --> I I --> J[Selected IP Rating] ``` #### Single-Phase Motor Type Selection ```mermaid flowchart TD A[Single-Phase Motor Required] --> B{Starting Torque Requirement?} B -->|Low: 30-50% FLT| C[Permanent Capacitor - 4APC] B -->|High: 160-230% FLT| D{Efficiency Priority?} D -->|Standard| E[Capacitor Start / Induction Run - 4APJC] D -->|High efficiency + power factor| F[Capacitor Start / Capacitor Run - 4APCC] C --> G[Fans, Blowers, Centrifugal Pumps] E --> H[Industrial, Agricultural, Demanding Starts] F --> I[High-Performance Applications] ``` #### Motor Mounting Decision Process ```mermaid flowchart TD A[Select Mounting Arrangement] --> B{Shaft Orientation?} B -->|Horizontal| C{Coupling Method?} B -->|Vertical| D[Vertical Foot Mount - V5/V6] C -->|Base mounted - belt/chain drive| E[Foot Mount - B3] C -->|Direct coupled - aligned| F{Space Constraint?} F -->|Standard| G[Flange Mount - B5] F -->|Compact / close-coupled| H[Face Mount - B14] C -->|Flexible - both options needed| I[Foot/Flange or Foot/Face Combo] ``` #### Combined Load Assessment Process ```mermaid flowchart TD A[Determine Applied Loads] --> B[Identify Frame Size and Pole Count] B --> C[Look Up Max Radial Load from Table] B --> D[Look Up Max Axial Load from Table] C --> E[Calculate Radial Load Proportion] D --> F[Calculate Axial Load Proportion] E --> G[Plot on Combined Load Chart] F --> G G --> H{Point Within Envelope?} H -->|Yes| I[Motor Selection Acceptable] H -->|No| J[Select Larger Frame Size and Re-check] ``` --- ### Key Terms Glossary - **TEFC (Totally Enclosed Fan Cooled)** — A motor enclosure type where an external fan provides cooling air over the motor casing, while the internal components are sealed from the environment - **IP Rating (Ingress Protection)** — A two-digit classification system indicating the level of protection an enclosure provides against solid objects (first digit) and water (second digit) - **Insulation Class** — A rating (e.g., Class B, Class F) defining the maximum temperature a motor's winding insulation can withstand continuously without degradation - **Frame Size** — A standardised dimensional designation ensuring physical interchangeability of motors from different manufacturers - **Radial Load** — A force applied perpendicular to the motor shaft axis, typically from belt tension, gear mesh forces, or coupled equipment weight - **Axial Load (Thrust Load)** — A force applied along the motor shaft axis, typically from fans, pumps, or helical gears - **Star (Y) Connection** — A three-phase winding configuration where one end of each winding is connected to a common neutral point; used for higher voltage operation - **Delta (Δ) Connection** — A three-phase winding configuration where windings are connected end-to-end in a closed loop; used for lower voltage operation - **Dahlander Connection** — A winding arrangement that allows a single set of windings to operate at two different speeds by reconfiguring the pole count - **Centrifugal Switch** — A speed-activated switch that disconnects the starting capacitor or auxiliary winding once the motor reaches a set percentage of operating speed - **FLT (Full Load Torque)** — The torque produced by a motor at its rated power and rated speed; used as a reference for expressing starting torque percentages --- ### Quick Revision - **TEFC motors** are sealed enclosures cooled by an external fan — suitable for dusty/wet environments - **IP ratings** use two digits: first = solid protection, second = water protection; higher numbers = more protection - **IP55** is a common industrial standard — dust-protected and jet-water-protected - **IP65** provides complete dust exclusion — required for severe environments - **Mounting codes** (B3, B5, B14, V1, etc.) define the physical attachment method and shaft orientation - **Star-delta starting** reduces inrush current by starting at reduced voltage (star) then switching to full voltage (delta) - **Dahlander motors** achieve two speeds from one winding; separate winding motors offer more speed flexibility - **Shaft loads** increase with frame size — always check both radial and axial limits from the data table - **Combined loading** reduces individual capacity — use the combined load chart to verify both loads simultaneously - **Single-phase permanent capacitor motors** have low starting torque (30–50% FLT) — suitable only for easy-start loads - **Capacitor start/induction run motors** provide high starting torque (160–230% FLT) — suitable for demanding applications - **Capacitor start/capacitor run motors** offer the best efficiency and power factor — ideal for high-performance needs - **Never run capacitor-type single-phase motors unloaded** — risk of damage to capacitors or windings - **Class F insulation** with **Class B temperature rise** is a common conservative rating approach — provides thermal margin - Standard operating conditions: ambient −30°C to +45°C, altitude up to 1000 m above sea level --- --- ## Chapter 2: Electric Motors — Gears, Motors & Geared Motor Units --- ### Overview This set of notes covers three interconnected areas of mechanical power transmission and drive system design: - **Geared motor units** — pre-engineered combinations of electric motors and gearboxes classified by drive type, including selection tables for output speed, torque, power, and unit sizing - **Spur and helical gears** — fundamental gear types used in mechanical power transmission, covering gear geometry, velocity ratios, tooth parameters, module selection, design principles, clearance, and force analysis - **Electric motors** — selection and specification of three-phase and single-phase electric motors, including performance data, efficiency characteristics, mounting arrangements, synchronous speeds, overhung load calculations, and a step-by-step motor selection method Together, these topics form the core knowledge required to design and specify mechanical drive systems from the prime mover (motor) through the transmission (gears/gearbox) to the driven load. --- ### Key Concepts - **Geared motor drive classifications** define standard combinations of motor power, gear ratio, output speed, output torque, and unit frame size for pre-engineered gearmotor assemblies - **Velocity ratio (VR)** is the fundamental relationship between driver and driven gear, determined by the ratio of teeth or pitch circle diameters - **Module (M)** is the key sizing parameter for gear teeth, linking pitch circle diameter to the number of teeth and governing tooth strength - **Hunting teeth** ensure even wear distribution by requiring no common factor between the number of teeth in the pinion and wheel - **Gear tooth forces** consist of tangential, separating (radial), and (for helical gears) axial components — all of which must be accounted for in shaft and bearing design - **Gear efficiency** is typically 95–96% per pair for well-machined, lubricated gears on rolling-element bearings; overall efficiency compounds across multiple stages - **Squirrel cage induction motors** are the most common type in engineering applications, self-adjusting to load via changes in current draw and slip - **Motor selection** follows a structured method: determine mechanical requirements → choose motor from performance tables → verify speed at design load → check overhung and thrust loads → extract dimensions --- ### Detailed Notes #### Geared Motor Units ##### Drive Classification System - Geared motor units are pre-engineered assemblies combining an electric motor with an integrated gearbox - Units are classified into **drive classifications** (e.g., Classification 2, 3, 4) which represent different ranges of output capability - Each classification provides a selection table cross-referencing: - **Nominal output speed** (rev/min) — ranging from approximately 20 to 288 rev/min - **Nominal gear ratio** — typically from 5:1 up to 70:1 - **Motor power** (kW) — ranging from 0.12 kW to 4.0 kW (varies by classification) - For each combination, the table specifies: - **Output power** (kW) - **Output torque** (Nm) - **Unit frame size** (e.g., JPM11, JPM17, JPM22, JPM26, JPM30) ##### Selection Considerations - As gear ratio increases, the available motor power range narrows (higher ratios support fewer high-power options) - As output speed decreases (higher ratio), output torque increases proportionally - Actual output speeds depend on the full-load speed of the motor and the exact gear ratio, and may differ from nominal speeds listed - Higher drive classifications generally support higher output torques and powers for equivalent speed ranges - Frame size increases with increasing power and torque requirements ##### Geared Motor Dimensions - Geared motors are available with **plug-in and solid output shafts** - Standard mounting is **foot mounting (Type 2)**, with dimensions specified for each frame size - Key dimensional parameters include: - **Overall envelope** (height, width, length) - **Shaft dimensions** (diameter, keyway, length) - **Mounting bolt patterns** (foot bolt spacing, flange PCD) - **Centre height** and **shaft centreline offsets** - Dimensions scale with frame size — larger frames (e.g., JPM30) have significantly larger envelopes and shaft diameters than smaller frames (e.g., JPM11) | Frame Size | B (mm) | B1 (mm) | C (mm) | D (mm) | E (mm) | Q (mm) | DO (mm) | DU (mm) | DV (mm) | |---|---|---|---|---|---|---|---|---|---| | JPM11 | 55 | 26.43 | 52 | 42 | 42 | 78 | 50 | 63 | 50 | | JPM17 | 85 | 40.55 | 78 | 60 | 67 | 98 | 73 | 98 | 80 | | JPM22 | 105 | 47.85 | 90 | 80 | 90 | 126 | 95 | 120 | 105 | | JPM26 | 117 | 50.33 | 97 | 92 | 102 | 140 | 110 | 135 | 120 | | JPM30 | 135 | 58.8 | 105 | 100 | 120 | 156 | 120 | 155 | 140 | --- #### Spur and Helical Gears ##### Types of Gears - Common gear types in engineering include: **spur, helical, double helical (herringbone), bevel, hypoid,** and **worm** - Two gears in mesh are called a **gear pair** - Mesh is normally external, but may be internal (one gear has teeth cut internally) - The smaller gear is the **pinion**; the larger is the **wheel** - The gear transmitting input torque/power is the **driver**; the output gear is the **driven** - In standard mechanical power transmission, the driver is typically the pinion — the wheel rotates slower, providing speed reduction - When more than two gears are in continuous mesh, this forms a **gear train** - **Simple gear train** — gears in series on separate shafts; intermediate gears are called **idler gears** (they do not change the overall velocity ratio) - **Compound gear train** — multiple gear pairs where intermediate shafts carry both a wheel and a pinion; the overall VR is the product of individual pair VRs - **Planetary (epicyclic) gear train** — compact arrangement with a sun gear, planet gears, and a ring gear ##### Spur vs Helical Gears - **Spur gears** have teeth cut parallel to the shaft axis - **Helical gears** have teeth cut at an angle (the **helix angle**, α) to the shaft axis - Typical helix angle: ~20° for single helical, ~30–35° for double helical (herringbone) - In a helical gear pair, one helix must be right-hand and the other left-hand - Helical gears are inherently stronger than spur gears of the same module, allowing a smaller module selection (one standard size down) - Helical gears produce an **axial force** component not present in spur gears ##### Velocity Ratio (VR) - For all gears except worm-and-wheel: **VR = number of teeth in wheel ÷ number of teeth in pinion** - For a compound gear train: **overall VR = product of individual pair VRs** - For a worm and wheel: **VR = number of teeth in wheel ÷ number of starts in worm** | Type of Gear Pair | VR Lower Limit | VR Upper Limit | |---|---|---| | Worm and wheel | 5 | 60 | | All other types | 1 | 5 | - Very high velocity ratios are undesirable due to the large number of teeth needed on the wheel, making accurate machining difficult and requiring large centre distances ##### Number of Teeth - It is impractical to have gears with too few teeth (below ~3 teeth causes profile issues) - **Rule of thumb minimums:** - Spur gears: ≥17 teeth on the pinion - Helical gears (20° helix angle): ≥14 teeth on the pinion - **Hunting teeth** — for maximum life with meshing gears, it is desirable to distribute wear uniformly among all teeth - The ideal condition (all teeth hunting) requires **no common factor** between the number of teeth in the pinion and the wheel - This ensures that the same teeth re-mesh only after the pinion has completed a number of revolutions equal to the number of teeth in the wheel - The velocity ratio in this case **cannot be reduced to a simpler ratio** | Teeth in Pinion | Teeth in Wheel | Revolutions of Pinion When Cycle Repeats | |---|---|---| | 18 | 38 | 19 | | 19 | 38 | 2 | | 20 | 38 | 19 | | 21 | 38 | 38 | | 18 | 40 | 20 | | 19 | 40 | 20 | | 20 | 40 | 2 | | 21 | 40 | 40 | - Note: 20/38 and 20/40 have very low cycle repeats (2) because they share a common factor — these combinations lead to uneven wear ##### Gear Parameters and Geometry - **Pitch Circle Diameter (PCD)** — the theoretical circle on which the gear teeth are considered to mesh; denoted as **d** for pinion and **D** for wheel - The relationship between VR and PCD: **VR = N/n = D/d** (where N = teeth in wheel, n = teeth in pinion) - **Nominal centre distance:** C = 0.5 × (d + D) — actual centre distance is usually slightly greater - **Addendum (A)** — height of tooth above the PCD line - **Dedendum (B)** — height of tooth below the PCD line - **Pressure angle (θ)** — angle made by the tangent to the gears at the point of contact; usually **20°** (assume unless stated otherwise) - **Pitch point (P)** — the point of contact on the PCD; must remain fixed as gears mesh to maintain constant velocity ratio - **Involute profile** — the standard tooth profile that keeps the pitch point fixed; can be visualised as the curve traced by unwinding a cord from a cylinder - For a rack and pinion, the mating profile on the pinion is involute while the rack profile is a straight-sided form at the pressure angle ##### Clearance - To minimise friction, teeth should contact only along the front face of the driver and back face of the driven - Two types of clearance are required: - **Radial clearance (bottom clearance)** — obtained by making dedendum > addendum; usually B = 1.25A - **Circumferential clearance** — very small when gears are new; increases with wear; obtained by making centre distance slightly larger than nominal - Circumferential clearance causes **backlash** — the back-and-forth play when one gear is held fixed and the other is rocked ##### Module (M) - **Module** is one of the most important parameters in gear design, defined as: **M = d/n = D/N** (PCD divided by number of teeth) - The module must be the same for both pinion and wheel in a gear pair - **Standard modules (first choice, in mm):** 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 - As module increases, tooth size increases → stronger teeth capable of transmitting more torque and power - **Standard proportions based on module:** - Addendum: A = M - Dedendum: B = 1.25 M - Tooth depth: A + B = 2.25 M - **Face width (W)** rules of thumb based on loading: - Light loads: W = 8M - Moderate loads: W = 10M - Heavy loads: W = 12M - The face width of the pinion is typically 5–10% larger than the wheel (depending on assembly tolerances) - Module selection can be done using a **module selection chart** (log-log plot of power vs pinion speed with module lines) - For spur gears with face width = 10M and 18 teeth on pinion - Can also be used for face widths 8–12M and pinions with 17–19 teeth - Can be used for helical gears with helix angles up to 20° by choosing one standard size smaller module ##### Gear Design Approach - A comprehensive gear design procedure references detailed engineering standards with dozens of variables and charts - The most critical factor: **the greater the loading, the larger the module** (and therefore the larger the teeth) - A simplified approach uses the module selection chart to determine appropriate module based on power and pinion speed ##### Gear Tooth Forces - Forces act at the **pitch point** (point of contact on the PCD) - The resultant transverse force **F** acts perpendicular to the tooth at the pitch point and represents the total load on the gear shaft at the gear location - This resultant decomposes into: - **Tangential force (Fₜ)** — the useful force that transmits torque - **Separating force (Fₛ)** — the radial force pushing gears apart along the line of centres; keeps gears in mesh - **θ** is the pressure angle between F and Fₜ (typically 20°) ###### Spur Gear Forces - **Tangential force:** Fₜ = 2T / d - Where T = torque (Nm), d = PCD (m) - **Separating force:** Fₛ = Fₜ × tan θ - **Resultant transverse force:** F = √(Fₜ² + Fₛ²) ###### Helical Gear Forces - Tangential force is the same as for spur gears: Fₜ = 2T / d - **Separating force (modified):** Fₛ = (Fₜ × tan θ) / cos α - Where α is the helix angle - **Axial force (additional):** Fₐ = Fₜ × tan α - **Resultant transverse force:** F = √(Fₜ² + Fₛ²) - The resultant transverse force for a helical gear is only slightly larger than for a spur gear, but the axial force is an important additional load that must be carried by the bearings ##### Worked Examples Summary **Example — Spur Gear Pair Design:** - Given: VR in range 2.5–2.7, pinion teeth = 18, module = 5 mm - Approach: Tabulate possible wheel teeth (45, 46, 47, 48) and check VR and hunting condition - Result: 18:47 ratio selected (VR = 2.556, all teeth hunting — no common factors) - PCD of pinion = 5 × 18 = 90 mm; PCD of wheel = 5 × 47 = 235 mm - Centre distance = 0.5 × (90 + 235) = 162.5 mm - Addendum = 5 mm, Dedendum = 6.25 mm, Tooth depth = 11.25 mm - Face widths (moderate load): Wheel = 50 mm, Pinion = 53.5 mm **Example — Spur Gear Force Calculation:** - Given: PCD = 100 mm, Torque = 800 Nm - Fₜ = 2 × 800 / 0.1 = 16 kN - Fₛ = 16 × tan 20° = 5.82 kN - F = √(16² + 5.82²) = 17 kN **Example — Helical Gear Force Calculation (20° helix angle):** - Fₜ = 16 kN (same as spur) - Fₛ = (16 × tan 20°) / cos 20° = 6.2 kN - F = √(16² + 6.2²) = 17.2 kN (only marginally greater than spur) - Fₐ = 16 × tan 20° = 5.82 kN (additional axial load on bearings) --- #### Electric Motors ##### Motor Types - The two most common motor types used in engineering are: - **Three-phase squirrel cage induction motor** — the workhorse of industrial applications - **Single-phase squirrel cage induction motor** — used for domestic and light commercial applications where three-phase supply is unavailable ##### Three-Phase Motors - Available configurations include: totally enclosed fan cooled, dust ignition proof, non-sparking, flameproof, two-speed, brake motors, geared motors, and slip ring motors - The standard off-the-shelf configuration is the **totally enclosed fan cooled** type with protection designation **IP55** or higher - Data in standard references typically covers sizes from 0.18 to 110 kW (frame sizes 63–280) - **Frame size** = distance in mm between the base of the motor feet and the centreline of the rotor — a common designation used by all manufacturers; as frame size increases, motor power increases ##### Synchronous Speeds (Three-Phase, 50 Hz) | Number of Poles | Synchronous Speed (rev/min) | |---|---| | 2 | 3000 | | 4 | 1500 | | 6 | 1000 | | 8 | 750 | ##### Single-Phase Motors - Available in three starting methods: - **Permanent capacitor** type - **Capacitor start / induction run** type - **Capacitor start / capacitor run** type - Three mounting arrangements: standard foot mount, flange mounted, and "C" type face mount - Only two synchronous speeds available: 2-pole (3000 rev/min) and 4-pole (1500 rev/min) ##### Motor Operating Characteristics - Under no-load conditions, the actual motor speed equals the synchronous speed (approximately) - Full-load speed is less than synchronous speed (the difference is called **slip**) - Between no load and full load, the speed-load relationship is very close to linear — linear interpolation can be used for intermediate loads with little error - **Squirrel cage motors self-adjust** to load: as load increases, current draw increases to provide the required torque - It is poor practice to **overload** the motor (excess current causes overheating and failure) - It is also poor practice to significantly **undersize** the load relative to motor capacity (motor runs at lower efficiency and wastes space/cost) - Electric motors, like most prime movers, have **lower efficiency at part load** than at full load ##### Performance Data - Performance tables list for each motor type: - Output power (kW), full-load speed (RPM) - No-load and full-load current (A), locked rotor current - **Efficiency** at 100% FL, 75% FL, and 50% FL - **Power factor** at 100% FL, 75% FL, and 50% FL - Full-load torque (Nm) - Starting torque, pull-up torque, maximum torque (multiples of FL torque) - Moment of inertia (J), net weight ##### Motor Mounting Arrangements - **B3 Footmount** — standard arrangement with feet for floor mounting - **B5 Flangemount** — flange mounted to driven equipment - **B14A / B14B Facemount** — face-mounted configuration - Additional variants exist for combined foot/flange mounting (Type F 160/280 series) - Dimensions are standardised and tabulated by frame size for all mounting types ##### Overhung Load and Thrust - When a gear, pulley, chain-wheel, or flywheel is directly attached to the motor shaft, it creates an **overhung (radial) load** - This load must not exceed the motor's allowable value, or bearing life will be reduced - **Overhung load formula:** **F = (2fT) / d = (60fP) / (π × d × N)** Where: - F = overhung load (N) - T = motor torque at design load (Nm) — not maximum/full-load torque - P = motor power at design load (W) — not maximum/full-load power - d = PCD of pulley, sprocket, or gear (m) - N = speed at design load (rev/min) - f = **drive application factor:** - Chain drive or toothed belt: f = 1.0 - Gear drive: f = 1.25 - Vee belt: f = 1.5 - Flat friction belt: f = 2.0 - If overhung load is excessive, options include: - Use a larger pulley or gear (increases d, reducing F) - Use a larger motor (higher allowable load) - Use an **intermediate (lay) shaft** with its own bearings coupled to the motor via a flexible coupling — this prevents the overhung load from reaching the motor bearings ##### Thrust (Axial) Load - If a mechanism produces a **thrust (axial) load** on the motor shaft, this must also not exceed the allowable value - When **both radial and axial loads** act simultaneously, the allowable thrust load is reduced: - If radial load equals maximum allowable → allowable thrust = table value × 0.68 - If radial load is 50% of maximum → allowable thrust = table value × 0.84 ##### Motor Selection Method (Three-Phase) 1. **Determine mechanical requirements** — torque, power, and speed 2. **Select motor from performance tables** — choose a motor at the appropriate synchronous speed with maximum power output (full load) ≥ required design power - "Full load" in manufacturer catalogues refers to the maximum continuous load rating - The actual load requirement (design power) is often less than maximum 3. **Calculate speed at design load** — use linear interpolation between no-load (synchronous) speed and full-load speed 4. **Check overhung load** — if a pulley, gear, or sprocket is directly attached, calculate F and verify it does not exceed allowable values 5. **Check thrust load** — if applicable, verify axial load is within limits (reducing for combined loading if needed) 6. **Extract performance and dimension data** — efficiency at design load (interpolated), torque at design load, current draw, shaft diameter, mounting bolt patterns, and overall dimensions ##### Worked Example — Motor Selection - **Given:** Design power = 12 kW at approximately 1450 rev/min, wedge belt pulley (PCD 100 mm, max bore 42 mm) directly on motor shaft - **Step 1:** Synchronous speed = 1500 rev/min → 4-pole motor required - **Step 2:** Selected motor: frame size 160, 4-pole, maximum output = 15 kW - **Step 3:** Speed at design load = 1500 − (12/15) × (1500 − 1455) = 1464 rev/min - **Step 4:** Overhung load: F = (60 × 1.5 × 12000) / (π × 0.1 × 1464) = 2348 N → within allowable limit of 2800 N - **Step 5:** No axial load in this case - **Step 6:** Design load is 80% of full load; efficiency at full load = 88%, at 75% = 87% → efficiency at design load ≈ 87.2%; torque at design load = 78.3 Nm | Parameter | Value | |---|---| | Motor type | Frame 160, 4-pole | | Number of poles | 4 | | Maximum power output | 15 kW | | Speed at design power | 1464 rev/min | | Torque at design power | 78.3 Nm | | Efficiency at design power | 87.2% | | Current draw at maximum load | 28.6 A | | Nominal output shaft diameter | 42 mm | | Mounting bolt centre distance (side) | 254 mm | | Mounting bolt centre distance (end) | 254 mm | --- ### Comparison Tables #### Spur Gears vs Helical Gears | Feature | Spur Gears | Helical Gears | |---|---|---| | Tooth orientation | Parallel to shaft axis | At an angle (helix angle α) to shaft axis | | Typical helix angle | 0° (N/A) | ~20° (single), ~30–35° (double) | | Noise | Higher (sudden tooth engagement) | Lower (gradual tooth engagement) | | Strength | Standard | Inherently stronger for same module | | Axial force | None | Present (Fₐ = Fₜ × tan α) | | Separating force formula | Fₛ = Fₜ × tan θ | Fₛ = (Fₜ × tan θ) / cos α | | Bearing requirements | Radial only | Radial + thrust bearings needed | | Module selection | Standard from chart | Can use one standard size smaller | | Minimum pinion teeth | ≥17 | ≥14 (at 20° helix) | #### Gear Train Types | Type | VR Calculation | Intermediate Gears Affect VR? | Compactness | |---|---|---|---| | Simple | N_wheel / n_pinion | No (idlers only change direction) | Low | | Compound | Product of individual pair VRs | Yes | Moderate | | Planetary | Depends on configuration | N/A (integrated) | High | #### Drive Application Factors for Overhung Load | Drive Type | Factor (f) | |---|---| | Chain drive or toothed belt | 1.0 | | Gear drive | 1.25 | | Vee belt | 1.5 | | Flat friction belt | 2.0 | --- ### Mermaid Diagrams #### Gear Pair Terminology and Relationships ```mermaid flowchart TD A[Gear Pair] --> B[Pinion - Smaller Gear] A --> C[Wheel - Larger Gear] B --> D[Driver - Transmits Input Power] C --> E[Driven - Receives Output Power] D --> F["VR = N/n = D/d"] F --> G["Speed Reduction: Output Speed = Input Speed / VR"] F --> H["Torque Multiplication: Output Torque = Input Torque × VR × η"] ``` #### Gear Design Process ```mermaid flowchart TD A[Define Requirements] --> B[Determine VR Needed] B --> C[Select Pinion Teeth Count ≥17 spur / ≥14 helical] C --> D[Calculate Wheel Teeth = Pinion Teeth × VR] D --> E{Check Hunting Teeth Condition} E -- No common factors --> F[Teeth Combination OK] E -- Common factors exist --> G[Adjust Wheel Teeth ±1] G --> D F --> H[Select Module from Chart Based on Power and Speed] H --> I["Calculate PCD: d = M × n, D = M × N"] I --> J["Calculate Centre Distance: C = 0.5 × (d + D)"] J --> K["Calculate Tooth Dimensions: A = M, B = 1.25M"] K --> L["Determine Face Width: W = 8M to 12M Based on Load"] L --> M[Calculate Gear Forces] M --> N[Design Complete — Specify Bearings and Shaft] ``` #### Gear Force Components ```mermaid flowchart LR A["Torque (T) on Gear"] --> B["Tangential Force: Fₜ = 2T/d"] B --> C["Separating Force (Spur): Fₛ = Fₜ × tan θ"] B --> D["Separating Force (Helical): Fₛ = Fₜ tan θ / cos α"] B --> E["Axial Force (Helical only): Fₐ = Fₜ × tan α"] C --> F["Resultant: F = √(Fₜ² + Fₛ²)"] D --> F E --> G[Must Be Carried by Thrust Bearings] ``` #### Electric Motor Selection Process ```mermaid flowchart TD A["Step 1: Determine Mechanical Requirements — Torque, Power, Speed"] --> B["Step 2: Choose Motor from Performance Tables — Synchronous Speed, Frame Size, Full Load Power ≥ Design Power"] B --> C["Step 3: Calculate Speed at Design Load — Linear Interpolation Between No-Load and Full-Load Speed"] C --> D["Step 4: Check Overhung Load — F = 60fP / (π × d × N) ≤ Allowable"] D --> E{Overhung Load OK?} E -- Yes --> F["Step 5: Check Thrust Load if Applicable"] E -- No --> G[Increase Pulley/Gear Size OR Use Larger Motor OR Add Intermediate Shaft] G --> D F --> H{Thrust Load OK?} H -- Yes --> I["Step 6: Obtain Performance Data — Efficiency, Torque, Current, Dimensions"] H -- No --> J[Increase Motor Size OR Use Intermediate Shaft with Thrust Bearing] J --> F I --> K[Motor Selection Complete] ``` #### Gear Efficiency in Compound Trains ```mermaid flowchart LR A[Input Power] --> B["Stage 1: η₁ = 96%"] B --> C["Stage 2: η₂ = 96%"] C --> D["Stage 3: η₃ = 96%"] D --> E["Output Power"] E --> F["Overall η = 0.96 × 0.96 × 0.96 = 0.885 = 88.5%"] ``` --- ### Key Terms Glossary - **Addendum (A)** — the height of a gear tooth above the pitch circle diameter; equals the module (A = M) - **Axial force (Fₐ)** — the force component along the shaft axis, present only in helical gears; Fₐ = Fₜ × tan α - **Backlash** — the play or looseness between meshing gear teeth caused by circumferential clearance; measurable by holding one gear fixed and rocking the other - **Compound gear train** — a gear train where intermediate shafts carry both a wheel and a pinion, allowing multiplication of velocity ratios - **Dedendum (B)** — the height of a gear tooth below the pitch circle diameter; B = 1.25M for standard proportions - **Design load (design power)** — the actual working load/power requirement of the driven machine, which is often less than the motor's full-load (maximum continuous) rating - **Drive application factor (f)** — a multiplier applied when calculating overhung loads to account for the type of drive connection (chain, gear, belt) - **Driver** — the gear in a pair that transmits input torque and power (usually the pinion) - **Driven** — the gear in a pair that receives output torque and power (usually the wheel) - **Frame size** — a standardised motor dimension (in mm) representing the distance from the motor base to the rotor centreline; universally used across manufacturers - **Gear pair** — two gears in mesh - **Gear train** — more than two gears in continuous mesh - **Helix angle (α)** — the angle at which helical gear teeth are cut relative to the shaft axis - **Hunting teeth** — a condition where the number of teeth in the pinion and wheel share no common factor, ensuring even wear distribution across all teeth - **Idler gear** — an intermediate gear in a simple gear train that changes direction of rotation but does not affect the velocity ratio - **Involute profile** — the standard tooth profile used in modern gearing that maintains a fixed pitch point and constant velocity ratio during meshing - **IP55** — a standard protection designation for electric motors indicating dust-tight and water-jet-resistant enclosure - **Module (M)** — the ratio of pitch circle diameter to number of teeth (M = PCD / teeth); the fundamental sizing parameter for gear teeth - **Nominal centre distance (C)** — half the sum of the two pitch circle diameters; C = 0.5 × (d + D); actual centre distance is usually slightly larger - **Overhung load** — the radial force on the motor shaft caused by a pulley, gear, sprocket, or flywheel mounted directly on it - **Pinion** — the smaller gear in a gear pair - **Pitch Circle Diameter (PCD)** — the theoretical circle on which gear teeth are considered to mesh; d for pinion, D for wheel - **Pitch point (P)** — the point on the pitch circle where contact occurs; must remain fixed for constant velocity ratio - **Planetary gear train** — a compact gear arrangement using sun, planet, and ring gears; also called epicyclic - **Pressure angle (θ)** — the angle between the resultant force and the tangential force at the pitch point; usually 20° - **Radial clearance** — the gap between the tip of one gear tooth and the root of the mating tooth; obtained by making dedendum > addendum - **Separating force (Fₛ)** — the radial force component that acts to push meshing gears apart along their line of centres - **Slip** — the difference between synchronous speed and actual full-load speed in an induction motor - **Squirrel cage motor** — the most common type of AC induction motor, named for its rotor construction; self-adjusts to load - **Synchronous speed** — the theoretical no-load speed of an AC motor, determined by supply frequency and number of poles - **Tangential force (Fₜ)** — the force component tangent to the pitch circle that transmits useful torque; Fₜ = 2T / d - **Velocity ratio (VR)** — the ratio of output gear teeth to input gear teeth (or equivalently, the ratio of PCDs); equals the speed reduction ratio - **Wheel** — the larger gear in a gear pair --- ### Quick Revision - **VR (general gears)** = teeth in wheel ÷ teeth in pinion = D / d - **VR (worm and wheel)** = teeth in wheel ÷ starts in worm - **VR limits:** worm 5–60; all others 1–5 - **Module:** M = d/n = D/N; standard first-choice values: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 - **Tooth proportions:** A = M, B = 1.25M, depth = 2.25M - **Face width:** W = 8M (light), 10M (moderate), 12M (heavy); pinion 5–10% wider - **Minimum pinion teeth:** spur ≥17, helical (20°) ≥14 - **Hunting teeth:** no common factor between pinion and wheel tooth counts - **Centre distance:** C = 0.5 × (d + D) - **Tangential force:** Fₜ = 2T / d (T in Nm, d in m) - **Separating force (spur):** Fₛ = Fₜ × tan θ - **Separating force (helical):** Fₛ = (Fₜ × tan θ) / cos α - **Axial force (helical):** Fₐ = Fₜ × tan α - **Resultant force:** F = √(Fₜ² + Fₛ²) - **Gear pair efficiency:** 95–96% per pair; compound overall = product of individual efficiencies - **Synchronous speeds (50 Hz):** 2-pole = 3000, 4-pole = 1500, 6-pole = 1000, 8-pole = 750 rev/min - **Motor speed at design load:** interpolate linearly between no-load (synchronous) and full-load speed - **Overhung load:** F = 60fP / (π × d × N); factors: chain/tooth belt 1.0, gear 1.25, vee belt 1.5, flat belt 2.0 - **Combined radial + axial loading:** reduces allowable thrust; multiply table value by 0.68 (full radial) or 0.84 (50% radial) - **Motor selection sequence:** Requirements → Table selection → Speed interpolation → Overhung load check → Thrust check → Extract data --- --- ## Chapter 3: Electric Motors — Single-Phase Performance & Dimensions --- ### Overview This document consolidates two major mechanical design reference topics. The first section covers **single-phase electric motor** performance data, including permanently connected capacitor motors, capacitor start/induction run motors, and capacitor start/capacitor run motors — with electrical characteristics, torque values, and physical dimensions for various frame sizes and mounting configurations. The second section addresses **shafts, keys, circlips, and seals** — covering material selection, dimensional standards, keyway stress calculations, circlip types and thrust load ratings, galvanic corrosion compatibility, and radial shaft seal selection including bore/shaft tolerance requirements and operating condition limits. --- ### Key Concepts - **Single-phase motors** are categorised by starting method: permanently connected capacitor (fan duty), capacitor start/induction run, and capacitor start/capacitor run — each with distinct torque and efficiency characteristics - **Motor frame sizes** follow standardised numbering (e.g., 63, 71, 80, 90, 100) and determine physical dimensions across mounting configurations - **Pole count** determines synchronous speed: two-pole motors run at 3000 RPM and four-pole motors run at 1500 RPM (at 50 Hz supply) - **Shaft and key sizing** is standardised — each shaft diameter has a corresponding standard key size (width × height) and defined tolerance - **Keyway stress design** uses rule-of-thumb multipliers based on allowable tensile stress for both shear and bearing calculations - **Circlips** are retaining rings used to prevent axial movement of components on shafts or within bores — available in internal, external, and push-on (E-clip) types - **Circlip thrust load capacity** is governed by two values: the load on the circlip itself and the load on the groove — the lower value governs the design - **Galvanic corrosion** between circlip and groove materials must be considered when selecting circlip material and finish - **Radial shaft seals** create a barrier between surfaces in relative motion — the sealing lip, spring, and case work together to retain lubricant and exclude contaminants - **Seal material selection** (designated by lip codes) depends on temperature range, chemical compatibility, shaft speed, and pressure --- ### Detailed Notes #### Single-Phase Motor Types - **Permanently Connected Capacitor (Fan Duty Only)** - Designated for fan duty applications only - A run capacitor remains in circuit at all times - Provides smooth, quiet operation but limited starting torque - Available in two-pole (3000 RPM) and four-pole (1500 RPM) configurations at 240 V, 50 Hz - Frame sizes range from 63 to 100L - **Capacitor Start / Induction Run** - Uses a start capacitor that is disconnected once the motor reaches approximately 75% of rated speed - Provides high starting torque with moderate running efficiency - Suitable for loads requiring significant breakaway torque - Available in two-pole and four-pole configurations at 240 V, 50 Hz - **Capacitor Start / Capacitor Run** - Uses both a start capacitor (for high starting torque) and a run capacitor (for improved running performance) - Offers the best combination of starting torque and running efficiency among single-phase types - Suitable for demanding applications requiring both high start and continuous run performance #### Motor Performance Parameters - **Output Power** — rated in watts (W), indicates continuous mechanical output - **Full Load Speed** — actual operating speed under rated load (always less than synchronous speed due to slip) - **Full Load Current** — current drawn at rated output; critical for circuit protection sizing - **Starting Current** — inrush current at startup; typically 3–7× full load current - **Full Load Torque** — continuous torque at rated speed (in Nm) - **Starting Torque** — torque available at zero speed; expressed as a ratio to full load torque - **Power Factor** — ratio of real power to apparent power at full load; typically 0.9–1.0 for capacitor-run motors - **Efficiency** — ratio of mechanical output to electrical input; ranges from approximately 60% to 80% depending on frame size and type - **Start Capacitor** — rated in µF at specified voltage; sized for starting duty - **Run Capacitor** — rated in µF at specified voltage; remains in circuit continuously #### Motor Mounting Configurations - **B3 Mounting (Foot Mount)** - Motor mounted horizontally on feet bolted to a base - Dimensions include overall length, height to shaft centre, foot hole spacing, and shaft extension details - All critical dimensions (A, AA, AB, AC, AG, B, BB, C, CA, H, HA, HD, AE, K, KA, L, LC, LD, HE, KK, D, E, F, G, GD) are standardised per frame size - **B5 Mounting (Flange Mount)** - Motor mounted via a flange on the drive end - Flange bolt circle (PCD), spigot diameter, and bolt hole sizes are standardised - Suitable for direct-coupling to pumps, gearboxes, and other driven equipment - Dimensions include flange face details, bolt patterns, and overall projection #### Motor Dimension Tables — Key Parameters | Parameter | Description | |---|---| | **A** | Overall foot-to-foot length | | **B / BB** | Foot bolt hole spacing (longitudinal / transverse) | | **C** | Shaft extension length | | **CA** | Total shaft + housing length | | **D** | Shaft diameter | | **E** | Key slot to shaft end | | **F** | Key width | | **G** | Key height | | **H** | Shaft centre height | | **K / KA** | Foot-to-shaft-end / foot-to-body dimensions | | **L / LC / LD** | Overall body length variations | | **AE** | Drive end flange diameter | | **GD** | Bolt hole diameter (flange) | --- #### Shafts - **Common Shaft Materials** - **Plain carbon steel** — grades 1020, 1030, 1040 (or 1045); most common and economical - **Stainless steel** — austenitic grades 304 and 316; martensitic grades 420 and 431; for corrosion resistance - **Alloy steel** — grades 4140 and 4340; for high-strength applications requiring heat treatment - **Shaft Sizes and Key Standards** - Standard bright steel shafts are available in metric diameters up to 120 mm (larger sizes up to 400 mm may also be available) - Each shaft diameter has a **corresponding standard key size** (width × height) - Shaft tolerance is supplied as a range (e.g., +0 / −0.08 mm for smaller shafts, +0 / −0.15 mm for larger shafts) #### Shaft Diameter to Key Size Reference | Shaft Diameter (mm) | Key Size (W × H, mm) | Shaft Tolerance (mm) | |---|---|---| | 8 | 2 × 2 | +0 / −0.08 | | 10 | 3 × 3 | +0 / −0.08 | | 12 | 4 × 4 | +0 / −0.08 | | 15 | 5 × 5 | +0 / −0.08 | | 16 | 5 × 5 | +0 / −0.08 | | 20 | 6 × 6 | +0 / −0.08 | | 22 | 6 × 6 | +0 / −0.08 | | 25 | 8 × 7 | +0 / −0.1 | | 27 | 8 × 7 | +0 / −0.1 | | 30 | 8 × 7 | +0 / −0.1 | | 33 | 10 × 8 | +0 / −0.1 | | 35 | 10 × 8 | +0 / −0.1 | | 39 | 12 × 8 | +0 / −0.1 | | 40 | 12 × 8 | +0 / −0.1 | | 45 | 14 × 9 | +0 / −0.1 | | 50 | 14 × 9 | +0 / −0.1 | | 55 | 16 × 10 | +0 / −0.12 | | 60 | 18 × 11 | +0 / −0.12 | | 65 | 18 × 11 | +0 / −0.12 | | 70 | 20 × 12 | +0 / −0.12 | | 75 | 20 × 12 | +0 / −0.12 | | 80 | 22 × 14 | +0 / −0.12 | | 90 | 25 × 14 | +0 / −0.12 | | 100 | 28 × 16 | +0 / −0.12 | | 110 | 28 × 16 | +0 / −0.15 | | 120 | 32 × 18 | +0 / −0.15 | #### Key and Keyway Stresses - **Design Rule of Thumb:** - **Allowable shear stress** in the key or shaft = **0.75 × allowable tensile stress** - **Allowable bearing stress** in the key or shaft = **1.5 × allowable tensile stress** - Keyway tolerance depends on the class of fit — may be free, normal, or close (interference) --- #### Circlips - **Function** — retaining rings that prevent axial movement of components on a shaft (external) or within a bore (internal) - **Common Profile Shapes** — rectangular, square, and round cross-sections ##### Circlip Types | Type | Application | Features | |---|---|---| | **Type 1300** | Internal (bore) | Lugs for plier assembly/disassembly | | **Type 1400** | External (shaft) | Lugs for plier assembly/disassembly | | **Type 1500 (E-clip)** | External (shaft) | Push-on fit from the side; no groove required | | **Type 1305** | Internal (bore) | No-groove design; not for repetitive disassembly | | **Type 1465** | External (shaft) | No-groove design; not for repetitive disassembly | ##### Circlip Standards - **Standard Series "E" Circlips (D1500 / N1500)** — incorporating metric series standards - D1500 = external type; N1500 = internal type - Standard material: carbon spring steel with phosphate and oil finish - Preferred sizes printed distinctly in reference tables - **Standard Internal Circlips (D1300)** — incorporating European specifications - All dimensions in mm - Tables provide groove dimensions, circlip dimensions, and thrust load values - **Standard External Circlips (D1400)** — incorporating European specifications - All dimensions in mm - Available with standard lugs or alternative lugs for larger sizes (over 125 mm typically without lugs) ##### Circlip Materials | Material | Code | Specifications | Max Temp (Short/Long) | Min Temp | Corrosion Resistance | |---|---|---|---|---|---| | Cold rolled carbon spring steel strip | CS / A | Standard carbon steel spec | 300°C / 200°C | −20°C | Phosphated; Moderate; Oiled — Poor | | Carbon steel wire | CS / A | Manganese 0.65–0.85% | 300°C / 200°C | −20°C | Phosphated; Moderate; Oiled — Poor | | Hard drawn carbon steel wire | CS / A | Standard wire spec | 200°C / 160°C | −20°C | Phosphated; Moderate; Oiled — Poor | | Phosphor bronze cold rolled strip | PB / E | Copper-tin alloy spec | 250°C / 150°C | −100°C | Good | | Phosphor bronze hard drawn wire | PB / E | Copper-tin alloy spec | 250°C / 150°C | −100°C | Good | | Beryllium copper cold rolled strip | BC / F | Copper-beryllium alloy spec | 250°C / 160°C | −100°C | Good | | Cold rolled stainless steel strip | AS / B | Austenitic stainless spec | 450°C / 360°C | −100°C | Good | | Cold rolled stainless steel strip (420 type) | RS / C | Martensitic stainless spec | 300°C / 200°C | −20°C | Fair | | Hard drawn stainless steel wire (302 type) | SS / D | Austenitic stainless wire spec | 250°C / 160°C | −100°C | Good | ##### Thrust Load Calculations - **Two thrust load figures** are quoted for each circlip size: - **T_c** = maximum safe thrust load on the **circlip** itself - **T_g** = maximum safe thrust load on the **groove** (shaft or bore) - Thrust load tables assume: - Pure shear in the circlip (abutting part is sharp-cornered, slide fit) - Standard circlip material - Steady loading conditions - Low carbon steel (mild steel) shaft with 300 MPa yield point - **For non-standard shaft material:** apply a correction factor to T_g - Factor = (actual shaft yield point) / 300 - Example: shaft yield 220 MPa → factor = 220/300 = 0.733 - Example: shaft yield 400 MPa → factor = 400/300 = 1.333 - **Design rule:** always use the **lower** value of T_c and T_g as the governing thrust load - Unless the shaft material has a very high yield point, the maximum safe thrust load will typically be governed by the shaft groove strength, not the circlip strength ##### Galvanic Corrosion Compatibility - **Critical consideration** when selecting circlip material and finish relative to the groove material - Galvanic corrosion occurs when dissimilar metals are in contact, especially in the presence of conductive solutions (electrolytes) | Severity Rating | Meaning | |---|---| | **** | Severe galvanic corrosion | | * (C) | Circlip tends to corrode | | * (G) | Groove material tends to corrode | - **Key Combinations to Avoid:** - Carbon steel circlip in copper/aluminium groove (severe corrosion) - Stainless steel circlip with most other metals (variable, often problematic) - Zinc-plated circlip in magnesium/aluminium groove (severe corrosion on groove) ##### Circlip Material Selection by Environment | Corrosive Environment | Satisfactory Resistance (Best → Worst) | Limited Application | |---|---|---| | Industrial / urban atmosphere | SS, AS, BC, PB, RS | CS | | Rural atmosphere | SS, AS, RS | CS | | Marine atmosphere | BC, PB, SS, AS | RS, CS | | Seawater and salt solutions | PB, BC, AS, SS | CS, RS | | Foodstuffs, fruit, etc. | SS, AS | RS | | Petroleum oils (crude) | RS, SS, AS | PB, BC | | Organic solvents | SS | RS, AS | | Steam 250°C | PB, SS, AS, RS | CS | | Steam 500°C | SS | RS | | Tap water | SS, AS, PB | CS, RS | --- #### Seals (Radial Shaft Seals) ##### Seal Function - A shaft seal is a barrier with **four functions:** 1. **Retaining** lubricants or liquids 2. **Excluding** contaminants 3. **Separating** fluids 4. **Confining** pressure ##### Three Basic Seal Types - **Static Seals** — barrier between non-moving surfaces (e.g., valve cover gaskets, O-rings) - **Axial Mechanical Seals** — face-type seals between radially mounted components; one usually stationary, spring-loaded against the other - **Dynamic Radial Seals** — barrier between surfaces in relative rotary motion; the most common type for rotating shaft applications ##### Dynamic Radial Seal Components - **Sealing Lip** — the primary contact element; an L-shaped shell with the lip contacting the shaft - **Garter Spring** — holds the lip in position against the shaft; keeps contact pressure consistent - **Case (Shell)** — the outer structure; press-fits into the bore housing - **Inner Shell (some designs)** — protects the lip from damage during installation - Advanced designs may include a **wave-pattern lip** (pumps lubricant back while dissipating heat) and **dust lip** for contaminant exclusion ##### Seal Material Selection (Lip Codes) | Lip Code | Material | Temperature Range | Key Characteristics | |---|---|---|---| | **R** | Nitrile (Buna-N) | −40°C to +107°C (continuous), intermittent to +121°C | Most common; excellent with mineral oils, greases, fuels; not for water-based cutting fluids above 66°C | | **D** | Duralip (Carboxylated Nitrile) | Similar to standard nitrile | Extreme abrasion resistance; for sand, grit, dirt exposure; intermittent dry running | | **H** | Duratemp (Hydrogenated Nitrile — HNBR) | Higher than standard nitrile | Improved heat, abrasion, ozone, and weathering resistance; for aerated hot oils | | **P** | Polyacrylate | −40°C to +149°C | For EP lubricants and higher temperatures; good oxidation resistance; not for water or below −40°C | | **S** | Silicone | −100°C to +163°C | High/low temperature range; low friction; poor compatibility with oxidised oils and abrasive contaminants | | **V** | Fluoroelastomer (LongLife) | −40°C to +204°C | Widest temperature and chemical resistance; premium material; resists most lubricants and chemicals; dry running intermittent only | | **E** | Vamac | −40°C to +163°C | Good abrasion resistance; swells more than nitrile at higher temperatures | | **F** | Felt | −65°C to +93°C | Limited to dust exclusion and heavy lubricant retention; for slow speeds and severe conditions | | **T** | TFE (PTFE-based) | −100°C to +260°C | Widest media resistance; excellent mechanical properties; low friction and wear | | **#** | Other / Special Compounds | Varies | Non-standard; contact manufacturer | - **Multi-Lip Codes** — first code = primary lip material, second code = auxiliary lip material (e.g., "RL" = nitrile primary + leather auxiliary; "RD" = nitrile primary + Duralip auxiliary) ##### Seal Group Designs | Group | Design Type | Description | |---|---|---| | 1 | V-Ring (VR1, VR2, VR3) | All-rubber; hand-fitted; no housing required; runs against seal case or housing face; for motors, conveyors, appliances, general machinery | | 2 | Non-spring-loaded (HM14, HM21, HM4) | Grease retention or dirt exclusion at slower speeds; lip facing outward for maximum dirt exclusion; heavy-duty type handles severe conditions | | 3 | Single lip, spring-loaded, no inner case (HMS4, HDW1, CRW1, HMS) | Most economical general purpose; for engines, transmissions, pumps, electric motors, drive axles, reducers; special material variants available for demanding conditions | | 4 | Single lip, spring-loaded, with inner case (CRWH1, CRS, CRSH, HMSH, HMSN) | Greater lip strength and protection; recommended where shaft assembly is against the lip; wide range of special materials available | | 5 | Dual lip, no inner case (HMSA7, CRWA1, HMSA5, CRSA, HMSA) | Medium dirt exclusion supplementing lube tube retention; spring-loaded; special materials for demanding conditions | | 6 | Dual lip, with inner case (CRWHA1, CRSHA, HMSHA) | Greater strength and lip protection; recommended where shaft assembly is against the seal lip; medium dirt exclusion | | 7 | Pressure-capable (CRWA5, CRW5, CRWHA5) | Single and dual lip designs for internal pressures up to 90 psi (~620 kPa); can replace some mechanical seals in smaller pump and general purpose applications | | 8 | Dual element (D7, C-type) | Dual lip to separate two fluids; maximum dirt exclusion; wide material variety | | 9 | External press-fit (X15, X12) | Press-fit on shaft or spindle; sealing element contacts bore; spring-loaded styles handle fluid retention; commonly used in agricultural equipment | | 10 | Heavy-duty dual metal-face (HDDF) | Premium construction; positive lubrication retention and dirt exclusion; installed by hand as a cartridge; for mixers, mining, grinders, rollers, or wherever abrasive contamination would cause failure | ##### Bore Requirements - **Bore Finish** — approximately 125 microinches Ra (3.2 µm) or smoother to avoid leakage; aluminium bores should be 100–200 microinches Ra (2.5–5.0 µm) - **Bore Configuration** — lead corner must be chamfered and burr-free; maximum radius 0.031" (0.8 mm) - **Bore Hardness** — no specific Rockwell hardness required, but must be sufficient to maintain interference with seal outer diameter - **Bore Material** — ferrous and aluminium are acceptable; for non-ferrous bore materials, consider differential thermal expansion - **Bore Tolerance (Metric, mm)** | Bore Diameter Range (mm) | Bore Tolerance (ISO/H8) | Metal Case Seal OD Tolerance | Rubber-Covered Seal OD Tolerance | |---|---|---|---| | Over 6 to 10 | +0.022 / −0.000 | +0.20 | +0.30 | | Over 10 to 18 | +0.027 / −0.000 | +0.20 | +0.30 | | Over 18 to 30 | +0.033 / −0.000 | +0.20 | +0.30 | | Over 30 to 50 | +0.039 / −0.000 | +0.20 | +0.30 | | Over 50 to 80 | +0.046 / −0.000 | +0.23 | +0.35 | | Over 80 to 120 | +0.054 / −0.000 | +0.25 | +0.35 | | Over 120 to 180 | +0.063 / −0.000 | +0.28 | +0.45 | | Over 180 to 250 | +0.072 / −0.000 | +0.35 | +0.45 | | Over 250 to 300 | +0.081 / −0.000 | +0.35 | +0.45 | | Over 300 to 315 | +0.081 / −0.000 | +0.45 | +0.55 | | Over 315 to 400 | +0.089 / −0.000 | +0.45 | +0.55 | | Over 400 to 500 | +0.097 / −0.000 | +0.45 | +0.55 | ##### Shaft Requirements - **Shaft Configurations** — burr-free chamfer or radius required; corners must be smooth and blended - **Shaft Finish** — recommended 10–20 microinches Ra (0.25–0.50 µm); plunge ground with machine lead angle of zero ±3 minutes - **Shaft Hardness** — minimum Rockwell C30 or higher to prevent handling damage and abrasive wear - **Shaft Diameter Tolerances (Metric, ISO)** | Nominal Shaft Diameter (mm) | Tolerance | |---|---| | Up to and including 4.000 | ±0.000 / −0.000 (per ISO) | | Over 6 to 10 | +0.000 / −0.090 | | Over 10 to 18 | +0.000 / −0.110 | | Over 18 to 30 | +0.000 / −0.130 | | Over 30 to 50 | +0.000 / −0.160 | | Over 50 to 80 | +0.000 / −0.190 | | Over 80 to 120 | +0.000 / −0.220 | | Over 120 to 180 | +0.000 / −0.250 | | Over 180 to 250 | +0.000 / −0.290 | | Over 250 to 315 | +0.000 / −0.320 | | Over 315 to 400 | +0.000 / −0.360 | | Over 400 to 500 | +0.000 / −0.400 | - **Shaft Material** — best performance on medium to high carbon steel or stainless steel; soft materials (brass, zinc, aluminium, magnesium, plastics) are not recommended except at low surface speeds (<100 FPM) in clean environments - **Shaft Surface Speed** — expressed in FPM (feet per minute) at the contact point; a better measure than RPM for seal selection ##### Shaft Eccentricity - **Shaft-to-Bore Misalignment (STBM)** — the amount by which the shaft is off-centre relative to the bore; caused by machining and assembly inaccuracies; measured as half of the Total Indicator Reading (TIR) - **Dynamic Run-Out (DRO)** — the amount by which the shaft does not rotate around its true centre; caused by misalignment, bending, imbalance, and manufacturing inaccuracies; measured as half of TIR on the shaft side ##### Recommended Operating Conditions Summary | Lip Code | Temperature Range | Max Shaft DRO | Max Misalignment (STBM) | Max Pressure | Max Shaft Speed | |---|---|---|---|---|---| | R (Nitrile) | −40°C to +100°C (static); −23°C to +149°C (dynamic) | End play ≤ tolerance | 1°–4° | 10 PSI (~69 kPa) | Back-up required: 0–1600 FPM (none), 1600–2000 FPM (axial), 2400–3000 FPM (axial + radial) | | F, L, P, R, S | −54°C to +163°C (varies) | 0.003" TIR @ 0–2000 RPM | 0.005" @ 0–2000 FPM | 3 PSI @ 0–2000 FPM (except 0 PSI for FF) | 500–2000 FPM depending on configuration | | P, R, S, V | −40°C to +204°C (varies) | 0.020" TIR (varies by speed) | 0.015" @ 0–1000 FPM; 0.010" @ 1000–3600 FPM | 10 PSI @ 0–1000 FPM; 5 PSI @ 1000–2000 FPM; 0 PSI @ 2000–3600 FPM | 3600 FPM (HDW type: 5000+ FPM) | ##### Seal Selection Example (Worked) - **Given:** shaft diameter 30 mm, gearbox application, max speed 2500 rev/min, operating temperature 60°C - **Step 1:** From size tables, select appropriate seal type for 30 mm shaft → suitable type identified - **Step 2:** From seal group chart, identify the seal as a Group 3 type (lip code V — fluoroelastomer for long life) - **Step 3:** Calculate shaft surface speed: - v = r × ω = 0.015 × π × 2500/30 = 3.93 m/s = 773 FPM - **Step 4:** Verify operating conditions: - Temperature 60°C is within allowable range (−40°C to +204°C) ✓ - Shaft tolerance (from tables): +0 / −0.13 mm ✓ - Shaft finish (from tables): 10–20 µinch = 0.254–0.508 µm ✓ - Maximum radial misalignment: 0.015" = 0.381 mm ✓ - Maximum oil pressure: 10 psi = 69 kPa ✓ --- ### Comparison Tables #### Single-Phase Motor Type Comparison | Feature | Permanently Connected Capacitor | Capacitor Start / Induction Run | Capacitor Start / Capacitor Run | |---|---|---|---| | **Starting Torque** | Low | High | High | | **Running Efficiency** | Moderate | Moderate | High | | **Power Factor** | Good | Moderate | Best | | **Noise Level** | Low (smooth running) | Moderate (switching transient) | Moderate (switching transient) | | **Typical Application** | Fan duty only | General purpose, pumps, compressors | Demanding continuous duty | | **Capacitor(s)** | Run only | Start only (switched out) | Start + Run | | **Cost** | Lowest | Moderate | Highest | #### Circlip Type Comparison | Feature | Internal (Type 1300) | External (Type 1400) | E-Clip (Type 1500) | |---|---|---|---| | **Location** | Inside bore | On shaft | On shaft | | **Installation** | Pliers (compress to insert) | Pliers (expand to fit) | Push-on from side | | **Groove Required** | Yes | Yes | No | | **Disassembly** | Easy (with pliers) | Easy (with pliers) | Difficult (destructive) | | **Thrust Capacity** | High | High | Low to moderate | | **Repetitive Assembly** | Yes | Yes | Not recommended | #### Seal Lip Material Comparison | Property | Nitrile (R) | Polyacrylate (P) | Silicone (S) | Fluoroelastomer (V) | TFE (T) | |---|---|---|---|---|---| | **Temperature Range** | −40 to +107°C | −40 to +149°C | −100 to +163°C | −40 to +204°C | −100 to +260°C | | **Oil/Grease Compatibility** | Excellent | Good (EP) | Poor (oxidised) | Excellent | Excellent | | **Chemical Resistance** | Moderate | Good | Moderate | Excellent | Best | | **Abrasion Resistance** | Moderate | Moderate | Low | Good | Excellent | | **Cost** | Low | Moderate | Moderate | High | Highest | | **Dry Running** | No | No | No | Intermittent only | Yes (limited) | --- ### Mermaid Diagrams #### Single-Phase Motor Selection Flowchart ```mermaid flowchart TD A[Application Requirement] --> B{Starting Torque Needed?} B -->|Low - Fan Duty Only| C[Permanently Connected Capacitor] B -->|High| D{Running Efficiency Critical?} D -->|No - Standard Duty| E[Capacitor Start / Induction Run] D -->|Yes - Demanding Duty| F[Capacitor Start / Capacitor Run] C --> G{Speed Requirement?} E --> G F --> G G -->|High Speed ~3000 RPM| H[Two-Pole Motor] G -->|Standard Speed ~1500 RPM| I[Four-Pole Motor] H --> J[Select Frame Size by Power Rating] I --> J J --> K[Verify Mounting Configuration: B3 Foot or B5 Flange] ``` #### Shaft Component Retention — Circlip Selection Process ```mermaid flowchart TD A[Component Requires Axial Retention] --> B{Retention Location?} B -->|Inside Bore| C[Internal Circlip - Type 1300] B -->|On Shaft| D{Groove Possible?} D -->|Yes| E{Repetitive Disassembly Needed?} D -->|No| F[E-Clip - Type 1500 Push-On] E -->|Yes| G[External Circlip - Type 1400 with Lugs] E -->|No| H[No-Groove Type 1465 or E-Clip] C --> I[Determine Size from Shaft/Bore Tables] G --> I F --> I H --> I I --> J[Check Thrust Load: T_c and T_g] J --> K{Shaft Material ≠ 300 MPa Yield?} K -->|Yes| L[Apply Correction Factor to T_g] K -->|No| M[Use Lower of T_c and T_g] L --> M M --> N[Select Circlip Material for Environment] N --> O[Check Galvanic Compatibility with Groove Material] ``` #### Radial Shaft Seal Selection Process ```mermaid flowchart TD A[Seal Required for Rotating Shaft] --> B[Determine Shaft Diameter] B --> C[Determine Operating Temperature] C --> D[Determine Shaft Speed / Surface Speed] D --> E[Determine Pressure Requirements] E --> F[Determine Media - Oil / Grease / Chemical] F --> G{Select Lip Material by Temperature & Media} G --> H[Select Seal Group by Application Type] H --> I[Verify from Operating Conditions Table] I --> J[Check Shaft Tolerance per ISO] J --> K[Check Shaft Finish - 10-20 µinch Ra] K --> L[Check Bore Tolerance per ISO/H8] L --> M[Verify Shaft Hardness ≥ Rc30] M --> N[Check Misalignment: STBM and DRO] N --> O[Confirm Seal Size from Catalogue Tables] ``` #### Seal Anatomy — Component Relationships ```mermaid flowchart LR A[Outer Case / Shell] -->|Press-fits into| B[Bore Housing] C[Sealing Lip] -->|Contacts| D[Rotating Shaft] E[Garter Spring] -->|Maintains pressure on| C F[Inner Shell] -->|Protects| C G[Dust Lip] -->|Excludes| H[External Contaminants] A --- C A --- E A --- F A --- G ``` --- ### Key Terms Glossary - **B3 Mounting** — foot-mounted motor configuration; motor bolted to base via feet - **B5 Mounting** — flange-mounted motor configuration; motor attached via drive-end flange - **Bore Tolerance** — the allowable dimensional variation of the housing bore into which a seal or bearing is fitted - **Capacitor Start / Capacitor Run** — single-phase motor using both a start and run capacitor for optimum torque and efficiency - **Capacitor Start / Induction Run** — single-phase motor using a start capacitor that disconnects at speed - **Circlip** — a retaining ring (snap ring) that fits into a groove to prevent axial movement - **DRO (Dynamic Run-Out)** — the deviation of a shaft from its true centre of rotation during operation - **E-Clip** — a push-on external retaining clip that does not require a machined groove - **Fluoroelastomer** — a premium seal lip material offering the widest temperature and chemical resistance range - **Full Load Torque** — the torque output of a motor at its rated full load speed - **Galvanic Corrosion** — electrochemical corrosion between dissimilar metals in electrical contact, accelerated by an electrolyte - **Garter Spring** — a circular spring inside a radial shaft seal that maintains lip contact pressure on the shaft - **Key** — a machine element inserted between a shaft and hub to transmit torque - **Keyway** — the slot or groove machined into a shaft or hub to receive a key - **Lip Code** — a letter designation identifying the elastomer material of a seal's sealing lip - **Nitrile (Buna-N)** — the most commonly used seal lip material; good for mineral oils and greases - **Permanently Connected Capacitor** — single-phase motor with a run capacitor always in circuit; suitable for fan duty only - **Power Factor** — the ratio of real (useful) power to apparent power in an AC circuit - **Radial Shaft Seal** — a dynamic seal that creates a barrier between a rotating shaft and a stationary housing - **STBM (Shaft-to-Bore Misalignment)** — the static offset of the shaft centreline from the bore centreline - **Synchronous Speed** — the theoretical speed of an AC motor determined by supply frequency and pole count (e.g., 3000 RPM for 2-pole at 50 Hz) - **T_c** — maximum safe thrust load on the circlip itself - **T_g** — maximum safe thrust load on the groove in the shaft or bore - **TIR (Total Indicator Reading)** — the full range of dial indicator movement when measuring eccentricity or run-out --- ### Quick Revision - Single-phase motors: **permanently connected capacitor** (fan duty, low start torque), **capacitor start/induction run** (high start torque, moderate efficiency), **capacitor start/capacitor run** (high start torque, best efficiency) - Two-pole = **3000 RPM** synchronous; four-pole = **1500 RPM** synchronous (at 50 Hz) - Motor mounting: **B3** = foot mount; **B5** = flange mount - Standard key sizes increase with shaft diameter — always refer to the shaft-to-key sizing table - Keyway stress rules: **shear = 0.75 × tensile**; **bearing = 1.5 × tensile** - Common shaft materials: plain carbon steel (1020–1045), stainless (304, 316, 420, 431), alloy (4140, 4340) - Circlip types: **1300** (internal with lugs), **1400** (external with lugs), **1500/E-clip** (push-on, no groove) - Circlip thrust design: always use the **lower** of T_c (circlip load) and T_g (groove load) - For non-300 MPa shaft material, **multiply T_g by (yield point / 300)** - Check **galvanic corrosion** compatibility between circlip material/finish and groove material - Seal lip material selection: **R** (nitrile, general purpose), **V** (fluoroelastomer, premium), **S** (silicone, wide temp), **T** (TFE, widest chemical resistance) - Shaft finish for seals: **10–20 microinches Ra** (0.25–0.50 µm), plunge ground, zero lead angle - Shaft hardness for seals: **minimum Rockwell C30** - Bore tolerance per **ISO/H8**; bore finish **125 microinches Ra** (3.2 µm) or smoother - Seal surface speed (FPM) is a better selection criterion than RPM - **STBM** = static misalignment; **DRO** = dynamic run-out; both measured as half of TIR --- --- # PART II — POWER TRANSMISSION: GEARS & GEARBOXES --- ## Chapter 4: Worm Gearboxes & Geared Motor Units --- ### Overview This document covers **worm gearbox selection and specification**, including single and double reduction configurations, and **geared motor unit selection** for industrial drive applications. It provides comprehensive rating data for various nominal gear ratios, centre distances, input speeds, and mounting configurations, along with a step-by-step method for selecting an appropriate geared motor unit based on application requirements such as torque, speed, load classification, overhung load, and thrust load. --- ### Key Concepts - **Worm Gearbox**: A gear system using a worm (screw-type gear) meshing with a worm wheel to achieve high reduction ratios in a compact form - **Nominal Ratio**: The designed speed reduction ratio between input and output shafts (e.g., 40:1, 50:1, 60:1, 70:1) - **Centre Distance**: The distance between the centrelines of the worm shaft and the wheel shaft; determines gearbox physical size and torque capacity - **Thermal Rating**: The maximum continuous input power (kW) a gearbox can handle without exceeding safe operating temperatures under standard conditions - **Mechanical Rating**: The maximum input power (kW) based on the strength of the gears, shafts, and bearings — typically higher than thermal rating - **Efficiency (%)**: The ratio of output power to input power; worm gearboxes have lower efficiency at higher ratios due to sliding contact - **Output Torque (Nm)**: The rotational force available at the output shaft — specified for both thermal and mechanical limits - **Single Reduction**: One worm and wheel pair providing a single stage of speed reduction - **Double Reduction**: Two stages of worm and wheel reduction in series for very high overall ratios - **Overhung Load (OHL)**: A radial force applied to the output shaft by an attached mechanism (e.g., pulley, sprocket, gear) - **Axial (Thrust) Load**: A force acting along the axis of the output shaft, caused by mechanisms such as helical gears - **Drive Classification**: A rating system (1 to 4) that accounts for the severity of service based on load type and operating hours - **Load Classification**: Categorisation of driven machinery as Steady (S), Medium Impulsive (M), or Highly Impulsive (H) - **Geared Motor Unit**: A pre-assembled combination of an electric motor and a gearbox, designed as a compact drive solution - **Force Feed Lubrication**: Required for operation in shaded (high-load) areas of rating tables; uses a pump to circulate lubricant - **Oil Cooler**: External cooling device that allows higher ratings beyond standard thermal limits - **Taper Lock Bush**: A mechanical fastening method for mounting pulleys, sprockets, or gears onto shafts using a tapered interference fit --- ### Detailed Notes #### Single Reduction Worm Gearbox Ratings ##### Nominal Ratio 40:1 - **Input Speed**: 1800 rev/min (output 45 rev/min) down to 100 rev/min (output 2.5 rev/min) - **Centre Distances Available**: 10, 12, 14, 17, 20, 24, 28 (units correspond to shaft separation) - **Key Observations**: - At **1800 rev/min input**, thermal input ranges from 28 kW (CD 10) to 216 kW (CD 28), mechanical input from 33 kW to 372 kW - **Efficiency** improves with increasing centre distance: 86% (CD 10) to 89% (CD 28) at 1800 rev/min input - At **lower input speeds** (e.g., 500 rev/min), thermal input drops significantly (10–105 kW), but mechanical input becomes proportionally larger relative to thermal - At **100 rev/min input**, only mechanical ratings are listed (no thermal rating), with efficiency dropping to 68–77% - **Maximum output torque** (single key): ranges from 11,200 Nm (CD 10) to 72,000 Nm (CD 28) - **Maximum output torque** (standard shaft): ranges from 15,800 Nm (CD 10) to 146,400 Nm (CD 28) ##### Nominal Ratio 50:1 - **Input Speed**: 1800 rev/min (output 36 rev/min) down to 100 rev/min (output 2 rev/min) - **Key Observations**: - Thermal input ratings are **lower** than 40:1 at the same centre distance due to increased sliding losses - At **1800 rev/min**, thermal input ranges from 23 kW (CD 10) to 170 kW (CD 28) - **Efficiency** is lower than 40:1: 83–86% at 1800 rev/min, dropping to 64–72% at 100 rev/min - At **250 rev/min input**, efficiency drops to 70–78% - **Maximum output torque** values remain the same as 40:1 (they are gearbox-size dependent, not ratio dependent) ##### Nominal Ratio 60:1 - **Input Speed**: 1800 rev/min (output 30 rev/min) down to 100 rev/min (output 1.6 rev/min) - **Key Observations**: - Further reduction in thermal input compared to 50:1: 21 kW (CD 10) to 149 kW (CD 28) at 1800 rev/min - **Efficiency** continues to decrease: 81–84% at 1800 rev/min, down to 61–69% at 100 rev/min - Mechanical ratings become increasingly dominant at low input speeds - At **250 rev/min input**, efficiency is 67–75% ##### Nominal Ratio 70:1 - **Input Speed**: 1800 rev/min (output 25.7 rev/min) down to 100 rev/min (output 1.4 rev/min) - **Key Observations**: - Lowest thermal input ratings among the four ratios: 18 kW (CD 10) to 133 kW (CD 28) at 1800 rev/min - **Efficiency** is the lowest: 78–82% at 1800 rev/min, dropping to 55–65% at 100 rev/min - At very low input speeds (100 rev/min), efficiency can be as low as 55% - Higher ratios generate more heat due to greater sliding between worm and wheel ##### General Trends Across Ratios | Parameter | Effect of Increasing Ratio (40:1 → 70:1) | |---|---| | **Thermal Input (kW)** | Decreases (more heat generated) | | **Mechanical Input (kW)** | Relatively stable for same CD | | **Efficiency** | Decreases (more sliding friction) | | **Output Torque** | Increases slightly (higher multiplication) | | **Output Speed** | Decreases (for same input speed) | ##### Important Notes from Rating Tables - Ratings in **shaded areas** require **force feed lubrication** - All ratings are based on **mineral oils**; synthetic lubricant ratings available on request - **Oil coolers** can provide higher ratings than those listed - **Two keys** must be specified for the wheel and output shaft when maximum output torque for **single key** is exceeded - **High tensile steel output shaft** must be specified when maximum output torque for **standard shaft** is exceeded --- #### Double Reduction Worm Gearbox Ratings (Mineral Oil) ##### Input Speed: 1450 rev/min - **Nominal Ratios Available**: 75:1 to 4900:1 - **Output Speeds**: 19.0 rev/min (ratio 75) down to 0.30 rev/min (ratio 4900) - **Centre Distances Available**: 10, 12, 14, 17, 20, 24, 28 - **Key Observations**: - At **ratio 75**, input power ranges from 14.7 kW (CD 10) to 156 kW (CD 28), efficiency 83–88% - At **ratio 150**, input power ranges from 13.3 kW (CD 10) to 186 kW (CD 28), efficiency 79–83% - At **ratio 500**, input power ranges from 6.2 kW (CD 10) to 68.2 kW (CD 28), efficiency 67–76% - At **ratio 1000**, input power ranges from 4.1 kW (CD 10) to 37 kW (CD 28), efficiency 59–70% - At **ratio 4900**, input power ranges from 1.2 kW (CD 10) to 12.0 kW (CD 28), efficiency 33–43% - **Output torque** reaches maximum capacity at larger centre distances (up to 165,000 Nm at CD 28) - **Efficiency drops dramatically** at very high ratios — as low as 33% at ratio 4900, CD 10 ##### Input Speed: 960 rev/min - Same ratio and centre distance options as 1450 rev/min - **Key Observations**: - Input power ratings are **lower** than at 1450 rev/min across all configurations - At **ratio 75**, input power ranges from 11.9 kW (CD 10) to 119 kW (CD 28), efficiency 81–87% - At **ratio 500**, input power ranges from 4.6 kW (CD 10) to 44.3 kW (CD 28), efficiency 64–74% - At **ratio 4900**, input power ranges from 0.9 kW (CD 10) to 8.2 kW (CD 28), efficiency 31–40% - Output torque values reach the same maximums as 1450 rev/min tables - Efficiency is slightly lower at 960 rev/min compared to 1450 rev/min for the same ratio --- #### Gearbox Dimensions and Configurations ##### Mounting Types | Code | Configuration | Mounting | Reduction | |---|---|---|---| | **TWU** | Underdriven | Foot | Single | | **TWO** | Overdriven | Foot | Single | | **TSMW** | Shaft Mounted | Shaft | Single | | **TWV** | Vertical | Foot | Single | | **TWDU** | Underdriven | Foot | Double | | **TWDO** | Overdriven | Foot | Double | | **TSMWD** | Shaft Mounted | Shaft | Double | | **TWDV** | Vertical | Foot | Double | ##### Unit Size Range - Available sizes: 10, 12, 14, 17 (single reduction also includes 20, 24, 28) - Sizes are designated by centre distance number - Double reduction units add a second worm/wheel stage, increasing overall envelope ##### Key Dimensional Parameters - **A** — Overall length (mm) - **B** — Height to shaft centre (mm) - **C** — Width across mounting feet (mm) - **D** — Mounting foot length (mm) - **F** — Mounting hole pattern (format: pitch × number / bolt size) - **G** — Output shaft details (bore, keyway, etc.) - **H, J** — Additional envelope dimensions - **K** — Bolt hole size (for mounting) - **Oil Capacity** — Approximate litres of lubricant required - **Weight** — Approximate mass in kg (quoted without oil) ##### Wormshaft and Wheelshaft Details - **E1** — Wormshaft diameter - **V1** — Wormshaft length - **W1** — Wormshaft bearing span - **X1, X2** — Wormshaft extension details - **Tapped Hole** — Thread size for input shaft connection (e.g., M20×42, M24×50, M30×60) - **E2** — Wheelshaft (output) diameter - **V2** — Wheelshaft length - **W2** — Wheelshaft bearing span - **Y1, Y2** — Wheelshaft extension details ##### Dimensional Data Summary (Single Reduction — Foot Mounted Underdriven) | Unit Size | A (mm) | B (mm) | C (mm) | D (mm) | Oil Capacity (L) | Weight (kg) | |---|---|---|---|---|---|---| | Size 10 | 254.0 | 171.5 | 419 | 349 | 8.8 | 365 | | Size 12 | 304.8 | 190.5 | 470 | 387 | 12.5 | 507 | | Size 14 | 355.6 | 215.9 | 552 | 457 | 18.6 | 840 | | Size 17 | 431.8 | 254.0 | 648 | 521 | 34.1 | 1397 | | Size 20 | 508.0 | 292.1 | 762 | 660 | 70.5 | 2034 | | Size 24 | 609.6 | 355.6 | 914 | 711 | 132.0 | 3632 | | Size 28 | 711.2 | 406.4 | 1041 | 813 | 168.0 | 5029 | ##### Important Configuration Notes - **Non-reversible units** require a **sprag clutch backstop** to be fitted - Units with central mounting pads use a bolt hole diameter designated as dimension **K** - **Shaft-mounted types** use output sleeve details instead of foot mounting dimensions - For units with **flange mounting motors**, refer to separate motor-specific data - **Double reduction units** have two output keys as a standard feature - Second reduction units may have blank central mounting pads --- #### Geared Motor Units ##### Overview - Designed for relatively **low power applications** (approximately 0.1 to 4.0 kW motor power input) - Only **foot-mounted** geared motor units are covered; output is via bored bush with key or output shaft extension - Units can also be specified as a **free-standing unit** (gearbox without motor) coupled to a designer's chosen motor - **Five gearbox sizes** available (designated by frame size number: 11, 17, 22, 26, 30) - **12 gear ratios** available per size, ranging from 5:1 to 70:1 - All units fitted with **4-pole motors** (nominal speed 1400–1420 rev/min), giving output speeds from 288 rev/min down to 20 rev/min - **11 motor sizes** available, ranging from 0.12 kW to 4.0 kW - Each gearbox size can be fitted with multiple motor sizes according to power requirements - Total of **104 power and speed combinations** available > **Note**: The smallest motor size (0.12 kW) is not a preferred size and may have extended lead times. --- #### Geared Motor Unit Selection Method **Step 1: Establish Mechanical Data** - Determine the type of output (driven) machinery - Establish maximum (design) torque, power, and speed (including tolerance range on speed if given) - Determine duration of service: continuous or intermittent - Determine average number of hours per day of operation **Step 2: Determine Load Classification** - From the load classification table, identify whether the driven machinery is: - **S (Steady)** — e.g., conveyors (uniformly loaded), fans, generators - **M (Medium Impulsive)** — e.g., car dumpers, dough mixers, machine tools, textile dryers - **H (Highly Impulsive)** — e.g., crushers, hammer mills, rubber mills, tumbling barrels **Step 3: Determine Drive Classification** - Cross-reference: - Load classification (S, M, or H) from Step 2 - Average hours per day of operation (Under 3 hours, 3–10 hours, Over 10 hours) - This yields a **Drive Classification** number from **1 to 4** | Driven Machinery | Under 3 hrs/day | 3–10 hrs/day | Over 10 hrs/day | |---|---|---|---| | **Steady (S)** | 1 | 1 | 2 | | **Medium Impulsive (M)** | 1 | 2 | 3 | | **Highly Impulsive (H)** | 2 | 3 | 4 | **Step 4: Select Unit from Data Tables** - Using the drive classification from Step 3, go to the appropriate data table - Select the unit based on required **output speed** and **output power** (or torque) - The data tables provide: output power (kW), output torque (Nm), and recommended gearbox size for each motor power and gear ratio **Step 5: Check Overhung Load** - If a gear, pulley, chain-wheel, flywheel, or other mechanism is directly attached to the output shaft, calculate the **overhung load** (radial force on the shaft) - Use the approximate formula: $F = \frac{2 \cdot f \cdot T}{d} = \frac{60 \cdot f \cdot P}{\pi \cdot d \cdot N}$ Where: - **F** = overhung load (N) - **T** = output shaft torque (Nm) — use design value, not selection table value - **P** = output shaft power (W) — use design value, not selection table value - **d** = pitch circle diameter (PCD) of pulley, sprocket, or gear (m) - **N** = output shaft speed (rev/min) - **f** = drive application factor: - 1.0 for chain drive or toothed belt - 1.25 for gear drive - 1.5 for vee (wedge) belt - 2.0 for flat friction belt - Compare calculated overhung load to the **allowable overhung load** from the capacity table - Overhung load capacities assume the load is applied **mid-way along the shaft** (at dimension A) - If the allowable value is exceeded, either choose a **larger unit** or use an **intermediate shaft (layshaft)** with its own bearings and a flexible coupling **Step 6: Check Thrust (Axial) Load** - If a helical gear or other mechanism creates an axial load on the output shaft, verify it does not exceed the **allowable axial load** from the capacity table - If exceeded, choose a larger gearbox or use an intermediate shaft with bearings to absorb the axial load **Step 7: Check Output Shaft Dimensions** - Verify the output shaft diameter is suitable for the attached mechanism (e.g., bore of pulley or sprocket) - Check mounting bolt sizes, bolt hole locations, and centre distances from the dimension data **Step 8: Specify the Unit** - Specify: gearbox size, gear ratio, output speed, and motor details (frame size, power rating) - Motor data includes: rated speed, current at rated voltage, moment of inertia, and rotor mass --- #### Motor Ratings and Performance Data | Rated Output (kW) | Frame Size | Speed (rev/min) | Current at 415V (A) | Current at 380V (A) | Load Moment of Inertia (kg·m²) | Rotor Moment of Inertia (kg·m²) | Rotor Mass (kg) | |---|---|---|---|---|---|---|---| | 0.12 | D63 | 1400 | 0.50 | 0.60 | 0.27 | 0.000365 | 0.97 | | 0.18 | D63 | 1400 | 0.57 | 0.62 | 0.27 | 0.000365 | 0.97 | | 0.25 | D71 | 1400 | 0.76 | 0.83 | 0.27 | 0.000543 | 1.44 | | 0.37 | D71 | 1400 | 1.05 | 1.15 | 0.40 | 0.000543 | 1.44 | | 0.55 | D80 | 1400 | 1.44 | 1.57 | 0.50 | 0.00131 | 2.17 | | 0.75 | D80 | 1400 | 1.90 | 2.10 | 0.70 | 0.00156 | 2.58 | | 1.1 | D90S | 1410 | 2.50 | 2.75 | 0.65 | 0.00343 | 4.06 | | 1.5 | D90L | 1420 | 3.45 | 3.75 | 0.78 | 0.00393 | 4.65 | | 2.2 | D100L | 1420 | 4.70 | 5.1 | 1.5 | 0.00980 | 7.18 | | 3.0 | D100L | 1420 | 6.2 | 6.8 | 2.0 | 0.0115 | 8.65 | | 4.0 | D112M | 1420 | 8.1 | 8.8 | 2.1 | 0.135 | 9.95 | --- #### Motor Flange and Shaft Dimensions | Motor Power (kW) | Frame | Shaft eD (mm) | Shaft E (mm) | Shaft F (mm) | Shaft G (mm) | Flange Dia eP (mm) | Flange eD (mm) | PCD S (mm) | Holes (M size) | C-Face eP (mm) | C-Face eN (mm) | Tapped PCD S (mm) | Bolt Size | |---|---|---|---|---|---|---|---|---|---|---|---|---|---| | 0.12–0.37 | D63–D71 | 14 | 30 | 5 | 11.0 | 16 | 160 | 110 | 10 | 130 | 105 | 70 | M6 | | 0.55–0.75 | D80 | 19 | 40 | 6 | 15.5 | 21.5 | — | — | — | 120 | 80 | — | M6 | | 1.1–1.5 | D90S–D90L | 24 | 50 | 8 | 20.0 | 27 | 200 | 130 | 12 | 140 | 95 | — | M8 | | 2.2–3.0 | D100L | 28 | 60 | 8 | 24.0 | 30 | 250 | 180 | 15 | 160 | 110 | — | M8 | | 4.0 | D112M | 28 | 60 | 8 | 24.0 | 30 | 250 | 180 | 15 | 160 | 110 | — | M8 | --- #### Overhung Load Capacities (N) | Output Speed (rev/min) | Size 11 OHL | Size 11 Axial | Size 17 OHL | Size 17 Axial | Size 22 OHL | Size 22 Axial | Size 26 OHL | Size 26 Axial | Size 30 OHL | Size 30 Axial | |---|---|---|---|---|---|---|---|---|---|---| | 300 | 900 | 1250 | 1700 | 2000 | 3000 | 6000 | 8000 | 4000 | 6000 | 9000 | | 200 | 950 | 1400 | 1750 | 2500 | 3200 | 7000 | 9000 | 4200 | 6200 | 10000 | | 150 | 1000 | 1650 | 1800 | 3000 | 3400 | 8000 | 10000 | 4400 | 6400 | 11000 | | 125 | 1050 | 1900 | 1850 | 3500 | 3600 | 9000 | 10000 | 4600 | 6600 | 12000 | | 100 | 1100 | 2200 | 1900 | 3800 | 4000 | 10000 | 10000 | 4700 | 6700 | 13000 | | 75 | 1200 | 2500 | 1950 | 4000 | 4000 | 11000 | 10000 | 4800 | 6800 | 13000 | | 50 | 1300 | 2800 | 2000 | 6000 | 4000 | 12000 | 10000 | 4900 | 6900 | 15000 | | 25 | 1350 | 3200 | 2050 | 7000 | 4000 | 13000 | 5000 | 14000 | 7000 | 15000 | | 15 | 1350 | 3800 | 2050 | 8000 | 4000 | 13000 | 5000 | 14000 | 7000 | 15000 | | 10 | 1350 | 4400 | 2050 | 9000 | 4000 | 13000 | 5000 | 14000 | 7000 | 15000 | | 5 | 1350 | 4800 | 2050 | 10000 | 4000 | 13000 | 5000 | 14000 | 7000 | 15000 | - Load capacities assume resultant load applied **mid-way** along the shaft (dimension A) - Dimension A varies by gearbox size: 60 mm (Size 11), 75 mm (Size 17), 95 mm (Size 22), 115 mm (Size 26), 140 mm (Size 30) --- #### Service Factors | Prime Mover Type | Duration of Service | Steady Load | Medium Impulsive | Highly Impulsive | |---|---|---|---|---| | Electric, Air, Hydraulic Motor or Steam Turbine (Steady Input) | 3 hrs/day max | 0.90 | 1.00 | 1.50 | | | 3–10 hrs | 1.00 | 1.25 | 1.75 | | | Over 10 hrs | 1.25 | 1.50 | 2.00 | | Multi-Cylinder IC Engine (Medium Impulsive Input) | 3 hrs/day max | 1.00 | 1.25 | 1.75 | | | 3–10 hrs | 1.25 | 1.50 | 2.00 | | | Over 10 hrs | 1.50 | 1.75 | 2.25 | | Single-Cylinder IC Engine (Highly Impulsive Input) | 3 hrs/day max | 1.25 | 1.50 | 2.00 | | | 3–10 hrs | 1.50 | 1.75 | 2.25 | | | Over 10 hrs | 1.75 | 2.00 | 2.50 | #### Starts per Hour Factor (f_s) | Maximum Starts per Hour | 5 | 50 | 100 | 300 | |---|---|---|---|---| | **Starts Factor** | 1.0 | 1.1 | 1.15 | 1.2 | --- #### Worked Example: Geared Motor Unit Selection **Problem**: An industrial textile dryer operates for 12 hours/day, driven by a geared motor unit via a wedge belt drive. The wedge belt pulley has a PCD of 160 mm and will be attached to the output shaft via a taper lock bush with a maximum bore size of 50 mm. The torque at the pulley is 200 Nm and the required speed is 35 ± 2 rev/min. **Solution**: 1. **Output torque** = 200 Nm at 35 ± 2 rev/min - Required output power: P = T × ω = 200 × (π × 35 / 30) = **0.733 kW** 2. **Load classification**: Textile dryer = **M (Medium Impulsive)** 3. **Drive classification**: Load M, 12 hrs/day (over 10 hours) → **Drive Classification 3** 4. **Unit selection**: From Drive Classification 3 data table, select a unit with output speed 36 rev/min, ratio 40:1, output torque 225 Nm — output speed 36 rev/min is within the tolerance of 35 ± 2 rev/min. Unit size: Size 30. 5. **Overhung load check**: - F = (2 × f × T) / d = (2 × 1.5 × 200) / 0.16 = **3750 N** - Allowable OHL for Size 30 at 50 rev/min = 6900 N; at 25 rev/min = 7000 N - 3750 N < 6900 N → **OK, no interpolation necessary** 6. **Thrust load**: No helical gear → **No axial load** → OK 7. **Output shaft diameter**: Size 30 output shaft = 40 mm (nominal) - Maximum pulley bore = 50 mm → 40 mm < 50 mm → **OK** - Bolt holes: 14.5 mm diameter → use M14 bolts - Bolt hole centre distances: 160 mm (side) and 130 mm (end) 8. **Specification**: Size 30, Ratio 40:1, Output Speed 36 rev/min, D90S frame motor (1.1 kW) --- ### Comparison Tables #### Single vs Double Reduction Gearboxes | Feature | Single Reduction | Double Reduction | |---|---|---| | **Ratio Range** | 5:1 to 70:1 | 75:1 to 4900:1 | | **Efficiency** | 55–89% (varies with ratio) | 31–88% (varies with ratio) | | **Complexity** | One worm/wheel set | Two worm/wheel sets in series | | **Size** | Smaller for same CD | Larger due to two stages | | **Cost** | Lower | Higher | | **Heat Generation** | Moderate | Higher (two friction stages) | | **Typical Application** | Moderate speed reduction | Very high speed reduction, very low output speeds | | **Output Speed Range** | 2–45 rev/min (with 4-pole motor) | 0.19–19 rev/min (with 4-pole motor) | #### Efficiency vs Ratio (Single Reduction, at 1800 rev/min Input, Approx. CD 20) | Nominal Ratio | Efficiency (%) | |---|---| | 40:1 | ~88% | | 50:1 | ~85% | | 60:1 | ~82% | | 70:1 | ~80% | #### Mounting Configuration Comparison | Feature | Foot Mount (Underdriven) | Foot Mount (Overdriven) | Shaft Mount | Vertical Foot Mount | |---|---|---|---|---| | **Input Position** | Below output | Above output | Side-mounted | Below output (vertical) | | **Output Shaft** | Horizontal | Horizontal | Hollow bore (sleeve) | Vertical | | **Foundation Required** | Yes | Yes | No (mounts on driven shaft) | Yes | | **Typical Use** | General purpose | Space-constrained applications | Conveyor drives, agitators | Vertical mixers, pumps | | **Torque Restraint** | Through mounting bolts | Through mounting bolts | External arm/bracket | Through mounting bolts | --- ### Mermaid Diagrams #### Geared Motor Unit Selection Process ```mermaid flowchart TD A[Step 1: Establish Mechanical Data] --> B[Determine output torque, power, speed] B --> C[Determine service duration and hours/day] C --> D[Step 2: Load Classification] D --> E{Driven Machinery Type?} E -->|Uniform/Light| F["Steady (S)"] E -->|Moderate Impact| G["Medium Impulsive (M)"] E -->|Heavy Impact| H["Highly Impulsive (H)"] F --> I[Step 3: Drive Classification] G --> I H --> I I --> J[Cross-reference: Load Class × Hours/Day] J --> K[Drive Classification 1–4] K --> L[Step 4: Select Unit from Data Table] L --> M[Match output speed and power/torque] M --> N[Step 5: Check Overhung Load] N --> O{F ≤ Allowable OHL?} O -->|Yes| P[Step 6: Check Thrust Load] O -->|No| Q[Choose larger unit OR use layshaft] Q --> P P --> R{Axial Load ≤ Allowable?} R -->|Yes| S[Step 7: Check Output Shaft Dimensions] R -->|No| T[Choose larger unit OR use layshaft] T --> S S --> U[Verify bore, bolt sizes, centre distances] U --> V[Step 8: Specify Unit] V --> W[Size + Ratio + Speed + Motor] ``` #### Worm Gearbox Operating Parameter Relationships ```mermaid flowchart LR A[Higher Gear Ratio] --> B[Lower Output Speed] A --> C[Lower Efficiency] A --> D[Higher Heat Generation] A --> E[Higher Output Torque per kW Input] F[Larger Centre Distance] --> G[Higher Torque Capacity] F --> H[Higher Power Capacity] F --> I[Larger Physical Size] F --> J[Higher Oil Capacity] F --> K[Higher Weight] L[Lower Input Speed] --> M[Lower Thermal Rating] L --> N[Lower Efficiency] L --> O[Mechanical Rating Dominates] ``` #### Overhung Load Calculation Decision Flow ```mermaid flowchart TD A[Is a mechanism attached to the output shaft?] -->|No| B[No overhung load check required] A -->|Yes| C[Identify mechanism type] C --> D[Determine drive application factor f] D --> E["f = 1.0 (chain/toothed belt)"] D --> F["f = 1.25 (gear drive)"] D --> G["f = 1.5 (vee belt)"] D --> H["f = 2.0 (flat belt)"] E --> I["Calculate F = (2 × f × T) / d"] F --> I G --> I H --> I I --> J{F ≤ Allowable OHL for unit size and speed?} J -->|Yes| K[Selection OK — proceed] J -->|No| L{Options} L --> M[Select larger gearbox unit] L --> N[Use intermediate layshaft with bearings and flexible coupling] ``` --- ### Key Terms Glossary - **Centre Distance (CD)**: The perpendicular distance between the worm shaft axis and the wheel shaft axis; determines the gearbox frame size and directly affects torque/power capacity - **Thermal Rating**: Maximum input power under continuous duty without exceeding safe temperature limits, based on standard ambient conditions and mineral oil lubrication - **Mechanical Rating**: Maximum input power based on gear tooth strength, shaft strength, and bearing capacity — typically exceeds thermal rating - **Worm**: A screw-shaped gear that meshes with a worm wheel; the driving element in a worm gearbox - **Worm Wheel**: A toothed wheel that meshes with the worm; the driven element producing the speed reduction - **Overhung Load (OHL)**: A radial force perpendicular to the shaft axis, generated by belt tension, chain pull, or gear mesh forces on an attached drive element - **Axial (Thrust) Load**: A force acting parallel to the shaft axis, commonly produced by helical gears or inclined conveyor drives - **Drive Application Factor (f)**: A multiplier applied to the overhung load formula to account for the dynamic characteristics of different drive types (belt, chain, gear) - **Taper Lock Bush**: A split, tapered sleeve used to clamp a pulley, sprocket, or coupling to a shaft without keyway modification; allows easy mounting and removal - **Sprag Clutch Backstop**: A one-way mechanical device fitted to non-reversible gearboxes to prevent reverse rotation under load (e.g., inclined conveyors) - **Force Feed Lubrication**: A system using an oil pump to circulate lubricant to gearbox components, required for high-load operating conditions - **Layshaft**: An intermediate shaft supported by its own bearings, interposed between the gearbox output shaft and the driven mechanism to absorb overhung or thrust loads - **PCD (Pitch Circle Diameter)**: The effective diameter of a pulley, sprocket, or gear at which the driving force acts - **Service Factor (f_d)**: A multiplier applied during selection that accounts for the severity of the application, prime mover type, and hours of operation - **Free-Standing Unit**: A gearbox supplied without a motor, intended to be coupled to a separately sourced motor by the system designer --- ### Quick Revision - **Worm gearbox efficiency decreases** as the gear ratio increases (40:1 ≈ 88% → 70:1 ≈ 80% at high input speeds) - **Thermal ratings limit continuous duty**; mechanical ratings limit short-duration peak loads - **Centre distance** is the primary determinant of gearbox size and torque capacity - **Shaded areas** in rating tables require force feed lubrication; oil coolers can extend ratings further - **Two keys** are required when single key torque limits are exceeded; **high tensile shafts** when standard shaft torque limits are exceeded - **Double reduction** achieves ratios from 75:1 to 4900:1 but with significantly lower efficiency (as low as 31%) - **Geared motor unit selection** follows an 8-step process: mechanical data → load classification → drive classification → unit selection → OHL check → thrust check → shaft dimensions → specification - **Overhung load formula**: F = 2fT/d — always use the **design** torque value, not the selection table value - **Drive application factors**: 1.0 (chain), 1.25 (gear), 1.5 (vee belt), 2.0 (flat belt) - **Load classifications**: S (Steady), M (Medium Impulsive), H (Highly Impulsive) — determined by the type of driven machinery - **Drive classifications** (1–4) combine load classification with daily operating hours - If overhung or thrust loads exceed allowable values, either **upsize the gearbox** or **use a layshaft** with its own bearings - **Non-reversible units** must have a **sprag clutch backstop** fitted - Motor sizes range from **0.12 kW (D63 frame)** to **4.0 kW (D112M frame)**, all 4-pole at nominal 1400–1420 rev/min - **Maximum output torques** are gearbox-size dependent, not ratio dependent: single key up to 72,000 Nm, standard shaft up to 146,400 Nm at largest centre distance --- --- ## Chapter 5: Couplings & Worm Gearbox Selection --- ### Overview This document consolidates mechanical design reference data for **shaft couplings** and **worm gearboxes**, two fundamental power transmission components. It covers selection criteria, dimensional data, performance ratings, and a step-by-step gearbox selection methodology with a worked example. The material is drawn from an industry-standard mechanical design data manual and is intended as a practical engineering reference for component specification and selection. --- ### Key Concepts - **Shaft Couplings** connect two rotating shafts to transmit torque, while accommodating varying degrees of misalignment (angular, axial, or parallel) - **Taper Bushes** are standardised locking devices used to mount couplings (and other components) onto shafts, using a taper-lock mechanism for secure, keyway-based attachment - **Worm Gearboxes** provide high reduction ratios in a compact form, using a worm (screw) and worm wheel (gear) arrangement — suited to high-power, low-speed applications - **Service Factors** adjust theoretical ratings to account for real-world operating conditions such as load type, duty cycle, and ambient temperature - **Overhung Loads** are radial forces imposed on a gearbox output shaft by belt, chain, or gear drives — a critical check in gearbox selection --- ### Detailed Notes #### 1. Coupling Types Four main coupling families are covered, each suited to different application requirements: ##### 1.1 Pin-Type Flexible Couplings (Taper Bore) - **Construction**: Two half-bodies joined by elastomeric-bushed pins; taper bore accepts standard taper bushes - **Product code convention**: Code ending in `/77` denotes one taper-bored half body; code ending in `/88` denotes a second taper-bored half body; a code ending in `/78` combines one of each to form a complete coupling - **Key parameters**: Number of pins (3–12), power rating at 100 RPM (kW), nominal torque (Nm), normal maximum speed (RPM), taper bush number, bore range, and setting width - **Bore range**: Minimum 32 mm to maximum 5.000" (125 mm) depending on size - **Speed range**: 2200–6800 RPM (decreasing with increasing coupling size) - **Torque range**: 194–18,536 Nm across the size range - **Note**: At maximum bore, keyways may be shallower than standard ##### 1.2 Tyre-Type Flexible Couplings - **Construction**: Two flanged half-bodies connected by a flexible rubber tyre element, providing high misalignment capacity and vibration damping - **Available body types**: "F" type (smaller sizes, ~40–60 range) and "H" type (larger sizes) - **Taper bore variants**: Available with product code `/77` (F-type half body) and `/88` (H-type half body) - **Key parameters**: Bore dimensions (A, B), setting distance (M), flange diameter (E), tyre width (W), clamping screw torque, and mass - **Bore range**: 12 mm minimum up to 150 mm maximum bore - **Tyre widths**: 67–274 mm depending on coupling size - **Clamping gap**: 2–6 mm (important for tyre installation and removal) - **Note**: Clamping screws must be withdrawn to release tyres; wrench clearance for taper bush screws is needed when the bush large end is outboard ###### Tyre Coupling Ratings Table | Coupling Size | Power at Shaft (kW) | Max Speed (rev/min) | Normal Torque (Nm) | Max Torque (Nm) | Torsional Stiffness (Nm/° at 20°C) | Misalignment — Angular (°) | Misalignment — Axial (mm) | End Float (mm) | |---|---|---|---|---|---|---|---|---| | TY40 | 0.26 | 4500 | 25 | 65 | 6.0 | 4 | 1.1 | 1.3 | | TY50 | 0.69 | 4500 | 86 | 165 | 12.5 | 4 | 1.3 | 1.7 | | TY60 | 1.33 | 4000 | 127 | 320 | 32.0 | 4 | 1.6 | 2.0 | | TY70 | 2.62 | 3600 | 250 | 625 | 60.0 | 4 | 1.9 | 2.3 | | TY80 | 3.93 | 3100 | 375 | 940 | 63.0 | 4 | 2.1 | 2.6 | | TY90 | 5.24 | 3000 | 500 | 1250 | 91.0 | 4 | 2.4 | 3.0 | | TY100 | 7.07 | 2600 | 675 | 1690 | 126.0 | 4 | 2.6 | 3.3 | | TY110 | 9.2 | 2300 | 875 | 2130 | 178 | 4 | 2.9 | 3.7 | | TY120 | 13.9 | 2060 | 1300 | 3540 | 298 | 4 | 3.2 | 4.0 | | TY140 | 24.3 | 1800 | 2320 | 5642 | 470 | 4 | 3.7 | 4.8 | | TY160 | 39.4 | 1600 | 3770 | 5340 | 776 | 4 | 4.2 | 5.3 | | TY180 | 65.8 | 1500 | 6270 | 16455 | 1030 | 4 | 4.8 | 6.0 | ##### 1.3 Disc-Type Flexible Couplings - **Construction**: Two hubs connected by a flexible disc element (typically stainless steel or composite laminate), providing torsional rigidity with angular and axial misalignment capacity - **Key parameters**: Taper bush number, power at 100 RPM (kW), nominal torque (Nm), maximum speed (RPM), bore range, and end float - **Bore range**: 12 mm minimum up to 110 mm maximum - **Speed range**: 900–2900 RPM (normal maximum speeds with 1° angular malalignment; higher speeds require manufacturer consultation) - **Torque range**: 71.6–4298 Nm - **Misalignment tolerance**: Maximum 1° angular, maximum 0.5 mm axial - **Size designations**: Use letter-number codes (e.g., D41N, D52S, D71W, D89N, D108W, D127S) where the letter suffix indicates the disc type (N = normal, S = standard, W = wide) ##### 1.4 Chain-Type Flexible Couplings - **Construction**: Two sprocket-like hubs enclosed by a duplex roller chain and a cover/housing; the chain allows for angular, axial, and parallel misalignment - **Key parameters**: Taper bush number, power at 100 RPM (kW), nominal torque (Nm), maximum speed (RPM), bore range, dimensions (B through F), and malalignment tolerances - **Bore range**: 12 mm minimum up to 140 mm maximum - **Speed range**: 700–3500 RPM (higher speeds require manufacturer consultation) - **Torque range**: 52.5–8595 Nm - **Misalignment tolerance**: 1° angular, 0.25–0.5 mm axial - **Taper bore variants available** for selected sizes --- #### 2. Taper Bushes — Range of Bores Taper bushes are the standardised interface between shaft and coupling (or sprocket, pulley, etc.). The metric range includes: | Bush Number | Bore Range (mm) | |---|---| | TB 1008 | 9, 10, 11 | | TB 1108 | 9, 10, 12, 14 | | TB 1210 | 12, 14, 16, 18, 19, 20, 22, 24, 25, 28 | | TB 1215 | 12, 14, 16, 18, 19, 20, 22, 24, 25, 28, 30, 32 | | TB 1610 | 14, 16, 18, 19, 20, 22, 24, 25, 28, 30, 32, 35, 38 | | TB 1615 | 14, 16, 18, 19, 20, 22, 24, 25, 28, 30, 32, 35, 38, 40 | | TB 2012 | 18, 19, 20, 22, 24, 25, 28, 30, 32, 35, 38, 40, 42 | | TB 2017 | 18, 19, 20, 22, 24, 25, 28, 30, 32, 35, 38, 40, 42, 42*, 44, 48, 50* | | TB 2517 | 20, 22, 24, 25, 28, 30, 32, 35, 38, 40, 42, 45, 48, 50, 55 | | TB 3020 | 25, 28, 30, 32, 35, 38, 40, 42, 45, 48, 50, 55, 60 | | TB 3030 | 35, 38, 38, 40, 42, 45, 48, 50, 55, 60, 65 | | TB 3525 | 35, 38, 40, 42, 45, 48, 50, 55, 60, 65, 65, 70, 75 | | TB 3535 | 38, 40, 42, 45, 48, 50, 55, 60, 65, 70, 75, 75, 80 | | TB 4030 | 40, 42, 42, 48, 50, 55, 60, 65, 70, 75, 80, 85 | | TB 4040 | 42, 48, 50, 55, 60, 65, 70, 75, 80, 85, 90, 90, 95, 100 | | TB 4535 | 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 100, 105, 110 | | TB 5050 | 70, 75, 80, 85, 85, 90, 95, 100, 105, 110, 115, 120, 125 | \* Asterisked bores indicate non-standard or shallow keyway variants - **Keyway note**: When ordering, specify both the bush number and the bore size required - **Shallow key depth**: Some bore sizes use a shallow key depth variant (marked with asterisk) --- #### 3. Key and Keyway Dimensions (Metric) Keys and keyways conform to the relevant industrial standard (originally referenced as BS 4235: Part 1: 1972). Parallel keyways are supplied as standard unless otherwise specified. | Shaft Diameter Over (mm) | Shaft Diameter Including (mm) | Key Width — J (mm) | Key Height — K (mm) | Keyway Depth — L (mm) | |---|---|---|---|---| | 6 | 8 | 2 | 2 | 1.0 | | 8 | 10 | 3 | 3 | 1.4 | | 10 | 12 | 4 | 4 | 1.8 | | 12 | 17 | 5 | 5 | 2.3 | | 17 | 22 | 6 | 6 | 2.8 | | 22 | 30 | 8 | 7 | 3.3 | | 30 | 38 | 10 | 8 | 3.3 | | 38 | 44 | 12 | 8 | 3.3 | | 44 | 50 | 14 | 9 | 3.8 | | 50 | 58 | 16 | 10 | 4.3 | | 58 | 65 | 18 | 11 | 4.4 | | 65 | 75 | 20 | 12 | 4.9 | | 75 | 85 | 22 | 14 | 5.4 | | 85 | 95 | 25 | 14 | 5.4 | | 95 | 110 | 28 | 16 | 6.4 | | 110 | 130 | 32 | 18 | 7.4 | | 130 | 150 | 36 | 20 | 8.4 | | 150 | 170 | 40 | 22 | 9.4 | | 170 | 200 | 45 | 25 | 10.4 | | 200 | 230 | 50 | 28 | 11.4 | --- #### 4. Worm Gearboxes ##### 4.1 General Information - **Application**: Designed for relatively high-power applications requiring significant speed reduction - **Types available**: Both single-reduction and double-reduction configurations - **Mounting configurations**: Underdriven, overdriven, shaft-mounted, vertical, and agitator types (note: agitator-type data is typically excluded from standard catalogues and requires manufacturer consultation) - **Single-reduction ratios**: Available from 5:1 to 70:1 - **Double-reduction ratios**: Available from 75:1 to 4900:1 - **Gear sizes**: Seven standard sizes are available, designated by a number code (e.g., W10, W12, W14, W17, W20, W24, W28) where the designation letter indicates a worm gearbox and the number represents the nominal centre distance between the worm shaft and wheel shaft in inches - **Input speed range**: Standard catalogues cover eight input speeds from 1800 to 100 rev/min for single-reduction; for double-reduction, only 1450 and 960 rev/min are typically listed (higher speeds up to 2800–3000 rev/min possible with manufacturer consultation) ##### 4.2 Rating Basis - **Power and torque ratings** are based on mineral oil lubrication and standard steel shafts with a single key - **Higher ratings** can be achieved through: synthetic oils/additives, oil coolers, high-tensile steel shafts, and two keys (requires manufacturer consultation) - **Actual vs nominal ratios**: Actual ratios may differ slightly from nominal ratios; always use the actual ratio for accurate speed calculations - **Efficiency**: Listed as efficiency at rated (maximum) power; at very low power, efficiency drops slightly; for normal operating conditions, efficiency can be treated as constant ##### 4.3 General Specification | Component | Material / Feature | |---|---| | **Gear case** | Close-grained cast iron, precisely machined joints and bearing bores | | **Wormshaft** | Integral alloy steel, case-hardened, ground and polished thread profiles | | **Wormwheel rim** | Phosphor bronze (centrifugally cast), complying with relevant standards, secured to cast iron centre by electron beam welding (for 10"–14" sizes) | | **Gear form** | Conforms to relevant national standards with proprietary modifications for improved tooth contact, uniform angular velocity, tapered oil entry, and reduced friction | | **Thread direction** | Right-hand standard; left-hand available on request | | **Shaft extensions** | Metric dimensions standard; imperial available for specific markets | | **Shaft material** | Carbon steel standard; high-tensile steel available for high-load applications | | **Bearings** | Metric taper roller bearings, face-to-face arrangement on both worm and wheel shafts for maximum stiffness; larger sizes use matched taper roller set at one end and deep groove ball bearing at opposite end | | **Oil seals** | Viton oil seals fitted as standard | | **Lubrication** | Sump oil lubrication (underdriven and overdriven types); grease lubrication required for vertical and agitator types; grease lubrication may be needed at lower speeds | | **Cooling** | Air cooling via radial fan directing air over ribbed gear case; fan-less units available where application permits | | **Backstop** | Sprag clutch backstop available internally or externally mounted with manual tension release | --- #### 5. Worm Gearbox Selection Method A systematic 15-step procedure is used to select a suitable worm gearbox: ##### Step 1 — Establish Mechanical Data - **Input (driver)**: Maximum (or design) torque, power, and speed - **Output (driven)**: Maximum (or design) torque, power, and speed (including tolerance range if given) - **Duration of service**: Continuous or intermittent, and average hours per day - **Maximum ambient temperature** around the gearbox **Important notes**: - Input and output values are inter-related by the gearbox — not all will be independently known at the start - Maximum torque/power excludes shock loading or hard-start factors (these are handled by the service factor) - Ambient temperature does not affect selection if the gearbox operates intermittently with sufficient cooling time between runs ##### Step 2 — Calculate Reduction Ratio - **Reduction ratio** = Input speed ÷ Output speed ##### Step 3 — Select Nominal Ratio - From the reduction ratio tables, select the closest **nominal ratio** to the required value - If the ratio exceeds 70:1, a double-reduction gearbox is required ##### Step 4 — Calculate Nominal Output Speed - **Nominal output speed** = Input speed ÷ Nominal ratio ##### Step 5 — Determine Load Classification - Classify the driven machine load as: **Steady (S)**, **Medium Impulsive (M)**, or **Highly Impulsive (H)** - Use the load classification table (see Section 6 below) ##### Step 6 — Determine Service Factor - From the mechanical service factor table, find the factor based on: prime mover type, load classification, duty duration (hours/day), and whether operation is continuous or intermittent ##### Step 7 — Calculate Selection Capacity - **If input conditions are given**: Selection input power = Design input power × Service factor - **If output conditions are given**: Selection output torque = Design output torque × Service factor ##### Step 8 — Preliminary Gearbox Selection - Go to the gearbox data tables for the relevant nominal ratio and input speed - Select the smallest gearbox with a capacity **greater than** the selection capacity from Step 7 ##### Step 9 — Verify Actual Ratio and Output Speed - From the reduction ratio tables, obtain the **actual ratio** for the selected gearbox size - Calculate actual output speed = Input speed ÷ Actual ratio - Verify the output speed falls within the required tolerance range - If not, consider an alternative mechanical drive system (e.g., chain drive) in conjunction with the gearbox ##### Step 10 — Check Thermal Rating (Continuous Operation) - If the gearbox operates continuously (or intermittently without sufficient cool-down time), obtain the **thermal service factor** from the thermal service factor table - The thermal service factor depends on ambient temperature ##### Step 11 — Verify Thermal Capacity - Multiply the thermal service factor by either the design input power or output torque - Compare this **selection thermal** value against the gearbox's **thermal rating** from the data tables - If the gearbox thermal rating is insufficient, either: - Select the next larger gearbox size (recheck actual ratio), or - Use auxiliary cooling (synthetic oil, oil coolers) ##### Step 12 — Check Overhung Load - If a belt, chain, gear, or other mechanism is attached to the output shaft, calculate the overhung (OH) load - **OH load formula**: F = (2 × f × T) / d, or equivalently F = (60 × f × P) / (π × d × N) - Where: F = overhung load (N), T = output shaft torque (Nm, design value not selection value), P = output shaft power (W, design value), d = PCD of pulley/sprocket/gear (m), N = output shaft speed (rev/min) - f = drive application factor: 1.0 (chain drive or toothed belt), 1.25 (gear drive), 1.5 (vee belt), 2.0 (flat friction belt) - Compare calculated OH load against the allowable value from the gearbox overhung load tables - If exceeded, select a larger gearbox or use an intermediate layshaft with its own bearings and a flexible coupling to the gearbox ##### Step 13 — Check Thrust Load - If a helical gear or other mechanism produces axial thrust on the output shaft, verify this does not exceed the gearbox's allowable thrust load - Alternative: use an intermediate shaft (layshaft) with its own bearings to absorb the axial load ##### Step 14 — Determine Efficiency and Calculate Unknowns - Read efficiency from the gearbox data tables at the selected ratio and input speed - Use efficiency to calculate any remaining unknown values: - Output power = Input power × Efficiency - Input power = Output power ÷ Efficiency - Input torque = Output torque ÷ (Ratio × Efficiency) ##### Step 15 — Specify the Gearbox - Specify the mounting type: underdriven, overdriven, shaft-mounted, or vertical - Read key dimensions from the manufacturer's dimension tables: input/output shaft diameters, centreline distances, bolt hole locations, etc. --- #### 6. Load Classification and Service Factors ##### 6.1 Load Classification by Application (Partial List) | Load Type | Example Applications | |---|---| | **Steady (S)** | Agitators (pure liquids), bottling machinery, brew kettles (continuous), centrifugal compressors/pumps, cooling towers, fans, generators, laundry washers/tumblers, light line shafts | | **Medium Impulsive (M)** | Agitators (liquids & solids, variable density), belt/bucket/chain/flight/screw conveyors, car dumpers, car pullers, classifiers, crane drives, dredges, feeders, hoists, lumber industry machinery, metal mills, mixers (concrete continuous), paper mills, reciprocating pumps, rubber/plastics machinery, shakers, stokers | | **Highly Impulsive (H)** | Brick presses, briquette machines, car dumpers (heavy duty), cane knives, crushers, hammer mills, heavy conveyors, log handling equipment, pug mills, rod/bar mills, roll cases, slab conveyors, tumbling barrels | **Note**: Applications marked with an asterisk (*) in original tables require specific manufacturer consultation. ##### 6.2 Mechanical Service Factors (Table 2) | Prime Mover / Input Type | Duration | Steady (S) | Medium Impulsive (M) | Highly Impulsive (H) | |---|---|---|---|---| | **Electric Motor (Steady Input)** | Intermittent ≤2 hr/day | 0.80 | 1.00 | 1.50 | | | 12 hr/day | 1.00 | 1.25 | 1.75 | | | 24 hr/day continuous | 1.25 | 1.50 | 2.00 | | **Multi-Cylinder IC Engine (Medium Impulsive Input)** | Intermittent ≤2 hr/day | 1.00 | 1.25 | 1.75 | | | 12 hr/day | 1.25 | 1.50 | 2.00 | | | 24 hr/day continuous | 1.50 | 1.75 | 2.25 | | **Single-Cylinder IC Engine (Highly Impulsive Input)** | Intermittent ≤2 hr/day | 1.25 | 1.50 | 2.00 | | | 12 hr/day | 1.50 | 1.75 | 2.25 | | | 24 hr/day continuous | 1.75 | 2.00 | 2.50 | **Note**: Linear interpolation is acceptable for service hours between those listed. ##### 6.3 Thermal Service Factors (Table 3) | Ambient Temperature (°C) | 10 | 20 | 30 | 40 | 50 | 60 | |---|---|---|---|---|---|---| | **Factor** | 0.87 | 1.0 | 1.16 | 1.35 | 1.62 | 1.97 | | Ambient Temperature (°F) | 50 | 68 | 86 | 104 | 122 | 140 | |---|---|---|---|---|---|---| | **Factor** | 0.87 | 1.0 | 1.16 | 1.35 | 1.62 | 1.97 | **Note**: A substantial increase in thermal rating is achievable using synthetic lubricants (consult manufacturer). --- #### 7. Reduction Ratios — Actual vs Nominal ##### 7.1 Single Reduction — Nominal & Exact Ratios | Nominal Ratio | Gear Size 10 | Gear Size 12 | Gear Size 14 | Gear Size 17 | Gear Size 20 | Gear Size 24 | Gear Size 28 | |---|---|---|---|---|---|---|---| | 5 | 5.125 | 5.11 | 5.10 | 5.10 | 5.09 | 5.08 | 5.08 | | 10 | 9.75 | 9.75 | 9.80 | 9.80 | 9.80 | 9.83 | 9.83 | | 15 | 14.66 | 14.66 | 14.75 | 14.75 | 14.75 | 14.75 | 14.75 | | 20 | 20.50 | 20.50 | 19.67 | 19.67 | 19.67 | 19.67 | 19.67 | | 25 | 24.5 | 24.5 | 24.5 | 24.5 | 24.5 | 24.67 | 24.67 | | 30 | 29.5 | 29.5 | 29.5 | 29.5 | 29.5 | 29.5 | 29.5 | | 40 | 40 | 40 | 39.5 | 39.5 | 39.5 | 39.5 | 39.5 | | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | | 70 | 70 | 70 | 70 | 70 | 70 | 70 | 70 | ##### 7.2 Double Reduction — Nominal & Exact Ratios | Nominal Ratio | Gear Size 10 | Gear Size 12 | Gear Size 14 | Gear Size 17 | Gear Size 20 | Gear Size 24 | Gear Size 28 | |---|---|---|---|---|---|---|---| | 75 | 76 | 75 | 76 | 76 | 76 | 75 | 75 | | 150 | 142 | 143 | 151 | 144 | 144 | 151 | 150 | | 250 | 237 | 239 | 239 | 239 | 239 | 241 | 242 | | 300 | 318 | 301 | 288 | 288 | 288 | 288 | 290 | | 500 | 502 | 502 | 482 | 482 | 482 | 482 | 482 | | 750 | 735 | 735 | 723 | 723 | 723 | 723 | 728 | | 1000 | 980 | 980 | 980 | 980 | 980 | 987 | 974 | | 1500 | 1475 | 1475 | 1475 | 1475 | 1475 | 1475 | 1475 | | 2000 | 2000 | 2000 | 2000 | 2000 | 2000 | 2000 | 1975 | | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 | | 3000 | 3000 | 3000 | 3000 | 3000 | 3000 | 3000 | 3000 | | 4200 | 4200 | 4200 | 4200 | 4200 | 4200 | 4200 | 4200 | | 4900 | 4900 | 4900 | 4900 | 4900 | 4900 | 4900 | 4900 | --- #### 8. Gearbox Data Tables (Selected Nominal Ratios) The gearbox data tables provide thermal and mechanical ratings for each combination of input speed, gear size, and nominal ratio. The tables include: input kW (thermal), output torque (Nm, thermal), input kW (mechanical), output torque (Nm, mechanical), and efficiency (%). **Key to input speeds for standard electric motors** (used for directly coupled motor input): - 4-pole motor: 1500 rev/min (actual ~1450 rev/min) - 6-pole motor: 1000 rev/min (actual ~960 rev/min) - 8-pole motor: 750 rev/min (actual ~720 rev/min) **Note on shaded areas in data tables**: Ratings in the shaded area require force-feed lubrication (not standard sump oil). ##### Example Data — Nominal Ratio 50/1 (Single Reduction, 1500 rev/min Input) | Gear Size | Input kW (Thermal) | Output Torque Nm (Thermal) | Input kW (Mechanical) | Output Torque Nm (Mechanical) | Efficiency % | |---|---|---|---|---|---| | 10 | 21 | 3687 | 53 | 9687 | 92 | | 12 | 28 | 4966 | 88 | 15985 | 92 | | 14 | 43 | 7731 | 121 | 21927 | 93 | | 17 | 61 | 11067 | 184 | 33427 | 93 | | 20 | 92 | 16760 | 245 | 44689 | 94 | | 24 | 140 | 25413 | 324 | 59256 | 94 | | 28 | 206 | 37618 | 466 | 85646 | 94 | --- #### 9. Overhung and Thrust Load Capacities ##### 9.1 Output Shaft Overhung Load Capacities (Newtons) Values vary by ratio, output speed, and centre distance. Sample data at 1450 rev/min input speed: | Ratio | Output Speed (rev/min) | Centre Distance 10 | Centre Distance 14 | Centre Distance 20 | Centre Distance 24 | Centre Distance 28 | |---|---|---|---|---|---|---| | 5 | 290 | 37,300 | 45,200 | 81,700 | 122,700 | 161,800 | | 10 | 145 | 44,900 | 53,600 | 93,600 | 141,400 | 187,000 | | 20 | 73 | 62,300 | 72,400 | 94,000 | 126,400 | 184,900 | | 30 | 48 | 70,900 | 87,500 | 112,200 | 150,700 | 284,300 | | 50 | 29 | 79,100 | 99,100 | 138,000 | 197,000 | 271,400 | | 70 | 21 | 79,700 | 91,700 | 101,000 | 147,900 | 198,000 | ##### 9.2 Output Shaft Thrust Load Capacities (Newtons) At both 1450 and 960 rev/min input speeds, thrust load capacities are constant across centre distances for ratios ≥ 20: | Ratio | Centre Distance 10 | Centre Distance 14 | Centre Distance 17 | Centre Distance 20 | |---|---|---|---|---| | 5 | 36,280 | 37,700 | 46,890 | 80,480 | | 10 | 49,370 | 54,210 | 65,280 | 107,530 | | 15 | 62,020 | 66,000 | 81,650 | 140,000 | | ≥20 | 65,000 | 66,000 | 94,500 | 140,000 | --- #### 10. Overhung Load Calculation — Derivation The overhung load formula is derived from belt/chain tension analysis: - For a belt or chain drive on the gearbox output shaft with slack-side tension T₁ and tight-side tension T₂: - **Overhung load**: F = T₁ + T₂ - **Torque**: T = (T₂ − T₁) × d/2 - If T₁ = 0 (zero slack-side tension): F = 2T/d - If T₁ ≠ 0, introduce the **drive application factor** (f): F = 2fT/d - f accounts for the fact that the total belt/chain force exceeds the net tangential force - Substituting power (P = Tω = T × πN/30): - **F = (60 × f × P) / (π × d × N)** **Drive application factors**: | Drive Type | Factor (f) | |---|---| | Chain drive or toothed belt | 1.0 | | Gear drive | 1.25 | | Vee belt | 1.5 | | Flat friction belt | 2.0 | For gear drives, the factor of 1.25 accounts for the pressure angle creating a separating force in addition to the tangential force, resulting in a resultant overhung load greater than the tangential component alone. --- #### 11. Worked Example — Worm Gearbox Selection **Problem**: An electric motor drives an overdriven worm gearbox. The output shaft has a chain pinion keyed to it, transmitting power via roller chain to a chain wheel on a non-uniformly loaded oven conveyor. **Given Data**: - Required power at oven conveyor chain wheel: 20 kW - Chain wheel speed: 15 ± 0.5 rev/min - Chain drive reduction ratio: 2:1 - Chain pinion PCD (keyed to gearbox output shaft): 270 mm - Electric motor: 4-pole, full load speed 1460 rev/min - Operating hours: 16 h/day average, continuous - Maximum ambient temperature: 45°C - Assumed chain drive efficiency: 96% - Gearbox lubricant: Mineral oil **Solution (Step-by-Step)**: 1. **Design output power** = 20 / 0.96 = 20.83 kW; required gearbox output speed = 30 ± 1 rev/min (due to 2:1 chain reduction) 2. **Reduction ratio** = 1460 / 30 = 48.7:1 → single-reduction gearbox (ratio < 70) 3. **Closest nominal ratio** = 50 4. **Nominal output speed** = 1460 / 50 = 29.2 rev/min 5. **Load classification** = M (medium impulsive) — non-uniformly loaded oven conveyor 6. **Service factor** = 1.33 (interpolated for 16 h/day continuous operation with electric motor and medium impulsive load) 7. **Output torque (mechanical)** = P/ω = 20,830 / (π × 29.2/30) = 6813 Nm; **Selection output torque** = 1.33 × 6813 = 9084 Nm 8. **Preliminary selection**: From ratio 50/1 table at 1500 rev/min input → W12 (output torque mechanical = 9838 Nm > 9084 Nm) 9. **Actual ratio** = 50/1 (same as nominal for W12); output speed = 29.2 rev/min → within 30 ± 1 range ✓ 10. **Thermal check**: Gearbox operates continuously at 45°C → thermal service factor = 1.485 (interpolated) 11. **Selection output torque (thermal)** = 6813 × 1.485 = 10,117 Nm; W12 thermal rating = 8156 Nm → **W12 FAILS thermal check** - Upgrade to **W14** (thermal rating = 11,696 Nm > 10,117 Nm) ✓ - Actual ratio for W14 at 50/1 is the same → output speed unchanged 12. **Overhung load check** (chain pinion on output shaft): f = 1 (chain drive), d = 0.270 m - OH load = (2 × 1 × 6813) / 0.270 = **50,470 N** - Allowable OH load for W14 at ratio 50/1 and 1450 rev/min input = 99,100 N → **OK** ✓ 13. **Thrust load**: No thrust load (chain drive, not helical gear) ✓ 14. **Efficiency** (from W14 data table at 1500 rev/min, ratio 50): 84% - Design output torque = 6813 Nm; Design output power = 20.83 kW - **Input power** = 20.83 / 0.84 = **24.8 kW** - **Input torque** = 6813 / (50 × 0.84) = **162 Nm** (or equivalently: 24,800 / (π × 1460/30) = 162 Nm) **Summary Table**: | Parameter | Input | Output | |---|---|---| | Speed (rev/min) | 1460 | 29.2 | | Power (kW) | 24.8 | 20.83 | | Torque (Nm) | 162 | 6813 | 15. **Specification**: Overdriven type, model designation TWO 14 (two-worm overdriven, size 14) - Nominal input shaft diameter: 75 mm - Nominal output shaft diameter: 120 mm - Side bolt hole centre distance: 597 mm (2 × dimension H) - End bolt hole centre distance: 431.8 mm (2 × dimension J) --- ### Comparison Tables #### Coupling Type Comparison | Feature | Pin-Type Flexible | Tyre-Type Flexible | Disc-Type Flexible | Chain-Type Flexible | |---|---|---|---|---| | **Torque range** | 194–18,536 Nm | 25–6270 Nm | 71.6–4298 Nm | 52.5–8595 Nm | | **Max speed** | 2200–6800 RPM | 1500–4500 RPM | 900–2900 RPM | 700–3500 RPM | | **Max bore** | Up to 125 mm | Up to 150 mm | Up to 110 mm | Up to 140 mm | | **Angular misalignment** | Low | High | 1° max | 1° max | | **Axial misalignment** | Low | 1.1–4.8 mm | 0.5 mm max | 0.25–0.5 mm | | **Vibration damping** | Moderate (elastomer pins) | High (rubber tyre) | Low (metallic disc) | Moderate (chain slack) | | **Maintenance** | Replace pin bushes | Replace tyre element | Replace disc pack | Replace chain/lubricate | | **Best suited for** | General purpose, moderate loads | High misalignment, vibration isolation | Torsional rigidity, precision drives | Moderate loads, easy assembly | #### Single vs Double Reduction Gearboxes | Feature | Single Reduction | Double Reduction | |---|---|---| | **Ratio range** | 5:1 to 70:1 | 75:1 to 4900:1 | | **Efficiency** | Higher (89–96%) | Lower (compound losses) | | **Size/cost** | Smaller, more economical | Larger, higher cost | | **Mounting types** | All five types | All five types | | **Application** | Moderate speed reduction | Very high speed reduction | | **Input speed** | Up to 1800 rev/min standard | 1450 and 960 rev/min standard | --- ### Mermaid Diagrams #### Worm Gearbox Selection Flowchart ```mermaid flowchart TD A[Step 1: Establish Mechanical Data<br/>Input/output torque, power, speed,<br/>duty cycle, ambient temp] --> B[Step 2: Calculate Reduction Ratio<br/>Ratio = Input Speed ÷ Output Speed] B --> C{Step 3: Ratio > 70?} C -- Yes --> D[Use Double-Reduction Gearbox] C -- No --> E[Use Single-Reduction Gearbox] D --> F[Step 3: Select Closest Nominal Ratio] E --> F F --> G[Step 4: Nominal Output Speed<br/>= Input Speed ÷ Nominal Ratio] G --> H[Step 5: Determine Load Classification<br/>S / M / H] H --> I[Step 6: Determine Service Factor<br/>from Table 2] I --> J[Step 7: Calculate Selection Capacity<br/>= Design Value × Service Factor] J --> K[Step 8: Preliminary Gearbox Selection<br/>Smallest gearbox exceeding selection capacity] K --> L[Step 9: Verify Actual Ratio & Output Speed<br/>Check tolerance range] L --> M{Step 10: Continuous<br/>operation?} M -- Yes --> N[Get Thermal Service Factor<br/>from Table 3] N --> O[Step 11: Check Thermal Rating<br/>Selection thermal ≤ Gearbox thermal?] O -- Fail --> P[Select Larger Gearbox<br/>or Add Auxiliary Cooling] P --> L O -- Pass --> Q{Step 12: External drive<br/>on output shaft?} M -- No --> Q Q -- Yes --> R[Calculate Overhung Load<br/>F = 2fT/d] R --> S{OH Load ≤<br/>Allowable?} S -- Fail --> T[Select Larger Gearbox<br/>or Use Layshaft] T --> L S -- Pass --> U{Step 13: Thrust<br/>load present?} Q -- No --> U U -- Yes --> V[Check Thrust Load<br/>≤ Allowable?] V -- Fail --> T V -- Pass --> W[Step 14: Determine Efficiency<br/>Calculate remaining unknowns] U -- No --> W W --> X[Step 15: Specify Gearbox<br/>Type, size, shaft diameters,<br/>mounting dimensions] ``` #### Coupling Selection Decision Tree ```mermaid flowchart TD A[Start: Coupling Selection] --> B{Primary<br/>Requirement?} B -- High misalignment<br/>& vibration damping --> C[Tyre-Type Coupling] B -- Torsional rigidity<br/>& precision --> D[Disc-Type Coupling] B -- General purpose<br/>moderate loads --> E[Pin-Type Coupling] B -- Easy assembly<br/>& moderate loads --> F[Chain-Type Coupling] C --> G{Max Torque<br/>≤ 6270 Nm?} G -- Yes --> H[Select from Tyre<br/>Coupling Range] G -- No --> I[Consider Pin-Type<br/>or alternative] D --> J{Max Speed<br/>≤ 2900 RPM?} J -- Yes --> K[Select from Disc<br/>Coupling Range] J -- No --> L[Consider Pin-Type<br/>for higher speeds] E --> M[Select from Pin-Type<br/>Coupling Range] F --> N[Select from Chain-Type<br/>Coupling Range] H --> O[Select Taper Bush<br/>& Verify Bore Range] K --> O M --> O N --> O I --> E L --> E O --> P[Verify Key & Keyway<br/>Dimensions] ``` #### Power Transmission System Overview ```mermaid flowchart LR A[Prime Mover<br/>Electric Motor /<br/>IC Engine] -->|Input Shaft| B[Worm Gearbox<br/>Speed Reduction<br/>Torque Multiplication] B -->|Output Shaft| C[Coupling<br/>Misalignment<br/>Compensation] C --> D[Driven Machine<br/>Conveyor / Pump /<br/>Mixer / etc.] B -.->|Overhung Load| E[Chain / Belt /<br/>Gear Drive] E --> D style A fill:#f0f0f0,stroke:#333 style B fill:#f0f0f0,stroke:#333 style C fill:#f0f0f0,stroke:#333 style D fill:#f0f0f0,stroke:#333 style E fill:#f0f0f0,stroke:#333 ``` --- ### Key Terms Glossary - **Bore**: The internal diameter of a coupling hub or bush that fits onto the shaft - **Centre Distance**: The distance between the centreline of the worm shaft and the centreline of the wheel shaft in a gearbox; used as the gearbox size designation - **Double Reduction**: A gearbox arrangement using two stages of worm/wheel reduction to achieve very high ratios (75:1 and above) - **Drive Application Factor (f)**: A multiplier applied in overhung load calculations to account for the type of drive mechanism (chain, gear, belt, etc.) - **End Float**: The maximum permissible axial movement of a coupling hub relative to its mating half - **Force-Feed Lubrication**: A pressurised oil supply system required when gearbox ratings exceed the sump-lubrication capacity (indicated by shaded areas in data tables) - **Keyway**: A machined slot in a shaft and hub into which a key is fitted to transmit torque and prevent relative rotation - **Load Classification**: Categorisation of the driven machine as Steady (S), Medium Impulsive (M), or Highly Impulsive (H), used to determine the service factor - **Nominal Ratio**: The catalogue or labelled reduction ratio of a gearbox; may differ slightly from the actual (exact) ratio - **Overhung Load**: The radial force acting on the gearbox output shaft due to belt/chain/gear tension from an externally mounted drive mechanism - **PCD (Pitch Circle Diameter)**: The effective diameter of a sprocket, pulley, or gear at which the driving force acts - **Service Factor**: A multiplier applied to the design load to account for operating conditions (load type, duty cycle, prime mover characteristics) - **Setting Width**: The axial distance between the two half-bodies of a coupling at the correct installed position - **Single Reduction**: A gearbox arrangement using one worm/wheel stage, suitable for ratios up to 70:1 - **Taper Bush**: A standardised conical locking device used to secure hubs (couplings, sprockets, pulleys) onto shafts using a keyway and set screws - **Thermal Rating**: The maximum continuous power or torque a gearbox can transmit without overheating, limited by heat dissipation capacity - **Thermal Service Factor**: A multiplier that adjusts the thermal rating requirement based on the ambient temperature around the gearbox - **Thrust Load**: An axial force acting along the output shaft, typically caused by helical gears or other mechanisms - **Torsional Stiffness**: The resistance of a coupling to angular deflection under torque, measured in Nm/° — higher values indicate a more rigid coupling - **Wormshaft**: The screw-like input element of a worm gearbox - **Wormwheel**: The gear element of a worm gearbox that meshes with the worm; typically made of phosphor bronze --- ### Quick Revision - **Four coupling types** covered: Pin-type (highest torque/speed range), Tyre-type (best misalignment/damping), Disc-type (best torsional rigidity), Chain-type (easiest assembly) - **Taper bushes** provide the standardised shaft-to-hub interface; always specify both bush number and bore size - **Key dimensions** are determined by shaft diameter according to the standard table - **Worm gearboxes**: Single reduction up to 70:1; double reduction from 75:1 to 4900:1 - **Seven gear sizes** available, designated by nominal centre distance - **Selection is a 15-step process**: Data → Ratio → Nominal ratio → Output speed → Load class → Service factor → Selection capacity → Preliminary selection → Verify ratio/speed → Thermal check → OH load check → Thrust check → Efficiency → Calculate unknowns → Specify - **Service factor** depends on three variables: prime mover type, load classification (S/M/H), and duty duration - **Thermal check** is critical for continuously operating gearboxes — the thermal rating often governs selection over the mechanical rating - **Overhung load formula**: F = 2fT/d = 60fP/(πdN) — always check against allowable values - **Drive application factors**: Chain = 1.0, Gear = 1.25, Vee belt = 1.5, Flat belt = 2.0 - **Efficiency** ranges from ~84% (high ratio, small gearbox) to ~96% (low ratio, large gearbox) - **If OH load exceeds allowable**: Use an intermediate layshaft with its own bearings and a flexible coupling to the gearbox to decouple the radial load - **Higher gearbox ratings** achievable via synthetic oils, oil coolers, high-tensile shafts, and dual keys --- --- # PART III — POWER TRANSMISSION: BELTS & CHAINS --- ## Chapter 6: Chain Drives & Couplings --- ### Overview - This note covers the **design, selection, and maintenance** of two critical mechanical power transmission systems: **chain drives** and **shaft couplings** - Chain drives transmit power between parallel shafts using a roller chain engaged with toothed sprockets - Couplings connect two shafts end-to-end, transmitting torque while accommodating various degrees of misalignment - Both systems are fundamental to industrial machinery, conveyor systems, and general mechanical power transmission - The note also briefly covers **taper lock bushes** used to secure sprockets and couplings to shafts - Content is drawn from a mechanical design data manual and includes selection procedures, rating charts, sprocket data, lubrication methods, and coupling comparison tables --- ### Key Concepts - **Chain Pitch** — the distance between adjacent chain link pins; the primary dimension used to classify chain size - **Drive Ratio** — the ratio of driven sprocket teeth to driver sprocket teeth (i = Z₂ / Z₁) - **Selection Power** — the adjusted power value used to select a chain from rating charts, calculated by applying service factors to the actual transmitted power - **Application Factor (f₁)** — accounts for dynamic overloads based on driver and driven machine characteristics - **Tooth Factor (f₂)** — modifies selection power based on the number of teeth on the driver sprocket (referenced to a 19-tooth baseline) - **Bearing Pressure** — the contact pressure between pin and bush surfaces; a key indicator of chain wear performance - **Taper Lock Bush** — a tapered sleeve that grips a shaft when tightened, providing a secure and re-usable mounting for sprockets and couplings - **Misalignment** — the deviation from perfect shaft alignment; classified as angular, axial (parallel), end float, or torsional - **Equivalent Selection Power (Pₑ)** — the adjusted power value used to select a coupling, normalised to a reference speed --- ### Detailed Notes #### Taper Lock Bushes - **Taper lock bushes** are the quickest and simplest method of securing sprockets and couplings to shafts (both imperial and metric) - The tapered surface of both bush and sprocket/coupling hub combine to create a **load-bearing connection** via the lock action of hardened high-tensile screws - Taper bush ranges from different manufacturers are generally **fully interchangeable** - When ordering, specify **both the bush number and bore size** required - Available in metric bore sizes ranging from small (e.g., 9 mm) up to very large bores depending on bush series - Standard bush series include: TB1008, TB1210, TB1215, TB1610, TB1615, TB2012, TB2017, TB2517, TB2525, TB3020, TB3030, TB3535, TB4040 - Each bush series accommodates a specific range of bore sizes and is matched to corresponding sprocket or coupling hub dimensions #### Chain Drives — Introduction - Two primary chain standards exist: **national standard (metric)** and **imperial standard (inch-based)** - Chains manufactured to both standards are available; the metric standard is more commonly used in many regions - There is no single unified national standard for roller chain in all countries — chains are made to comply with one or both international standards - Chain size is specified by the **chain pitch** (distance between adjacent link pins) - Both standards use imperial (inch) pitch sizes; metric pitch equivalents are listed in catalogues - Chain may be specified by inch or mm pitch; all other catalogue dimensions are given in **metric (mm) units** #### Types of Roller Chain - **Simple (Simplex)** — single strand; most common for general power transmission - **Duplex** — two parallel strands; higher load capacity - **Triplex** — three parallel strands; highest standard load capacity - **Quadruplex** — four parallel strands; for very heavy-duty applications - Other varieties include: straight-sided chain, double pitch chain, cranked link chain, plastic bush chain, O-ring chain, hollow bearing pin chain, and sidebow chain - The most common type for power transmission is the **high-waisted precision steel roller chain** - Chains used for **conveying** rather than power transmission have different data and attachments #### Roller Chain Construction - A precision steel roller chain consists of a series of **journal bearings** held in precise relationship by constraining link plates - Each bearing consists of a **bearing pin** and **bush** on which the chain roller revolves - The bearing pin and bush are **case-hardened** to allow articulation under high pressures - The design permits both **load-carrying pressures** and **gearing action** to be transmitted via the chain rollers - Chains are classified according to **pitch**, **roller diameter**, and **width between inner plates** - These dimensions collectively determine the form and width of the sprocket teeth #### Chain Drive Expected Life - When properly selected, installed, lubricated, and maintained with loads not exceeding design values, a quality roller chain is expected to have an operating life of **8 million cycles or 15,000 hours** - The rating charts in selection procedures assume a **minimum life expectancy of 15,000 hours** with proper installation and lubrication #### Standards Reference Guide | Transmission Chain Type | ISO Standard | National Metric Standard | Imperial Standard | Other Standards | |---|---|---|---|---| | Short Pitch Transmission Chain & Sprockets | 606 | 228 | B29.1M | DIN8187 / DIN8188 | | Short Pitch Bush Chain & Sprockets | 1395 | 228 | — | DIN8154 | | Double Pitch Roller Chain & Sprockets | 1275 | 4687 | B29.3M | DIN8181 | | Oilfield Chain & Sprockets | 606 | — | B29.1M | API Spec 7F | | Cycle Chain | 9633 | — | — | — | | Motorcycle Chain | 10190 | 7615 | — | — | | Cranked Link Chain & Sprockets | 3512 | — | B29.1M | DIN8182 | --- #### Chain Drive Selection Method ##### Symbols, Terms, and Units - **Z₁** = Number of teeth on **driver** sprocket (pinion) - **Z₂** = Number of teeth on **driven** sprocket (wheel) - **C** = Centre distance (mm) - **P** = Chain pitch (mm) - **i** = Drive ratio - **L** = Chain length (pitches) ##### Selection Summary (Step-by-Step) | Step | Action | Details | |---|---|---| | **1** | Select drive ratio and sprockets | Z₁ = 19 teeth minimum | | **2** | Establish application factor f₁ | Account for dynamic loads | | **3** | Determine tooth factor f₂ | f₂ = 19 / Z₁ | | **4** | Calculate selection power | Selection Power = Power × f₁ × f₂ (kW) | | **5** | Select chain drive from rating charts | Use smallest pitch of simple chain that meets the selection power | | **6** | Calculate chain length | Use chain length formula | | **7** | Calculate exact centre distance | Use revised centre distance formula | | **8** | Choose lubrication method | Based on chain speed and power | --- ##### Step 1 — Select Drive Ratio and Sprockets - Use standard sprocket sizes to choose a ratio based on available tooth counts - Best practice: use an **odd number of teeth combined with an even number of chain pitches** - Ideally, sprockets should have a **minimum of 19 teeth** - If operating at high speed or subject to impulsive loads, the smaller sprocket should have **at least 25 teeth** and should be **hardened** - Maximum recommended teeth on any sprocket: **114 teeth** - Drive ratio formula: **i = Z₂ / Z₁** - For large ratio drives, check that the **angle of lap on Z₁ is not less than 120°** | Driven Sprocket (Z₂) | Driver Sprocket (Z₁) Teeth → | 15 | 17 | 19 | 21 | 23 | 25 | |---|---|---|---|---|---|---|---| | **25** | | — | — | — | — | — | 1.00 | | **38** | | 2.53 | 2.23 | 2.00 | 1.80 | 1.65 | 1.52 | | **57** | | 3.80 | 3.35 | 3.00 | 2.71 | 2.48 | 2.28 | | **76** | | 5.07 | 4.47 | 4.00 | 3.62 | 3.30 | 3.04 | | **95** | | 6.33 | 5.59 | 5.00 | 4.52 | 4.13 | 3.80 | | **114** | | 7.60 | 6.70 | 6.00 | 5.43 | 4.96 | 4.56 | --- ##### Step 2 — Establish Application Factor (f₁) - **f₁** accounts for dynamic overloads depending on the **characteristics of both the driver and driven machines** - Can be selected directly or by analogy using the application factor chart | Driven Machine Characteristics | Smooth Running Driver | Slight Shocks Driver | Moderate Shocks Driver | |---|---|---|---| | **Smooth Running** (centrifugal pumps, compressors, printing machines, uniformly loaded conveyors, escalators, liquid agitators, mixers, rotary driers, fans) | 1.0 | 1.1 | 1.3 | | **Moderate Shocks** (pumps & compressors 3+ cyl, concrete mixing machines, non-uniformly loaded conveyors, solid agitators & mixers) | 1.4 | 1.5 | 1.7 | | **Heavy Shocks** (planers, excavators, roll & ball mills, rubber processing machines, presses & shears, 1 & 2 cyl pumps & compressors, oil drilling rigs) | 1.8 | 1.9 | 2.1 | **Driver classifications:** - **Smooth Running** — electric motors, steam & gas turbines, internal combustion engines with hydraulic coupling - **Slight Shocks** — internal combustion engines with 6+ cylinders, or engines with mechanical coupling, electric motors with frequent starts - **Moderate Shocks** — internal combustion engines with fewer than 6 cylinders, with mechanical coupling --- ##### Step 3 — Tooth Factor (f₂) - The tooth factor modifies the final power selection based on the **size of the driver sprocket** - Formula: **f₂ = 19 / Z₁** - The rating curves in standard charts are based on a **19-tooth sprocket**; smaller sprockets increase the chain load per tooth | Z₁ (Driver Teeth) | f₂ | |---|---| | 15 | 1.27 | | 17 | 1.12 | | 19 | 1.00 | | 21 | 0.91 | | 23 | 0.83 | | 25 | 0.76 | --- ##### Step 4 — Calculate Selection Power $\text{Selection Power} = \text{Power (kW)} \times f_1 \times f_2$ - This adjusted power value is then used with the rating charts --- ##### Step 5 — Select Chain Drive - From the rating chart, select the **smallest pitch of simple chain** that can transmit the selection power at the speed of the driver sprocket Z₁ - This normally results in the **most economical drive** - If the selection power exceeds the capacity of the simple chain, consider a **multiplex chain** (duplex or triplex) of the same pitch size --- ##### Step 6 — Calculate Chain Length - Chain length in pitches (L) for a two-point drive at any centre distance: $L = \frac{Z_1 + Z_2}{2} + \frac{2C}{P} + \frac{\left(\frac{Z_2 - Z_1}{2\pi}\right)^2 \times P}{C}$ - **Round up** the calculated number of pitches to a **whole number of even pitches** - Odd numbers of pitches require a **cranked link** (offset link), which is **not recommended** - If a jockey sprocket is used for adjustment, add **two pitches** to the chain length - **C** is the contemplated centre distance in mm; should generally be between **30–50 pitches** - Example: For 1/2″ pitch chain, C = 1.5 × 25.4 × 40 = 1524 mm --- ##### Step 7 — Calculate Exact Centre Distance - The actual centre distance for the chain length (L) calculated above will generally be **greater** than originally contemplated - Revised centre distance formula: $C = \frac{P}{8} \left[ 2L - Z_1 - Z_2 + \sqrt{(2L - Z_2 - Z_1)^2 - \frac{\pi}{3.88}(Z_2 - Z_1)^2} \right]$ Where: - **P** = Chain pitch (mm) - **L** = Chain length (pitches) - **Z₁** = Number of teeth in driver sprocket - **Z₂** = Number of teeth in driven sprocket --- ##### Step 8 — Choose Lubrication Method - The recommended lubrication method is based on **chain speed and power transmitted**, found in the rating charts --- #### Rating Chart Construction - Rating charts appear complex but are constructed from **three simple lines**: - **Link plate fatigue** line — dominates at lower speeds (failure if maximum power recommendation is exceeded) - **Pin galling** line — occurs due to boundary lubrication breakdown at very high speeds - **Bush and roller fatigue** curve — at the intersection of the fatigue and galling lines, this curve dominates - The **rounded tops** of each selection curve account for these intersections - For driver sprocket speeds **less than 10 rpm**: multiply the transmitted power by 10/n and read from the 10 rpm column (where n = driver sprocket speed) - **1 Kilowatt = 1.34 hp** --- #### Chain Suspension Force - The force between one link and the next due to chain mass is small and is **internally balanced** within the chain - This causes the chain to adopt a **sagging catenary shape** between the sprockets - Allowance must be made in installation for **slightly different postures** adopted by the chain between zero and maximum load --- #### Lubrication - Chain drives must be protected against **dirt and moisture** - Use **good quality non-detergent mineral-based oil** - A **periodic change of oil** is desirable - Heavy oils and greases are generally **too stiff** to enter chain working surfaces and **should not be used** - The lubricant must reach the **bearing areas** of the chain by being directed between the inner and outer link plates, preferably at the point where the chain enters the sprocket on the **bottom strand** ##### Lubricant Viscosity by Temperature | Ambient Temperature (°C) | SAE Rating | Viscosity Standard | |---|---|---| | −5 to +5 | 20 | 46 to 68 | | 5 to 40 | 30 | 100 | | 40 to 50 | 40 | 150 to 220 | | 50 to 60 | 50 | 320 | - For the majority of applications, a **multigrade oil (e.g., SAE 20/50)** would be suitable ##### Use of Grease - Grease lubrication is **not recommended**; if used, the following conditions apply: - Limit chain speed to **4 m/s** - Normal greases applied to the outside surfaces only **seal the bearing surfaces** and will not work — causes premature failure - Grease must be **heated until fluid** and the chain **immersed** and allowed to soak until all air bubbles cease - Regular cleaning and regreasing at intervals is required depending on power and speed - Temperatures above **80°C** will cause damage to many greases and reduce effectiveness ##### Abnormal Ambient Temperatures - For elevated temperatures up to **250°C**, use dry lubricants such as colloidal graphite, MoS₂ in white spirit, or poly-alkaline glycol carriers - For low temperatures between **−5°C and −40°C**, special low-temperature initial greases and subsequent oil lubricants are necessary --- #### Four Lubrication Methods | Type | Method | Description | Application Range | |---|---|---|---| | **Type 1** | Manual Operation | Oil applied periodically with brush or oil can every ~8 hours; keep chain wet with oil | Low speed, low power | | **Type 2** | Drip Lubrication | Oil drips from a drip lubricator directed between link plate edges; sufficient volume and frequency for penetration | Moderate speed/power | | **Type 3** | Bath or Disc Lubrication | Lower chain strand runs through oil sump in the drive housing; OR a disc picks up oil and deposits it on the chain via deflection plates. Disc peripheral speeds: **180–2440 m/min** | Medium to high speed/power | | **Type 4** | Stream Lubrication | Continuous supply from a circulating pump or central system directed onto the chain via spray pipes; oil emerges in line with chain edges; positioned to deliver oil just before the chain engages the driver sprocket. Provides effective **cooling and impact damping** at high speeds | High speed, high power | --- #### Effect of Temperature on Chain Drives - Chain and chaincase temperatures during operation are an important control factor - Depending on severity of use, special attention to lubrication method may be required - Chain temperatures above **100°C** should be avoided if possible - Chain can generally give acceptable performance up to around **250°C** in some circumstances - Improving lubrication cooling effectiveness: increase oil volume to **up to 4.5 litres per minute per chain strand** and incorporate external cooling for the oil --- #### Bearing Pressures - When a chain has been correctly selected, the expected failure mode over a very long period is **wear** - A key indicator of likely wear performance is **bearing pressure** — the magnitude of contact pressure between the key mating surfaces (pin and bush) - Bearing pressure is calculated by dividing the **working load** by the **bearing area** - Bearing areas for standard chains are quoted in manufacturer designer data ##### Bearing Pressure vs Chain Velocity (General Guidance) | Chain Velocity | Simple Chain (N/mm²) | Multiplex Chain (N/mm²) | |---|---|---| | **Slow** | ~40 | ~60 | | **Medium** | ~35 | ~50 | | **High** | ~20 (contact manufacturer) | ~30 (reduced life) | - These values give an **indication only** and should not replace the standard chain selection methods --- #### Transmission Sprockets — Data Summary - Sprocket data is provided for various standard pitches - Materials available: **Steel** (standard) and **Heavy Duty Cast Iron** - Bore types: **Plain bore** and **Taper bore** (using taper lock bushes) - Chain configurations: **Simple**, **Duplex**, and **Triplex** ##### Sprocket Data by Pitch Size | Pitch (mm) | Pitch (inches) | Tooth Width Simple (mm) | Tooth Width Duplex (mm) | Tooth Width Triplex (mm) | |---|---|---|---|---| | 12.7 | 0.500 | B1 = 7.2 | B2 = 21.0 | B3 = 34.9 | | 15.875 | 0.625 | B1 = 9.2 | B2 = 25.6 | B3 = 42.2 | | 19.05 | 0.750 | B1 = 11.1 | B2 = 30.4 | B3 = 49.8 | | 25.4 | 1.000 | B1 = 16.2 | B2 = 47.7 | B3 = 79.6 | | 31.75 | 1.250 | B1 = 18.5 / 24.1 (1.5″ pitch) | B2 = 54.6 / 72.0 | B3 = 91.0 / 120.3 | | 44.45 | 1.750 | B1 = 29.4 | B2 = 88.4 | B3 = 148.0 | | 50.8 | 2.000 | B1 = 29.4 | B2 = 88.4 | B3 = 148.0 | - Sprockets are available with **welded hubs** for certain larger sizes - **Rebore, keyway, and setscrew modification services** are available from manufacturers --- #### Sprocket Modifications and Specials - Standard sprockets are available for simple, duplex, and triplex configurations up to 2.00″ pitch - Manufacturers also produce sprockets with **intermediate numbers of teeth** to suit single or multi-strand chains - **Special design sprockets** can be manufactured to specific requirements using normal or special materials - Sprockets to suit chain manufactured to imperial standards are available and are made to order ##### Rebore, Keyway, and Setscrew Modification - Catalogued stock sprockets are supplied either **taper bored** or **pilot bored** (larger unfinished bore allowing machining to tolerance) - Pilot bore allows standard tolerances to be machined; a bore to closer tolerance can also be supplied on request - Keyways to imperial or metric specifications, and setscrews can be machined - A **rebore, keyway, and setscrew modification service** is available from manufacturers --- ### Couplings #### Preamble - Couplings connect the output shaft of a prime mover (motor, engine) to the input shaft of a driven machine (gearbox, pump, conveyor) - Multiple types of coupling exist; the main variation is in **cost, misalignment tolerance, and power capacity** - Six common coupling types are covered here: **Spiderflex, Pinflex, Tyreflex, Discflex, Chainflex,** and **Rigid** - Additional specialised types include: high-misalignment gear types, brake drum gear types, disc brake types, shear pin gear types, buffer shear pin types, telescopic types, and hydraulic couplings - **Power ratings** for flexible couplings are based on a reference speed of **100 rev/min** - To select a coupling, multiply the actual power at the actual operating speed by the factor **100/N** (where N is operating speed in rpm) --- #### Misalignment Types - **Rigid couplings** are NOT designed to accept misalignment or movement between shafts — only suitable where no misalignment or movement will occur - **Flexible couplings** are designed to meet four misalignment conditions and should always be used wherever a prime mover is directly coupled to a gearbox or machine shaft | Misalignment Type | Description | |---|---| | **Angular** | Shaft axes are inclined at an angle to each other; measured at the coupling faces | | **Axial (Parallel)** | Shaft axes are parallel but laterally displaced (offset) | | **End Float** | Ability to accommodate relative axial displacement of connected shafts; achieved by sliding or flexure of resilient components | | **Torsional Flexibility** | Design feature to permit shock and impulsive loadings to be absorbed suitably | - Flexible couplings are **not designed to absorb excessive misalignment** caused by careless assembly - Shafts should still be **aligned as accurately as possible** in accordance with good engineering practice --- #### Selection Method — Rigid Couplings - Rigid couplings are rated to transmit the **same torque and power** as a mild steel shaft of the same diameter - Misalignment is **not a consideration** in their selection - Selection involves: 1. **Matching the coupling to the shaft size** involved 2. **Ensuring the speed is within** the maximum speed listed - Rigid couplings are available with or without **taper lock bushes** --- #### Selection Method — Flexible Couplings (11-Step Process) | Step | Action | |---|---| | **1** | Set out all relevant data: max power (design power), operating speed, max speed (if different), nature of prime mover and load, average operating hours/day, starts/day, maximum design misalignment, shaft sizes | | **2** | Classify the load as: Steady (S), Medium Impulsive (M), or Highly Impulsive (H) using the load classification table | | **3** | Obtain the **service factor (f_D)** from the service factor table | | **4** | Obtain the **start factor (f_S)** from the start factor table | | **5** | Calculate selection power: **Ps = P × f_D × f_S** (where P = design power in kW) | | **6** | Calculate equivalent selection power: **Pe = (Ps × 100) / N** (where N = operating speed in rev/min) | | **7** | Go to coupling tables for the type to be used; select the smallest suitable coupling for the equivalent selection power (Pe) from Step 6. If no type specified, list all suitable types | | **8** | Check that the **design misalignment** is less than the **allowable misalignment** for the coupling. If not, select another type | | **9** | Check that the **maximum coupling bore** (or taper bush bore) is greater than the actual shaft size. If not, select a larger coupling | | **10** | Check that the **maximum coupling speed** is greater than the maximum operating speed. If not, select a different coupling | | **11** | Detail the coupling selection with catalogue numbers for coupling and taper bush (if used). Check standard bore size from the taper bush table | --- #### Service Factors ##### Table 2 — Service Factor (f_D) | Prime Mover (Drive Input) | Duration of Service | Steady Load | Medium Impulsive | Highly Impulsive | |---|---|---|---|---| | **Electric, Air & Hydraulic Motors or Steam Turbine** (Steady input) | Intermittent — 3 hrs/day max | 0.90 | 1.00 | 1.50 | | | 3–10 hrs/day | 1.00 | 1.25 | 1.75 | | | Over 10 hrs/day | 1.25 | 1.50 | 2.00 | | **Multi-cylinder Internal Combustion Engine** (Medium impulsive input) | Intermittent — 3 hrs/day max | 1.00 | 1.25 | 1.75 | | | 3–10 hrs/day | 1.25 | 1.50 | 2.00 | | | Over 10 hrs/day | 1.50 | 1.75 | 2.25 | | **Single-cylinder Internal Combustion Engine** (Highly impulsive input) | Intermittent — 3 hrs/day max | 1.25 | 1.50 | 2.00 | | | 3–10 hrs/day | 1.50 | 1.75 | 2.25 | | | Over 10 hrs/day | 1.75 | 2.00 | 2.50 | ##### Table 3 — Start Factor (f_S) | Starts Per Hour | 0–1 | 1–30 | 30–60 | 60+ | |---|---|---|---|---| | **Factor (f_S)** | 1.0 | 1.2 | 1.3 | 1.5 | **Note:** For applications with excessive vibration, contact the manufacturer's technical department. --- #### Coupling Types Comparison | Coupling Type | Max Power @ 100 RPM (kW) | Max Speed (RPM) | Angular Misalignment | Radial Misalignment | Key Feature | |---|---|---|---|---|---| | **Spider** | 1.12 | 11,000 | Low | Low | Low cost, compact | | **Spiderflex** | 35 | 7,700 | 0.5°–2.5° | 0.3–0.5 mm | Nitrile element, oil resistant | | **Pinflex** | 258 | 6,800 | 0.25° | 0.13 mm | High torque, steel pin construction | | **Tyreflex** | 65.8 | 4,500 | 4° | 1.6 mm | Highest angular misalignment tolerance | | **Discflex** | 45 | 2,900 | 1° | 0.5 mm | Moderate misalignment | | **Chainflex** | 90 | 3,500 | 1° | 0.25 mm | Uses roller chain as flexible element | | **Torque Limiter** | 78 | 5,750 | — | — | Overload protection | | **Rigid** | 98 | 4,760 | None | None | Highest stiffness, zero misalignment tolerance | | **Gearflex (Double)** | 50,485 | 7,100 | Highest | Highest | Extreme power capacity | | **Gearflex (Single)** | 50,485 | 7,100 | — | — | Single engagement variant | --- #### Coupling Type Details ##### Spiderflex Coupling - Available in **B type** (plain bore) and **F/H type** (taper bore) - Flexible element: **Nitrile rubber** — temperature range **−40 to +100°C**, oil resistant, low absorption of liquids, partially resistant to chemicals - Shore hardness: **A88** - Permissible misalignment varies with size (e.g., 0.3–0.5 mm radial, 0.5°–2.5° angular) - End float range: +0.2 to +1.7 mm depending on coupling size - Weight range: 1.0 to 63 kg ##### Pinflex Coupling - Pin-based flexible coupling with **varying pin counts** (3 to 16 pins depending on size) - Maximum angular misalignment: **0.25°** - Maximum axial misalignment: **0.13 mm** - Power range: 2.03 kW (3-pin, size 1/3) up to 258.80 kW (16-pin, size 8/16) at 100 RPM - Steel half-bodies as standard - Available with bore range from unbored up to very large bores depending on size ##### Tyreflex Coupling - Provides the **highest angular misalignment tolerance** of all common flexible couplings (up to **4°**) - Also provides the **highest radial misalignment** tolerance (up to **1.6 mm**) - Best choice when significant misalignment must be accommodated ##### Discflex Coupling - Moderate misalignment capability (1° angular, 0.5 mm radial) - Compact design ##### Chainflex Coupling - Uses a **duplex roller chain** wrapped around sprocket-like hubs - Provides 1° angular and 0.25 mm radial misalignment capacity - Maximum speed: 3,500 RPM - Power up to 90 kW at 100 RPM ##### Rigid Coupling - Available in **plain bored** and **taper bored** versions - Rated to transmit the **same torque as a mild steel shaft** of the same diameter - No misalignment tolerance — shafts must be perfectly aligned - Selection is based on matching shaft diameter and checking maximum speed --- #### Rigid Coupling Data | Catalogue No. | Max Speed (RPM) | Bore Range Min–Max (mm) | Taper Bush | Weight (kg) | |---|---|---|---|---| | RR35 | 4,760 | — to 35 | — | 3.6 | | RR45 / RRT12 | 3,980 | 11 to 45/42 | TB1215 | 6.4 / 6 | | RR65 / RRT20 | 2,950 | 18 to 65/50 | TB2012 | 14.9 / 11.5 | | RR75 / RRT25 | 2,510 | 19 to 75/60 | TB2525 | 25 / 24 | | RR90 / RRT30 | 2,150 | 35 to 90/75 | TB3030 | 40 / 39 | | RR115 / RRT40 | 1,690 | 40 to 115/100 | TB4040 | 82 / 79 | --- #### Worked Example — Flexible Coupling Selection **Given:** - Power: 7.5 kW at 1440 rev/min from an electric motor - Driven machine: chain conveyor (non-uniformly fed) - Operating: 18 hours per day, 15 starts per hour - Shaft diameter: 38 mm (both motor and gearbox) - Maximum angular misalignment: 2° - Maximum axial misalignment: 0.2 mm - Taper bushes to be installed from coupling faces **Solution:** 1. **Data** — as given 2. **Load classification** — Medium Impulsive (M) (chain conveyor, non-uniformly fed) 3. **Service factor** — f_D = 1.5 (electric motor, over 10 h/day, medium impulsive) 4. **Start factor** — f_S = 1.2 (1–30 starts/hour) 5. **Selection power** — Ps = 7.5 × 1.5 × 1.2 = **13.5 kW** 6. **Equivalent selection power** — Pe = (13.5 × 100) / 1440 = **0.9375 kW** 7. **Suitable coupling types identified:** - Spiderflex: RSCT110 - Pinflex: PFT1/3 - Tyreflex: TY60 - Discflex: DT52N - Chainflex: C33M 8. **Check allowable misalignment (2° angular, 0.2 mm radial):** | Coupling | Allowable Angular (°) | Allowable Radial (mm) | Meets Requirement? | |---|---|---|---| | Spiderflex RSCT110 | 1° | 0.3 | ❌ Angular insufficient | | Pinflex PFT1/3 | 0.25° | 0.13 | ❌ Both insufficient | | **Tyreflex TY60** | **4°** | **1.6** | **✅ Both met** | | Discflex DT52N | 1° | 0.5 | ❌ Angular insufficient | | Chainflex C33M | 1° | 0.25 | ❌ Angular insufficient | 9. **Check max bore** — Tyreflex TY60: max bore = 42 mm → ✅ (shaft is 38 mm) 10. **Check max speed** — Tyreflex TY60: 4,000 rev/min → ✅ (operating at 1,440 rev/min) 11. **Final selection** — Tyreflex TY60/77 (F type) with taper bush TB1610. From taper bush table, 38 mm is a standard shaft size. Therefore: **TB1610/38** --- ### Mermaid Diagrams #### Chain Drive Selection Process ```mermaid flowchart TD A[Start: Known Power, Speed, Machine Characteristics, Centre Distance] --> B[Step 1: Select Drive Ratio & Sprockets\nZ₁ ≥ 19 teeth minimum\ni = Z₂ / Z₁] B --> C[Step 2: Establish Application Factor f₁\nUsing driver/driven characteristics chart] C --> D[Step 3: Determine Tooth Factor f₂\nf₂ = 19 / Z₁] D --> E[Step 4: Calculate Selection Power\nSelection Power = Power × f₁ × f₂ kW] E --> F[Step 5: Select Chain Drive\nUse rating chart — smallest pitch simple chain\nIf exceeded → consider multiplex] F --> G[Step 6: Calculate Chain Length\nUsing chain length formula\nRound to even number of pitches] G --> H[Step 7: Calculate Exact Centre Distance\nUsing revised centre distance formula] H --> I[Step 8: Choose Lubrication Method\nBased on chain speed & power from rating charts] I --> J[Selection Complete] ``` #### Flexible Coupling Selection Process ```mermaid flowchart TD A[Start: Known Power, Speed, Prime Mover Type, Load Type, Misalignment Requirements] --> B[Step 1: Set Out All Relevant Data] B --> C[Step 2: Classify Load\nSteady / Medium Impulsive / Highly Impulsive] C --> D[Step 3: Obtain Service Factor f_D] D --> E[Step 4: Obtain Start Factor f_S] E --> F[Step 5: Calculate Selection Power\nPs = P × f_D × f_S] F --> G[Step 6: Calculate Equivalent Selection Power\nPe = Ps × 100 / N] G --> H[Step 7: Select Smallest Suitable Coupling\nfrom coupling tables] H --> I{Step 8: Design Misalignment\n≤ Allowable Misalignment?} I -- Yes --> J{Step 9: Max Bore\n≥ Actual Shaft Size?} I -- No --> H J -- Yes --> K{Step 10: Max Coupling Speed\n≥ Operating Speed?} J -- No --> H K -- Yes --> L[Step 11: Detail Selection\nCatalogue No. + Taper Bush No.] K -- No --> H ``` #### Roller Chain Construction ```mermaid flowchart LR subgraph Chain Link Assembly A[Outer Plates] --- B[Bearing Pin] B --- C[Bush] C --- D[Roller] D --- E[Inner Plates] end subgraph Function F[Pin + Bush = Journal Bearing\nCase-hardened for high pressures] G[Roller = Engages Sprocket Teeth\nReduces wear on sprocket] H[Link Plates = Constrain Bearings\nTransmit tensile load] end ``` #### Coupling Types — Misalignment Capability Map ```mermaid quadrantChart title Coupling Misalignment Capability x-axis "Low Angular" --> "High Angular" y-axis "Low Radial" --> "High Radial" Rigid: [0.01, 0.01] Pinflex: [0.08, 0.08] Chainflex: [0.25, 0.15] Discflex: [0.25, 0.30] Spiderflex: [0.35, 0.25] Tyreflex: [0.95, 0.95] ``` #### Lubrication Method Selection ```mermaid flowchart TD A[Determine Chain Speed & Power] --> B{Low Speed / Low Power?} B -- Yes --> C[Type 1: Manual\nBrush or oil can every 8 hours] B -- No --> D{Moderate Speed / Power?} D -- Yes --> E[Type 2: Drip Lubrication\nOil drips between link plate edges] D -- No --> F{Medium-High Speed / Power?} F -- Yes --> G[Type 3: Bath or Disc\nChain runs through oil sump\nor disc picks up oil] F -- No --> H[Type 4: Stream Lubrication\nContinuous pump supply\nProvides cooling & impact damping] ``` --- ### Key Terms Glossary | Term | Definition | |---|---| | **Chain Pitch (P)** | Distance between adjacent bearing pin centres; the primary chain classification dimension | | **Drive Ratio (i)** | Ratio of driven sprocket teeth to driver sprocket teeth: i = Z₂ / Z₁ | | **Selection Power** | Adjusted power value (Power × f₁ × f₂) used to select chain from rating charts | | **Application Factor (f₁)** | Multiplier accounting for dynamic overloads based on driver and driven machine characteristics | | **Tooth Factor (f₂)** | Multiplier based on driver sprocket size: f₂ = 19 / Z₁ (baseline = 19-tooth sprocket) | | **Simplex / Duplex / Triplex** | Single, double, or triple strand roller chain configurations | | **Bearing Pressure** | Contact pressure between pin and bush; indicator of chain wear life (working load / bearing area) | | **Catenary** | Natural sagging curve of a chain strand between sprockets under self-weight | | **Taper Lock Bush** | Tapered sleeve that grips a shaft via high-tensile screws; provides secure, re-usable mounting | | **Equivalent Selection Power (Pₑ)** | Coupling selection power normalised to 100 RPM reference: Pₑ = (Ps × 100) / N | | **Service Factor (f_D)** | Coupling multiplier based on prime mover type, load characteristics, and duration of service | | **Start Factor (f_S)** | Coupling multiplier based on number of starts per hour | | **Angular Misalignment** | Inclination angle between two connected shaft axes | | **Axial (Parallel) Misalignment** | Lateral offset between two parallel shaft axes | | **End Float** | Ability of a coupling to accommodate relative axial displacement of connected shafts | | **Torsional Flexibility** | Coupling's ability to absorb shock and impulsive torque loadings | | **Pin Galling** | Failure mode at high speeds caused by breakdown of lubrication at the pin/bush interface | | **Link Plate Fatigue** | Failure mode at lower speeds caused by cyclic stress on chain link plates exceeding fatigue limit | | **Jockey Sprocket** | Additional sprocket used to take up slack and adjust chain tension; adds 2 pitches to chain length | --- ### Quick Revision - **Chain pitch** is the primary classification dimension for roller chains — measured pin centre to pin centre - **Minimum 19 teeth** on the driver sprocket for standard applications; **25+ teeth** for high speed or impulsive loads - **Maximum recommended sprocket teeth: 114**; use **odd teeth + even pitches** combination - **Selection Power = Power × f₁ × f₂** — always calculate before consulting rating charts - **f₁** depends on driver AND driven machine characteristics; **f₂ = 19/Z₁** (baseline 19-tooth) - **Round chain length to even number of pitches** — odd pitches require cranked links (not recommended) - **Centre distance typically 30–50 pitches**; recalculate exact centre distance after determining chain length - **Angle of lap ≥ 120°** on the smaller sprocket for large ratio drives - **Grease is NOT recommended** for chain lubrication — use mineral oil; 4 types of lubrication methods based on speed/power - **Chain temperatures above 100°C should be avoided**; acceptable up to 250°C with dry lubricants - **Expected chain life: 15,000 hours / 8 million cycles** under proper conditions - **Flexible couplings** accommodate four types of misalignment: angular, axial, end float, torsional - **Rigid couplings** tolerate ZERO misalignment — selection based on shaft size and speed only - **Coupling selection power: Pₑ = (P × f_D × f_S × 100) / N** — normalised to 100 RPM - **Tyreflex** has the highest misalignment tolerance (4° angular, 1.6 mm radial) among common flexible types - **Gearflex** provides the highest power capacity (50,000+ kW at 100 RPM) for extreme applications - **Taper lock bushes** are interchangeable between manufacturers and provide secure, re-usable shaft mounting - Always verify: **misalignment within limits**, **bore ≥ shaft size**, **max speed ≥ operating speed** when selecting couplings - **1 kW = 1.34 hp** for power conversion --- --- ## Chapter 7: Belt Drives — Power Ratings & Pulleys --- ### Overview - This reference covers **wedge belt power ratings**, **taper lock pulley specifications**, and **pulley groove dimensions** for standard V-belt drive systems - Power ratings are provided per belt for **SPB** and **SPC** wedge belt profiles, as well as **CRE-type** wedge belts (SPZ, SPA, SPB cross-sections) - Taper lock pulley catalogues cover **SPZ & Z**, **SPA & A**, **SPB & B**, and **SPC & C** belt profiles with full dimensional data - Pulley groove dimensions define the **face width**, **groove geometry**, and **tolerances** for each belt section - All data supports the **selection, specification, and verification** of belt drive components in mechanical power transmission systems --- ### Key Concepts - **Rated Power per Belt**: The power (in kW) a single belt can transmit at a given speed ratio and pulley pitch diameter — used to determine the number of belts required - **Additional Power per Belt for Speed Ratio**: An incremental power value added to the base rating when the speed ratio between driver and driven shafts exceeds 1.0 - **Small Pulley Pitch Diameter (PCD)**: The effective diameter at which the belt contacts the pulley — determines belt speed and power capacity - **Belt Speed**: The linear velocity of the belt (m/s), directly related to pulley diameter and shaft RPM — higher belt speeds generally increase power capacity up to a limit - **Taper Lock Pulley**: A pulley that uses a **split taper bush** (cone-shaped locking sleeve) to clamp onto the shaft — enables tool-free installation and removal without keyway damage - **Bush Number**: Identifies the specific taper lock bush size — defines bore range, shaft compatibility, and mounting bolt pattern - **Number of Grooves**: The number of V-grooves machined into the pulley — must match or exceed the number of belts in the drive - **Pulley Type**: Refers to the physical construction style (e.g., solid, spoked, plate) — different types suit different speed, weight, and balance requirements - **Groove Dimensions**: Standardised measurements (groove angle, depth, pitch, top width) that ensure correct belt seating and power transmission --- ### Detailed Notes #### Power Ratings — SPB Wedge Belts - **Application**: SPB belts are a **narrow-section wedge belt** profile used in medium-to-heavy industrial drives - Power ratings are tabulated for **small pulley pitch diameters** ranging from **140 mm to 315 mm** - **Shaft speeds** (Rev/min of faster shaft) range from **100 to 3000 RPM** - **Belt speeds** indicated on the right-hand column range from **2.33 m/s up to 40 m/s** (depending on RPM and pulley diameter) - As pulley diameter increases at a given RPM, the rated power per belt increases due to higher belt speed and better wrap angle - An **additional power table** is provided per belt for speed ratios — this accounts for the extra load capacity gained when the driven pulley is larger than the driver (speed ratio > 1.0) - The additional power values are tabulated for speed ratios from **1.00 to 1.05** up to **3.39 and over** - **Note**: Only pulleys of a specified manufacture standard should be used where belt speed falls between **30 and 40 m/s** — confirm selection and supply with the belt manufacturer #### Power Ratings — SPC Wedge Belts - **Application**: SPC belts are the **largest standard narrow-section wedge belt** profile — used for high-power industrial drives - Power ratings cover **small pulley pitch diameters** from **224 mm to 560 mm** - **Shaft speeds** range from **100 to 2000 RPM** - **Belt speeds** range up to **40 m/s** - The same additional power per speed ratio table structure applies as for SPB belts - SPC belts transmit significantly **higher power per belt** than SPB — e.g., at 1440 RPM with a 450 mm pulley, a single SPC belt can transmit approximately **52–54 kW** - The same belt speed caution (30–40 m/s range) applies for pulley manufacturer confirmation #### Power Ratings — CRE Wedge Belts (SPZ, SPA, SPB) - **CRE-type** belts are a category of **classical/conventional wedge belts** with smaller cross-sections - Three sub-profiles are covered: ##### SPZ Profile - Smallest CRE profile — suited for **light-duty drives** - Power ratings for small pulley pitch diameters from **56 mm to 97 mm** - Shaft speeds from **100 to 2800 RPM** - Maximum rated power per belt is modest (typically under **5 kW** per belt) ##### SPA Profile - Mid-range CRE profile — suited for **moderate-duty drives** - Power ratings for small pulley pitch diameters from **80 mm to 132 mm** - Shaft speeds from **100 to 2800 RPM** - Rated power per belt ranges from approximately **0.23 kW** (small pulley, low speed) up to approximately **9 kW** at higher speeds and larger pulleys ##### SPB Profile (CRE Type) - Largest CRE profile covered — suited for **medium-duty drives** - Power ratings for small pulley pitch diameters from **112 mm to 132 mm** - Shaft speeds from **100 to 2800 RPM** - Rated power per belt is higher than SPA — up to approximately **13 kW** per belt at optimal conditions --- #### Taper Lock Pulleys — SPZ & Z Belts - Pulleys are catalogued with **pitch diameters from 56 mm to 200 mm** - **Number of grooves**: 1 to 5 depending on pitch diameter - **Bush numbers** include 1008, 1108, 1210, 1610, and 2012 - **Maximum bore sizes** range from **25 mm (metric) / 1 inch** up to **50 mm (metric) / 2 inches** - **Pulley types** include solid (Type 1), plate (Type 2), and spoked variants (Types 6NR, 6, etc.) - Key dimensional parameters provided: - **F** — Pulley face width (mm) - **J** — Hub projection or mounting face dimension (mm) - **K** — Keyway or clearance dimension (mm) - **L** — Bush length or overall hub depth (mm) - **M** — Bolt circle or mounting feature dimension (mm) - **N** — Additional mounting or clearance dimension (mm) - **Outside Diameter (O)** — Overall outer diameter of the pulley (mm) - **Type 6NR pulleys** are non-preferred sizes and should be avoided in new designs where possible #### Taper Lock Pulleys — SPA & A Belts - Pulleys are catalogued with **pitch diameters from 80 mm to 800 mm** - **Number of grooves**: 1 to 6 depending on pitch diameter - **Bush numbers** include 1210, 1610, 2012, 2517, 3020, 3525, 4030, 4535 - **Maximum bore sizes** range from **32 mm / 1¼ inch** up to **115 mm / 4½ inches** - Larger pulleys (diameter ≥ 400 mm) support up to **6 grooves** and use larger bush sizes (3525, 4030, 4535) - **Type 6NR** pulleys appear throughout — these use a specific non-standard retaining method - Pulleys with an asterisk (*) designation are **non-preferred sizes** - Outside diameters range from **86 mm** (smallest single-groove) to **806 mm** (largest multi-groove) #### Taper Lock Pulleys — SPB & B Belts - Pulleys are catalogued with **pitch diameters from 112 mm to 1000 mm** - **Number of grooves**: 2 to 8 depending on pitch diameter - **Bush numbers** include 2012, 2517, 3020, 3525, 4030, 4535 - **Maximum bore sizes** range from **50 mm / 2 inches** up to **125 mm / 5 inches** - SPB pulleys begin at **2 grooves minimum** (no single-groove SPB taper lock pulleys listed) - For the largest pulleys (≥ 630 mm PCD), up to **8 grooves** are available - Outside diameters range from **119 mm** to **1007 mm** - Pulley types progress from solid/plate at smaller sizes to spoked at larger sizes #### Taper Lock Pulleys — SPC & C Belts - Pulleys are catalogued with **pitch diameters from 200 mm to 1250 mm** - **Number of grooves**: 3 to 8 depending on pitch diameter - **Bush numbers** include 2517, 3020, 3525, 4535, 5040 - **Maximum bore sizes** range from **60 mm / 2½ inches** up to **125 mm / 5 inches** - SPC pulleys begin at **3 grooves minimum** — reflecting the higher power capacity of this belt section - For the largest pulleys (≥ 800 mm PCD), up to **8 grooves** are available - Outside diameters range from **210 mm** to **1260 mm** - All pulleys use **Type 7 construction** (spoked) at larger sizes for weight reduction --- #### Pulley Groove Dimensions - Groove dimensions are standardised to ensure correct belt fit, seating depth, and power transmission - Dimensions vary by **belt section** and **pulley PCD range** (single groove vs. dual groove) --- ### Tables #### Pulley Groove Dimension Standards | Belt Section | Groove Type | PCD Range (mm) | A' (±0.5°) | D (±0.3, −0.0) | e* (±0.15) | l (±0.3) | b (±0.13) | lp | W | R (NOM) | |---|---|---|---|---|---|---|---|---|---|---| | **SPZ** | Single Groove | Up to 80 | 34° | 11.0 | 12 | 8 | 2.0 | 8.5 | 9.7 | 17.25 | | **SPZ** | Dual Groove | Over 80 | 38° | 11.0 | 12 | 8 | 2.0 | 8.5 | 9.9 | 17.25 | | **SPA** | Single Groove | Up to 118 | 34° | 13.75 | 15 | 10 | 2.75 | 11 | 12.7 | 21.25 | | **SPA** | Dual Groove | Over 118 | 38° | 13.75 | 15 | 10 | 2.75 | 11 | 12.9 | 21.25 | | **SPB** | Single Groove | Up to 190 | 34° | 17.5 | 19 | 12.5 | 3.5 | 14 | 16.1 | 27.25 | | **SPB** | Dual Groove | Over 190 | 38° | 17.5 | 19 | 12.5 | 3.5 | 14 | 15.4 | 27.25 | | **SPC** | Single Groove | Up to 315 | 34° | 23.8 | 25.5 | 17 | 4.8 | 19 | 21.9 | 37.25 | | **SPC** | Dual Groove | Over 315 | 38° | 23.8 | 25.5 | 17 | 4.8 | 19 | 22.3 | 37.25 | > **Note**: The *e** dimension tolerance is measured between any two grooves. All dimensions in millimetres. #### Belt Profile Comparison — Power Capacity Range | Belt Profile | Type | Typical PCD Range (mm) | Approx. Max Power per Belt (kW) | Typical Application | |---|---|---|---|---| | **SPZ** | CRE / Classical | 56–97 | ~5 | Light-duty drives, fans, small pumps | | **SPA** | CRE / Classical | 80–132 | ~9 | Moderate-duty drives, compressors | | **SPB** (CRE) | CRE / Classical | 112–132 | ~13 | Medium-duty industrial drives | | **SPB** | Narrow Wedge | 140–315 | ~31 | Medium-to-heavy industrial drives | | **SPC** | Narrow Wedge | 224–560 | ~60 | Heavy-duty, high-power industrial drives | #### Taper Lock Bush Size Summary | Bush Number | Typical Max Bore (Metric, mm) | Typical Max Bore (Imperial, inches) | Common Belt Profiles | |---|---|---|---| | **1008** | 25 | 1 | SPZ | | **1108** | 28 | 1⅛ | SPZ | | **1210** | 32 | 1¼ | SPZ, SPA | | **1610** | 42 | 1⅝ | SPZ, SPA | | **2012** | 50 | 2 | SPA, SPB | | **2517** | 60 | 2½ | SPA, SPB, SPC | | **3020** | 75 | 3 | SPA, SPB, SPC | | **3525** | 100 | 4 | SPB, SPC | | **4030** | 115 | 4½ | SPA, SPB | | **4535** | 125 | 5 | SPB, SPC | | **5040** | 125 | 5 | SPC | #### Minimum Groove Count by Belt Section (Taper Lock Pulleys) | Belt Section | Minimum Grooves | Maximum Grooves | Notes | |---|---|---|---| | **SPZ / Z** | 1 | 5 | Single-groove pulleys available at small diameters | | **SPA / A** | 1 | 6 | Single-groove available; 6-groove at large diameters | | **SPB / B** | 2 | 8 | No single-groove taper lock SPB pulleys | | **SPC / C** | 3 | 8 | Minimum 3 grooves; reflects high-power application | --- ### Mermaid Diagrams #### Belt Profile Selection Flowchart ```mermaid flowchart TD A[Determine Required Power per Belt] --> B{Power Level?} B -->|< 5 kW| C[SPZ Profile] B -->|5–13 kW| D{Application Type?} B -->|13–31 kW| F[SPB Narrow Wedge] B -->|> 31 kW| G[SPC Narrow Wedge] D -->|Light/Moderate Duty| D1[SPA Profile] D -->|Medium Duty| D2[SPB CRE Profile] C --> H[Select Pulley PCD from Rating Tables] D1 --> H D2 --> H F --> H G --> H H --> I[Verify Belt Speed ≤ 40 m/s] I --> J{Belt Speed 30–40 m/s?} J -->|Yes| K[Confirm Pulley Suitability with Manufacturer] J -->|No| L[Proceed with Standard Selection] K --> L L --> M[Select Taper Lock Pulley from Catalogue] M --> N[Verify Bush Size and Bore Compatibility] N --> O[Check Groove Dimensions Match Belt Section] ``` #### Taper Lock Pulley Selection Process ```mermaid flowchart TD A[Identify Belt Section] --> B[Determine Number of Belts Required] B --> C[Select Pulley Pitch Diameter from Power Rating Table] C --> D[Look Up Taper Lock Pulley Catalogue] D --> E{Check Number of Grooves Available} E -->|Sufficient| F[Identify Bush Number] E -->|Insufficient| G[Increase Pulley Diameter or Change Belt Section] G --> C F --> H[Verify Max Bore ≥ Shaft Diameter] H -->|Yes| I[Check Pulley Type Suitability] H -->|No| J[Select Next Larger Bush or Pulley] J --> F I --> K[Record Key Dimensions: F, J, K, L, M, N, O] K --> L[Confirm Outside Diameter Fits Available Space] L --> M[Specify Catalogue Code for Procurement] ``` #### Pulley Groove Geometry — Key Dimensions ```mermaid flowchart LR A[Belt Section Identified] --> B[Determine PCD Range] B --> C{PCD ≤ Threshold?} C -->|Yes| D["Single Groove Angle: 34°"] C -->|No| E["Dual Groove Angle: 38°"] D --> F[Apply Standard Groove Dimensions] E --> F F --> G["Key Dimensions: A' = Groove Angle D = Groove Depth e = Groove Pitch l = Belt Seat Width b = Tolerance Band lp = Datum Length W = Top Width R = Nominal Radius"] ``` --- ### Key Terms Glossary - **Wedge Belt**: A V-shaped belt with a trapezoidal cross-section that wedges into the pulley groove for friction-based power transmission - **Narrow-Section Wedge Belt**: An optimised V-belt profile (SPB, SPC) with a higher power-to-width ratio compared to classical sections - **CRE Belt**: A classical/conventional wedge belt cross-section (SPZ, SPA, SPB) — smaller and less power-dense than narrow-section equivalents - **Pitch Diameter (PCD)**: The effective working diameter of the pulley at the belt's neutral axis — used for all speed and power calculations - **Outside Diameter (O)**: The overall outer diameter of the pulley including the groove lands - **Taper Lock Bush**: A split, tapered sleeve that locks a pulley concentrically onto a shaft using clamping bolts — allows keyless or keyed mounting - **Bush Number**: A standardised code identifying the taper lock bush dimensions, bore range, and bolt pattern - **Speed Ratio**: The ratio of driven pulley PCD to driver pulley PCD — determines the torque multiplication and speed reduction - **Belt Speed (m/s)**: The linear speed of the belt, calculated as `π × PCD × RPM / 60,000` — critical for power rating selection and centrifugal load limits - **Groove Angle (A')**: The included angle of the V-groove — typically 34° for smaller pulleys and 38° for larger pulleys within the same belt section - **Groove Pitch (e)**: The centre-to-centre distance between adjacent grooves on a multi-groove pulley - **Face Width (F)**: The total width across the pulley face, encompassing all grooves and edge margins - **Non-Preferred Pulley Size**: A catalogue entry marked with an asterisk (*) indicating it is not the standard/recommended size — may have longer lead times or limited availability - **Type 6NR**: A pulley construction variant using a non-standard retaining method — typically found in older or transitional designs --- ### Quick Revision - **SPB wedge belts** cover PCDs from **140–315 mm** and can transmit up to approximately **31 kW per belt** — used for medium-to-heavy industrial drives - **SPC wedge belts** cover PCDs from **224–560 mm** and can transmit up to approximately **60 kW per belt** — the largest standard narrow-section profile - **CRE belts** (SPZ, SPA, SPB) are smaller classical profiles suited for **light to medium duty** — max power per belt ranges from ~5 kW (SPZ) to ~13 kW (SPB CRE) - **Belt speed must not exceed 40 m/s** — for speeds between 30–40 m/s, confirm pulley suitability with the manufacturer - **Additional power** is added per belt when the **speed ratio exceeds 1.0** — this accounts for improved belt wrap on the smaller pulley - **Taper lock pulleys** use a **split taper bush** for shaft mounting — bush number determines max bore and shaft compatibility - **Groove angles** change with pulley PCD: **34° for smaller pulleys**, **38° for larger pulleys** within each belt section - **Minimum groove counts** vary by belt section: SPZ/Z = 1, SPA/A = 1, SPB/B = 2, SPC/C = 3 - **Pulley types** progress from solid/plate construction at small diameters to **spoked construction** at large diameters for weight reduction - **Non-preferred sizes** (marked with *) should be avoided in new designs — use standard catalogue entries for availability and cost efficiency - Always verify: **belt section → power rating → pulley PCD → number of grooves → bush size → bore compatibility → groove dimensions** --- --- # PART IV — SHAFTS, KEYS, BEARINGS & SEALS --- ## Chapter 8: Shafts, Keys, Circlips, Seals & Rolled Steel Sections --- ### Overview - This chapter covers the **mechanical design of shafts** — rotating members supported by bearings that transmit torque and power - Topics include **shaft load classification**, **failure modes**, **design approaches**, **stress formulas**, **load estimation methods**, and **design procedures** for determining minimum shaft diameter - Also covered: **circlip and seal sizing** (metric long-life series), and **rolled steel section selection** for beams and columns - Key design philosophy: calculate equivalent torque and moment from combined loading, apply shock/fatigue factors, then determine shaft diameter using strength-of-materials formulas - Two primary design approaches are presented — one based on **endurance limit** and another based on **basic strength of materials** with generous safety factors --- ### Key Concepts - **Shaft**: A rotating member supported by bearings that transmits torque and power - **Steady Loads**: Torsional, bending, and axial loads that occur continuously during operation - **Shock Loads**: Intermittent, sudden increases in load (e.g., initial engagement in rolling or pressing operations) - **Inertia Loads**: Loads arising from acceleration or deceleration of the shaft and attached equipment - **Equivalent Torque (T_E)**: A combined measure incorporating both torque and bending moment — used to find shaft diameter from shear stress - **Equivalent Moment (M_E)**: A combined measure used to find shaft diameter from bending stress - **Shock/Fatigue Factors (K_T, K_M)**: Multipliers applied to steady torque and moment to account for dynamic loading effects - **Stress Concentration**: Localised increase in stress at geometric discontinuities such as keyways, shoulders, grooves, or holes - **Endurance Limit**: The stress level below which a material can theoretically sustain an infinite number of load cycles without fatigue failure - **Drive Application Factor (f)**: A multiplier used to account for the difference between actual transverse shaft load and the simplified calculated value --- ### Detailed Notes #### Shaft Definition and Characteristics - **Definition**: A rotating member supported by bearings that transmits torque and power - Rotation may be **continuous**, **intermittent**, **uni-directional**, or **reversing** - Shafts attached to wheels are often called **axles** - Usually **circular in cross-section** — solid or hollow; sometimes square for specific applications - Typically **rigid**; flexible shafts (cables) exist for specialised applications but are not covered here - Usually **long relative to diameter** - Commonly made from **steel or other metals**; non-metallic shafts are sometimes used - **Torque and power** are transmitted from an input location (e.g., a prime mover) to an output location (e.g., a driven load) - Input may come from a motor, engine, or intermediate shaft via gears, belts, or chains - Output may be transmitted directly to a load or via power transmission devices #### Shaft Loads and Stresses ##### Steady Loads - **Primary design loads** that occur relatively continuously during operation - Three types act on shafts, often simultaneously: | Load Type | Example Source | Resultant Stress | |-----------|--------------|-----------------| | **Torsional** | Motor, gear, belt, or chain drive | Torsional shear stress | | **Bending** | Transverse load from weight, gear forces, belt/chain tension | Bending stress (axial tension and compression) | | **Axial** | Propeller or weight load on a vertical shaft | Axial tension and compression | ##### Shock Loads - **Intermittent** in nature, causing sudden increases in load - Common in rolling mills, punching/cropping presses, and similar applications - Shafts must be designed to **withstand shock loads** even if they occur only momentarily - Load-limiting devices (shear pins, overload protection) are often fitted to protect the shaft ##### Inertia Loads - Occur during **acceleration or deceleration** (speed changes) - Magnitude depends on: - **Rate of acceleration/deceleration** (magnitude) - **Mass moment of inertia** of the shaft and coupled equipment/transmission devices - Typically occur during **start-up** and **shut-down** phases - For electric motors: - **Soft-start** (current-limiting device fitted): starting torque ≤ **1.5–2× rated load torque** - **Hard-start** (no current limiter): starting torque can be **3–5× rated load torque** #### Shaft Failure Modes ##### Failure Due to Excessive Load - Occurs when shaft stress **exceeds the yield stress** - Relatively rare due to **load-limiting devices** (shear pins, overload protection) in most systems - If overload causes **yielding without fracture**, the shaft may remain serviceable - Design goal: prevent stress from exceeding yield stress; **permanent deformation = failure** ##### Failure Due to Fatigue - **Most common failure mode** for shafts with high revolution counts - Can occur even when stresses are **well below yield point** - Most likely when loads **continually fluctuate**, especially with **stress reversal** - **Two mechanisms of stress reversal**: - **Change in load direction**: Most common for torsional stress reversal (e.g., vehicle transmission shafts reversing between drive and braking) - **Rotation of the shaft**: Most common for bending stress reversal (e.g., a horizontal shaft with a downward load — top and bottom alternate between tension and compression each half-revolution) #### Shaft Design Approaches ##### Approach 1: Endurance-Based - Calculate **peak loads** (including inertia and shock) and **stress concentrations** as accurately as possible - Allowable shaft stresses include an **allowance for shaft size** — larger diameter = lower allowable stress - For shafts with many revolutions: design to prevent **fatigue failure** using the **endurance limit** - Endurance limit is determined from standardised fatigue tests on polished specimens (typically 8–10 mm diameter) - A **small factor of safety** (typically ~1.2) is applied, based on the endurance limit - Based on relevant national rotating shaft design standards ##### Approach 2: Strength-of-Materials-Based (Recommended) - Calculate the **maximum design load** likely under operating conditions - Apply **shock/fatigue factors** and a **relatively generous factor of safety** - Account for **inertia loads** and **non-uniformity of material properties** - Use **basic strength of materials formulas** to calculate shaft stresses or diameter - More fundamental approach; provides **better understanding of stresses** involved - Avoids complex formulas with unstated assumptions - Based on recognised engineering code methodology #### Core Stress Formulas ##### Combined Shear Stress (Formula 1) $f_s = \frac{16 \, T_E}{\pi \, d^3}$ - Used to find shaft diameter from **torsional shear stress** ##### Combined Axial Stress (Formula 2) $f_s = \frac{32 \, T_E}{\pi \, d^3}$ - Used to find shaft diameter from **bending (axial) stress** ##### Equivalent Torque (Formula 3) $T_E = \sqrt{T^2 + M^2}$ - Combines torque (T) and bending moment (M) into a single equivalent value ##### Equivalent Moment (Formula 4) $M_E = 0.5 \, (T_E + M)$ - Used for bending stress calculations ##### Design Torque and Moment (with shock/fatigue factors) $T = K_T \cdot T_S \qquad M = K_M \cdot M_S$ - Where T_S and M_S are the **steady torque and moment** - K_T = shock/fatigue factor in **torsion** - K_M = shock/fatigue factor in **bending** #### Shock/Fatigue Factor Values | Loading Condition | K_T (Torsion) | K_M (Bending) | |-------------------|:---:|:---:| | **Static or gradually applied load** | 1.0 | 1.5 | | **Suddenly applied with minor shock** | 1.0–1.5 | 1.5–2.0 | | **Suddenly applied with heavy shock** | 1.5–3.0 | 2.0–3.0 | - **K_M = 1.5 minimum** even for static loads — accounts for bending stress reversal due to shaft rotation (constant load direction and magnitude) - These factors apply to **bending, torsion, or combined bending and torsion** (the most common loading) - For significant **axial loads**, more complex formulas (e.g., from relevant engineering codes) should be used, including column effects for compression #### Allowable Stresses and Factors of Safety - For **steel shafts** using the fundamental design approach: - **Bending** (tension or compression): the **smaller** of **40% f_y** or **24% f_ult** - **Torsion** (shear): the **smaller** of **30% f_y** or **18% f_ult** - Where: - **f_y** = yield strength - **f_ult** = ultimate tensile strength - The allowable shear stress is based on the assumption that **shear strength ≈ 75% of tensile strength** #### Stress Concentration at Keyways - **Keyways** are one of the most important sources of stress concentration in shafts - Located where gears, sprockets, or pulleys are fitted — usually the **most highly stressed locations** - **Design rule of thumb**: allowable stresses with a keyway are **75% of allowable stresses without** the keyway - For other stress concentrations (steps, holes), consult relevant engineering design standards and handbooks #### Estimating Shaft Loads ##### 1. Weight (Gravitational Load) - Applies when a **heavy pulley, flywheel, or similar component** is mounted on a non-vertical shaft - Causes a **transverse bending force**: $F = m \cdot g$ - Assumed: shaft supported by **low-friction bearings** (frictional torque negligible) ##### 2. Chain Drive - Chain tension creates a **transverse force** on the shaft at the sprocket - **Force at sprocket**: $F = T_2 + T_1$ — (Formula 5) — tight side + slack side tension - **Torque at sprocket**: $T = (T_2 - T_1) \cdot d/2$ — (Formula 6) - Where d = **pitch circle diameter (PCD)** of the sprocket (in metres) - When transmitting power, **slack side tension is usually negligible** → T_1 ≈ 0 ##### 3. Belt Drive (Vee or Wedge) - Same approach as chain drive, but **slack side tension is NOT zero** (friction-dependent) - Formulas 5 and 6 apply for belt drives as well - For **parallel belts**: F = T_2 + T_1 (correct); for **non-parallel belts**: use **vector sum** (but scalar sum errs on the safe side) - When both T_2 and T_1 are unknown, use one of three methods: ###### Method (a): Assume Slack Side Tension | Belt Section | Slack Side Tension (N) | |:---:|:---:| | SPZ | 100 | | SPA | 150 | | SPB | 350 | | SPC | 750 | - Based on mid-load power at 1000 rev/min, tension ratio 12:1, smallest recommended PCD for belt size ###### Method (b): Assume Belt Tension Ratio | Drive Ratio | Belt Tension Ratio | |:---:|:---:| | 1 | 16.3 | | 2 | 12 | | 3 | 10.4 | | 4 | 9.5 | | 5 | 9 | | 6 | 8.6 | - Based on 90% of tension ratio at slip point on smaller pulley; wedge angle 38°, friction coefficient 0.3, centre distance = sum of pulley PCDs; centrifugal effects excluded - Linear interpolation can be used for intermediate values ###### Method (c): Assume a Drive Application Factor - If slack side tension were zero: $F = 2T/d$ - Actual force is **greater** because T_1 ≠ 0 → apply factor **f**: $F = \frac{2 \, f \, T}{d}$ - For **vee or wedge belt drives**, f is typically taken as **1.5** - For **chain drives**: if T_1 = 0, then f = 1 - **Note**: f = 1.5 gives a result ~20% higher than other methods; f = 1.25 gives closer correlation ##### 4. Gear Drive - Force on the shaft = **resultant transverse force at the gear tooth contact point** - Three force components: - **F_t** (tangential force): produces the torque; $F_t = 2T/d$ — (Formula 8) - **F_s** (separating/radial force): keeps gears in mesh; acts through gear centrelines - **F** (resultant transverse force): vector sum of F_t and F_s - **Pressure angle (θ)**: angle between F and F_t — typically **20°** unless stated otherwise ###### Spur Gear Formulas $F_s = F_t \cdot \tan\theta \qquad \text{(Formula 9)}$ $F = \sqrt{F_t^2 + F_s^2} \qquad \text{(Formula 10)}$ ###### Helical Gear Formulas - Helical gears have teeth cut at an angle (**helix angle α**) to the shaft axis - Stronger and quieter than spur gears, but produce an **additional axial force** $F_s = \frac{F_t \cdot \tan\theta}{\cos\alpha} \qquad \text{(Formula 11 — separating force)}$ $F_a = F_t \cdot \tan\alpha \qquad \text{(Formula 12 — axial force)}$ - The resultant transverse force is still $F = \sqrt{F_t^2 + F_s^2}$ #### Design Procedure 1. **Estimate all loads** acting on the shaft (weight, drive forces, gear forces, etc.) 2. Draw **torque, shear force, and bending moment diagrams** - Shear force diagram is optional but useful to draw before the bending moment diagram 3. **Identify the critical location** — position of maximum combined stress (usually where torque and bending moment are both at maximum, typically at gear/sprocket/pulley locations) 4. Determine the **design torque and moment** by applying shock/fatigue factors (K_T, K_M) 5. Calculate **equivalent torque (T_E)** and **equivalent moment (M_E)** 6. Calculate **allowable stresses** (with keyway reduction if applicable) 7. Determine **minimum shaft diameter** using Formulas 1 and 2 8. Select the **closest standard shaft size** (round up) ##### Single-Plane vs Multi-Plane Bending - **Single-plane**: all resultant transverse forces act in the **same plane** → one bending moment diagram needed - **Multi-plane**: transverse forces act in **different planes** (e.g., horizontal and vertical) → draw bending moment diagrams for **each plane**, then combine: $M = \sqrt{M_v^2 + M_h^2} \qquad \text{(Formula 13 — resultant bending moment)}$ - Where M_v = vertical plane moment, M_h = horizontal plane moment ##### Design Notes - Treatment **excludes significant axial loads** — in most shafts, direct axial stress is small relative to bending and torsional stresses - Examples use **single-diameter shafts**; the same principles apply to **stepped shafts** — each step diameter is determined from the maximum stress at that section - For stepped shafts: apply a **stress-concentration factor** at each step (depends on ratio of diameters and internal radius) #### Rolled Steel Sections ##### Overview - **Hot rolled sections** are available in standard profiles: universal beams, universal columns, parallel flange channels, equal/unequal angles, and merchant bar (rounds, squares, flats) - Hot rolled sections have a **commercial finish** — not suitable for rotating shafts (use **bright steel** for shafts) - Available in several grades: | Grade | Minimum Yield (MPa) | Minimum UTS (MPa) | |:---:|:---:|:---:| | 250 | 250 | 410 | | 300 plus | 300 | 440 | | 350 | 350 | 480 | ##### Beam Selection Procedure 1. Determine the **maximum bending moment (M)** from loading and span 2. Calculate the **allowable bending stress** using the design factor: - e.g., for a design factor of 2 on yield: $f_b = f_y / 2$ 3. Calculate the **required section modulus**: $Z = M / f_b$ 4. Select the **smallest standard section** with Z ≥ required Z from beam tables 5. **Check self-weight**: recalculate reactions, moment, and Z including beam self-weight 6. Verify the selected section is still adequate ##### Column Selection Procedure 1. Determine the **effective length (L_e)** based on end conditions: - Both ends pinned: L_e = L - One fixed, one free (cantilever): L_e = 2L - One fixed, one pinned: L_e = 0.7L - Both ends fixed: L_e = 0.5L 2. Calculate the **design critical load** = applied load × design factor 3. Calculate the **limiting slenderness ratio**: $\left(\frac{L_e}{r}\right)_{lim} = \sqrt{\frac{2\pi^2 E}{f_y}}$ 4. Select a trial section from column tables; use the **smaller radius of gyration (r_y)** for buckling analysis 5. Calculate actual $L_e/r$ and compare with limiting value 6. If $L_e/r$ > limiting value → **slender column** → use **Euler formula**: $F_{cr} = \frac{\pi^2 E A}{(L_e/r)^2}$ 7. Check that $F_{cr}$ ≥ design critical load; iterate if necessary --- ### Comparison Tables #### Shaft Design Approaches Compared | Feature | Approach 1 (Endurance-Based) | Approach 2 (Strength-Based) | |---------|-----------------------------|-----------------------------| | **Basis** | Endurance limit from fatigue testing | Basic strength of materials | | **Factor of Safety** | Small (~1.2) | Relatively generous | | **Load Handling** | Peak loads calculated accurately | Maximum likely operating loads + factors | | **Complexity** | Complex formulas | Simpler, more transparent formulas | | **Understanding** | May use formulas with unstated assumptions | Better understanding of stress state | | **Standards** | Based on rotating shaft design standards | Based on engineering code methodology | | **Best For** | High-cycle fatigue-critical applications | General shaft design | #### Shaft Failure Modes Compared | Failure Mode | Cause | Likelihood | Prevention | |-------------|-------|-----------|-----------| | **Excessive Load** | Stress exceeds yield | Rare (load limiters fitted) | Shear pins, overload protection | | **Fatigue** | Cyclic stress reversal below yield | Most common | Design below endurance limit; minimise stress concentrations | #### Belt Load Estimation Methods Compared | Method | Input Required | Accuracy | Notes | |--------|---------------|----------|-------| | **(a) Assume T_1** | Belt section type | Moderate | Uses standard slack side tension values | | **(b) Assume tension ratio** | Drive ratio | Moderate | Based on near-slip conditions | | **(c) Application factor** | Factor f | Approximate | f = 1.5 typical; overstates by ~20% vs other methods | #### Spur vs Helical Gear Forces | Parameter | Spur Gear | Helical Gear | |-----------|-----------|-------------| | **Tangential force (F_t)** | 2T/d | 2T/d | | **Separating force (F_s)** | F_t · tan θ | F_t · tan θ / cos α | | **Axial force (F_a)** | None | F_t · tan α | | **Resultant transverse (F)** | √(F_t² + F_s²) | √(F_t² + F_s²) — very similar to spur | | **Noise** | Higher | Lower | | **Strength** | Lower | Higher | --- ### Mermaid Diagrams #### Shaft Design Process ```mermaid flowchart TD A[Identify All Shaft Loads] --> B[Estimate Load Magnitudes] B --> C{Load Type?} C -->|Weight| D[F = mg] C -->|Chain Drive| E["F = T₂ + T₁ <br/> T = (T₂ - T₁) · d/2"] C -->|Belt Drive| F[Use Method a, b, or c] C -->|Gear Drive| G["F_t = 2T/d <br/> F_s = F_t · tan θ <br/> F = √(F_t² + F_s²)"] D --> H[Draw Shear Force & Bending Moment Diagrams] E --> H F --> H G --> H H --> I[Identify Critical Location] I --> J["Apply Shock/Fatigue Factors <br/> T = K_T · T_S <br/> M = K_M · M_S"] J --> K["Calculate T_E = √(T² + M²) <br/> M_E = 0.5(T_E + M)"] K --> L["Calculate Allowable Stresses <br/> Bending: min(0.4·f_y, 0.24·f_ult) <br/> Shear: min(0.3·f_y, 0.18·f_ult)"] L --> M{Keyway Present?} M -->|Yes| N[Multiply Allowable Stresses × 0.75] M -->|No| O[Use Full Allowable Stresses] N --> P["Solve for d from: <br/> f_s = 16·T_E / (π·d³) <br/> f = 32·M_E / (π·d³)"] O --> P P --> Q[Select Larger Diameter <br/> Round Up to Standard Size] ``` #### Shaft Load Classification ```mermaid flowchart LR A[Shaft Loads] --> B[Steady Loads] A --> C[Shock Loads] A --> D[Inertia Loads] B --> B1[Torsional] B --> B2[Bending] B --> B3[Axial] C --> C1[Intermittent <br/> Sudden Increase] D --> D1[Start-Up / Shut-Down] D1 --> D2["Soft-Start: 1.5–2× rated"] D1 --> D3["Hard-Start: 3–5× rated"] ``` #### Shaft Failure Decision Tree ```mermaid flowchart TD A[Shaft Under Load] --> B{Stress > Yield?} B -->|Yes| C[Excessive Load Failure] C --> C1[Permanent Deformation] C1 --> C2{Shaft Broken?} C2 -->|No| C3[May Still Be Serviceable] C2 -->|Yes| C4[Replace Shaft] B -->|No| D{Cyclic Stress Reversal?} D -->|Yes| E{Stress > Endurance Limit?} E -->|Yes| F[Fatigue Failure Over Time] E -->|No| G[Infinite Life — No Failure] D -->|No| G ``` #### Multi-Plane Bending Resolution ```mermaid flowchart TD A[Forces on Shaft in Multiple Planes] --> B[Resolve into Vertical & Horizontal Components] B --> C[Draw Vertical Plane BM Diagram → M_v] B --> D[Draw Horizontal Plane BM Diagram → M_h] C --> E["Resultant: M = √(M_v² + M_h²)"] D --> E E --> F[Proceed with Design Using Resultant M] ``` #### Beam Selection Flowchart ```mermaid flowchart TD A[Given: Span, Loading, Grade, Design Factor] --> B[Calculate Max Bending Moment M] B --> C["Allowable Stress f_b = f_y / Design Factor"] C --> D["Required Z = M / f_b"] D --> E[Select Smallest Section with Z ≥ Required] E --> F[Check Self-Weight] F --> G{Z Still Adequate?} G -->|Yes| H[Section Confirmed] G -->|No| I[Select Next Larger Section] I --> F ``` --- ### Key Terms Glossary | Term | Definition | |------|-----------| | **Shaft** | A rotating member supported by bearings that transmits torque and power | | **Axle** | A shaft to which wheels are attached | | **Steady Load** | A primary design load occurring continuously during operation | | **Shock Load** | An intermittent, sudden increase in load | | **Inertia Load** | A load arising from acceleration or deceleration of the shaft | | **Equivalent Torque (T_E)** | √(T² + M²) — combines torque and bending moment for shear stress calculation | | **Equivalent Moment (M_E)** | 0.5(T_E + M) — combines torque and bending moment for bending stress calculation | | **K_T** | Shock/fatigue factor applied to torsion | | **K_M** | Shock/fatigue factor applied to bending | | **Endurance Limit** | Maximum stress for infinite fatigue life under cyclic loading | | **Stress Concentration** | Localised stress increase at geometric discontinuities | | **Keyway** | A groove cut in the shaft to accept a key for torque transmission; major source of stress concentration | | **PCD (Pitch Circle Diameter)** | The effective diameter of a gear, sprocket, or pulley used in force/torque calculations | | **Pressure Angle (θ)** | Angle between the tangential and resultant forces at a gear tooth; typically 20° | | **Helix Angle (α)** | Angle of tooth cut relative to the shaft axis in helical gears | | **Tangential Force (F_t)** | Force at the gear tooth that produces torque; F_t = 2T/d | | **Separating Force (F_s)** | Radial force keeping meshing gears engaged | | **Drive Application Factor (f)** | Multiplier accounting for actual vs simplified transverse shaft load; typically 1.5 for belt drives | | **Yield Strength (f_y)** | Stress at which permanent deformation begins | | **Ultimate Tensile Strength (f_ult)** | Maximum stress a material can sustain before fracture | | **Section Modulus (Z)** | A geometric property of a cross-section relating bending moment to bending stress; Z = M/f_b | | **Radius of Gyration (r)** | A geometric property used in column buckling analysis; relates moment of inertia to cross-sectional area | | **Slenderness Ratio (L_e/r)** | Ratio of effective column length to radius of gyration; determines buckling behaviour | | **Euler Formula** | Critical buckling load formula for slender columns: F_cr = π²EA/(L_e/r)² | | **Universal Beam (UB)** | An I-shaped hot rolled section optimised for bending (deep, narrow flanges) | | **Universal Column (UC)** | An I-shaped hot rolled section optimised for axial compression (square-ish profile, wide flanges) | --- ### Quick Revision #### Shaft Design — Must-Know Formulas - **Combined shear stress**: $f_s = 16 T_E / (\pi d^3)$ - **Combined bending stress**: $f = 32 M_E / (\pi d^3)$ - **Equivalent torque**: $T_E = \sqrt{T^2 + M^2}$ - **Equivalent moment**: $M_E = 0.5(T_E + M)$ - **Design torque**: $T = K_T \cdot T_S$ - **Design moment**: $M = K_M \cdot M_S$ #### Allowable Stresses (Steel Shafts) - **Bending**: smaller of 40% f_y or 24% f_ult - **Shear**: smaller of 30% f_y or 18% f_ult - **With keyway**: multiply both by **0.75** #### Shock/Fatigue Factors — Quick Reference - **Static/gradual**: K_T = 1.0, K_M = 1.5 - **Sudden + minor shock**: K_T = 1.0–1.5, K_M = 1.5–2.0 - **Sudden + heavy shock**: K_T = 1.5–3.0, K_M = 2.0–3.0 #### Shaft Load Formulas - **Weight**: F = mg - **Chain/belt drive force**: F = T_2 + T_1 - **Chain/belt torque**: T = (T_2 - T_1) · d/2 - **Belt drive with factor**: F = 2fT/d (f ≈ 1.5 for belt drives) - **Gear tangential force**: F_t = 2T/d - **Spur gear separating force**: F_s = F_t · tan θ - **Helical gear separating force**: F_s = F_t · tan θ / cos α - **Helical gear axial force**: F_a = F_t · tan α - **Resultant gear force**: F = √(F_t² + F_s²) - **Multi-plane resultant moment**: M = √(M_v² + M_h²) #### Column Design — Quick Reference - **Limiting slenderness ratio**: $(L_e/r)_{lim} = \sqrt{2\pi^2 E / f_y}$ - **Euler critical load**: $F_{cr} = \pi^2 E A / (L_e/r)^2$ - Use the **smaller radius of gyration** for buckling checks - If $L_e/r$ > limiting value → **slender** → Euler applies #### Key Design Reminders - K_M is **never less than 1.5** (even for static loads) due to bending stress reversal from rotation - **Fatigue** is the most common shaft failure mode — not overload - Soft-start motors: **1.5–2×** rated torque; hard-start: **3–5×** rated torque - Shaft diameter is determined by the **more critical** of shear stress and bending stress — check **both** - For stepped shafts: apply **stress concentration factors** at each step - Hot rolled sections → **not for rotating shafts**; use **bright steel** instead --- --- ## Chapter 9: Rolling Element Bearings --- ### Overview - **Topic:** Rolling element bearing selection, life calculation, and design methodology - **Scope:** Covers bearing types, load rating systems, life prediction methods (basic, adjusted, and advanced), bearing selection procedures for multiple bearing categories, and supporting reference data - **Core Principle:** Bearing life is a statistical estimate influenced by load, lubrication, cleanliness, and material — the more factors accounted for, the more accurate the prediction - **Key Takeaway:** Three progressively refined methods exist for calculating bearing life, each incorporating additional real-world factors beyond basic load capacity --- ### Key Concepts #### Dynamic Load Rating and Bearing Life - **Basic Dynamic Load Rating (C):** The constant radial load under which a group of identical bearings will achieve a basic rating life of 1 million revolutions - **L₁₀ Life:** The life that 90% of a sufficiently large group of identical bearings can be expected to attain or exceed under given operating loads - The **average life** of a bearing is approximately **5 times** the L₁₀ life - L₁₀ life is expressed in **millions of revolutions** #### Three Methods for Determining Bearing Life - **Method 1 — Basic L₁₀ Life:** Accounts only for the loads on the bearing; simplest and most conservative - **Method 2 — Adjusted Rating Life (Lna):** Extends Method 1 by incorporating reliability, material type, and lubricant viscosity - **Method 3 — New Life Theory (Lnaa):** Further extends Method 2 by adding the concept of a **fatigue load limit** and **contamination factor**, enabling infinite life prediction under ideal conditions #### Factors Affecting Bearing Life - **Steel type:** Standard bearing steels meet international specifications; premium steels can exceed standard life properties - **Lubrication:** Encompasses lubricant type (oil/grease), additives, viscosity, temperature, circulation method, and change intervals - **Cleanliness:** Encompasses environmental contaminants, particulate ingress, water contamination, lubricant filtration, and sealing method --- ### Detailed Notes #### Bearing Types Overview - **37 common types** of rolling element bearings exist, categorised into radial and thrust families - Selection depends on factors such as: load direction, shaft speed, accuracy, noise, friction, self-alignment capability ##### Radial Bearings - **Deep groove ball bearings** — Single row, double row, with shields or seals, with snap ring groove in outer ring - **Self-aligning ball bearings** — Cylindrical or tapered bore, with seals, with extended inner ring - **Angular contact ball bearings** — Single row, paired mounting, precision, double row, four-point contact - **Cylindrical roller bearings** — Multiple sub-types (NJ, NJP, NNU, NN), single/double/four row, full complement - **Needle roller bearings** — Drawn cup, open/closed ends, with flanges, with/without inner ring, with seals - **Spherical roller bearings** — Cylindrical or tapered bore - **Taper roller bearings** — Single row, four row, crossed ##### Thrust Bearings - **Thrust ball bearings** — Single/double direction, with flat/spherical housing washers, with sealing rings - **Angular contact thrust ball bearings** — Single/double direction - **Cylindrical roller thrust bearings** - **Needle roller thrust bearings** - **Spherical roller thrust bearings** - **Taper roller thrust bearings** — Single/double direction #### Bearing Type Selection Characteristics | Characteristic | Deep Groove Ball | Self-Aligning Ball | Angular Contact Ball | Cylindrical Roller | Needle Roller | Spherical Roller | Taper Roller | Thrust Ball | Cylindrical Roller Thrust | Needle Roller Thrust | Spherical Roller Thrust | |---|---|---|---|---|---|---|---|---|---|---|---| | **Radial load** | + | + | + | ++ | ++ | ++ | ++ | — | — | — | — | | **Axial load** | +½ | +½ | +↑ | — to +½ | — | + (limited) | ++ | ++ | ++ | ++ | ++ | | **Combined load** | + | + | ++ | — to + | — | + | ++ | — | — | — | + | | **Moment load** | — | + | + | — | — | + | — | — | — | — | — | | **High speed** | ++ | ++ | ++ | ++ | ++ | + | + | + | + | — | + | | **High running accuracy** | ++ | + | ++ | ++ | + | + | + | + | + | + | + | | **Quiet running** | ++ | + | ++ | + | — | + | + | + | — | — | — | | **High stiffness** | + | + | ++ | ++ | ++ | ++ | ++ | + | + | + | ++ | | **Low friction** | ++ | ++ | ++ | ++ | ++ | + | + | + | + | — | + | | **Self-aligning** | — | ++ | — | — | — | ++ | — | — | — | — | ++ | | **Locating bearing** | + | + | ++ | + to ++ | — | + | ++ | + | + | + | + | | **Non-locating bearing** | + | + | — | ++ | + | + | — | — | — | — | — | > **Legend:** ++ = excellent, + = good, — = poor/unsuitable, ½ = limited in one direction #### Bearing Selection Procedures ##### Selection of Deep Groove Ball Bearings (Method 1 — Basic L₁₀ Life) 1. **Determine required life** in operating hours - Consider continuous vs intermittent operation and expected equipment life - Common default for mechanical design: **10 years** 2. **Convert design life** from hours to millions of revolutions: - **L = (60 × N × h) / 10⁶** - Where: L = design life (millions of revolutions), N = average speed (rev/min), h = design life (hours) 3. **Determine average radial load (Fr) and axial load (Fa)** - Loads are typically shaft reaction forces at the bearing - Apply **shock factors** to steady loads where dynamic loads occur 4. **Calculate the ratio Fa/Fr** 5. **Select a bearing** from data tables for the known shaft size - In the absence of other knowledge, select a bearing around the **mid-range** of those available - Record the static load rating **Co** and dynamic load rating **C** 6. **Calculate the ratio Fa/Co** and read off the value of **e** from the calculation factors graph - For normal clearance bearings, project from the Fa/Co value to the Y line and down to the e scale 7. **Calculate the equivalent dynamic bearing load P:** - If **Fa/Fr ≤ e** → then **P = Fr** - If **Fa/Fr > e** → then **P = X·Fr + Y·Fa** where X = 0.56 - Values of Y can be read from the graph by projecting across from the Fa/Co value to the Y line - *Note: This graph is drawn for normal clearance bearings* 8. **Calculate the bearing L₁₀ life:** - **L₁₀ = (C / P)³** 9. **Compare L₁₀ to L:** - If **L₁₀ < L** → bearing is too small; repeat steps 5–8 with a higher load capacity bearing - If **L₁₀ ≈ L** → bearing is acceptable - If **L₁₀ > L** → bearing may be oversized; repeat with a lower load capacity bearing 10. **Calculate equivalent static bearing load Po:** - **Po = 0.6·Fr + 0.5·Fa** - Check that **Po < Co**; if not, select another bearing - *Note: If Po < Fr then set Po = Fr* 11. **Check minimum radial load:** - For satisfactory operation: **Fr > 0.01·C** - *More accurate methods based on lubricant viscosity and operating speed exist in manufacturer catalogues* 12. **Check maximum shaft speed** does not exceed the speed rating of the bearing ##### Selection of Self-Aligning Ball Bearings (Method 1 — Basic L₁₀ Life) - Steps 1–4 are **identical** to the deep groove ball procedure - Step 5: Use bearing data tables specific to self-aligning ball bearings (with or without adaptor sleeves) - Record C, Co, and calculation factors: **e, Y₁, Y₂, Y₀** - Step 6: Calculate equivalent dynamic bearing load P: - If **Fa/Fr ≤ e** → then **P = Fr + Y₁·Fa** - If **Fa/Fr > e** → then **P = 0.65·Fr + Y₂·Fa** - Steps 7–8: Calculate L₁₀ life using **L₁₀ = (C / P)³** and compare to required life - Step 9: Calculate equivalent static bearing load: - **Po = Fr + Y₀·Fa** - Check that **Po < Co** - *Note: If Po < Fr then set Po = Fr* - Step 10: Minimum radial load check: **Fr > 0.01·C** - Step 11: Check maximum shaft speed - Step 12: If tapered bore with adaptor sleeve, check axial load limit: - **Fa < 3·B·d** - Where: Fa = axial load (N), B = bearing width (mm), d = internal diameter (mm) ##### Selection of Cylindrical Roller Bearings (Method 1 — Basic L₁₀ Life) - Steps 1–4 follow the same pattern - *Note: Fa/Fr ratio should not exceed 0.5* - Step 5: Use cylindrical roller bearing data tables; record Co and C - Step 6: Calculate equivalent dynamic bearing load P: - For bearings **without flanges** (type NU): **P = Fr** - For bearings **with flanges:** - If **Fa/Fr ≤ e** → then **P = Fr** - If **Fa/Fr > e** → then **P = 0.92·Fr + Y·Fa** - Where: e = 0.2, Y = 0.6 for series 10, 2, 3, and 4; e = 0.3, Y = 0.4 for series 22 and 23 - Step 7: Calculate L₁₀ using: **L₁₀ = (C / P)^(10/3)** - *Note: Roller bearings use the exponent 10/3 rather than 3* - Steps 8–9: Compare life, check static load: - **Po < Co/1.5** (for cylindrical roller bearings) - *Note: Po = Fr for cylindrical roller bearings* - Step 10: Minimum radial load: **Fr > 0.02·C** - Step 11: Check maximum shaft speed ##### Selection of Spherical (Self-Aligning) Roller Bearings (Method 1 — Basic L₁₀ Life) - Steps 1–4 follow the same pattern - Step 5: Use spherical roller bearing data tables; record Co, C, and calculation factors **e, Y₁, Y₂, Y₀** - Step 6: Calculate equivalent dynamic bearing load P: - If **Fa/Fr ≤ e** → then **P = Fr + Y₁·Fa** - If **Fa/Fr > e** → then **P = 0.67·Fr + Y₂·Fa** - Step 7: Calculate L₁₀ using: **L₁₀ = (C / P)^(10/3)** - *Roller bearing exponent 10/3 applies* - Steps 8–9: Compare life, check static load: - **Po = Fr + Y₀·Fa** - Check that **Po < Co/1.5** - Step 10: Minimum radial load: **Fr > 0.02·C** - Step 11: Check maximum shaft speed #### Method 2 — Adjusted Rating Life - Uses the formula: **Lna = a₁ × a₂ × a₃ × L₁₀** - Where: - **a₁** = life adjustment factor for **reliability** - **a₂** = life adjustment factor for **material** - **a₃** = life adjustment factor for **operating conditions** ##### Reliability Factor (a₁) - For the standard 90% reliability: **a₁ = 1** - For higher reliability levels, manufacturer handbooks provide corresponding a₁ values (always < 1) ##### Material Factor (a₂) - For standard bearing steels (as defined by international standards): **a₂ = 1** - Premium manufacturer steels may have higher life properties ##### Operating Conditions Factor (a₃) - Determined primarily by bearing **lubrication** (assuming normal operating temperatures and cleanliness) - Some manufacturers combine a₂ and a₃ into a single factor **a₂₃** ##### Determining a₂₃ 1. Calculate the **mean diameter** of the bearing: **dₘ = 0.5 × (d + D)** - Where d = bore diameter, D = outer diameter 2. From Diagram 1, read the **required kinematic viscosity (ν₁)** for adequate lubrication at the given rotational speed and mean diameter 3. Calculate the **viscosity ratio:** **κ = ν / ν₁** - Where ν = actual kinematic viscosity of the lubricant at operating temperature 4. From Diagram 3, read the value of **a₂₃** based on κ 5. Apply: **Lna = a₁ × a₂₃ × L₁₀** ##### Notes on Viscosity and Temperature - Viscosity and temperature of lubricants are interrelated; for liquid lubricants, viscosity **decreases** with temperature - Typical pre-lubricated deep groove ball bearing grease has a viscosity of **100 mm²/s at 40°C** - Operating temperature depends on ambient temperature, bearing load, shaft speed, housing design, and similar factors - Measurement of similar bearings under operating conditions is a good method for estimating operating temperature - Diagram notes: shaded area on Diagram 3 is for lubricants **with additives**; diagrams are valid for mineral oils and greases under **normal cleanliness** conditions #### Method 3 — New Life Theory - Introduces the concept of a **fatigue load limit (Pu)** — the load below which fatigue will not occur (given adequate lubrication and cleanliness) - For loads below Pu, the bearing theoretically lasts **indefinitely** - The formula: **Lnaa = a₁ × a_SKF × L₁₀** - Where: - **a₁** = reliability factor (same as Method 2) - **a_SKF** = life adjustment factor based on new life theory ##### Determining a_SKF 1. Calculate the **viscosity ratio κ** (same as Method 2) 2. Determine the **contamination factor ηc** from the contamination table 3. Calculate: **ηc × Pu / P** 4. From Diagram 4 (ball bearings) or Diagram 5 (roller bearings), read **a_SKF** based on κ and ηc·Pu/P 5. Apply: **Lnaa = a₁ × a_SKF × L₁₀** (assuming a₁ = 1 for 90% reliability: **L_SKF = a_SKF × L₁₀**) > **Key insight:** If κ > 4, use the κ = 4 curve. As ηc·Pu/P tends to zero, a_SKF tends to 0.1 for all values of κ #### Contamination Factor (ηc) Reference Table | Condition | ηc | |---|---| | Very clean — debris size on the order of the lubricant film thickness | 1 | | Clean — typical of bearings greased for life and sealed | 0.8 | | Normal — typical of bearings greased for life and shielded | 0.5 | | Contaminated — bearings without seals, particle ingress likely from surroundings | 0.5 – 0.1 | | Heavily contaminated | 0 | #### Worked Example — Comparing All Three Methods **Given:** - Shaft diameter: 45 mm - Speed: 5000 rev/min - Bearing designation: 6309 (deep groove ball) - Radial load: 8 kN, no axial load - Lubrication: oil with viscosity 20 mm²/s at operating temperature - Reliability: 90% (normal) **Method 1 — Basic L₁₀ Life:** - From bearing tables for 6309 (45 mm shaft): C = 52.7 kN - Since no axial load: P = Fr = 8 kN - **L₁₀ = (52.7 / 8)³ = 286 million revolutions** **Method 2 — Adjusted Life:** - a₁ = 1 (90% reliability) - From tables: D = 100 mm → dₘ = 0.5 × (45 + 100) = 72.5 mm - From Diagram 1 at 5000 rpm: required viscosity ν₁ = 7 mm²/s - Actual viscosity ν = 20 mm²/s → κ = 20/7 = 2.9 - From Diagram 3 with κ = 2.9: a₂₃ = 2 - **Lna = 1 × 2 × 286 = 572 million revolutions** - *The longer life is due to lubricating oil viscosity being ~3× the minimum required* **Method 3 — New Life Theory:** *(a) Clean conditions:* - From tables: Pu = 1.34 kN, ηc = 0.8 (normal cleanliness) - ηc × Pu/P = 0.8 × 1.34/8 = 0.134 - From Diagram 4 with κ = 2.9: a_SKF ≈ 8 - **Lnaa = 8 × 286 = 2288 million revolutions** - *This is 4× higher than the adjusted life method prediction* *(b) Contaminated conditions (ηc = 0.2):* - ηc × Pu/P = 0.2 × 1.34/8 = 0.0335 - From Diagram 4 with κ = 2.9: a_SKF ≈ 1.2 - **Lnaa = 1.2 × 286 = 343 million revolutions** - *Contamination causes a considerable reduction in predicted life* --- ### Comparison Tables #### Life Calculation Methods Comparison | Feature | Method 1 (Basic L₁₀) | Method 2 (Adjusted Lna) | Method 3 (New Life Lnaa) | |---|---|---|---| | **Factors considered** | Load only | Load + reliability + material + lubrication | All of Method 2 + fatigue load limit + contamination | | **Formula** | L₁₀ = (C/P)^p | Lna = a₁ · a₂₃ · L₁₀ | Lnaa = a₁ · a_SKF · L₁₀ | | **Exponent (p)** | 3 (ball), 10/3 (roller) | Same as Method 1 | Same as Method 1 | | **Can predict infinite life?** | No | No | Yes (if load < Pu with adequate lubrication/cleanliness) | | **Accuracy** | Conservative estimate | Better estimate | Most accurate estimate | | **Complexity** | Lowest | Moderate | Highest | | **When to use** | Quick preliminary sizing | Standard engineering design | Critical applications, contaminated environments | #### Bearing Exponents by Type | Bearing Type | Life Equation Exponent | |---|---| | Ball bearings (all types) | 3 | | Roller bearings (cylindrical, spherical, taper) | 10/3 | #### Equivalent Dynamic Load Formulas by Bearing Type | Bearing Type | Condition | Formula | |---|---|---| | **Deep groove ball** | Fa/Fr ≤ e | P = Fr | | **Deep groove ball** | Fa/Fr > e | P = 0.56·Fr + Y·Fa | | **Self-aligning ball** | Fa/Fr ≤ e | P = Fr + Y₁·Fa | | **Self-aligning ball** | Fa/Fr > e | P = 0.65·Fr + Y₂·Fa | | **Cylindrical roller (no flanges)** | All cases | P = Fr | | **Cylindrical roller (with flanges)** | Fa/Fr ≤ e | P = Fr | | **Cylindrical roller (with flanges)** | Fa/Fr > e | P = 0.92·Fr + Y·Fa | | **Spherical roller** | Fa/Fr ≤ e | P = Fr + Y₁·Fa | | **Spherical roller** | Fa/Fr > e | P = 0.67·Fr + Y₂·Fa | #### Equivalent Static Load Formulas by Bearing Type | Bearing Type | Static Load Formula | Check Condition | |---|---|---| | **Deep groove ball** | Po = 0.6·Fr + 0.5·Fa | Po < Co | | **Self-aligning ball** | Po = Fr + Y₀·Fa | Po < Co | | **Cylindrical roller** | Po = Fr | Po < Co/1.5 | | **Spherical roller** | Po = Fr + Y₀·Fa | Po < Co/1.5 | > **Note:** For all types, if Po < Fr, then set Po = Fr #### Minimum Radial Load Requirements | Bearing Type | Minimum Load Condition | |---|---| | Deep groove ball | Fr > 0.01·C | | Self-aligning ball | Fr > 0.01·C | | Cylindrical roller | Fr > 0.02·C | | Spherical roller | Fr > 0.02·C | #### Self-Aligning Ball Bearing Adaptor Sleeve Axial Load Limit | Parameter | Requirement | |---|---| | **Axial load limit** | Fa < 3·B·d | | Fa | Axial load on the bearing (N) | | B | Width of the bearing (mm) | | d | Internal diameter of the bearing (mm) | --- ### Mermaid Diagrams #### Bearing Selection Decision Process ```mermaid flowchart TD A[Start: Define Operating Requirements] --> B[Determine required life in hours] B --> C[Convert hours to millions of revolutions<br/>L = 60·N·h / 10⁶] C --> D[Determine radial load Fr and axial load Fa] D --> E[Calculate Fa/Fr ratio] E --> F[Select bearing type based on<br/>load direction, speed, alignment needs] F --> G[Select specific bearing from data tables<br/>Record C, Co, and calculation factors] G --> H[Calculate equivalent dynamic load P] H --> I[Calculate L₁₀ = C/P raised to p<br/>p=3 ball, p=10/3 roller] I --> J{L₁₀ vs L?} J -->|L₁₀ < L| K[Bearing too small<br/>Select higher capacity] K --> G J -->|L₁₀ ≈ L| L[Bearing OK] J -->|L₁₀ >> L| M[Bearing oversized<br/>Select lower capacity] M --> G L --> N[Check static load Po < Co or Co/1.5] N --> O[Check minimum radial load] O --> P[Check maximum shaft speed] P --> Q[Bearing Selection Complete] ``` #### Three Life Calculation Methods ```mermaid flowchart LR subgraph Method1["Method 1: Basic L₁₀"] M1A[Load data only] --> M1B["L₁₀ = (C/P)^p"] end subgraph Method2["Method 2: Adjusted Life Lna"] M2A[Load data] --> M2D M2B[Reliability a₁] --> M2D M2C[Material + Lubrication a₂₃] --> M2D M2D["Lna = a₁ · a₂₃ · L₁₀"] end subgraph Method3["Method 3: New Life Lnaa"] M3A[Load data] --> M3E M3B[Reliability a₁] --> M3E M3C[Viscosity ratio κ] --> M3E M3D[Contamination ηc + Fatigue limit Pu] --> M3E M3E["Lnaa = a₁ · a_SKF · L₁₀"] end Method1 -.->|Adds reliability,<br/>material, lubrication| Method2 Method2 -.->|Adds fatigue limit<br/>and contamination| Method3 ``` #### Factors Affecting Bearing Life ```mermaid flowchart TD A[Bearing Life] --> B[Steel Type] A --> C[Lubrication] A --> D[Cleanliness] B --> B1[Standard ISO steel: a₂ = 1] B --> B2[Premium steels: a₂ > 1] C --> C1[Lubricant type: oil / grease] C --> C2[Additives present?] C --> C3[Viscosity at operating temp] C --> C4[Circulation and filtration method] C --> C5[Change interval] D --> D1[Environmental contaminants] D --> D2[Metallic particles / dirt / dust] D --> D3[Water contamination] D --> D4[Lubricant filtration quality] D --> D5[Sealing method effectiveness] ``` #### Viscosity Ratio (κ) Determination Process ```mermaid flowchart TD A[Calculate mean diameter<br/>dₘ = 0.5 × d + D] --> B[Use Diagram 1:<br/>Find required viscosity ν₁<br/>from speed and dₘ] B --> C[Determine actual lubricant<br/>viscosity ν at operating temp] C --> D[Calculate κ = ν / ν₁] D --> E{κ value?} E -->|κ < 1| F[Inadequate lubrication<br/>Reduced life] E -->|κ ≈ 1| G[Marginal lubrication<br/>Standard life] E -->|κ > 1| H[Good lubrication<br/>Extended life] E -->|κ > 4| I[Use κ = 4 curve<br/>Maximum benefit reached] ``` --- ### Imperial-Metric Equivalents Reference | Category | Conversion | |---|---| | **Length** | 1 inch = 25.4 mm | | **Length** | 1 foot = 12 inches = 304.8 mm | | **Length** | 1 yard = 3 ft = 914 mm | | **Mass** | 1 pound = 0.454 kg | | **Mass** | 1 ton = 1.016 t | | **Volume** | 1 gallon = 4.456 L | | **Pressure** | 1 psi = 6.89 kPa | | **Temperature** | F = 1.4·C + 32 | | **Heat Energy** | 1 BTU = 1.055 kJ | | **Power** | 1 hp = 747 W | --- ### Key Terms Glossary - **L₁₀ Life:** The rated life at which 90% of a group of identical bearings will survive under a specified load; expressed in millions of revolutions - **Basic Dynamic Load Rating (C):** The constant radial load that produces a basic rating life of 1 million revolutions for a bearing - **Basic Static Load Rating (Co):** The static load that produces a specified permanent deformation at the most heavily stressed rolling element/raceway contact - **Fatigue Load Limit (Pu):** The load below which metal fatigue will not occur in a bearing with adequate lubrication and cleanliness (used in Method 3) - **Equivalent Dynamic Bearing Load (P):** A calculated constant radial load that would produce the same life as the actual combined radial and axial loads - **Equivalent Static Bearing Load (Po):** A calculated static radial load that would cause the same total permanent deformation as the actual combined loads - **Viscosity Ratio (κ):** The ratio of actual lubricant kinematic viscosity to the required minimum kinematic viscosity at operating temperature (κ = ν/ν₁) - **Contamination Factor (ηc):** A factor (0 to 1) representing the level of particulate contamination in the bearing operating environment - **Adjusted Rating Life (Lna):** Bearing life calculated using Method 2, incorporating reliability, material, and lubrication adjustment factors - **a₁:** Life adjustment factor for reliability (= 1 for 90% reliability) - **a₂:** Life adjustment factor for material (= 1 for standard bearing steels) - **a₃:** Life adjustment factor for operating conditions (primarily lubrication) - **a₂₃:** Combined material and operating conditions factor - **a_SKF:** Life adjustment factor used in the new life theory (Method 3) - **Deep Groove Ball Bearing:** Most common bearing type; handles radial and moderate axial loads; low friction; high speed capability - **Self-Aligning Ball Bearing:** Accommodates shaft misalignment and deflection; uses a spherical outer ring raceway - **Cylindrical Roller Bearing:** Handles heavy radial loads; higher capacity than ball bearings of equivalent size; line contact between rollers and raceways - **Spherical Roller Bearing:** Handles heavy radial and moderate axial loads while accommodating misalignment; uses barrel-shaped rollers - **Adaptor Sleeve:** A tapered sleeve used to mount bearings with tapered bores onto cylindrical shafts - **Shock Factor:** A multiplier applied to steady loads to account for dynamic/impact loading conditions --- ### Quick Revision - **Design life equation:** L = (60 × N × h) / 10⁶ — converts hours to millions of revolutions - **Ball bearing life:** L₁₀ = (C/P)³ - **Roller bearing life:** L₁₀ = (C/P)^(10/3) - **Average bearing life** ≈ 5 × L₁₀ life - **Three life methods:** Basic L₁₀ (load only) → Adjusted Lna (+ reliability, material, lubrication) → New Life Lnaa (+ fatigue limit, contamination) - **Adjusted life formula:** Lna = a₁ × a₂₃ × L₁₀ - **New life formula:** Lnaa = a₁ × a_SKF × L₁₀ - **Viscosity ratio:** κ = ν/ν₁ — higher κ means better lubrication and longer life (cap at κ = 4) - **Contamination factor ηc:** 1 = very clean, 0.8 = sealed/greased for life, 0.5 = shielded, 0.1–0.5 = contaminated, 0 = heavily contaminated - **If Fa/Fr ≤ e:** simpler formula applies (usually P = Fr or P = Fr + Y₁·Fa) - **If Fa/Fr > e:** more complex formula with combined load factors applies - **Static load checks:** Deep groove ball: Po < Co; Roller bearings: Po < Co/1.5 - **Minimum radial load:** Ball bearings Fr > 0.01·C; Roller bearings Fr > 0.02·C - **Always check:** shaft speed does not exceed bearing speed rating - **37 standard bearing types** — selection based on load direction, speed, accuracy, noise, friction, self-alignment - **Key factors affecting life beyond load:** steel type, lubrication quality, and cleanliness --- --- ## Chapter 10: Journal Bearings, Belt Drives & Bearings Reference --- ### Overview - This document consolidates key mechanical design reference data covering three foundational topics in machine element design: **rolling element bearings**, **journal (plain) bearings**, and **belt drives** - The material is drawn from a technical education data manual used in mechanical engineering coursework - It provides selection procedures, design formulas, worked examples, comparison tables, and catalogue reference data for practical design applications - Understanding these components is essential for designing rotating machinery, power transmission systems, and general mechanical assemblies --- ### Key Concepts - **Rolling Element Bearings** — bearings that use balls or rollers to reduce friction between rotating and stationary parts; include cylindrical roller bearings and spherical roller bearings - **Journal Bearings** — also known as plain bearings or bushes; rely on a lubricant film between the shaft (journal) and the bearing surface rather than rolling elements - **Thick-Film Lubrication** — a condition in journal bearings where the lubricant film is thick enough that the journal does not contact the bearing surface, resulting in minimal wear - **Bearing Modulus (M)** — a dimensionless parameter used to assess whether thick-film lubrication will occur in a journal bearing - **Belt Drives** — power transmission systems that use flexible belts running over pulleys to transfer rotational energy between shafts - **Wedge Belts** — V-shaped cross-section belts (including vee, wedge, banded, multi-pull, link, cogged raw edge, and synchronous types) used in modern power transmission - **Service Factor** — a multiplier applied to the normal running power to account for the type of driven machine, prime mover, and operating hours --- ### Detailed Notes #### Chapter 1: Rolling Element Bearings ##### Cylindrical Roller Bearings (Single Row) - **Bore diameter ranges covered:** 30–55 mm - **Key parameters listed for each bearing designation:** - **Principal dimensions:** bore diameter (d), outer diameter (D), width (B) - **Basic load ratings:** dynamic (C) and static (C₀) — measured in Newtons (N) - **Fatigue load limit (Pᵤ)** — threshold below which fatigue life is theoretically infinite - **Speed ratings:** reference speed for grease and oil lubrication (r/min) - **Mass** — in kilograms - **Bearing dimensions:** inner ring (d₁, d₂), outer ring (D₁), fillet radii (r₁₂ min, r₃₄ min), and abutment dimensions (dₐ min, Dₐ max, rₐ max) - **Bearing type designations** include NU, NJ, NUP, and N series — each denoting a specific internal configuration of rollers and flanges - **Angle rings** are listed separately with their own designation codes, masses, and dimensions (B₁, B₂) ##### Spherical Roller Bearings (Single Row) - **Bore diameter ranges covered:** 20–55 mm - **Available bore types:** cylindrical bore, tapered bore (designated with "K" suffix) - **Designation codes:** CC, E, EK — indicating different internal designs and load capacities - **Key parameters** are the same as cylindrical roller bearings plus additional **calculation factors:** - **e** — a limiting value for the ratio of axial to radial load - **Y₁, Y₂** — axial load factors used in equivalent dynamic load calculations - **Y₀** — static axial load factor - **Abutment and fillet dimensions** include: dₐ (min), Dₐ (max), rₐ (max), plus additional dimensions for shoulder diameters and chamfer limits - A footnote indicates that **permissible axial displacement** from the normal position of one bearing ring relative to the other is specified in manufacturer catalogues --- #### Chapter 2: Journal (Plain) Bearings ##### Definition and Construction - A **journal bearing** (also called a bush or plain bearing) consists of a bearing surface surrounding a rotating shaft (the journal), housed within a stationary housing - The **journal** is not necessarily larger in diameter than the shaft — it is often the same diameter - **Two main types of journal bearings:** - **Pressure-lubricated type** — lubricant is pumped into the bearing under pressure (e.g., automotive engine bearings); requires complex design and is outside the scope of standard data manuals - **Non-pressure-lubricated type** — relies on self-lubrication or simple oil/grease supply; suitable for off-the-shelf selection - **Flange-type bearings** have a flange on one side to accommodate thrust loads in addition to radial loads ##### Bearing Materials - **Journal material:** typically a hard material with a fine, smooth, ground or lapped finish - **Bearing material:** a dissimilar, softer material with a relatively open and porous finish - **Why dissimilar materials are required:** - Prevents localised welding and seizure - Soft material allows **embeddability** of foreign particles - Porous, open finish **retains lubricant** - **Common bearing materials:** - **Metallic:** bronze (copper-tin alloy), white-metal alloys (lead-tin-aluminium-antimony-copper), cast iron (historically used, now rare) - **Non-metallic:** nylon, phenolics, PTFE (polytetrafluoroethylene) - **Common lubricants:** oils and greases; some special bearings use water or even air (dry operation) ##### Porous Bronze Bearings - Manufactured using **powder metallurgy** — pure copper and tin powders are sintered together - **Self-lubricating:** pre-impregnated with a standard lubricating oil (approximately 30% oil by volume) - Under many operating conditions, **no additional lubrication is required** - In some cases, **auxiliary lubrication** is recommended to extend bearing life ##### Performance Factors for Good Operation - **Surface finish of the shaft (journal):** - Should be a fine ground finish, preferably lapped - **Surface hardness of the shaft:** - Recommended minimum: steel with 0.35–0.45% carbon content (equivalent to a medium carbon grade) - For heavy-duty applications, the shaft should be hardened - **Grade of lubricant:** - Higher viscosity → longer bearing life - However, higher viscosity → greater friction - High-viscosity lubricants should only be used with high loads - Bearing life can be extended by cutting a **grease groove** into the bearing and pumping grease in - Standard pre-impregnation uses a light machine oil (approximately 20 centipoise at 65°C) - **Heat dissipation:** - Friction generates heat, which reduces lubricant viscosity and increases wear - Housing material and design should promote heat dissipation - Example: a thermosetting plastic housing will not dissipate heat as readily as a metallic housing - **Shock loads:** - Porous bronze bearings handle moderate radial shock loads due to oil-cushioned operation - Excessive prolonged radial shock increases metal-to-metal contact and reduces bearing life - Large out-of-balance forces in rotating members also reduce life - **Clearance:** - Bearings are typically a light press fit in the housing - A shouldered tool is usually used for installation via an arbour press - Running clearance between journal and bush: **rule-of-thumb is 1/1000 of the journal diameter** - Example: 25 mm journal → 0.025 mm running clearance - **Length-to-diameter ratio (L/d):** - Recommended range: **0.5 to 1.5** - Too small → high bearing pressure, difficult lubricant retention, side leakage - Too large → high friction, potential misalignment causing metal-to-metal contact ##### Advantages of Journal Bearings (vs. Rolling Element Bearings) - Low cost - Quiet operation with minimal noise - Little radial space required - High speed capability - Can operate with non-oil lubricants (water, grease, or even dry/air) ##### Disadvantages of Journal Bearings (vs. Rolling Element Bearings) - Relatively low radial load carrying capacity - Zero thrust load capability (unless a flange type is used with a stepped shaft) - Low misalignment capability (self-aligning types exist in small sizes but require the misalignment to be taken up between the outer bearing surface and the housing) - Shaft material and surface finish are critical to performance - Large sizes (above ~50 mm) are generally not available off-the-shelf ##### Summary of Best Applications - Journal bearings are most suitable for **relatively high-speed shafts with moderate radial loads and low or zero thrust loads**, particularly when **cost, noise, and space** are important considerations --- #### Thick-Film Lubrication Theory ##### Lubrication Regimes - **Boundary lubrication:** at rest or very low speeds, the journal contacts the lower face of the bearing; considerable wear occurs - **Thin-film (transition) lubrication:** as speed increases, oil is dragged around by the shaft, the shaft begins to "float" on a thin oil film; the journal may occasionally contact the bearing (especially during shock loads); moderate wear may occur - **Thick-film lubrication:** at high speed, the oil film becomes thick enough that **no contact occurs** between journal and bearing; **no wear occurs** because there is no metal-to-metal contact ##### Frictional Torque vs. Speed - At rest/low speed: **high friction** due to metal-to-metal contact (boundary lubrication) - As speed increases: **friction decreases** as metal contact diminishes - Once floating (thick-film regime): **friction increases again** because fluid friction increases with velocity (as with any fluid flow) - **The most desirable operating point** is the region around the **onset of thick-film lubrication** — below this point, wear occurs and frictional torque is high ##### Bearing Modulus (M) - Defined as: $M = \frac{\mu \cdot v}{p}$ - Where: - **μ** = dynamic viscosity of the lubricant (centipoise, cp) at operating temperature - **v** = linear (surface) velocity of the journal (m/s) - **p** = bearing pressure calculated on the **projected area** (MPa) - **Note:** 1 cp = 1000 Pa·s (i.e., 1 centipoise = 0.001 Pa·s) - **Design rule-of-thumb:** thick-film lubrication onset occurs at a bearing modulus of approximately **75** - If **M > 75** → thick-film lubrication is likely - If **M < 75** → consider increasing lubricant viscosity or other design changes to raise M - If **M >> 75** → thick-film lubrication is assured, but friction will be high — consider reducing lubricant viscosity --- #### Selection Procedure for Porous Bronze Journal Bearings 1. **Obtain relevant data:** journal (shaft) diameter, running speed, and radial load 2. **Select a bearing length** from the standard size table; as a first trial, assume **L/d = 1** (i.e., bearing length equals shaft diameter) 3. **Calculate bearing pressure (p):** $p = \frac{F}{A} = \frac{F}{d \times L}$ - Where: p = bearing pressure (MPa), F = radial bearing load (N), d = journal diameter (mm), L = bearing length (mm) 4. **Calculate surface velocity (v):** $v = r \cdot \omega = \frac{d}{2000} \times \frac{2\pi N}{60}$ - Where: N = rotational speed (rev/min), d = diameter (mm), v = surface velocity (m/s) 5. **Check bearing pressure against maximum allowable:** - For velocities ≤ 1 m/s, use the **velocity vs. maximum pressure table** - For velocities > 1 m/s, use the **maximum bearing pressure vs. shaft speed chart** (which provides curves for different shaft diameters) - If the calculated pressure exceeds the maximum, try a longer bearing to reduce pressure 6. **Calculate the p·v factor:** - Multiply bearing pressure (MPa) by surface velocity (m/s) - If p·v > 0.53 → auxiliary lubrication is needed - If p·v slightly exceeds 0.53, it may be possible to reduce p·v below 0.53 by increasing the bearing length (which reduces pressure) 7. **Check for thick-film lubrication:** - Calculate the bearing modulus M - Standard porous bronze bearings are pre-impregnated with a light machine oil having a viscosity of approximately **20 cp at 65°C** - If M > 75 → thick-film operation is likely - If M < 75 → consider increasing viscosity or other design modifications - If M >> 75 → thick-film operation is assured but friction is high; consider reducing viscosity 8. **Record the catalogue number** and relevant design data for the selected bearing --- #### Maximum Bearing Pressure Reference | **Surface Velocity (m/s)** | **Maximum Pressure (MPa)** | |---|---| | Slow and intermittent | 27.5 | | Continuous and < 0.125 | 13.8 | | 0.25 – 0.5 | 2.8 | | 0.5 – 0.75 | 1.9 | | 0.75 – 1.0 | 1.4 | | Over 1.0 | Use pressure vs. speed chart for specific shaft diameter | --- #### Worked Example: Porous Bronze Bearing Selection - **Given:** 30 mm diameter shaft, 1450 rev/min, 500 N total radial load shared equally between two bearings → 250 N per bearing, continuous running - **Step 1:** Load per bearing = 500/2 = 250 N - **Step 2:** Choose 30 mm bearing length (L/d = 1) - **Step 3:** p = 250 / (30 × 30) = 0.278 MPa - **Step 4:** v = (30/2000) × (2π × 1450/60) = 2.278 m/s - **Step 5:** Since v > 1 m/s, use the pressure vs. speed chart → for 30 mm at 1450 rev/min, maximum pressure = 0.47 MPa → 0.278 < 0.47 → **OK** - **Step 6:** p·v = 0.278 × 2.278 = 0.633 → exceeds 0.53 → **auxiliary lubrication required** - **Step 7:** M = (20 × 2.278) / 0.278 = 164 → well above 75 → **thick-film lubrication assured** - **Step 8:** Selected bearing has a nominal inside diameter of 30 mm and outside diameter of 38 mm with a length of 30 mm; auxiliary lubrication (e.g., reservoir with felt washer) is required ##### Auxiliary Lubrication Methods - **Felt washer soaked in oil** with a steel retainer - **Felt wick and oil well** arrangement - **Oil reservoir and felt washer (or wool)** surrounding the bearing - **Felt pad with spring pressure** and a screw cap filled with light grease --- #### Standard Metric Bearing Size Tables ##### Cylindrical Bearings (Standard Sizes) | **Inside Dia. (Nom. mm)** | **Outside Dia. (Nom. mm)** | **Available Lengths (mm)** | |---|---|---| | 4 | 8 | 4, 6 | | 6 | 10 | 6, 10 | | 8 | 12 | 6, 8, 12 | | 10 | 16 | 8, 10, 16, 25 | | 12 | 18 | 8, 12, 16, 20, 25 | | 14 | 20 | 10, 14, 20, 30 | | 16 | 22 | 12, 16, 20, 25, 30 | | 18 | 24 | 12, 18, 30 | | 20 | 26 | 15, 20, 25, 30 | | 22 | 28 | 15, 20, 25, 30 | | 25 | 32 | 20, 25, 30, 35 | | 27 | 35 | 20, 25, 30, 35 | | 30 | 38 | 20, 25, 30, 35 | | 33 | 41 | 20, 25, 30, 35 | | 35 | 45 | 25, 35, 40 | | 39 | 49 | 25, 35, 40 | | 45 | 55 | 35, 50, 55 | | 50 | 60 | 35, 50 | ##### Flange Bearings (Standard Sizes) - Flange bearings have a flange with a specified **flange diameter** and **flange thickness** to allow thrust load support and ease of mounting - Available from 12 mm to 70 mm flange diameter with thicknesses from 2 mm to 5 mm ##### Non-Standard Metric Cylindrical Bearings - Available for nominal inside diameters from 3 mm to 25 mm - Outside diameters range from 5 mm to 30 mm - Lengths range from 5 mm to 50 mm --- #### Chapter 3: Belt Drives ##### Types of Belts - **Vee belts:** older type of V-shaped design; now largely superseded by wedge belts but the term "vee belt" is still commonly used for both types - **Wedge belts:** similar to vee belts but with a deeper profile; slightly more expensive but have higher power ratings; now more commonly specified for new designs; pulleys are interchangeable with vee belt pulleys - **Banded belts:** multiple belts joined together at the top to form a composite belt; eliminates belt twist, whip, and turnover - **Multi-pull belts:** similar to banded belts but with a different profile - **Link belts:** hybrid between vee belts and chain drives; made of reinforced urethane linked sections; resistant to heat, oil, and chemicals; can be made to any length; uses the same pulleys as vee/wedge belts - **Cogged raw edge (CRE) belts:** similar to vee belts but with a cogged edge on the underside; can be used with smaller pulleys; commonly used in automotive and high-speed drives; same pulleys as vee/wedge belts - **Synchronous belts:** flat belts with a toothed profile that mates with gear teeth on the pulleys; prevents belt slip and maintains pulley synchronisation; lower load capacity than vee or wedge belts ##### Key Design Notes - Modern design data is given for **wedge belts** (not vee belts) - Pulleys use a **taper lock** design — when specifying, both the pulley catalogue number and the bush catalogue number are needed - Belt designation tables give **belt length**, **combined arc of contact**, and **belt length correction factor** - No specific national standard exists for vee or wedge belts, but commercial products comply with both relevant national and international standards --- #### Wedge Belt Selection and Drive Design Procedure 1. **Determine the service factor** from the service factor table based on: - Type of driven machine (light duty through extra heavy duty) - Type of prime mover (soft start vs. heavy start) - Hours of operation per day - For speed-increasing drives, multiply by an additional factor based on the speed ratio 2. **Calculate design power:** - Design power = Normal running power × Service factor - Normal running power = maximum power at the driver end (excludes shock loading and hard start factors) 3. **Select the belt section** using the belt selection chart (log-log plot of design power vs. rev/min of faster shaft): - Common sections: SPZ, SPA, SPB, SPC - When two or three sections may be suitable, check all possibilities for pulley size, number of belts, and cost before deciding - General rule: when two sections are suitable, choose the **larger** section (fewer belts needed with appropriately sized pulleys) 4. **Determine the speed ratio:** - Speed ratio = rev/min of faster shaft ÷ rev/min of slower shaft - If a speed tolerance applies, calculate the minimum and maximum driven shaft speeds - **Maximum speed ratio** obtainable with a single set of pulleys is approximately **6:1** 5. **Select the minimum pulley diameter** from Table 1: - For intermediate values, choose the next closest larger size - If faster shaft speed > 2880 rev/min, the minimum pulley is that given for 2880 rev/min 6. **Select suitable pulley pitch diameters:** - Start with the minimum driver pulley diameter - Select approximately five of the next larger pitch diameters available - Multiply each driver pulley diameter by the speed ratio to determine the theoretical driven pulley diameter - Choose the closest available pitch diameter for the driven pulley - Calculate actual driven pulley speed = driver speed × (driver PCD / driven PCD) - Discard any combinations that give a driven speed outside the tolerance range 7. **Choose the most suitable pulley combination:** - Smaller pulleys → more compact drive, lower belt speed - Larger pulleys → higher power rating per belt, fewer belts required - Consider space constraints — maximum pulley sizes may be dictated by the available space 8. **Calculate belt speed:** $v = r \cdot \omega = \frac{d}{2} \times \frac{\pi \times N}{30}$ - Where: d = pitch diameter (m), N = rev/min - **Belt speed must not exceed 40 m/s** — if it does, select smaller pulleys 9. **Estimate centre distance (if not specified):** - A good design rule: **centre distance ≈ sum of the two pulley pitch diameters (C ≈ D + d)** 10. **Calculate the required belt pitch length:** $L = 2C + \frac{(D - d)^2}{4C} + \frac{\pi}{2}(D + d)$ - Where: L = pitch length (mm), C = approximate centre distance (mm), D = large pulley pitch diameter (mm), d = small pulley pitch diameter (mm) 11. **Choose a standard belt length** closest to the calculated value from the belt section table: - Generally choose the **next larger** rather than smaller size 12. **Calculate exact centre distance:** $C = A + \sqrt{A^2 - B}$ - Where: $A = \frac{L}{4} - \frac{\pi}{8}(D + d)$ $B = \frac{(D - d)^2}{8}$ - L = standard belt length chosen 13. **Obtain basic power rating per belt:** - From the rated power tables for the chosen belt section - **Basic power per belt = Rated power + Additional power** - For speeds intermediate to those listed, use **linear interpolation** 14. **Apply combined correction factor:** - From the combined arc of contact and belt length correction factor table - **Corrected power per belt = Basic power per belt × Combined correction factor** 15. **Calculate the number of belts:** - Number of belts = Design power ÷ Corrected power per belt - Round to the **nearest whole number** - Rule of thumb: if the fractional part is ≥ 0.3, round up; if < 0.3, round down (subject to design accuracy and safety factor assessment) 16. **Obtain catalogue numbers** for pulleys and bushes: - Verify that pulleys are available with the required number of grooves - Verify that the maximum bush bore does not exceed the shaft sizes being used - If not available, it is usually preferable to **redesign the drive** rather than manufacture custom pulleys --- #### Worked Example: Wedge Belt Drive Design - **Given:** 6-cylinder diesel engine at 1050 rev/min driving a reciprocating gas compressor at 650 rev/min ± 3%; maximum power = 50 kW; operation > 16 hours/day; engine shaft = 70 mm diameter; compressor shaft = 80 mm diameter - **Step 1:** Service factor = 1.4 (Class 3 heavy duty, internal combustion engine with ≥ 4 cylinders, over 16 hours/day) - **Step 2:** Design power = 50 × 1.4 = 70 kW - **Step 3:** Either SPB or SPC section is suitable; select the **larger SPC section** - **Step 4:** Speed ratio = 1050/650 = 1.615 (reduction); driven speed range = 630.5 to 669.5 rev/min - **Step 5:** Minimum pulley diameter = 250 mm (from Table 1) - **Step 6:** Six combinations evaluated (driver pulleys from 250 to 335 mm); all give acceptable driven speeds within the tolerance range - **Step 7:** Selected combination: driver = 315 mm PCD, driven = 500 mm PCD → driven speed = 661.5 rev/min; larger pulleys chosen for higher power rating - **Step 8:** Belt speed = (0.315/2) × (π × 1050/30) = 17.3 m/s → OK (< 40 m/s) - **Step 9:** Centre distance = 315 + 500 = 815 mm - **Step 10:** Required belt pitch length = 2921 mm - **Step 11:** Closest standard belt lengths: 2800 and 3150 mm → choose 3150 mm - **Step 12:** Exact centre distance = 930.3 mm - **Step 13:** Basic power per belt = 26.725 + 2.405 = 29.13 kW - **Step 14:** Combined correction factor = 0.9 → Corrected power per belt = 29.13 × 0.9 = 26.217 kW - **Step 15:** Number of belts = 70 / 26.217 = 2.67 → **use 3 belts** - **Step 16:** Driver pulley: 315 mm PCD, 3 grooves, shaft 70 mm; Driven pulley: 500 mm PCD, 3 grooves, shaft 80 mm — both verified as available from catalogue --- #### Service Factor Table (Summary) | **Duty Class** | **Description** | **Soft Start, 10 & under hrs** | **Soft Start, Over 10–16 hrs** | **Soft Start, Over 16 hrs** | **Heavy Start, 10 & under hrs** | **Heavy Start, Over 10–16 hrs** | **Heavy Start, Over 16 hrs** | |---|---|---|---|---|---|---|---| | **Class 1 — Light** | Agitators (uniform), blowers/fans (≤ 7.5 kW), centrifugal compressors, belt conveyors (uniform) | 1.0 | 1.1 | 1.2 | 1.1 | 1.2 | 1.3 | | **Class 2 — Medium** | Agitators/mixers (variable), blowers/fans (> 7.5 kW), rotary compressors/pumps, generators, laundry/printing/sawmill machinery | 1.1 | 1.2 | 1.3 | 1.2 | 1.3 | 1.4 | | **Class 3 — Heavy** | Brick machinery, bucket elevators, reciprocating compressors/pumps, conveyors (heavy), hoists, mills, pulverisers, punches, presses, quarry plant, rubber machinery, textile machinery | 1.2 | 1.3 | 1.4 | 1.4 | 1.5 | 1.6 | | **Class 4 — Extra Heavy** | Crushers (gyratory, jaw, roll), ball/rod mills | 1.3 | 1.4 | 1.5 | 1.5 | 1.6 | 1.8 | **Soft start:** electric motors (star-delta, shunt wound, direct-on-line, series & compound wound), internal combustion engines with ≥ 4 cylinders, all prime movers fitted with centrifugal clutches, dry or fluid couplings, or electronic soft start devices **Heavy start:** electric motors (direct-on-line, series & compound wound), internal combustion engines with < 4 cylinders, prime movers not fitted with soft start devices **For speed-increasing drives**, multiply the service factor by an additional factor: - Speed ratio 1.00–1.24 → multiply by 1.00 - Speed ratio 1.25–1.74 → multiply by 1.05 - Speed ratio 1.75–2.49 → multiply by 1.11 - Speed ratio 2.50–3.49 → multiply by 1.18 - Speed ratio 3.50 and over → multiply by 1.25 --- #### Belt Section Selection Guide (Table 2 Summary) | **Belt Section** | **Typical Design Power Range (kW)** | **Typical Speed Range (rev/min)** | |---|---|---| | **SPZ** | 1 – 50 | 200 – 10,000 | | **SPA** | 2 – 100+ | 100 – 10,000 | | **SPB** | 5 – 300+ | 100 – 7,000 | | **SPC** | 20 – 900+ | 100 – 4,000 | - Overlapping regions exist — when two sections may be suitable, evaluate both before selecting - The selection chart is a log-log graph with rev/min of the faster shaft on the x-axis and design power on the y-axis --- #### Combined Arc of Contact and Belt Length Correction Factor - **Correction factors** are provided for each belt section (SPZ, SPA, SPB, SPC) based on: - **Speed ratio** (1–1.5, >1.5–2, >2–2.5, >2.5–3, >3) - **Belt length** (varies by section) - **Values range from 0.8 to 1.15** — shorter belts and higher speed ratios receive lower correction factors; longer belts and lower speed ratios receive higher factors - A correction factor of **1.0** represents a nominal (baseline) condition --- #### Power Rating Tables - **Rated power per belt** is given for each belt section (SPZ, SPA, SPB, SPC) as a function of: - **Rev/min of the faster shaft** (100 to 6000 rev/min) - **Small pulley pitch diameter** (varies by section) - **Additional power per belt** is also given for each speed ratio range (1.00–1.06 through to higher ratios) - **Total basic power per belt = Rated power + Additional power** - **Belt speed range:** only use pulleys from the specified manufacturer when belt speed falls between 30 and 40 m/s; confirm selection and supply with the manufacturer --- ### Comparison Tables #### Journal Bearings vs. Rolling Element Bearings | **Feature** | **Journal (Plain) Bearings** | **Rolling Element Bearings** | |---|---|---| | **Cost** | Low | Moderate to high | | **Noise** | Very quiet | Can be noisy at high speed | | **Radial space** | Minimal | Larger cross-section | | **Speed capability** | Very high | Moderate to high | | **Radial load capacity** | Low to moderate | High | | **Thrust load capacity** | None (unless flanged) | Available in thrust configurations | | **Misalignment tolerance** | Low | Moderate (self-aligning types) | | **Shaft requirements** | Critical (material, finish, hardness) | Standard shafts acceptable | | **Lubrication** | Can use oil, grease, water, or dry | Oil or grease | | **Maximum size (off-the-shelf)** | ~50 mm | Very large sizes available | | **Maintenance** | May need lubrication top-up | Sealed types are maintenance-free | #### Belt Section Comparison | **Belt Section** | **Profile Depth** | **Power Capacity** | **Pulley Size** | **Typical Application** | |---|---|---|---|---| | **SPZ** | Smallest | Lowest | Smallest pulleys | Low-power, high-speed drives | | **SPA** | Medium | Medium | Medium pulleys | General-purpose industrial drives | | **SPB** | Large | High | Large pulleys | Heavy industrial drives | | **SPC** | Largest | Highest | Largest pulleys | Heavy-duty, high-power drives | #### Lubrication Regime Comparison | **Regime** | **Speed** | **Film Thickness** | **Contact** | **Wear** | **Friction** | |---|---|---|---|---|---| | **Boundary** | At rest / very low | Negligible | Full metal-to-metal | High | High (static) | | **Thin-film (Transition)** | Low to moderate | Thin | Occasional contact | Moderate | Decreasing | | **Thick-film** | High | Full separation | No contact | None | Increasing (fluid friction) | --- ### Mermaid Diagrams #### Journal Bearing Selection Procedure ```mermaid flowchart TD A[Obtain shaft diameter, speed, and radial load] --> B[Select bearing length from standard table<br>First trial: L/d = 1] B --> C[Calculate bearing pressure<br>p = F / d × L] C --> D[Calculate surface velocity<br>v = d/2000 × 2πN/60] D --> E{Is v ≤ 1 m/s?} E -- Yes --> F[Check p against<br>velocity vs. max pressure table] E -- No --> G[Check p against<br>pressure vs. speed chart] F --> H{Is p ≤ max allowable?} G --> H H -- No --> I[Increase bearing length L<br>and recalculate] I --> C H -- Yes --> J[Calculate p·v factor] J --> K{Is p·v ≤ 0.53?} K -- Yes --> L[No auxiliary lubrication needed] K -- No --> M[Auxiliary lubrication required] L --> N[Calculate bearing modulus<br>M = μv / p] M --> N N --> O{Is M ≥ 75?} O -- Yes --> P[Thick-film lubrication assured<br>Record catalogue number] O -- No --> Q[Consider increasing lubricant<br>viscosity or redesign] Q --> N ``` #### Wedge Belt Drive Design Procedure ```mermaid flowchart TD A[Determine service factor<br>from duty class table] --> B[Calculate design power<br>= Running power × Service factor] B --> C[Select belt section<br>from selection chart] C --> D[Determine speed ratio<br>and driven speed tolerance] D --> E[Select minimum pulley<br>diameter from Table 1] E --> F[Select suitable pulley<br>pitch diameter combinations] F --> G[Check all combinations give<br>driven speed within tolerance] G --> H[Choose most suitable<br>pulley combination] H --> I[Calculate belt speed<br>v = rω] I --> J{Is v < 40 m/s?} J -- No --> K[Select smaller pulleys<br>and recalculate] K --> F J -- Yes --> L[Estimate or specify<br>centre distance] L --> M[Calculate required<br>belt pitch length] M --> N[Choose closest standard<br>belt length ≥ calculated] N --> O[Calculate exact<br>centre distance] O --> P[Obtain basic power per belt<br>= Rated + Additional power] P --> Q[Apply combined<br>correction factor] Q --> R[Calculate number of belts<br>= Design power ÷ Corrected power] R --> S[Round to nearest<br>whole number] S --> T[Obtain pulley and bush<br>catalogue numbers] T --> U{Are pulleys available<br>with required grooves?} U -- Yes --> V[Design complete] U -- No --> W[Redesign drive<br>with different pulleys] W --> F ``` #### Lubrication Regimes in Journal Bearings ```mermaid flowchart LR A[Rest / Very Low Speed] --> B[Boundary Lubrication<br>Metal-to-metal contact<br>High wear] B --> C[Low to Moderate Speed] C --> D[Thin-Film Lubrication<br>Transition regime<br>Moderate wear] D --> E[High Speed] E --> F[Thick-Film Lubrication<br>No contact, no wear<br>Fluid friction only] style B fill:#ff6b6b,color:#000 style D fill:#ffd93d,color:#000 style F fill:#6bcb77,color:#000 ``` #### Belt Drive Types Classification ```mermaid graph TD A[Belt Drive Types] --> B[V-Section Belts] A --> C[Flat/Toothed Belts] B --> D[Vee Belts<br>Older design, still common] B --> E[Wedge Belts<br>Deeper profile, higher rating] B --> F[Banded Belts<br>Multiple belts joined at top] B --> G[Multi-Pull Belts<br>Similar to banded, different profile] B --> H[Link Belts<br>Urethane linked sections<br>Heat/oil/chemical resistant] B --> I[CRE Belts<br>Cogged edge, smaller pulleys<br>High-speed drives] C --> J[Synchronous Belts<br>Toothed profile, no slip<br>Lower load capacity] style A fill:#4a90d9,color:#fff style B fill:#5ba8c8,color:#fff style C fill:#5ba8c8,color:#fff ``` --- ### Key Terms Glossary - **Journal** — the portion of a shaft that rotates within a bearing; often the same diameter as the shaft itself - **Bush** — another name for a journal (plain) bearing, typically a cylindrical sleeve pressed into a housing - **Bearing Modulus (M)** — ratio of (lubricant viscosity × surface velocity) to bearing pressure; used to predict lubrication regime - **Boundary Lubrication** — a condition where the lubricant film is too thin to prevent metal-to-metal contact between the journal and the bearing - **Thick-Film Lubrication** — a condition where the lubricant film is thick enough to fully separate the journal from the bearing, eliminating wear - **Projected Area** — the product of the journal diameter and bearing length (d × L); used to calculate bearing pressure - **p·v Factor** — the product of bearing pressure and surface velocity; if it exceeds a threshold value (typically 0.53 for porous bronze bearings), auxiliary lubrication is needed - **Embeddability** — the ability of a soft bearing material to absorb foreign particles without damaging the journal surface - **Powder Metallurgy** — a manufacturing process where metal powders are compacted and sintered to form solid components (used for porous bronze bearings) - **Porous Bronze** — a self-lubricating bearing material made from sintered copper and tin powders, pre-impregnated with oil - **Dynamic Viscosity (μ)** — a measure of a fluid's resistance to flow; measured in centipoise (cp) where 1 cp = 0.001 Pa·s - **Service Factor** — a multiplier applied to normal running power to account for the severity of operating conditions in belt drive design - **Speed Ratio** — the ratio of the faster shaft speed to the slower shaft speed in a belt drive - **Pitch Diameter (PCD)** — the effective diameter of a pulley at which the belt runs; determines the actual speed ratio - **Design Power** — the product of normal running power and the service factor; the effective power used for belt selection - **Combined Correction Factor** — a factor applied to the basic power rating per belt to account for the arc of contact and belt length - **Arc of Contact** — the angle of wrap of the belt around the smaller pulley; smaller arcs reduce the effective power transmission - **Taper Lock** — a type of bush used to mount pulleys onto shafts; enables easy installation and removal without keyway damage - **Centre Distance** — the distance between the centres of the driver and driven pulleys - **Fatigue Load Limit (Pᵤ)** — the load below which rolling element bearing fatigue life is theoretically infinite - **Basic Dynamic Load Rating (C)** — the constant radial load that a rolling element bearing can theoretically endure for 1 million revolutions - **Basic Static Load Rating (C₀)** — the maximum radial load a non-rotating rolling element bearing can sustain without permanent deformation --- ### Quick Revision - **Journal bearings** are low-cost, quiet, high-speed capable, but limited in radial load capacity and require careful attention to shaft finish, material hardness, and lubrication - **Three lubrication regimes** exist: boundary (high wear), thin-film/transition (moderate wear), and thick-film (no wear) — the design goal is to achieve thick-film lubrication - **Bearing modulus M = μv/p** — if M > 75, thick-film lubrication is likely; if M < 75, redesign or increase viscosity - **p·v factor threshold = 0.53** — if exceeded, auxiliary lubrication is mandatory for porous bronze bearings - **L/d ratio** for journal bearings should be in the range **0.5 to 1.5** - **Running clearance rule-of-thumb:** 1/1000 of journal diameter - **Wedge belt design** starts with the service factor, then progresses through design power → belt section → speed ratio → pulley selection → belt length → correction factor → number of belts - **Belt speed must not exceed 40 m/s** - **Maximum speed ratio** with a single set of pulleys is approximately **6:1** - **Centre distance rule-of-thumb:** C ≈ D + d (sum of pulley pitch diameters) - When two belt sections are suitable, **choose the larger section** for fewer belts - When choosing a standard belt length, **prefer the next larger** rather than smaller size - **Rolling element bearings** are characterised by dynamic and static load ratings, speed ratings, and fatigue load limits — selection depends on bore size, load, speed, and required life - **Spherical roller bearings** include additional calculation factors (e, Y₁, Y₂, Y₀) for combined radial and axial loading --- --- # PART V — JOINTS, SPRINGS & MACHINE ELEMENTS --- ## Chapter 11: Springs, Bolted Joints, Welded Joints, Power Screws & Machine Elements --- ### Overview - **Scope:** Comprehensive reference covering rolled steel sections, helical springs, bolted joints, welded joints, power screws, and machine element design - **Purpose:** Provides standard design data, formulas, worked examples, and selection procedures for common mechanical components - **Application:** Useful for mechanical design, machine element selection, stress analysis, and joint design in engineering practice --- ### Key Concepts #### Rolled Steel Sections - Standardised structural steel profiles (parallel flange channels, equal angles, unequal angles) with tabulated dimensional and mechanical properties - Properties include cross-sectional area, second moment of area, section modulus, radius of gyration, and torsion constant - Used for structural and machine frame design where bending, shear, and buckling resistance are required #### Helical Springs - Elastic elements that store and release energy, classified by load type (tension, compression, torsion, bending) - Governed by the relationship between force and deflection (spring constant *k*) - Design involves selecting wire diameter, mean coil diameter, number of coils, free length, and verifying stress against allowable limits #### Bolted Joints - Mechanical fastening method using threaded fasteners loaded in tension, shear, or combined loading - Design requires consideration of preload, safety factors, bolt material strength, and joint type (friction vs. bearing) - Tightening torque and bolt selection are critical for joint integrity #### Welded Joints - Permanent joints formed by fusing materials together, analysed using butt weld and fillet weld methods - Weld stress is calculated as force per unit length of weld (line method) or as conventional stress on the weld throat area - Bending and torsion in welds require section property calculations of the weld group #### Power Screws - Threaded devices that convert rotary motion to linear motion (or vice versa) - Key parameters include pitch, lead, thread form, friction angle, and helix angle - Efficiency depends on friction coefficient, helix angle, and thread geometry #### Machine Element Design - Encompasses the design of knuckle joints, levers, couplings, and similar connections - Requires stress analysis (tensile, shear, bending, bearing) and appropriate selection of proportions based on strength of materials --- ### Detailed Notes #### Rolled Steel Sections ##### Parallel Flange Channels (PFC) - **Designation format:** depth (mm) followed by "PFC" (e.g., 380 PFC, 300 PFC) - **Key properties tabulated:** - Mass per metre (kg/m) - Depth of section, flange width, flange thickness, web thickness - Root radius, depth between flanges - Gross cross-sectional area - Second moment of area (*Ix*, *Iy*) about both axes - Section modulus (*Sx*, *Sy*) — elastic - Radius of gyration (*rx*, *ry*) - Torsion constant (*J*) and warping constant - **Section capacity tables** provide form factors, yield stress values, and load capacities about both axes for various steel grades ##### Equal Angles (EA) - **Designation format:** leg size × leg size × thickness (e.g., 200 × 200 × 26 EA) - **Properties include:** - Mass per metre, actual thickness - Gross area of cross-section - Coordinate of centroid (*pn*, *pp*) - Second moment of area about x-axis, y-axis, and principal axes - Section modulus, radius of gyration - Torsion constant (*J*) - **Note:** The principal axes (n-n and p-p) are rotated at 45° relative to the geometric axes for equal angles ##### Unequal Angles (UA) - **Designation format:** long leg × short leg × thickness (e.g., 150 × 100 × 12 UA) - **Additional properties** compared to equal angles: - Centroid coordinates differ for each axis direction - Principal axis orientation angle (*α*) must be considered - Properties tabulated about both geometric and principal axes --- #### Helical Springs ##### Classification by Load Type | **Load Type** | **Spring Forms** | |---|---| | Tension | Helical cylindrical; flexible rod or bar | | Compression | Helical cylindrical; helical spiral; multi-disc; flexible block | | Torsion | Helical (cylindrical or spiral); flexible bar, rod or block; flat spiral | | Bending | Bar; flat leaf (single or multiple) | ##### Common Spring Materials - Plain high carbon spring steel - Alloy steel (including stainless steel) - Spring brass, bronze, or monel metal - Non-metal solids such as neoprene rubber - Gases such as air or nitrogen (gas springs) ##### Spring Constant *k* $k = \frac{F}{x}$ - **F** = total force (N) and **x** = total deflection (mm), OR - **F** = change in force (N) and **x** = change in deflection (mm) - Units: **N/mm** - The force-deflection diagram is a straight line passing through the origin (zero load = zero deflection) ##### Pre-load - Most springs are **pre-loaded** — they carry a certain load (or exert a force) when working deflection is zero - **x₁** = pre-load deflection - **x₂** = total (maximum) deflection - **x** = working deflection (change in deflection) = x₂ − x₁ - **F₁** = pre-load force - **F₂** = maximum force - **F** = change in force = F₂ − F₁ ##### Pre-load Worked Example - **Given:** A valve spring exerts 200 N closed and 250 N open; working deflection = 8 mm - **Solution:** - Change in force: F = 250 − 200 = 50 N - Spring constant: k = 50 / 8 = **6.25 N/mm** - Pre-load deflection: x₁ = 200 / 6.25 = **32 mm** - Total deflection: x₂ = 32 + 8 = **40 mm** ##### Stock Spring Selection Procedure 1. Calculate the spring constant k = F / x 2. Determine the maximum force 3. Look up a catalogue for a spring matching k and maximum force requirements 4. Record outside diameter, wire diameter, free length, spring rate, and maximum deflection ##### Spring Design (Custom Springs) ###### Spring Index *C* $C = \frac{D}{d}$ - **D** = mean diameter of spring (mm) - **d** = wire diameter (mm) | **Spring Size** | **D (mm)** | **d (mm)** | **C** | |---|---|---|---| | Small | < 8 | < 1 | 4–8 | | Medium | 8–24 | 1–4 | 8–12 | | Large | > 24 | > 4 | 12–15 | ###### Allowable Stress *f_all* - Depends on **wire material properties**, **wire diameter** (smaller wire → higher allowable stress), and **service conditions** | **Duty** | **Number of Cycles** | **Type of Load** | |---|---|---| | Light | < 10⁴ | Static or gradually applied | | Average (medium) | 10⁴ – 10⁶ | Gradually applied – light shock | | Heavy | > 10⁶ | Light–heavy shock | - For a safety factor: maximum calculated stress should not exceed **85%** of the value read from allowable stress curves ###### Calculated Stress *f* - Helical springs are stressed in **torsional shear + bending** - Torsion shear stress formula: $f = \frac{16T}{\pi d^3}$ - Since torque T = F × D/2: $f = \frac{8FD}{\pi d^3}$ - Including the **Wahl factor K** (accounts for combined torsional shear and bending): $f = \frac{8KFD}{\pi d^3} \quad \text{(Formula 3)}$ - Or in terms of spring index C: $f = \frac{8KFC}{\pi d^2} \quad \text{(Formula 4)}$ - **Wahl Factor:** $K = \frac{4C - 1}{4C - 4} + \frac{0.615}{C} \quad \text{(Formula 5)}$ - **Key notes:** - Stress *f* is caused by load **F** (not change in load) - Spring stress is **independent of the number of coils** - Do not confuse K (Wahl factor) with k (spring constant) ###### Number of Coils $n = \frac{Gd}{8C^3 k} \quad \text{(Formula 6)}$ - **G** = modulus of rigidity of the spring wire (typically 78.6 GPa for spring steel) - The smaller the spring constant, the greater the number of coils needed - A large deflection also means a small spring constant → more coils - Stress is **independent** of the number of coils (same wire diameter, mean diameter → same stress regardless of coil count) ###### Initial Length (Free Length) of a Spring $L = Nd + x_2 \quad \text{(Formula 7)}$ - Where **N** = total number of coils, **d** = wire diameter, **x₂** = total deflection - The loop/end lengths depend on the form of attachment provided for each end of the spring ###### Free Length for Compression Springs $L = Nd + x_2 (1 + C_a) \quad \text{(Formula 8)}$ - **C_a** = clash allowance — the amount by which the design deflection is increased to eliminate the possibility of coil clash under load - Typical clash allowance: **20%** (0.2) - However, a check of catalogue springs usually reveals that they have a clash allowance between **30% and 40%** ###### Buckling of Compression Springs - As free length increases in proportion to diameter, the spring becomes more slender and may buckle under load - If **L/D > 10**, the spring will most likely buckle under any load or deflection - If **L/D < 10**, the spring will most likely buckle under any load (deflection dependent — check using buckling ratio graph) - Use the **x₂/L ratio** (maximum deflection to free length ratio) to determine if buckling is likely by reference to the buckling graph ##### Design Procedure Summary 1. Assume a spring index C using typical values table and obtain a trial value for the mean diameter D and wire diameter d 2. Determine the maximum allowable stress (if not given) using service condition tables and the allowable stress graph 3. Calculate the Wahl factor K 4. Calculate the stress in the spring using Formula 3 or Formula 4 5. Compare the calculated stress to the maximum allowable stress — if too high, trial a larger wire diameter and repeat; if too small, trial a smaller diameter 6. Determine the spring constant (spring rate) k 7. Determine the total number of coils *n* and hence the number of active coils *N* 8. Calculate the free length of the spring (compression: Formula 8; extension: Formula 7) 9. If buckling is likely, check whether some guidance or support is needed 10. Summarise the design preferably with a sketch showing all relevant data ##### Compression vs Extension Springs — Stock Catalogues - **Compression springs:** Catalogue includes outside diameter, wire diameter, free length, spring rate (R in N/mm), solid height, and approximate number of coils - **Extension springs:** Catalogue includes outside diameter, wire diameter, free length, initial tension (T₁), spring rate, and approximate extended length - **Catalogue numbering** is based on imperial (inch) sizes (e.g., C0360-025-2000 = compression spring, 0.360 in OD, 0.025 in wire dia, 2.000 in free length) --- #### Bolted Joints ##### Types of Bolted Joints | **Joint Type** | **Load Transfer Mechanism** | **Key Characteristic** | |---|---|---| | Friction type | Load transferred by friction between clamped members | Bolt in tension only; no bearing on bolt shank | | Bearing type | Load transferred by bolt shank bearing against hole wall | Bolt in shear; bearing stress on shank | ##### Types of Fasteners - **Set screws** — held in location by a thrust collar or bearing - **Cap screws** — head bears directly on the member - **Head bolts and nuts** — many types including hexagon head, cup oval, square neck, hexagon socket head cap screws - **Studs** — threaded at both ends ##### Bolt Material and Grade - Standard metric bolt grades include property classes 4.6, 4.8, 5.8, 8.8, 10.9, and 12.9 - **Reading the grade:** First number × 100 = ultimate tensile strength (MPa); first × second × 10 = yield stress (MPa) - Example: Grade 8.8 → UTS = 800 MPa, Yield = 640 MPa - Standard bolts are available in both imperial (inch) and metric sizes - Thread forms: ISO metric (coarse pitch) with fine pitch available in both systems ##### Bolt Dimensions - **Nominal diameter D** = outside diameter of the thread (equals the pitch diameter of a hypothetical zero-thread-depth bolt) - **Pitch diameter** = diameter of the thread at the point where tooth and space widths are equal - **Root diameter d₁** = inside diameter of the thread (also known as minor diameter) - **Pitch p** = axial distance between successive threads - **Lead L** = distance advanced by nut (or screw) for 1 rotation (for single-start thread, L = p) ##### Stress Area - The **stress area** (also known as the tensile area, **A_t**) is used for bolt strength calculations - It is based on the mean of the root diameter and pitch diameter - **A_t** = (π/4) × d₁² where d₁ is approximately equal to the mean of root and pitch diameters ##### Bolt Loading — Tension ###### Design Procedure for Direct Tensile Load 1. Determine the total required preload: **F = S × L** (Safety Factor × Applied Load) 2. Select bolt size and material from tables to find a bolt with tensile area giving preload stress within the yield stress 3. Select appropriate number of bolts: **N = F / (Y × A_s)** where Y = yield stress, A_s = stress area 4. Specify tightening torque from recommended assembly torque tables 5. Position bolts as near as possible to the line of direct tensile loading ###### Safety Factors for Bolted Joints | **Nature of Loading** | **Safety Factor** | |---|---| | Steady stress | 1.5 – 2 | | Repeated stress, gradually applied | 2 – 3.5 | | Repeated stress with shock | 4.5 – 6 | ##### Bolt Loading — Shear - Shear load is taken on the **shank** of the bolt (not the thread) - Shear stress: **f_s = F / A_s** where A_s = shear area = (π/4) × d² (shank diameter) - Maximum permissible shear stress (from Table 13) is typically **200 MPa** for standard bolt grades assuming bolt is less than 16 mm diameter - For precision high-tensile grade (class 8.8), shear capacity is significantly higher ##### Bolt Loading — Combined Tension and Shear - When a bolt carries **both** tensile and shear loads, stresses must be combined - Combined stress formula: $f_{max} = \sqrt{(f/2)^2 + f_s^2} + f/2$ - Where **f** = direct tensile stress, **f_s** = shear stress - The bolt must be satisfactory in **both** tension and shear separately as well as combined ##### Bolted Bracket in Bending - Direct shear load per bolt: **F₁** = F / (number of bolts) - Bending moment about the bolt group centroid: **M = F × y** - Force on each bolt due to bending: **F₁ = M / (Σy²)** where y = distance from centroid to each bolt centreline - The most highly stressed bolts are those furthest from the pivot point (centroid) - Resolve forces into vertical and horizontal components, then combine vectorially ##### Bolted Bracket in Torsion - Direct shear load per bolt: **F₁** = F / N - Torsional moment about the centroid: **T = F × e** (e = eccentricity) - Force on each bolt due to torsion: perpendicular to the radius from centroid to bolt - The most highly stressed bolt is the one at the greatest radial distance from the centroid - Combine direct and torsional forces vectorially ##### Flexible Gasket Joints - For joints with gaskets (sealing liquids or gases under pressure): - Design pressure load on bolts: **Q = A × P** (area × pressure) - Total preload required: **W = Q + F** where F = preload to seat the gasket - Typically, **W = Q × 1.1** (add 10% for gasket seating) - Select bolt type with proof load stress appropriate to the application ##### Friction Type Joints - Bolts fitted in **clearance holes** — load transferred by friction between clamped surfaces - Higher bolt tension → higher clamping force → higher friction resistance - Bolt preload should be **reduced** by a factor of 0.806 when using flexible gasket joints ##### Tightening Methods | **Method** | **Accuracy** | **Relative Cost** | |---|---|---| | Feel (operator judgement) | ±35% | 1 | | Torque wrench | ±25% | 1.5 | | Turn-of-the-nut | ±15% | 3 | | Pre-load indicating washers | ±10% | 3.5 | | Load indicating | ±3 – 5% | 15 | | Strain gauges | ±1% | 20 | ##### How a Bolted Joint Carries Load - **Tension:** External load resisted by bolt pre-tension; the joined members are stiffer than the bolt so they compress much less than the bolt extends — pre-load force maintains clamping; external load adds only a small increment to bolt tension - **Shear:** In friction joints, load is carried entirely by friction between clamped members; in bearing joints, the bolt shank bears against the hole wall - External load should **not exceed the preload** — if it does, the joint separates and the bolt carries the full external load (dangerous for fatigue) ##### General Rules to Reduce Fatigue Failure 1. Tighten bolt effectively to ensure an induced tension or preload in excess of the maximum external load 2. Observe general rules should be followed to minimise possibility of fatigue failure of bolts under high alternating or fluctuating stresses --- #### Welded Joints ##### Types of Welds - **Butt welds:** Full penetration weld joining two plates edge-to-edge - **Fillet welds:** Triangular cross-section weld joining two surfaces at approximately right angles ##### Butt Weld Assumptions - Welding has been carried out by a competent trade welder in accordance with correct welding procedures for the material being welded - A welding rod has been used that has a strength at least equal to the un-welded plate - Weld runs for the full width of the plate and if long welds are to be made, it is preferable that they be intermittent rather than continuous ##### Weld as a Line Method - The weld is designed as a **separate component** with stress area A = t × L - Where **L** = length of weld, **t** = throat thickness - Line stress **f** is defined as: $f = \frac{F}{L} \quad \text{(units: N/mm)}$ - For an applied load F (any direction), the stress in the weld is: $f^s = \frac{f}{t} = \frac{F}{t \times L} \quad \text{(units: MPa)}$ ##### Conventional Design Method - The weld is designed as a separate component with stress area A = t × L - Where **t** = throat thickness of the weld - Two methods may be used for design of fillet welds: 1. **Weld as a line** — treats the weld as having no thickness; section modulus Z has units of mm² 2. **Conventional method** — treats the weld as an area; section modulus Z has units of mm³ ##### Fillet Weld Throat Thickness - For a standard fillet weld, the angle of the weld is 45° - **Leg length s** = size of fillet weld specified by the leg length - **Throat thickness t** = s × 0.707 (= s × sin 45°) - Preferred weld sizes (in mm): 2, 3, 4, 5, 6, 8, 10, 12, 16 ##### Design of Fillet Welds - Fillet weld should be on **both sides** wherever possible to minimise distortion and stress - For greater strength: plates should use an E48xx rod (UTS of 410 MPa) - For low carbon and mild steel plates: a commonly used electrode welding rod is the E41xx × UTS 410 or E3 × 410 MPa - Under conditions of **steady or static** load, the allowable weld stress is often taken as 0.3 × UTS - For **dynamic or cyclic** loads: an appropriate design (safety) factor should be applied ##### Allowable Weld Stress - If the shear stress of the welding rod is not known, a rule-of-thumb is to use **75%** of the tensile strength - For static or gradually applied loads: allowable weld stress would be 0.3 × 410 = **123 MPa** (for E41xx rod) - For dynamic/cyclic loads: apply an appropriate safety factor ##### Bending Loads in Fillet Welds - Direct loads only: the **line method** has no advantage - However, when there are bending or torsion loads: the **line method** is very useful - The weld as a line method is illustrated in worked examples ###### Bending Stress Formula (Weld as Line) $f = \frac{Z}{M} = \frac{I}{y \cdot W} \quad \text{where } Z \text{ is the section modulus with units mm²}$ - If the weld is not treated as a line, the section modulus of area I or Z would vary with each different weld size — using the weld as a line avoids this ###### Torsion Loads in Fillet Welds $f = \frac{T}{J} \times r$ - Where: **r** = radius (distance from centroid to outer fibre), **f** = polar second moment of area of the section with units mm³, **T** = torque (Nmm) ##### Locating the Centroid of a Weld Group - Break the weld into component lengths - Calculate the centroidal distance using the first moment of area approach: $y_c = \frac{A_1 y_1 + A_2 y_2 + \ldots}{A_1 + A_2 + \ldots}$ - Where y is the vertical centroidal distance and A = weld length × 1 (for line method) ##### Section Modulus Formulas for Common Weld Configurations - A comprehensive table of formulas exists for 12 standard weld configurations including: - Single line along one edge - Two parallel lines (top and bottom) - C-shapes, L-shapes, rectangular, and circular weld groups - Each providing formulas for **Z** (bending about x-axis) and **J** (polar moment for torsion) --- #### Power Screws ##### Purpose - Convert **rotary motion to linear motion** (or vice versa) - Used in vices, clamps, jacks, presses, machine tool lead screws, and similar mechanisms ##### Terminology - **Pitch p** = axial distance between successive threads - **Lead L** = distance advanced by the screw (or nut) for 1 rotation; for single-start thread: **L = p**; for multi-start: **L = n × p** where n = number of starts - **Pitch diameter d** = diameter of a theoretical thread with zero thread depth but has the same lead as the actual screw - **Root diameter d₁** = inside diameter of the thread (also known as minor diameter) - **Nominal diameter D** = outside diameter of the thread - **Friction angle φ** = angle whose tangent equals the coefficient of friction: **tan φ = μ** - **Helix angle θ** = angle of the thread helix: **tan θ = nπ / (π × d)** = L / (π × d) ##### Thread Forms and Dimensions | **p (mm)** | **D (mm)** | |---|---| | 3 | 10.25 | | 4 | 15 | | 5 | 20 | | 6 | 25 | | 8 | 30.35 | | 10 | 40.45 | | 12 | 50.55 | | 14 | 70.75 | | 15 | 80.85 | | 16 | 90.95 | | 17 | 100 | - Several thread form variations exist: **square**, **modified square**, **trapezoidal metric** (ACME equivalent), and **buttress** - Square thread has highest efficiency but is difficult to manufacture - Trapezoidal metric thread (face angle of 15°, included angle of 30°) is the most commonly used - Buttress thread: designed for heavy loads in one direction only ##### Thread Depth and Relationships - For the trapezoidal thread: **thread depth t = 0.5 p**, pitch diameter **d = D − 0.5p**, minor diameter **d₁ = D − 1.5 × D** (approximately) - For the buttress thread: similar relationships with a face angle of 5° and included angle of 30° ##### Screw Torque and Thrust ###### For a Square Thread (Downward Thrust) - **Raising load** (Formula 4): $T = F \times \frac{d}{2} \times \tan(\theta + \phi')$ - **Lowering load** (Formula 5): $T = F \times \frac{d}{2} \times \tan(\phi' - \theta)$ - Where **φ'** = effective friction angle, **θ** = helix angle ###### For Non-Square Face Angle - If the thread face is inclined at angle **α** (in place of φ), use **φ'** in these formulas where: $\tan \phi' = \frac{\cos \alpha}{\mu}$ - The friction angle φ is given by: **tan φ = μ** ##### Coefficient of Friction - Depends primarily on: **surface finish quality**, **type and frequency of lubrication**, and **number of revolutions or cycles** - Lowest coefficient: accurately machined threads with good surface finish and operating for some period with good lubrication (oil of suitable viscosity) — can be as low as **0.1** - Average value (mean of two extremes): **μ = 0.125** - Start-up or initial friction is higher; for start-up conditions, values should be increased by one-third (multiply by 4/3) ##### Thread-Pitch Diameter Relationship - Unlike fastening screws, power screws do **not** have standardised metric pitch/diameter sizes - A useful guide table relates pitch *p* to approximate nominal diameters ##### Efficiency of a Screw Thread $\eta = \frac{W}{W_0} = \frac{2\pi \times T}{F \times L}$ - Where **W** = work input (rotational), **W₀** = work output (linear), **F** = thrust load, **T** = applied torque, **L** = lead - For 1 revolution of the thread: output = F × L; input = T × 2π ##### Self-Locking - A screw is **self-locking** when the helix angle θ equals or is less than the friction angle φ: **θ ≤ φ** - Overhauling occurs when **θ > φ** (the load would lower the screw without applied torque) - Multi-start threads will **not** self-lock (because the helix angle is too large) — a two-start thread would have θ = 11.1° which is not self-locking at typical μ values - Self-locking is an important safety feature in many applications such as lifting devices ##### Collar Friction - Each of the three methods used for converting rotary motion to linear motion (collar, thrust bearing, or ball screw) has different friction characteristics - If bedding is used: **T = μ × F × r_m** where r_m = mean radius of the thrust face - For collar friction: Formula 8 applies: **T = μ × F × r_m** - Where r_m = mean radius = (D₁ + D₂)/4 for a flat bearing surface ##### Stress Analysis of Power Screws - **Axial stress in the root:** f = F / A₁ where A₁ = (π/4) × d₁² (tensile area based on root diameter) - **Shear stress in the thread:** f_s = bh / (F × 1.5) where b = thread length in nut, h = thread height - **Bending stress in the thread:** f_b = (I × b × h) / (F × 3) — the thread is treated as a short cantilever - **Bearing pressure in the thread:** p_b = F / (I × b) where I = thread depth, b = thread engaged length - **Number of threads in nut:** n = d/p (Formula 9) - **Thread length in nut:** b = n × p (Formula 10) - **Bearing pressure:** p_b = (I × b) / F (Formula 11) - Maximum allowable bearing pressure depends on speed and lubrication | **Rubbing Speed (m/s)** | **Max Pressure (MPa)** | |---|---| | < 0.05 | 20 | | 0.05 – 0.1 | 10 | | 0.1 – 0.2 | 5 | | > 0.2 | 2.5 | ##### Buckling of Power Screws - The effective length and radius of gyration must be used to check if the screw column will buckle - **k = a / d₁** (radius of gyration / stress diameter ratio) - Relationship between effective length and k depends on the degree of end restraint: - Both ends rigidly held: L_e = 0.7 L - Both ends pin-jointed (equivalent to cantilever): L_e = 2 L - One end rigid, other free: L_e = 0.85 L - Flexible end supports (pin-joint equivalent): L_e = L - Check for buckling using Johnson's formula (for short/intermediate columns) or Euler's formula (for long columns) ##### Johnson's Column Formula $F_{cr} = f_y \times A_1 \left[ 1 - \frac{4\pi^2 E}{(k/L_e)^2 \times f_y} \right]$ - This formula applies for the critical buckling force; a safety factor should be applied (typically 5) - For a maximum slenderness ratio of 100, the maximum length (or travel) is approximately 600 mm --- #### Machine Elements — Knuckle Joints ##### Description - A **knuckle joint** connects two rods that are in the same line of action - Consists of an **eye** (fork end), a **fork** (clevis), and a **pin** - Loads are typically tensile or compressive along the rod axis ##### Good Proportions (Based on Rod Diameter *d*) | **Parameter** | **Dimension** | |---|---| | Pin diameter | d | | Eye outer diameter | 2d | | Fork outer diameter | 2d | | Eye width (boss width) | 1.34d | | Fork width (each prong) | 0.75d | | Pin head diameter | 1.5d + 3 | | Internal width = nut thickness | 3 + eye width | | Radial thickness (initial) | 5–10 mm | ##### Stress Analysis of a Knuckle Joint ###### Pin - **Bending stress:** $f_{bending} = \frac{2 \times p \times a}{F}$ - Where **a** = distance between supports (related to fork and eye widths), **F** = applied force - **Shear stress:** $f_{shear} = \frac{a \times e}{F}$ - The pin is in **double shear** (two shear planes) ###### Eye - **Bending stress = 2pa / F** - **Shear stress = ae / F** - **Fork tensile stress = 2(d − D) × a / F** ###### Fork - **Bending stress = bq / F** - **Shear stress = 2be / F** - **Fork tensile stress = (d − D) × b / F** ##### Notes on Knuckle Joint Design - Joint proportions may be **cast** or **fabricated** — they may also be relatively small - Joints may be case or fabricated; if they are relatively small, they may be cast - If the knuckle joint is of standard proportions with the same strength material, the rods are integral with the eye and fork - In the knuckle joint illustrated, there is no separate bearing and rotational or oscillating motion occurs between the pin and eye or pin and fork - For practice, you may be asked to calculate stresses in the eye, fork, and pin — with all stresses compared to allowable --- #### Machine Elements — Levers ##### Design Principles - A lever transmits force using a **fulcrum** (pivot point) - The level of mechanical advantage depends on the relative distances of force application points from the fulcrum - Critical design factor is usually the **bending stress** at the fulcrum (maximum bending moment location) - A U-beam (I-beam section) may be used; bending stress is usually the most critical stress - Fulcrum, roller arms (rocker arms) may also be forged - The design of a lever follows standard design procedures and is best illustrated by example ##### Lever Cross-Sections - Typical cross-sections: **rectangular**, **circular**, **I-section**, **T-section** - The lever can be cast or fabricated - If the lever has an integral boss, bending stress may be a maximum just outside the boss ##### Design Considerations - Often the lever transmits forces using knuckle joints or similar connections - If the boss is designed with grease nipples or oil holes, the lever can be designed without a separate bearing - A critical design factor is the **bearing pressure** at the fulcrum — particularly if the lever is required to perform a large number of operating cycles - In some cases, rolling element bearings are used; in other cases, plain journal bearings are used, with the design practice to fit the boss with grease nipples so lubrication can be applied --- ### Comparison Tables #### Joint Types Comparison | **Feature** | **Bolted Joint** | **Welded Joint** | **Knuckle Joint** | |---|---|---|---| | **Type** | Removable (non-permanent) | Permanent | Semi-permanent (pin removable) | | **Load Types** | Tension, shear, combined | Tension, shear, bending, torsion | Tension/compression (axial) | | **Stress Analysis** | Based on bolt tensile/shear area | Based on weld throat area or line method | Based on pin shear, bending; eye/fork tensile | | **Key Design Factor** | Preload and safety factor | Weld size (throat thickness) and electrode strength | Pin diameter and component proportions | | **Advantages** | Easy to assemble/disassemble; adjustable preload | High strength; sealed joint; no stress concentration from holes | Allows limited angular movement; simple to manufacture | | **Disadvantages** | Stress concentration at bolt holes; requires access from both sides | Permanent; residual stress; distortion; requires skilled welder | Limited to axial loads; pin wear over time | #### Spring Type Comparison | **Feature** | **Compression Spring** | **Extension Spring** | |---|---|---| | **Load direction** | Axial compressive | Axial tensile | | **Free state** | Extended (longest length) | Coils touching (shortest length) | | **Pre-load** | Achieved by compressing to installed length | Built-in initial tension from coil contact | | **Ends** | Ground/squared ends (closed) | Hooks or loops at both ends | | **Free length formula** | L = Nd + x₂(1 + Cₐ) | L = body length + hook allowances | | **Failure mode** | Buckling (if L/D > 10); clash | Hook failure; overstress | --- ### Mermaid Diagrams #### Helical Spring Design Process ```mermaid flowchart TD A[Start: Define Requirements] --> B[Determine F, x, and service conditions] B --> C[Assume Spring Index C from Table] C --> D[Calculate trial D and d] D --> E[Determine allowable stress f_all] E --> F[Calculate Wahl Factor K] F --> G[Calculate actual stress f] G --> H{f ≤ 0.85 × f_all?} H -->|No - too high| I[Increase wire diameter d] I --> D H -->|Yes| J[Calculate spring constant k] J --> K[Calculate number of coils n] K --> L[Calculate free length L] L --> M{Compression spring?} M -->|Yes| N{Check L/D ratio for buckling} N -->|L/D > 10| O[Add guidance/support or redesign] N -->|L/D ≤ 10| P[Check x₂/L ratio on buckling graph] M -->|No| Q[Check hook stress for extension] O --> R[Finalise Design and Summarise] P --> R Q --> R ``` #### Bolted Joint Design Process ```mermaid flowchart TD A[Start: Define Load and Joint Type] --> B{Joint Type?} B -->|Tension| C[Calculate total preload F = S × L] B -->|Shear| D[Calculate shear load per bolt] B -->|Combined| E[Calculate both tension and shear] C --> F[Select bolt material and grade] D --> F E --> F F --> G[Determine tensile/shear area from tables] G --> H[Calculate stress and compare to allowable] H --> I{Stress OK?} I -->|No| J[Select larger bolt or higher grade] J --> G I -->|Yes| K[Determine number of bolts N] K --> L[Select tightening method and torque] L --> M[Position bolts per design rules] M --> N[Check for fatigue if cyclic loading] N --> O[Finalise Design] ``` #### Power Screw Design Process ```mermaid flowchart TD A[Start: Define Load F and Travel] --> B[Select thread form] B --> C[Choose pitch p and diameter D from table] C --> D[Calculate helix angle θ] D --> E[Determine friction coefficient μ] E --> F[Calculate friction angle φ] F --> G{Self-locking required?} G -->|Yes| H{θ ≤ φ?} H -->|No| I[Reduce lead / use single start] I --> C H -->|Yes| J[Calculate raising torque] G -->|No| J J --> K[Calculate lowering torque] K --> L[Calculate efficiency η] L --> M[Check thread stresses] M --> N[Check bearing pressure] N --> O{Buckling concern?} O -->|Yes| P[Check slenderness ratio and critical load] O -->|No| Q[Finalise Design] P --> Q ``` #### Welded Joint Analysis Process ```mermaid flowchart TD A[Start: Define Load Type and Magnitude] --> B{Weld Type?} B -->|Butt Weld| C[Design as plate: f = F / A] B -->|Fillet Weld| D{Loading Type?} D -->|Direct only| E[f = F / (t × L)] D -->|Bending| F[Use line method: calculate Z] D -->|Torsion| G[Use line method: calculate J] D -->|Combined| H[Calculate direct + bending/torsion stresses] C --> I[Compare to allowable stress] E --> I F --> J[f_bending = M / Z then divide by t] G --> K[f_torsion = T × r / J then divide by t] H --> L[Combine stresses vectorially] J --> I K --> I L --> I I --> M{f ≤ f_allowable?} M -->|No| N[Increase weld size or length] N --> E M -->|Yes| O[Specify weld size, length, and electrode] ``` --- ### Key Terms Glossary | **Term** | **Definition** | |---|---| | **Spring constant (k)** | Ratio of force to deflection (N/mm); represents stiffness of a spring | | **Wahl factor (K)** | Correction factor for combined torsional shear and bending stress in helical springs | | **Spring index (C)** | Ratio of mean coil diameter to wire diameter (D/d); indicates coil tightness | | **Pre-load** | Initial force or tension applied to a spring or bolt before external working load is added | | **Clash allowance (Cₐ)** | Additional deflection allowance (typically 20%) to prevent coil-to-coil contact in compression springs | | **Proof load stress** | Maximum stress a bolt can sustain without permanent deformation (typically 85–90% of yield) | | **Stress area (Aₜ)** | Effective cross-sectional area of a bolt thread used for calculating tensile strength | | **Throat thickness (t)** | Shortest distance from root to face of a fillet weld; equals leg length × 0.707 | | **Line stress (f)** | Force per unit length of weld (N/mm) — used in the weld-as-a-line design method | | **Helix angle (θ)** | Angle of the thread helix relative to a plane perpendicular to the screw axis | | **Friction angle (φ)** | Angle whose tangent equals the coefficient of friction between mating thread surfaces | | **Self-locking** | Condition where a screw will not move under load without applied torque (θ ≤ φ) | | **Lead (L)** | Axial distance a screw advances per revolution; for single-start: L = pitch | | **Pitch (p)** | Axial distance between adjacent thread forms | | **Knuckle joint** | A pin-connected joint between two coaxial rods allowing limited angular movement | | **Section modulus (Z)** | Geometric property relating bending moment to stress; Z = I/y | | **Radius of gyration (r)** | Geometric property relating second moment of area to cross-sectional area; r = √(I/A) | | **Buckling** | Sudden lateral deflection failure of a slender member under compressive load | | **Modulus of rigidity (G)** | Shear modulus of the material (78.6 GPa for spring steel) | | **Bearing pressure** | Contact pressure between mating surfaces (e.g., thread flanks, pin and eye) | --- ### Quick Revision - **Spring constant:** k = F/x — the slope of the force-deflection line; units N/mm - **Spring stress formula:** f = 8KFD / (πd³) or f = 8KFC / (πd²) — always use the Wahl factor K - **Wahl factor:** K = (4C−1)/(4C−4) + 0.615/C — always greater than 1; accounts for curvature and direct shear - **Number of coils:** n = Gd / (8C³k) — more coils = softer spring (lower k) - **Compression spring free length:** L = Nd + x₂(1 + Cₐ) — include clash allowance (typically 20%) - **Buckling check:** If L/D > 10, the spring will likely buckle — provide guidance or redesign - **Bolt grade reading:** First digit × 100 = UTS; first × second × 10 = yield (e.g., 8.8 → 800/640 MPa) - **Bolt preload:** F = Safety Factor × Design Load; select bolt so stress < yield stress - **Bolt shear:** Use shank area (not thread area); shear stress = F/A - **Combined bolt stress:** f_max = √((f/2)² + f_s²) + f/2 - **Weld throat:** t = 0.707 × s (leg length); preferred sizes: 2, 3, 4, 5, 6, 8, 10, 12, 16 mm - **Weld line stress:** f = F/L (N/mm); convert to MPa by dividing by throat t - **Power screw torque (raising):** T = F × (d/2) × tan(θ + φ') - **Power screw torque (lowering):** T = F × (d/2) × tan(φ' − θ) - **Self-locking condition:** θ ≤ φ (helix angle ≤ friction angle) - **Power screw efficiency:** η = (F × L) / (2π × T) - **Knuckle joint proportions:** Pin diameter = rod diameter d; eye OD = 2d; fork OD = 2d - **Fillet weld in bending:** Use section modulus Z (mm² in line method) — select from table of standard configurations - **Fillet weld in torsion:** Use polar moment J (mm³ in line method) — combine direct and torsional line stresses vectorially --- ---