KEVOS® MAKEOS · Power Transmission
Ball Screw Critical Speed and Buckling
Is this ball screw below its critical speed and buckling load?
Critical (whirling) speed and Euler buckling load of a ball or lead screw from root diameter, unsupported length and end fixity, against the operating speed and axial load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Root diameter | mm | Root (minor) diameter of the screw from the catalogue. |
| Unsupported length | mm | Distance between bearings, or from the bearing to the nut at its furthest position. |
| End mounting | choice | Bearing arrangement at the screw ends. |
| Elastic modulus | GPa | Modulus of the screw steel. |
| Density | kg/m³ | Density of the screw material. |
| Maximum operating speed | rpm | Highest screw speed in service. |
| Maximum compressive axial load | N | Largest compressive load on the screw. |
| Allowed share of critical speed | % | Maximum share of critical speed your design rule or the screw maker allows (often 80%). |
| Allowed share of buckling load | % | Maximum share of buckling load your design rule allows (often 50%). |
Method and formulas
- I = π d_r⁴ ÷ 64; A = π d_r² ÷ 4.
- Critical speed n = (λ² ÷ 2πL²) √(EI ÷ ρA) × 60, with λ = 4.730, 3.927, π or 1.875 for fixed–fixed, fixed–supported, supported–supported and fixed–free.
- Buckling P = π²EI ÷ (KL)², with K = 0.5, 0.7, 1 or 2.
- Example: a 21 mm root, 1200 mm fixed–supported screw has a critical speed of 2,750.4 rpm and a buckling load of 27.508 kN.
Limitations
- Uniform shaft at the root diameter; the nut and support stiffness affect real values.
- Nut life, DN limit and drive torque are separate checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a ball screw axis before ordering
- Choose end bearing arrangement
- Find the longest screw for a speed
Who it is for
- Design engineers
- Maintenance engineers
- Automation engineers
What you get
- Critical speed and allowed speed
- Buckling load and allowed load
- Utilisation of each
Interpreting the result
- If the speed is too high, use a larger diameter, a fixed–fixed mounting, a shorter length or a rotating nut.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2561–2568. Topic reference; no source tables or recommended settings are reproduced.
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