KEVOS® MAKEOS · Power Transmission
Overhung Gear Shaft Sizing (Gear Forces, Bending, Shaft Diameter, Stress)
For a spur or helical gear overhung on a shaft, what forces does the gear put on the shaft, what diameter does the shaft need, and is my chosen diameter within stress?
Sizing of a shaft carrying an overhung spur or helical gear: tangential, radial and axial gear forces from the power, speed and pitch diameter (as the gear forces tool), the resultant bending moment at the bearing from the overhang and the axial-force couple, the diameter needed by the ASME-style shock-factor method with a keyway allowance (as the shaft diameter tool), and the combined axial, bending and torsional stress and safety factor of the chosen diameter (as the combined shaft stress tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power transmitted | kW | Power through the gear. |
| Shaft speed | rpm | Speed of the shaft. |
| Gear pitch diameter | mm | Pitch diameter of the gear on this shaft. |
| Normal pressure angle | ° | Normal pressure angle of the teeth. |
| Helix angle (0 = spur) | ° | Helix angle; 0 for a spur gear. |
| Overhang (bearing to gear centre) | mm | Distance from the centre of the nearest bearing to the gear’s mid-face. |
| Shaft | ||
| Shaft diameter at the bearing | mm | Diameter of the shaft at the bearing (the critical section). |
| Shock and fatigue factor, bending | Combined shock and fatigue factor on bending. | |
| Shock and fatigue factor, torsion | Combined shock and fatigue factor on torsion. | |
| Allowable shear stress | MPa | Allowable shear stress for the shaft method. |
| Keyway at the section | choice | Whether a keyway is cut at the section. |
| Yield strength | MPa | Yield strength of the shaft. |
| Required safety factor on yield | Safety factor on yield you need for the combined stress. | |
Method and formulas
- T = 9549 P ÷ n; F_t = 2T ÷ d; F_r = F_t tan α_n ÷ cos β; F_a = F_t tan β (as the gear forces tool).
- Moment at the bearing M = √[(F_t a)² + (F_r a + F_a d ÷ 2)²].
- Diameter d = ∛[16 √((K_m M)² + (K_t T)²) ÷ π τ] with τ × 0.75 for a keyway (as the shaft diameter tool); combined stress σ = F ÷ A + M ÷ Z, τ = T ÷ 2Z, von Mises (as the combined shaft stress tool).
- Example: the gear pushes 2,469.6 N tangentially and 930.59 N radially; the shaft needs 35.91 mm, and at 40 mm the stress gives a factor of 11.405.
Limitations
- Moment taken at the bearing nearest the gear; check other sections and deflection separately.
- Shock-factor method; detailed fatigue design uses endurance limits and notch factors.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a pinion shaft on a gearbox or motor
- Check a shaft after a power increase
- Show the effect of overhang on shaft size
Who it is for
- Design engineers
- Machine designers
- Students
What you get
- Gear forces and torque
- Bending moment at the bearing
- Diameter needed and the stress in the chosen diameter
Interpreting the result
- Halving the overhang halves the bending moment: keep gears close to their bearings.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160, 2195–2200, 295–303, 212–218. Topic reference; no source tables or recommended settings are reproduced.
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Open the Overhung Gear Shaft Sizing (Gear Forces, Bending, Shaft Diameter, Stress) calculator
