Shaft Diameter (Torsion)
Find the minimum solid shaft diameter d for torque T at allowable shear τ.
Inputs
Formula
τ = 16T/(πd³) → d = ³√(16T/(πτ))
Preliminary size from torsion only; refine with bending.
Fundamentals
Find the minimum solid shaft diameter d for torque T at allowable shear τ.
This tool computes Shaft Diameter (Torsion) from the formula: τ = 16T/(πd³) → d = ³√(16T/(πτ))
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
| Torque T | Input parameter |
| Allowable shear τ | Input parameter |
| Min diameter d | Output result |
How to use
- Fill in Torque T, Allowable shear τ in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Min diameter d in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：τ = 16T/(πd³) → d = ³√(16T/(πτ))
输入变量：
- Torque T
T— N·mm - Allowable shear τ
tau— MPa
输出结果：
- Min diameter d
d— mm
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 τ = 16T/(πd³) → d = ³√(16T/(πτ))，取 Torque T = 50,000 N·mm；Allowable shear τ = 40 MPa。
代入计算得：Min diameter d = 18.53 mm。
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 |
|---|---|---|---|
| Torque T (N·mm) | T | N·mm | 50000 |
| Allowable shear τ (MPa) | tau | MPa | 40 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Min diameter d | d | mm |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: τ = 16T/(πd³) → d = ³√(16T/(πτ))
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases