Eigenvalue Analysis Techniques for Magnetic Bearing Supported Rotating Machinery

Conventional eigenvalue analysis techniques for rotating machines use a linearized force coefficient bearing model that fits experimental data for fluid film bearings and seals. In this model, real and constant stiffness, damping, and added mass coefficients define the frequency dependence of the fluid film bearing force/displacement transfer function. This model can not adequately represent the more complicated frequency dependence of a magnetic bearing transfer function. Therefore, application of standard eigenvalue techniques to magnetic bearing supported rotors requires equivalent coefficients that are frequency dependent. In this paper, a typical fluid film bearing transfer function is compared to a typical magnetic bearing transfer function (PID controller) to illustrate the differences and to explain how equivalent coefficients are defined for magnetic bearings. The iterative procedure required to use the equivalent coefficients in standard rotordynamic eigenvalue analysis programs is discussed. Iteration can be eliminated by modifying a conventional eigenvalue analysis program to include the electromechanical equations of the magnetic bearing controller, an approach that provides a direct description of the frequency dependence of the magnetic bearing transfer function. The controller model applied by Chen and the more general approach applied by Maslen are discussed.