KEVOS® MAKEOS · Gears
Worm Gear Geometry and Efficiency
What ratio, lead angle, centre distance and efficiency does this worm drive have, and will it back-drive?
Ratio, lead and lead angle, wheel diameter, centre distance, forward efficiency and back-driving efficiency of a worm and wheel from module, starts, teeth and friction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Axial module of worm | mm | Axial module of the worm, equal to the transverse module of the wheel. |
| Worm starts | starts | Number of threads (starts) on the worm. |
| Wheel teeth | teeth | Number of teeth on the wheel. |
| Worm pitch diameter | mm | Pitch diameter of the worm. |
| Normal pressure angle | ° | Normal pressure angle (often 20°). |
| Coefficient of friction | Friction coefficient at the running sliding speed and lubrication, from the gear maker (about 0.02–0.08 for bronze wheels in oil). |
Method and formulas
- Ratio = z₂ ÷ z₁; lead = π mx z₁; lead angle γ = atan(lead ÷ π d₁).
- Wheel diameter d₂ = mx z₂; centre distance a = (d₁ + d₂) ÷ 2.
- Worm driving η = (cos αn − μ tan γ) ÷ (cos αn + μ cot γ).
- Wheel driving η′ = (cos αn − μ cot γ) ÷ (cos αn + μ tan γ); η′ ≤ 0 means self-locking.
- Example: a 1-start worm with 40 teeth gives 40:1, a 5.7106° lead angle and 64.923% efficiency.
Limitations
- Bearing and churning losses are not included.
- Static self-locking is not reliable under vibration; use a brake where safety matters.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Select a worm reduction
- Check whether a worm drive will hold a load
- Estimate gearbox efficiency and heat
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Ratio
- Lead and lead angle
- Wheel pitch diameter and centre distance
- Efficiency worm driving
- Efficiency wheel driving and self-locking
Interpreting the result
- Low efficiency means heat: check the gearbox thermal rating at continuous duty.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2191–2194. Topic reference; no source tables or recommended settings are reproduced.
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