论文标题:滚动轴承—转子系统的非线性动力学研究
Investigations of Light-induced Photorefractive Spatial Channel Waveguides
论文作者 赵凌燕
论文导师 袁茹,论文学位 硕士,论文专业 机械设计及理论
论文单位 西北工业大学,点击次数 133,论文页数 86页File Size2717k
2003-03-01论文网 http://www.lw23.com/lunwen_361975387/ 非线性动力学;轴承-转子系统;径向内部间隙;混沌;Laypunov指数
nonlinear dynamics;bearing-rotor system;radial internal clearance;chaos;Laypunov exponent
本文以转子动力学和非线性动力学理论为基础，针对非线性轴承—转子系统的具体特点，建立了系统的非线性动力学模型，比较了Runge-Kutta法和Gill法在轴承—转子动力学分析中的有效性和稳定性，得出了Gill法优于Runge-Kutta法的结论，并用Gill法研究了有径向内部间隙的深沟球轴承支承的水平刚性转子系统的非线性振动。 取球轴承的径向内部间隙为主要的研究参数，分析了平衡和不平衡这两种转子系统的动力学响应特性。计算结果表明，系统在某些参数域中可能发生倍周期分岔、概周期及混沌振动。用数值积分方法得到系统在特殊参数域中的周期解、分岔图、轴心轨迹、幅值谱及Poincaré映射图，并且用Laypunov指数的数值计算方法对平衡转子系统的混沌性态进行了判断。数值分析的结果为该类轴承—转子系统的设计提供了理论参考。 对于平衡转子系统，周期响应、亚谐波响应和混沌响应的出现在很大程度上依赖于径向内部间隙。随着间隙的增大，不稳定区和混沌响应区变宽。阻尼增大导致响应的幅值减小，并且降低了不稳定性。 不平衡转子系统的非线性是由于赫兹接触和轴承的径向内部间隙，系统的激励频率为变柔度频率和转子的旋转频率。结果表明，当轴承—转子系统的转速变化时，动态响应出现了不稳定和混沌，在通向混沌的道路上出现了倍周期和跳跃现象。
In allusion to the characteristics of a nonlinear bearing-rotor system, a system model was established based on rotor dynamics and nonlinear dynamics theory. The applicability and the stability of the numerical methods to the investigation of the system is investigated and the calculation shows that the four order variable step size Gill method is better than Runge-Kutta method in numerical stability. The nonlinear vibration of a horizontal rigid rotor supported by a deep groove ball bearing having radial internal clearance is studied by the Gill numerical integral method.The radial internal clearance of a deep groove ball bearing is taken as the main parameter, the effect of which on the dynamics response of the two kinds of rotor system(balanced or unbalanced) is studied. The results of a parametric study have resulted in the observation that the systems may undergo period doubling bifurcation, quasi-periodic and chaotic motions. In some typical parameter regions the periodic results, the bifurcation diagrams, the shaft centerline orbit, the phase portrait, the Poincare maps and the frequency spectrums of the systems are acquired by with numerical integral method. At the same time, a method to calculate the Laypunov exponents of a balanced rotor system is used to determine whether the system is in a state of chaos motion. The analytic results in this paper provide the theoretical reference for design this kind of bearing-rotor system.For the balanced rotor system, radial internal clearance is an important parameter for determining the dynamics response. It is seen that with increase in clearance the regions of unstable and chaotic response become wider. Increase damping results in lowered amplitude response and also reduced instability.For the unbalanced rotor system, the non-linearity is both due to Herzian contact and the radial internal clearance of bearing. The system is excited by the varying compliance frequency and the rotational frequency. The results have shown the appearance of instability and chaos in the dynamics response of the system as the speed of the bearing-rotor system is changed. Period doubling and intermittency have been observed as the route to chaos.
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