Worm Gear Drive
Compute the ratio, output speed, efficiency η and output torque of a worm drive from worm starts Z1 and wheel teeth Z2. Lead angle γ and friction μ set efficiency.
Inputs
Formula
Fundamentals
Compute the ratio, output speed, efficiency η and output torque of a worm drive from worm starts Z1 and wheel teeth Z2. Lead angle γ and friction μ set efficiency.
This tool computes Worm Gear Drive from the formula: i = Z2/Z1; η = tanγ/(tanγ + μ/cosα); T2 = T1·i·η
History
Design theory of gears, threads and bearings matured with machine tools and standardisation (AGMA, ISO) since the Industrial Revolution.
Engineering applications
Used for transmission design, joint strength checks and component selection.
Glossary
| Worm starts Z1 | Input parameter |
| Wheel teeth Z2 | Input parameter |
| Lead angle γ | Input parameter |
| Ratio i | Output result |
| Output speed | Output result |
How to use
- Fill in Worm starts Z1, Wheel teeth Z2, Lead angle γ, Friction μ, Input speed n1, Input torque T1 in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Ratio i, Output speed, Efficiency η, Output torque in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：i = Z2/Z1; η = tanγ/(tanγ + μ/cosα); T2 = T1·i·η
输入变量：
- Worm starts Z1
Z1 - Wheel teeth Z2
Z2 - Lead angle γ
gamma— ° - Friction μ
mu - Input speed n1
n1— rpm - Input torque T1
T1— N·m
输出结果：
- Ratio i
i - Output speed
n2— rpm - Efficiency η
eta - Output torque
T2— N·m
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 i = Z2/Z1; η = tanγ/(tanγ + μ/cosα); T2 = T1·i·η，取 Worm starts Z1 = 2；Wheel teeth Z2 = 40；Lead angle γ = 10 °；Friction μ = 0.05；Input speed n1 = 1,440 rpm；Input torque T1 = 10 N·m。
代入计算得：Ratio i = 20；Output speed = 72 rpm；Efficiency η = 0.7682；Output torque = 153.6 N·m。
Key Points
- Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
- Compare stress with allowable stress and keep a safety factor (≥1.5, ≥2 for critical parts).
- For high speed/load also check lubrication, heat and fatigue life, not just static strength.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Worm starts Z1 | Z1 | 2 | |
| Wheel teeth Z2 | Z2 | 40 | |
| Lead angle γ (°) | gamma | ° | 10 |
| Friction μ | mu | 0.05 | |
| Input speed n1 (rpm) | n1 | rpm | 1440 |
| Input torque T1 (N·m) | T1 | N·m | 10 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Ratio i | i | |
| Output speed | n2 | rpm |
| Efficiency η | eta | |
| Output torque | T2 | N·m |
Applications
- Common engineering use cases