【摘要】 以转子动力学和非线性动力学理论为基础 ,针对非线性转子 -轴承系统的具体特点 ,建立了采用短轴承模型的弹性转子 -轴承 -基础系统模型 ,并用数值积分和庞加莱映射方法对其在某些参数域中进行了非线性振动研究。对系统动力学特性随转速及偏心质量变化时的非线性行为进行了分析 ,计算结果显示 ,系统在某些参数域中可能发生倍周期分叉、概周期及混沌运动。用数值方法得到系统在特殊参数域中的分叉图、频谱图、相图、轴心轨迹、及庞加莱映射图 ,并用分形几何理论对混沌系统的状态进行了判断。数值分析结果为该类转子 -轴承系统的设计和安全运行提供了理论参考。更多还原

【Abstract】 In allusion to the specific features of a nonlinear rotor bearing system, the nonlinear vibration of an elastic rotor bearing foundation system on the assumption of short bearing model is formulated and its characteristics are studied in some parameter ranges based on rotor dynamics and nonlinear dynamics theory with the Poincaré maps and numerical integral method. The nonlinear behavior of the system is analyzed along with the changing of the rotational speed and unbalance weight. The result of calculation shows that it may undergo the period doubling, quasi periodic and chaotic motions. In some typical parameter regions the bifurcation diagrams, the shaft centerline orbit, the phase portrait, the Poincaré maps and the frequency spectrums of the system are acquired with numerical integral method. At the same time, the stability being influenced by the physical dimensions of bearing is analyzed. The fractal dimension concept is used to determine whether the system is in a state of chaos motion. The analysis result in the paper provides a theoretical reference for designing and safely operating of this kind of systesms.更多还原