Unstable Vibrations in a Rotating Shaft System with Nonlinearity of Unsymmetry subjected to Base Excitation

本文从理论和实验两方面研究了轴的非线性或非对称性，并附加基础激励的旋转轴系统的不稳定振动。两个主要主题总结如下：1.本文研究了非线性转轴系统在基底激励下的强迫振动问题。由于滚珠轴承中的间隙，轴具有非线性弹簧特性。利用极坐标表示的非线性分量，分析了旋转轴的响应。结果，很明显，轴的轨道是椭圆形的，并且轴的响应曲线根据轴速度而复杂地变化。在稳态解不稳定的激励频率范围内，存在振幅随时间缓慢变化的非同步振荡。这种振荡包含 ...更多信息 许多分量的频率在激励频率的两侧以相等的跨度对齐。在实验中，我们得到了与理论值定性一致的结果.弹性支承非对称轴在大临界转速附近的不稳定振动本文研究弹性支承非对称轴。在该系统中，转子安装在轴的中间，并且基座可在横向于轴的方向上移动。考虑阻尼的影响，分析了主临界转速附近的不稳定振动。从理论上分析发现，在主临界转速附近的不稳定区域最多可分为六个区域，这取决于基座的质量、基座的刚度和轴的不对称性。存在两种类型的振动模式，在这些分开的，不稳定的区域。在实验中，我们得到了五种类型的响应曲线，其中包含n个不稳定区（n=1，2。. . ., S）附近的主要临界速度，通过改变质量的基础。理论计算值与实验结果吻合较好。少

This research is presented theoretically and experimentally on unstable vibrations in a rotating shaft system with nonlinearity or unsymmetry of the shaft, where base excitation is added. Two main themes are summarized as follows :1. Forced oscillations in a nonlinear rotating shaft system subjected to base excitationThe response of a rotating shaft, whose base is excited by a sinusoidal force, is studied. The shaft has nonlinear spring characteristics due to the clearance in the ball bearings. By using the nonlinear components represented by the polar coordinates, we analyze the response of the rotating shaft. As a result, it becomes clear that the orbit of the shaft is elliptic, and that the response curve of the shaft varies intricately depending on the shaft speed. It is also found that the non-synchronous oscillation, whose amplitude varies slowly with time, occurs within the region of the excitation frequency, where the steady state solution is unstable. This oscillation contains … More many components whosc frequencies align in equal spans on both sides of the excitation frequency. In experiments, we obtained qualitatively the same results as the theoretical values.2. Unstable Vibrations of an Unsymmetrical Shaft Supported by a Flexible Base Near the Major Critical SpeedWe deal with an unsymmetrical shaft supported by a flexible base. In this system, a rotor is mounted in the middle of the shaft, and the base is movable in a transversal direction to the shaft. We analyze the unstable vibration near the major critical speed by taking into account the effects of damping. From a theoretical analysis, it is found that the unstable region near the major critical speed is divided at most into six zones which depend on the mass of the base, the stiffness of the base, and the unsymmetry of the shaft. There exist two types of vibration modes in these divided, unstable zones. In experiments, we obtained five types of response curves which contained n unstable zones(n=1, 2. . . ., S)near the major critical speed, by changing the mass of the base. and got good agreement between the theoretical values and experimental results. Less