Gearboxes and Geared Motors: Selection and Integration: Mechanical Design Reference

Mechanical Design Reference

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

. Coupling Types

Four main coupling families are covered, each suited to different application requirements:

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

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

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)

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

. Taper Bushes — Range of Bores

Taper bushes are the standardised interface between shaft and coupling (or sprocket, pulley, etc.). The metric range includes:

* 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)

. 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.

. Worm Gearboxes

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)

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

General Specification

. 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.

. Load Classification and Service Factors

Load Classification by Application (Partial List)

Note: Applications marked with an asterisk (*) in original tables require specific manufacturer consultation.

Mechanical Service Factors (Table 2)

Note: Linear interpolation is acceptable for service hours between those listed.

Thermal Service Factors (Table 3)

Note: A substantial increase in thermal rating is achievable using synthetic lubricants (consult manufacturer).

. Reduction Ratios — Actual vs Nominal

Single Reduction — Nominal & Exact Ratios

Double Reduction — Nominal & Exact Ratios

. 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)

. Overhung and Thrust Load Capacities

Output Shaft Overhung Load Capacities (Newtons)

Values vary by ratio, output speed, and centre distance. Sample data at 1450 rev/min input speed:

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:

. 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.

. 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:

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

Single vs Double Reduction Gearboxes

Mermaid Diagrams

Worm Gearbox Selection Flowchart

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]