基于嵌入式谱随机有限元法的转子系统随机不平衡响应特性分析

Stochastic unbalance response characteristics of rotor systems based on intrusive spectral stochastic finite element method

原始不平衡量在转轴中沿轴线呈任意空间分布,因而实际转子的不平衡量需用分布不平衡量和点不平衡量两种方式共同表达。考虑两种不平衡量的随机性,以随机场和随机变量的方式模拟转子中存在的两类不平衡量,并采用嵌入式谱随机有限元方法建立随机不平衡量下的转子系统不平衡响应随机分析模型。结果显示,提供的随机表征方法能较好地模拟两类转子不平衡量的随机性;不平衡量的随机性影响着转子不平衡响应的变异性,可以发现:(1)共振频率附近的位移响应幅值标准差也较大;(2)位移响应幅值的变异系数受低频段内共振频率的影响较小,但随着共振频率阶次的增高影响也逐渐增大;(3)位移响应相位角的标准差变化情况与位移幅值的变异系数变化情况是基本类似的。

Mass unbalance in a flexible shaft is distributed arbitrarily along its axis, so distributed mass unbalance and lumped mass unbalance should be considered and presented, respectively for mass unbalance simulation of real rotor systems. Taking the random nature of these two unbalances in a flexible shaft into account, they are represented as random fields and random variables. Here, stochastic analysis of unbalance response of rotor systems with random mass unbalances were performed using the intrusive spectral stochastic finite element method. Numerical results illustrated that the presented stochastic representation methods of distributed and lumped mass unblances are suitable to simulate the random nature of mass unbalances. Results showed that the variations of unblance responses are largely affected by the randomness of unbalances, for example,① the standard devitations of displacement amplitudes near the resonance frequencies become larger ;② the effects of resonance frequences with in a lower frequency band on the variation coefficient of displacement amplitudes are less, but the effects increase with increase in resonance frequency order ; （3） the change curve of the standard deviation of displacement phase angle is similar to that of the variation coefficient of displacement amplitudes.