Path-Following Analysis versus WMSL-Method – An Application for Nonlinear Magnetic Bearing Characteristics

In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems, [1], under extreme operating conditions a simple nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, fully nonlinear force to displacement and force to current characteristics are considered. The AMB system is excited by unbalance forces of the rotor. The behaviour of the system is discussed especially for the case of large rotor eccentricities, causing large rotor displacements. On the one hand, a path-following analysis, see [2, 3, 4], for the equations of motion is carried out to calculate bifurcation diagrams of the vibration amplitude with the the rotor speed as the chosen bifurcation parameter. On the other hand, the weighted mean square linearization method (WMSL-method), see [5, 6], is extended to a two-dimensional approach in order to obtain approximated stiffness and damping coefficients. These coefficients depend on the vibration amplitudes and allow the application of equivalent linear solution methods. In that way, a more or less precise approximation of the nonlinear system behaviour is achieved and approximated bifurcation diagrams including unstable paths can be calculated. However, no information about the stability of the obtained solutions is obtained by this approach. Some well known linearization methods, like the method of harmonic balance for example, ar