Numerical analysis of a nonlinear double disc rotor-seal system

Abstract

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.

A coupling vibration model of multi-stage pump rotor system based on FEM

“…The motion equations of rigid disc can be obtained by Eq. (11) and they have been described in [3]: The motion equations of elastic shaft can be derived from FEM and each element can be expressed as: J and e K are 4 × 4 matrices. Combining the motion equations of the rigid discs and elastic shaft elements, the motion equations of rotor system can be expressed as:…”

“…The multi-stage pump rotor system can be simplified into a rotor-bearing-seal system. As an important factor influencing the vibration status of the rotor system, the dynamic characteristics of bearings and the dynamic vibration of bearing-rotor system have been the target of many researchers [2,3].…”

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

“…Based on lots of experiments, Muszynska and Bently regarded the circulating velocity as the key factor inducing the instability in a rotor system [14,15]. This nonlinear force model was widely used to calculate the sealing force and to predict the dynamic characteristics of a rotor system because the small disturbance limit condition could not be obeyed [16,17]. The numerical results exhibited rich forms of multiperiodic, quasi-periodic and chaotic motion and implied that the nonlinear sealing force had great influence on the dynamic characteristics of the rotor system.…”

Nonlinear dynamics of rub-impact on a rotor-rubber bearing system with the Stribeck friction model

“…Shi et al [11] examine the dynamic response of a vertical rotor-bearing system with nonlinear bearing forces and discuss the influence of system parameters. In addition, many works have discussed chaotic motion [12,13] and destructive self-excited dry friction backward whirl [14,15].…”