BIZOMAT 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). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Axial module of worm
- What it is
- The axial module of the worm, equal to the transverse module of the wheel. Times π it gives the worm’s axial pitch.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not use the normal module of the worm thread here.
What this means: Worm starts
- What it is
- The number of thread starts on the worm, which with the wheel teeth sets the ratio.
- Units and format
- Enter a number in starts: a number of thread starts. The form accepts 1 starts to 12 starts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 starts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More starts lower the ratio and raise lead angle and efficiency; self-locking becomes less likely.
- Get it right
- Count the separate thread ends at the end of the worm.
What this means: Wheel teeth
- What it is
- The number of teeth on the worm wheel. Ratio equals wheel teeth divided by worm starts.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 10 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the ratio, wheel diameter and centre distance.
- Get it right
- Count teeth on the wheel, not threads on the worm.
What this means: Worm pitch diameter
- What it is
- The pitch diameter of the worm, where the lead angle is measured and the wheel meshes.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger worm diameter lowers the lead angle and the efficiency.
- Get it right
- Use the pitch diameter, not the outside diameter of the worm.
What this means: Normal pressure angle
- What it is
- The pressure angle of the worm thread in the normal plane, from the worm drawing or the gear maker.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the normal angle, not the axial angle, if the drawing gives both.
What this means: Coefficient of friction
- What it is
- The friction coefficient between the worm and wheel at the running sliding speed and lubrication, from the gear maker.
- Units and format
- Enter a plain number with no unit. The form accepts 0.005 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction lowers efficiency in both directions and makes self-locking more likely.
- Get it right
- Friction is higher at start-up than at running speed, so starting efficiency is lower.
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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