Shaft torque and shaft diameter
Torque from the transmitted power and speed — for a motor, pump, gearbox or coupling — and the smallest diameter of a solid shaft for an allowable torsional stress.
T = P / ω = 9549 · P / nd = ∛(16 · T / (π · [τ]))T = P / ω holds for any shaft. The starting and breakdown torques of an induction motor are 1.5–3 times the rated torque, so couplings are selected with a service factor. The torsion-based diameter is preliminary: the final shaft check covers combined bending and torsion and fatigue. Inverse: P = T · n / 9549.
Source: Shigley's Mechanical Engineering Design — torsion of shafts
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
To size a shaft or coupling, use the motor rating.
Induction motors at 50 Hz: about 2 950, 1 470, 980 and 735 rpm (2, 4, 6 and 8 poles).
For a preliminary design of steel shafts, 15–30 MPa: the low value allows for bending and the stress concentration at the keyway.
Unit converter for this formulaPower · Rotational speed · Pressure · Torque · Length
- kW1
- W1,000
- MW0.001
- PS (metric hp)1.35962
- kcal/h859.845
- hp1.34102
- BTU/h3,412.14
PS is the metric horsepower (735.5 W), hp the mechanical horsepower (745.7 W).
- d — Smallest solid shaft diameter–
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Basic rating life of a bearing in millions of revolutions and in operating hours from the dynamic load rating and the equivalent load, and the life at a higher reliability.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.