Critical Speed Equation (Nc)
There are two main methods used to calculate critical speed—the Rayleigh–Ritz method and Dunkerley's method. Both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. In general, the Rayleigh–Ritz equation overestimates and the Dunkerley equation underestimates the natural frequency. The equation illustrated below is the Rayleigh–Ritz method applied to a shaft. The static deflection expresses the relationship between rigidity of the shaft and inertial forces; it includes all the loads applied to the shaft when placed horizontally. However, the relationship is valid no matter what the orientation of the shaft is.
- Critical speed,
where:
- g = gravitational acceleration (≈ 9.81 m⁄s²)
- δst = vertical static deflection of the shaft when placed horizontally
- Nc is in rpm
Critical speed depends upon the magnitude and location of the shaft unbalance, the length of the shaft, its diameter, and the kind of bearing support. Good practice suggests that the maximum operating speed should not exceed 75% of the critical speed.
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