Shaft Critical Speed
Estimate the first critical speed n_cr from static deflection δ by Rayleigh's method (δ in mm, g=9.81).
Inputs
Formula
ncr = (30/π)·√(g/δ)
Keep operating speed clear of the ±20% resonance band.
Fundamentals
Estimate the first critical speed n_cr from static deflection δ by Rayleigh's method (δ in mm, g=9.81).
This tool computes Shaft Critical Speed from the formula: ncr = (30/π)·√(g/δ)
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
| Static deflection δ | Input parameter |
| Critical speed ncr | Output result |
How to use
- Fill in Static deflection δ in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Critical speed ncr in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：ncr = (30/π)·√(g/δ)
输入变量：
- Static deflection δ
delta— mm
输出结果：
- Critical speed ncr
ncr— rpm
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 ncr = (30/π)·√(g/δ)，取 Static deflection δ = 0.5 mm。
代入计算得：Critical speed ncr = 1,338 rpm。
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 |
|---|---|---|---|
| Static deflection δ (mm) | delta | mm | 0.5 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Critical speed ncr | ncr | rpm |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: ncr = (30/π)·√(g/δ)
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