Critical Speed Calculator Overview
This calculator estimates the first critical (whirling) speed of a rotating shaft — the speed at which the shaft begins to vibrate due to resonance. It helps engineers and designers ensure that operating speeds remain well below the natural frequency of the shaft to prevent vibration and potential failure.
How It Works
The critical speed Nc is determined using the relationship between the shaft’s stiffness, mass, and boundary conditions:
Where:
- d = Shaft root diameter (m)
- L = Distance between bearings (m)
- E = Modulus of elasticity (Pa)
- ρ = Density of material (kg/m³)
- β1 = End fixity constant, based on support type
End Fixity Options
The calculator adjusts the result using a fixity factor (F) to account for different bearing and support conditions:
| Option | End Condition | Factor (F) | Description |
|---|---|---|---|
| A | Fixed–Free (Cantilever) | 0.36 | Lowest stiffness; one end fixed, one free |
| B | Simply Supported | 1.00 | Both ends supported but free to rotate |
| C | Fixed–Pinned | 1.47 | One end fixed, one pinned |
| D | Fixed–Fixed | 2.23 | Both ends fixed; highest stiffness |
Output
The calculator provides the critical speed in revolutions per minute (rpm). It assumes a uniform solid shaft, operating in its first bending mode, and is suitable for quick design checks or educational purposes.