Nonstationary Vibrations of a Rotating Machinery Through Critical Speeds and Active Damping

由于各种原因，旋转机械具有非线性弹簧特性。在本研究中，研究了由非线性弹簧特性引起的通过临界速度的非平稳振动。在转子安装在弹性轴上的实验装置中，观察到了各种亚谐和求和-微分谐振动。在理论和实验分析中，我们提出了利用数字信号处理技术的复数FFT方法。利用复FFT方法、相平面分析和渐近方法，得到以下结果：(1)对于给定的角加速度，在较大临界速度的情况下，非平稳振动的最大幅值Gamma max只有一个值。当加速度大于某一值时，转子可以通过临界转速。加速度越大，最大振幅越小。(2)在1/2阶次简谐振动的情况下，即使角加速度相同，最大振幅Gamma max也在0和(Gamma Max)_1之间变化。(3)在非对称非线性引起和-差谐振荡的情况下，对于给定的角加速度，最大幅值Gamma max在(Gamma Max)_1和(Gamma Max)_2之间随机变化。(4)在1/3阶次简谐振动的情况下，只要加速度值很小或很大，转子就可以通过临界转速。否则，非平稳幅值被拉向平稳幅值，转子不能通过临界转速。主动减振技术目前正在开发中，目前还没有取得完整的结果。

Rotating machinery has nonlinear spring characteristics for various reasons. In this research, nonstationary oscillations through critical speeds caused by nonlinear spring characteristics are investigated.1. In an experimental apparatus in which a rotor was mounted on an elastic shaft, various kinds of subharmonic and summed-and-differential harmonic oscillations are observed.2. In the theoretical and experimental analyses, we originated Complex-FFT method which utilizes a digital signal processing technique. By using Complex-FFT method, phase plane analyses, and the asymptotic methods, the following results are obtained : (1) In the case of the major critical speed, the maximum amplitude gamma max in nonstationary oscillation has only one value for a given angular acceleration. The rotor can pass the critical speed when the acceleration is higher than a certain value. The bigger the acceleration, the smaller the maximum amplitudes. (2) In the case of subharmonic oscillation of order 1/2, the maximum amplitude gamma max varies between 0 and (gamma max)_1 in randam even if the angular acceleration is the same. (3) In the case of summed-and-differential harmonic oscillation caused by unsymmetrical nonlinearity, the maximum amplitude gamma max varies between two values (gamma max)_1 and (gamma max)_2 in random for a given angular acceleration. (4) In the case of subharmonic oscillation of order 1/3, the rotor can pass the critical speed if the value of accelaration is very small or very large. Otherwise, the nonstationary amplitude is drawn toward stationary amplytude and the rotor cannot pass the critical speed.3. The active damping technique is now under development and we could not obtain a completed results.