BIZOMAT MAKEOS · Gears
Worm Gear Drive Design (Efficiency, Forces and Heat)
What torque and forces does this worm drive deliver, how much heat does it make, will the housing stay cool enough, and is it self-locking?
Design check of a worm gear drive: ratio, lead angle and efficiency from module, starts, teeth, worm diameter and friction (as the worm gear tool), sliding velocity, input and output torque, tangential, axial and separating forces on worm and wheel, power lost as heat and the oil temperature from the housing surface and heat transfer coefficient, and a self-locking check when the load must be held.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Input power | kW | Power into the worm shaft. |
| Worm speed | rpm | Speed of the worm. |
| Axial module | mm | Axial module of the worm (equal to the wheel’s transverse module). |
| Worm starts | Number of starts (threads) on the worm. | |
| Wheel teeth | Number of teeth on the wheel. | |
| Worm pitch diameter | mm | Pitch diameter of the worm. |
| Normal pressure angle | ° | Normal pressure angle of the thread. |
| Friction coefficient at the sliding speed | Friction coefficient between worm and wheel at the sliding speed found (falls as sliding speed rises; your value from the gear maker). | |
| Housing surface area | m² | Outside surface area of the gearbox housing. |
| Heat transfer coefficient | W/m²·K | Heat transfer coefficient from housing to air (higher with a fan on the worm shaft). |
| Ambient temperature | °C | Surrounding air temperature. |
| Highest oil temperature | °C | Highest oil temperature allowed for the lubricant. |
| Must the drive hold the load by itself? | choice | Whether the drive must hold the load without a brake. |
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: Input power
- What it is
- The power fed into the worm shaft by the motor.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 10000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.1 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Torques, forces and heat generated rise in direct proportion.
- Get it right
- Use the power at the worm, not the output power wanted; the tool applies the efficiency itself.
What this means: Worm speed
- What it is
- The rotational speed of the worm, usually the motor speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For the same power, a higher speed lowers the torques and forces.
- Get it right
- The friction coefficient depends on sliding speed, so check it matches the sliding speed in the results.
What this means: Axial module
- What it is
- The tooth size of the worm measured along its axis, equal to the transverse module of the wheel.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.5 mm to 50 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.
- Effect on the result
- Sets the lead and the wheel pitch diameter; a larger module gives a larger lead angle.
- Get it right
- Use the axial module, not the normal module, which is smaller on a worm with a lead angle.
What this means: Worm starts
- What it is
- The number of separate threads wound around the worm. More starts mean a longer lead.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 8. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 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, raise the lead angle and efficiency, and make self-locking less likely.
- Get it right
- Count thread ends at the end of the worm, not the turns along it.
What this means: Wheel teeth
- What it is
- How many teeth the worm wheel has. Divided by the worm starts it gives the ratio.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 200. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth raise the ratio and output torque and lower output speed.
- Get it right
- Count the teeth on the wheel, not the gearbox ratio label.
What this means: Worm pitch diameter
- What it is
- The diameter of the worm at its pitch line, where it meshes with the wheel teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 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 gives a smaller lead angle and a higher sliding speed.
- Get it right
- Use the pitch diameter, not the outside diameter of the thread.
What this means: Normal pressure angle
- What it is
- The pressure angle of the worm thread measured in the plane normal to the thread.
- 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.
- Effect on the result
- A larger angle raises the separating force.
- Get it right
- Use the normal pressure angle, not the axial one, from the gear data.
What this means: Friction coefficient at the sliding speed
- What it is
- The sliding friction coefficient between worm and wheel at the sliding speed found, from the gear maker.
- Units and format
- Enter a plain number with no unit. The form accepts 0.005 to 0.3. 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, adds heat and makes self-locking more likely.
- Get it right
- It falls as sliding speed rises; recheck it against the sliding speed in the results.
What this means: Housing surface area
- What it is
- The outside surface area of the gearbox housing that gives off heat to the surrounding air.
- Units and format
- Enter a number in m²: square metres. The form accepts 0.000001 m² to 100 m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The oil temperature rise above ambient is inversely proportional to area.
- Get it right
- Count only surfaces exposed to air; a face bolted to a frame gives off little.
What this means: Heat transfer coefficient
- What it is
- The heat flow from each square metre of housing to the air for each kelvin of temperature difference.
- Units and format
- Enter a number in W/m²·K: watts per square metre per kelvin. The form accepts 0.000001 W/m²·K to 200 W/m²·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 W/m²·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The oil temperature rise above ambient is inversely proportional to it.
- Get it right
- It is higher with a fan on the worm shaft or in moving air; use a value for your installation.
What this means: Ambient temperature
- What it is
- The temperature of the air around the gearbox.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -40 °C to 60 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The oil temperature rises one for one with ambient.
- Get it right
- Use the hottest ambient expected in service, not a room average.
What this means: Highest oil temperature
- What it is
- The highest oil temperature allowed for the lubricant and seals.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 150 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the oil temperature, only the check.
- Get it right
- Take it from the lubricant or gearbox maker.
What this means: Must the drive hold the load by itself?
- What it is
- Whether the worm must hold the load without a brake when the motor stops, which requires the drive to be statically self-locking.
- Units and format
- Choose one of 2 options from the list: No (a brake holds it, or it does not matter); Yes (must be statically self-locking).
- Example
- The form opens with “No (a brake holds it, or it does not matter)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Yes makes a drive that can be back-driven fail the check.
- Get it right
- Static self-locking is not reliable under vibration; for safety-critical holding a brake is the competent solution.
Method and formulas
- Lead = π m z₁; tan γ = lead ÷ (π d₁); efficiency η = (cos αₙ − μ tan γ) ÷ (cos αₙ + μ cot γ) (as the worm gear tool).
- Sliding speed v_s = π d₁ n₁ ÷ (60 000 cos γ).
- T₁ = P₁ ÷ ω₁; T₂ = P₁ η ÷ ω₂; wheel tangential force (worm thrust) F_t2 = 2T₂ ÷ d₂; worm tangential force (wheel thrust) F_t1 = 2T₁ ÷ d₁; separating force ≈ F_t2 tan αₙ ÷ cos γ.
- Heat = P₁(1 − η); oil temperature = ambient + heat ÷ (k A).
- Example: 1.1 kW at 1450 rpm through 40:1 gives 188.13 N·m at 64.923% efficiency; the oil runs at about 51.795 °C.
Limitations
- Mesh friction only; bearing and churning losses add heat.
- Static self-locking is not reliable under vibration: use a brake for safety-critical holding.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a worm reducer for continuous duty
- Find bearing loads on worm and wheel shafts
- Decide whether a worm drive can hold a load without a brake
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Ratio, lead angle, efficiency and sliding speed
- Torques and forces on worm and wheel
- Heat, oil temperature and self-locking checks
Interpreting the result
- More starts raise the lead angle and efficiency but lose self-locking.
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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Open the Worm Gear Drive Design (Efficiency, Forces and Heat) calculator