Gear Bending Stress (Lewis)
Estimate root bending fatigue stress σ_F via the Lewis formula with tooth form factor Y_Fa, stress correction Y_Sa and load factor K.
Inputs
Formula
Fundamentals
Estimate root bending fatigue stress σ_F via the Lewis formula with tooth form factor Y_Fa, stress correction Y_Sa and load factor K.
This tool computes Gear Bending Stress (Lewis) from the formula: σF = Ft/(b·m) · YFa·YSa·K
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
| Tangential force Ft | Input parameter |
| Face width b | Input parameter |
| Module m | Input parameter |
| Bending stress σF | Output result |
How to use
- Fill in Tangential force Ft, Face width b, Module m, Form factor YFa, Stress correction YSa, Load factor K in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Bending stress σF in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：σF = Ft/(b·m) · YFa·YSa·K
输入变量：
- Tangential force Ft
Ft— N - Face width b
b— mm - Module m
m— mm - Form factor YFa
YFa - Stress correction YSa
YSa - Load factor K
K
输出结果：
- Bending stress σF
sigmaF— MPa
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 σF = Ft/(b·m) · YFa·YSa·K，取 Tangential force Ft = 2,000 N；Face width b = 30 mm；Module m = 3 mm；Form factor YFa = 2.8；Stress correction YSa = 1.6；Load factor K = 1.5。
代入计算得：Bending stress σF = 149.3 MPa。
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 |
|---|---|---|---|
| Tangential force Ft (N) | Ft | N | 2000 |
| Face width b (mm) | b | mm | 30 |
| Module m (mm) | m | mm | 3 |
| Form factor YFa | YFa | 2.8 | |
| Stress correction YSa | YSa | 1.6 | |
| Load factor K | K | 1.5 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Bending stress σF | sigmaF | MPa |
Applications
- Common engineering use cases