精细积分法在迷宫密封转子系统非线性动力学特性计算中的应用

A new high precision direct integration scheme for nonlinear rotor-seal system

基于M uszynska密封力模型,建立了迷宫密封转子系统的非线性动力学模型,将精细积分法推广应用于非线性情况,计算了迷宫密封不平衡转子系统的动力学特性,依据F loquet理论讨论其分岔特性。研究表明:在2N类算法计算指数矩阵基础上提出的精细积分法和传统的数值计算方法相比,其精度高,在分析中通过取不同步长计算对比,表明该方法在某些情况下可以采取较大时间步长,有效提高了计算速度。

In this paper, the mechanical model of labyrinth seal rotor system with Muszynska seal forces is established. A new efficient and high precision direct integration scheme is proposed based on 2^N type algorithm for the computing of exponential matrix. According to the proposed model and numerical integration method, the response of the unbalanced rotor-seal system is investigated. Combining precise integration method with Poincare mapping method, the bifurcation diagrams associated with various rotor speeds are presented and the course of the system shifting from the steady state to the unsteady state is analyzed. The study demonstrates that precise integration method can be effectively applied to nonlinear numerical analysis of rotor-seal system. The scheme is significantly less sensitive to the size of time step compared with other existing methods, time reduced substantially. so a large time step may be used and the computing