Stability and bifurcation of a non-linear bearing-flexible rotor coupling dynamic system

Abstract

The non-linear coupling dynamic behaviour of a hydrodynamic bearing-flexible rotor system is analysed. A local iteration method consisting of the improved Wilson-θ method, the predictor-corrector mechanism, and the Newton-Raphson method is proposed to calculate the non-linear dynamic response. Using the proposed method, the iterations are executed only on non-linear degrees of freedom. The iteration process shows improved convergence by taking the prediction value as the initial value. The stability and bifurcation type of periodic responses are determined by the Floquet theory. According to the physical characteristics of the oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at each step of the iterative process. Non-linear oil film forces and their Jacobians are calculated simultaneously without an increase in computational costs, and compatible accuracy is obtained. Numerical results reveal periodic, quasi-periodic, coexisting, and jump solutions of rich and complex non-linear behaviours of the system and show that the proposed methods not only save computational costs but also have high precision. simulation for the symmetrical single-disc flexible rotor-bearing system [4]. Based on the symmetrical flexible rotor model with a single disc, the journal orbit of the rotor and the stability of the system are determined using the shooting method and the generalized shooting method [5,6]. Non-linear dynamic behaviours of a large flexible rotor system are obtained by the Newmark method and the predictor-corrector mechanisms [7,8]. From references [3] and [9], it is seen that the predictor-corrector mechanism and the Newton shooting method are used to calculate the unbalance periodic responses and bifurcation point of the system. In this article, an improved Wilson-θ method is developed to obtain a local iteration method for calculating non-linear responses. The iteration for non-linear responses needs to be performed only on non-linear degrees of freedom by the proposed method. According to the physical characteristics of the oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at each step of the iterative process. Non-linear oil film forces and their Jacobians JMES1190

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Nonlinear vibration and stability analysis of a flexible rotor supported on angular contact ball bearings

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