1. Define design torque
Rated torque is not always maximum torque. Starts, jams, shocks and process variations can impose a higher value.
Practical tip: clearly document whether the entered torque is rated, maximum or already factored.
2. Select a coherent allowable stress
Allowable stress should not be an arbitrary fraction without considering material, treatment, temperature and loading type.
For a cyclic shaft, a fatigue approach is often more restrictive than a static check.
3. Understand the diameter effect
τmax = 16T/(πD³)For a solid shaft, stress varies as 1/D³. Increasing D by 10% therefore reduces stress by roughly 25%, all else equal.
This is powerful, but it increases mass, inertia and package size.
4. Solid or hollow?
A hollow shaft can offer a good mass-to-stiffness compromise because material near the axis contributes little to polar moment.
However, d/D or wall thickness must be prescribed. Then check manufacturing, assembly, possible welds and local buckling.
5. Checklist before approval
The theoretical diameter is only the beginning.
- Select an actually available size and recalculate.
- Check twist angle and stiffness.
- Include stress concentrations from shoulders and grooves.
- Check bending plus torsion with Von Mises at the same point.
- Perform fatigue analysis if torque or bending varies.
- Check critical speed, bearings, keyways and joints.
Numerical application
Example: hollow shaft under 2 kN·m
Use τallow = 80 MPa and d/D = 0.6.
- Apply D = ∛[16T/(πτallow(1−k⁴))].
- Obtain Dmin = 52.690 mm.
- Provisionally round to 53 mm.
- Recalculate d = 31.8 mm and τ = 78.61 MPa.
Result: 53 mm satisfies the simplified static check, but it must still be compared with available sizes, fatigue and geometric details.
Method linked to MIT notes on torsion and examples. Open exact source ↗
For checking and further study
Direct references
Each link points to the exact course, standard or publication page used, rather than a generic homepage.