The Motion of the Rotor Acrossing Critical Speed Levitated by AMBs with Anisotropic Stiffness

The stiffness and damping ratios in x and y radial degrees of freedom (DOF) of active magnetic bearing (AMB) may be different due to the machining and assembly errors. Therefore, the critical speeds in the two radial DOFs will not be equal. To study the rotor motion when its speed is between the two unequal radial critical speeds, a model of a rigid Jeffcott rotor levitated by AMBs with anisotropic bearing stiffness and damping ratio was built in this paper. The differential equation of motion of the model was derived from Lagrange equation firstly. Then the motion of the rotor geometric center was given. Through plotting the orbit of the rotor geometric center, it is found that the backward whirling movement of the rotor can be observed when the product of the damping ratios in x and y DOFs is lower than a critical value.