KEVOS® MAKEOS · Strength
Shaft Design: Strength, Twist and Critical Speed
What shaft diameter satisfies strength, torsional stiffness and critical speed together for this drive?
Shaft sizing that checks three criteria at once: diameter for combined bending and torsion with shock factors (maximum-shear theory, with the handbook’s 75% working stress allowance for a keyway), diameter for a twist limit per metre, and diameter that keeps the first critical speed of the shaft with a central mass a margin above running speed — reporting which governs.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | ||
| Power | kW | Power transmitted. |
| Speed | rpm | Shaft speed. |
| Maximum bending moment | N·m | Largest bending moment on the shaft from belt pull, gear forces and weights. |
| Shock factor, bending | Combined shock and fatigue factor for bending (1.5 for gradually applied, rotating loads). | |
| Shock factor, torsion | Combined shock and fatigue factor for torsion. | |
| Material and limits | ||
| Allowable shear stress | MPa | Allowable shear stress for the shaft material. |
| Keyway at the critical section | choice | Whether the critical section has a standard keyway. |
| Twist limit | °/m | Allowable angle of twist per metre of length. |
| Shear modulus | GPa | Shear modulus. |
| Elastic modulus | GPa | Elastic modulus. |
| Density | kg/m³ | Density of the shaft material. |
| Critical speed | ||
| Bearing span | mm | Distance between bearings. |
| Central mass (pulley, rotor) | kg | Mass carried at mid-span. |
| Required critical ÷ running speed | How far above running speed the first critical speed must be. | |
Method and formulas
- Torque T = P ÷ ω; strength: d = [16 ÷ (π τ) √((K_m M)² + (K_t T)²)]^(1/3), with τ × 0.75 for a keyway.
- Twist: J ≥ T ÷ (G θ), d = (32 J ÷ π)^(1/4).
- Critical speed ≈ 946 ÷ √δ rpm (δ in mm), with δ the static deflection of the simply supported shaft under the central mass plus its own weight; solved for d.
- Example: 15 kW at 1450 rpm with 150 N·m of bending needs a 41.295 mm shaft; twist governs.
Limitations
- Simply supported span with one central mass; overhung loads and several masses need a fuller analysis.
- Stress concentrations other than a standard keyway need their own factors.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a drive shaft for a motor, pulley or fan
- Check whether stiffness or whirling governs rather than strength
- Decide a shaft size before detailed design
Who it is for
- Design engineers
- Mechanical engineers
- Engineering managers
What you get
- Diameter for strength
- Diameter for twist
- Diameter for critical speed and the governing size
Interpreting the result
- When twist governs, a slightly larger diameter is often cheaper than a stronger material.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303. Topic reference; no source tables or recommended settings are reproduced.
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