Structural static stability and dynamic chaos of active electromagnetic bearing systems: Analytical investigations and numerical simulations

Abstract

The complete nonlinear dynamics of an active magnetic bearing (AMB) with proportional and derivative controller is revisited analytically. Through the stability analysis of the second-order nonlinear differential equation governing the dynamics of the system, a state diagram is obtained in the proportional gain and precontrol current space. This diagram is fundamental and may help in making important design decisions namely in the identification of a controller for the complete range of the rotor mass, in order to ensure structural stability. In particular, we find that there exists a threshold for the proportional gain whose expression depends both on the inner radius of the bearing and on the bias current, and below which no stable dynamics of the system can occur. In the operating range, we show that the system exhibits a rich dynamics characterized by the possibility for the existence of many kinds of nonlinear localized excitations in the transient state, which may lead to an irregular or a chaotic behavior of the shaft. In this regime, the expressions of the critical running speed obtained by means of the Melnikov theory indicate its dependence on the AMB characteristic parameters.