Numerical analysis of nonlinear rotor–seal system

The seal characteristic is an important factor affecting the performance of the rotor system. The nonlinear model of the rotor–seal system is established using Muszynskaʹs nonlinear seal forces. An efficient and high-precision direct integration scheme is presented based on the 2N type algorithm for the computation of exponential matrices. The nonlinear phenomena in the unbalanced rotor–seal system are investigated using the adopted model and numerical integration method. The influence of the seal on the nonlinear characteristics of the rotor system is analyzed by the bifurcation diagrams and Poincaré maps. Various nonlinear phenomena in the rotor–seal system, such as periodic motion, double-periodic motion, quasi-periodic motion and Hopf bifurcation are investigated and the stability is judged by Floquet theory and bifurcation theorem. The influence of parameters on the critical instability speed of the balanced rotor–seal system is also included. The high-precision direct integration method is effectively applied to the nonlinear numerical analysis of the rotor–seal system. The scheme has high precision and a large time step may be adopted to save computing resources.