Nonlinear Dynamic Analysis And Optimization Of Bearing-Rotor System

On the background of design of aviation turbine engine, nonlinear dynamic analysis and optimization of bearing-rotor system are studied in this dissertation. This system is a very important component in engineering and it is widely used in power, mechanical, and transportation project fields. Due to many complicated nonlinear factors existing in the system and coupling among these factors, there are still quite great gaps between theoretical research on nonlinear dynamics analysis, optimal design and practical engineering. Thus theoretical researches on model, method for nonlinear dynamic analysis and optimal dynamical design have important theoretical signficances and practical engineering value to modern machine production of rotating machinery. Several aspects as nonlinear dynamic analysis method for bearing-single rotor system, nonlinear dynamic model of rolling bearing-dual rotor system and dynamical optimization of bearing-rotor system are focused on in this thesis.The contents of the dissertation are as follows:(1) We propose an improved shooting method for nonlinear dyanmic analysis of rolling bearing-unbalanced single rotor system.The unbalanced rotor bearing system is excited by two periodic forces with different periods, eccentric force of the rotor and nonlinear varying bearing force. When the shooting method is used to obtain the periodic solutions of the system, the integral interval is long and the computation efficiency is low because the integral interval should be the least common multiple of the above two exciting periods. Aiming at the above problems, an improved shooting method is proposed based on combination of higher Poincare map and Newton-Raphson iteration. The stability and bifurcation are judged through Floquet theory. Compared with current shooting method and fixed point algorithm, the proposed method has shorter integral interval and higher efficiency under the same solving precision.(2) We develop a new five-degree-freedom dynamical analysis model of rolling bearing-dual rotor system, which is widely used in aerospace engineering. Compared with current models, rotational freedoms of rotors are introduced. Furthermore, in the proposed model, the nonlinear displacement, deformation and load of bearings are formulated mathematically considering five degrees of freedom and coupling of dual rotors. The nonlinear equations of motions of dual rotors with five degrees of freedom are solved using Runge-Kutta-Fehlberg algorithm. In order to investigate the effect of introduced five degrees of freedom and nonlinear dynamic bearing model, we compare the simulation results of proposed model with two present models. The quantitative results are given. The simulation results show the rotational freedom of rotors and nonlinear dynamic model of deep groove ball bearings have great effects on the system dynamic simulation and verify Gupta's prediction (1993).(3) We propose an optimization model of rotor-bearing system with bearing nonlinear dynamics constraints and an optimization method. Comparing with present similar works, we make following improving works. Firstly, influence of clearance is involved in the optimization model. Secondly, a hybrid algorithm based on evolutionary algorithm/line search method is proposed. Numerical results of classic example show: the clearance has great influence on optimization results. The proposed algorithm overcomes the difficulty in choosing initial value of line search method and the premature of evolutionary algorithm. The proposed method has higher success rate under the same calculation accuracy. At the end of the dissertation, we adopt the proposed optimization method to optimize an aero-gas-turbine-engine bearing-rotor system in engineering and the optimal results are obtained.This study is helpful to the model, solution and optimization of the rolling bearing-rotor system. And also this work can provide theoretical and software support for dynamic analysis and optimal design of bearing-rotor system.