Bolt Preload (Torque)
Back-calculate preload F0 from tightening torque T, nut factor K and nominal diameter d, then estimate preload stress from stress area As.
Inputs
Formula
Fundamentals
Back-calculate preload F0 from tightening torque T, nut factor K and nominal diameter d, then estimate preload stress from stress area As.
This tool computes Bolt Preload (Torque) from the formula: F0 = T/(K·d); σ0 = F0/As
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
| Tightening torque T | Input parameter |
| Nut factor K | Input parameter |
| Nominal dia. d | Input parameter |
| Preload F0 | Output result |
| Preload stress σ0 | Output result |
How to use
- Fill in Tightening torque T, Nut factor K, Nominal dia. d, Stress area As in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Preload F0, Preload stress σ0 in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：F0 = T/(K·d); σ0 = F0/As
输入变量：
- Tightening torque T
T— N·m - Nut factor K
K - Nominal dia. d
d— mm - Stress area As
As— mm²
输出结果：
- Preload F0
F0— N - Preload stress σ0
sigma0— 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 F0 = T/(K·d); σ0 = F0/As，取 Tightening torque T = 100 N·m；Nut factor K = 0.2；Nominal dia. d = 12 mm；Stress area As = 84.3 mm²。
代入计算得：Preload F0 = 41,670 N；Preload stress σ0 = 494.3 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 |
|---|---|---|---|
| Tightening torque T (N·m) | T | N·m | 100 |
| Nut factor K | K | 0.2 | |
| Nominal dia. d (mm) | d | mm | 12 |
| Stress area As (mm²) | As | mm² | 84.3 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Preload F0 | F0 | N |
| Preload stress σ0 | sigma0 | MPa |
Applications
- Common engineering use cases