Suppose the mass of the rotor is M, the eccentric mass is M, and the eccentric distance is e. If the vertical distance from the center of mass of the rotor to the connecting center line of the two bearings is not zero, the deflection is a, as shown in figure 1-1.

FIG. 1-1 rotor mechanics model

With eccentric mass m and eccentric distance e, centrifugal force, centrifugal torque or both will be generated when the rotor rotates.The size of centrifugal force and eccentric mass m, eccentric distance e and rotation angular velocity, namely F = me omega

.It is well known that alternating forces (with periodic changes in direction and magnitude) cause vibration, which is why unbalance causes vibration.As the rotor rotates once, the direction of centrifugal force changes once. Therefore, the frequency of unbalanced vibration is consistent with the rotation speed, and the amplitude-frequency characteristics and phase-frequency characteristics of vibration are also shown.