Compare an ideal worm-to-wheel reduction from tooth count and worm starts, then apply an entered efficiency to torque and power. The sketch places a worm inside a ring, but it does not determine a compatible internal mesh. The calculation assumes the worm is the input; the reference video uses the worm as its output.
Internal Worm-gear Wheel Interactive Calculator
Explore reduction, ideal output speed, efficiency-adjusted torque and input-power loss using a user-entered efficiency.
Equation Used
- One worm revolution advances the wheel by the entered number of starts z relative to N teeth.
- Input torque and speed are steady compatible magnitudes.
- Entered efficiency represents total mechanical power efficiency at that operating point.
- Output torque is inferred from Pout=eta Pin and ideal speed ratio.
- No module/diameters, lead/helix angle, pressure angle, handedness, center distance, enveloping geometry, contact ratio, backlash, friction law, self-locking/backdrive, startup, thermal balance, tooth/bearing/shaft/housing loads, strength, wear, lubrication or safety model.
Efficiency is an input assumption, not a prediction. Torque output follows a steady power balance and ignores startup, breakaway and thermal variation. Ring tooth count and worm starts alone cannot define an internal worm mesh or determine backdrivability.
Enclosed worm and inward-facing ring
A z-start worm advances z wheel teeth per worm revolution, so ideal reduction is N/z. With entered overall efficiency eta, output power is eta times input power and torque follows from output speed.
The sketch places a worm inside the ring and uses the entered z/N phase ratio. Its tooth marks and moving worm lines are symbolic, with no solved helical contact. Playback speed does not represent entered rpm.
Use as an ideal ratio check
The outputs can verify tooth-count ratio and an assumed-efficiency energy balance. They cannot select a worm set, establish self-locking, calculate operating efficiency, predict temperature or rate capacity.
Efficiency must be supplied
Pin=Tin omega_in. Ideal output speed is nin/R. Assuming Pout=eta Pin gives Tout=Tin R eta. Mechanical loss is Pin(1−eta).
Actual efficiency depends strongly on lead angle, friction, lubrication, materials, speed, load and temperature.
Worked example
For N=60, z=1, nin=1,000 rpm, Tin=2 N·m and assumed eta=65%, ideal reduction is 60:1, output speed is 16.67 rpm, efficiency-adjusted torque is 78 N·m and assumed mechanical loss is about 73.30 W.
What the ratio and efficiency assumption cannot determine
A real internal worm pair needs compatible helix, lead, axis placement and tooth surfaces. Efficiency depends on operating conditions and must come from appropriate data. The power balance cannot establish contact stresses, temperature rise, capacity or whether the wheel can drive the worm.
Frequently asked questions
Does a high ratio make the drive self-locking?
No. Backdrivability depends on lead angle, friction and operating conditions.
Is entered efficiency valid at every load and speed?
No. It is one operating-point assumption, not a prediction.
Does the reference video use the same input and output?
No. Nguyen Duc Thang’s description takes output from a sprocket fixed to the worm. This calculator instead assumes worm input and wheel output; its reduction and torque results must not be applied directly to that video arrangement.
Mechanism reference
Nguyen Duc Thang’s mechanism collection, page 56, describes Internal worm wheel 1 as a 60-tooth internal helical ring engaging a one-start worm, with output taken from a sprocket fixed to the worm. The calculator uses the opposite power-flow assumption: worm input and wheel output.
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