Compound Gear Train
Compute the overall ratio of a two-stage compound train i = (Z2/Z1)·(Z4/Z3) and the output speed/torque.
Inputs
Formula
Fundamentals
Compute the overall ratio of a two-stage compound train i = (Z2/Z1)·(Z4/Z3) and the output speed/torque.
This tool computes Compound Gear Train from the formula: i = (Z2/Z1)·(Z4/Z3); n2 = n1/i; T2 = T1·i
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
| Stage1 pinion Z1 | Input parameter |
| Stage1 gear Z2 | Input parameter |
| Stage2 pinion Z3 | Input parameter |
| Overall ratio i | Output result |
| Output speed | Output result |
How to use
- Fill in Stage1 pinion Z1, Stage1 gear Z2, Stage2 pinion Z3, Stage2 gear Z4, 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 Overall ratio i, Output speed, Output torque in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：i = (Z2/Z1)·(Z4/Z3); n2 = n1/i; T2 = T1·i
输入变量：
- Stage1 pinion Z1
Z1 - Stage1 gear Z2
Z2 - Stage2 pinion Z3
Z3 - Stage2 gear Z4
Z4 - Input speed n1
n1— rpm - Input torque T1
T1— N·m
输出结果：
- Overall ratio i
i - Output speed
n2— rpm - 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)·(Z4/Z3); n2 = n1/i; T2 = T1·i，取 Stage1 pinion Z1 = 20；Stage1 gear Z2 = 60；Stage2 pinion Z3 = 20；Stage2 gear Z4 = 80；Input speed n1 = 1,500 rpm；Input torque T1 = 10 N·m。
代入计算得：Overall ratio i = 12；Output speed = 125 rpm；Output torque = 120 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 |
|---|---|---|---|
| Stage1 pinion Z1 | Z1 | 20 | |
| Stage1 gear Z2 | Z2 | 60 | |
| Stage2 pinion Z3 | Z3 | 20 | |
| Stage2 gear Z4 | Z4 | 80 | |
| Input speed n1 (rpm) | n1 | rpm | 1500 |
| Input torque T1 (N·m) | T1 | N·m | 10 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Overall ratio i | i | |
| Output speed | n2 | rpm |
| Output torque | T2 | N·m |
Applications
- Common engineering use cases