Nonlinear dynamics of the six-pole rotor-AMB system under two different control configurations

Abstract

The nonlinear dynamics of the six-pole rotor active magnetic bearings system is studied in this article for the first time. Two control configurations based on a proportional-derivative feedback current controller are proposed to mitigate lateral vibrations of the considered system. The first configuration is designed in such a way that only four electromagnetic poles are responsible for the system vibration control in the $$ Y $$ -direction, while all six poles control the lateral vibration in the $$ X $$ -direction. A second configuration is proposed in which the same four poles of the first configuration control the system vibration in the $$ Y $$ -direction, while the other two poles are responsible for controlling the system vibration in the $$ X $$ -direction. According to the suggested control methods, a mathematical model is derived that simulates lateral oscillations of the system. Using the perturbation analysis, four autonomous and coupled first-order nonlinear differential equations that govern the system oscillation amplitudes and the corresponding phase angles in both $$ X $$ and $$ Y $$ -directions are extracted. Various bifurcation diagrams are obtained using rotor spinning-speed and disk eccentricity as a bifurcation control parameter. The conditions at which the system can whirl either forward or backward are investigated. Numerical validations for the obtained bifurcation diagrams are introduced which illustrate excellent agreement with the analytical results. Based on the acquired analytical and numerical results, it is found that the first control configuration has the best dynamical behavior for controlling the vibration of such systems.