Dunkerley's method[1][2] is used in mechanical engineering to determine the critical speed of a shaft-rotor system.
The elastic properties of the shaft will act to restore the “straightness”.
In order to save the machine from failure, operation at such whirling speeds must be avoided.
The whirling frequency of a symmetric cross section of a given length between two points is given by: where: E = Young's modulus, I = second moment of area, m = mass of the shaft, L = length of the shaft between points.
A shaft with weights added will have an angular velocity of N (RPM) equivalent as follows: