Worm Gear Efficiency and Self-Locking Calculator
Efficiency, reverse efficiency, self-locking, output torque and speed, centre distance and heat loss of a worm and wheel from the starts, teeth, module, worm diameter and friction.
Results
The dashed line marks the value you entered.
What this tool does
A worm drive reduces speed a great deal in one stage, but all the tooth contact is sliding, so efficiency depends mainly on the lead angle and on friction: a single-start worm with a high ratio can fall well under 50 %, while multi-start worms with large lead angles can pass 90 %. When friction is greater than tan λ × cos φn the wheel cannot drive the worm — it self-locks, which is why worms are common in hoists. Do not rely on it alone to hold a load: vibration can lower friction and let it creep back, and a brake is the proper answer. The friction coefficient depends strongly on speed, materials and lubrication.
Formula
tan λ = starts × m ÷ d1 · η = (cos φn − μ tan λ) ÷ (cos φn + μ cot λ) · reverse η = (cos φn − μ cot λ) ÷ (cos φn + μ tan λ) · self-locking if tan λ ≤ μ ÷ cos φn
Variables
| Symbol | Meaning | Unit |
|---|---|---|
za | Starts (threads) on the worm | — |
zb | Teeth on the worm wheel | — |
mx | Axial module | mm |
dw | Pitch diameter of the worm | mm |
mu | Coefficient of friction between the parts | — |
pa | Normal pressure angle | ° |
n1 | Worm speed | rpm |
pw | Input power | kW |
EF | Efficiency, worm driving | % |
LA | Lead angle | ° |
RT | Reduction ratio | — |
ER | Efficiency when driven backwards | % |
SL | Does it self-lock? | — |
TO | Output torque | N·m |
NO | Output speed | rpm |
CD | Centre distance | mm |
HL | Heat to dissipate | W |
Worked example
- Starts (threads) on the worm1
- Teeth on the worm wheel30
- Axial module4 mm
- Pitch diameter of the worm40 mm
- Coefficient of friction between the parts0.05
- Normal pressure angle20 °
- Worm speed1450 rpm
- Input power1.5 kW
- Efficiency, worm driving64.9 %
- Lead angle5.71 °
- Reduction ratio30.00
- Efficiency when driven backwards46.5 %
- Does it self-lock?No — the wheel can drive the worm
- Output torque192.4 N·m
- Output speed48.3 rpm
- Centre distance80.0 mm
- Heat to dissipate526 W
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.