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Nonlinear dynamic analysis of a rotor/bearing/seal system. (English) Zbl 1400.37105

Summary: In this study a new dynamic model of a rotor system is established based on the Hamilton principle and the finite element method (FEM). We analyze the dynamic behavior of the rotor system with the coupled effects of the nonlinear oil film force, the nonlinear seal force, and the mass eccentricity of the disk. The equations of the motion are solved effectively using the fourth order Runge-Kutta method in MATLAB. The dynamic behavior of the system is illustrated by bifurcation diagrams, largest Lyapunov exponents, phase trajectory diagrams, and Poincaré maps. The numerical results show that the rotational speed of the rotor, the pressure drop in the seal, the seal length, the seal clearance, and the mass eccentricity of the disk are the key parameters that significantly affect the dynamic characteristics of the rotor system. The motion of the rotor system exhibits complex types of periodic, quasi-periodic, double-periodic, multi-periodic, and chaotic vibrations. This analysis can be used to guide the design of seal parameters and to diagnose the vibration of rotor/bearing/seal systems.

MSC:

37N05 Dynamical systems in classical and celestial mechanics
70H05 Hamilton’s equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
70K50 Bifurcations and instability for nonlinear problems in mechanics
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)

Software:

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References:

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