Chaos of flexible rotor system with critical speed in magnetic bearing based on the improved precise Runge-Kutta hybrid integration

Magnetic rotor-bearing system has drawn great attention because of its several advantages compared to existent rotor-bearing system, and explicit Runge-Kutta method has achieved good results in solving dynamic equation. However, research on flexible rotor of magnetic bearing is relatively less. Moreover, explicit Runge-Kutta needs a smaller integral step to ensure the stability of the calculation. In this article, we propose a nonlinear dynamic analysis of flexible rotor of active magnetic bearing established by using the finite element method. The precise Runge-Kutta hybrid integration method and the largest Lyapunov exponent are used to analyze the chaos of the rotor system at the first- and second-order critical speed of the rotor. Experiment on chaos analysis has shown that compared with the explicit Runge-Kutta method, the precise Runge-Kutta hybrid integration method can improve the convergence step of calculation significantly while avoiding iterative solution and maintain high accuracy which is four times the increase of the integral step.