Pulley Groove Geometry — Key Dimensions
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
SHAFTS, KEYS, BEARINGS & SEALS
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
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:
| 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
- Used to find shaft diameter from torsional shear stress
- Used to find shaft diameter from bending (axial) stress
- Combines torque (T) and bending moment (M) into a single equivalent value
- Used for bending stress calculations
Design Torque and Moment (with shock/fatigue factors)
- 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
| 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:
- 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: — (Formula 5) — tight side + slack side tension
- Torque at sprocket: — (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
| 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
| 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:
- Actual force is greater because T_1 ≠ 0 → apply factor f:
- 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; — (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
- 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
- The resultant transverse force is still
Design Procedure
- Estimate all loads acting on the shaft (weight, drive forces, gear forces, etc.)
- Draw torque, shear force, and bending moment diagrams
- Shear force diagram is optional but useful to draw before the bending moment diagram
- 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)
- Determine the design torque and moment by applying shock/fatigue factors (K_T, K_M)
- Calculate equivalent torque (T_E) and equivalent moment (M_E)
- Calculate allowable stresses (with keyway reduction if applicable)
- Determine minimum shaft diameter using Formulas 1 and 2
- 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:
- 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:
| 250 |
250 |
410 |
| 300 plus |
300 |
440 |
| 350 |
350 |
480 |
Beam Selection Procedure
- Determine the maximum bending moment (M) from loading and span
- Calculate the allowable bending stress using the design factor:
- e.g., for a design factor of 2 on yield:
- Calculate the required section modulus:
- Select the smallest standard section with Z ≥ required Z from beam tables
- Check self-weight: recalculate reactions, moment, and Z including beam self-weight
- Verify the selected section is still adequate
Column Selection Procedure
- 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
- Calculate the design critical load = applied load × design factor
- Calculate the limiting slenderness ratio:
- Select a trial section from column tables; use the smaller radius of gyration (r_y) for buckling analysis
- Calculate actual and compare with limiting value
- If > limiting value → slender column → use Euler formula:
- Check that ≥ design critical load; iterate if necessary
Shaft Design Approaches Compared
| 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
| 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
| (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
| 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 |
Shaft Design Process
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
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
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
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
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
| 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) |
- Combined shear stress:
- Combined bending stress:
- Equivalent torque:
- Equivalent moment:
- Design torque:
- Design moment:
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
- 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:
- Euler critical load:
- Use the smaller radius of gyration for buckling checks
- If > 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
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
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
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