Numerical analysis of a nonlinear double disc rotor-seal system

Based on the finite element method (FEM) and the Lagrange equation, a novel nonlinear model of a double disc rotor-seal system, including the coupled effects of the gravity force of the discs, Muszynska’s nonlinear seal fluid dynamic force, and the mass eccentricity of the discs, is proposed. The fourth order Runge-Kutta method is applied to solve the motion equations of the system and numerically determine the vibration response of the center of the discs. The dynamic behavior of the system is analyzed using bifurcation diagrams, time-history diagrams, axis orbit diagrams, Poincaré maps, and amplitude spectrums. With the rotor speed increasing, the system presents rich forms including periodic, multi-periodic, quasi-periodic, and chaotic motion. We also discuss the effects of the distance between the two discs, the mass of the discs, seal clearance, seal length, and seal drop pressure on the dynamic behavior of the system. The numerical results demonstrate that a symmetrical disc structure, small disc mass, proper seal clearance, long seal length and high seal drop pressure can enhance the stability of a double disc rotor-seal system. The results provide a theoretical foundation for the design of multi-stage sealing systems.