Mechanical Design Data and Machine-Element Reference: Comparison Tables

Comparison Tables

Spur Gears vs Helical Gears

Gear Train Types

Drive Application Factors for Overhung Load

Gear Pair Terminology and Relationships

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

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

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 in the supplied reference]

Electric Motor Selection Process

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

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

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

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

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

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

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

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)

• 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

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)

• 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

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)

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)

• 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

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 ✓