不确定双圆盘转子系统振动响应分析

采用基于随机矩阵最大熵法的非参数方法对不确定性转子系统进行动力学建模,研究了模型不确定性与参数不确定性对不确定双圆盘转子系统固有频率波动的影响,分析了转子系统振动响应在不同转速范围内对模型不确定性与参数不确定性的敏感度,从而将一般参数建模方法所无法考虑的建模误差考虑在内。结果表明:模型与参数不确定性对系统固有频率波动的影响大小不同,转轴弹性模量变异系数为0.04时分别使1阶固有频率产生了1.19%与3.58%的波动,2阶固有频率产生了1.82%与3.64%的波动;支承刚度变异系数为0.04时分别使1阶固有频率产生了0.01%与6.17%的波动,2阶固有频率产生了0.68%与6.18%的波动。不同转速范围内,转子系统振动响应对两种不确定性的敏感度也不同:在低于120 rad/s与高于430 rad/s的范围内,系统响应对两种不确定性均不敏感;在120～200 rad/s以及270～430 rad/s范围内,模型不确定性比参数不确定性对响应波动的影响大。该研究成果能够为复杂转子系统随机响应的预测提供一定的理论参考。 

Vibration responses analysis for double disks rotor system with uncertainties

The nonparametric method based on the maximum entropy method of random matrix was used to model the dynamics of uncertain rotor system. The effects of model uncertainties and parametric uncertainties on the fluctuation of natural frequencies of an uncertain double disk rotor system were studied with nonparametric method. The sensitivity of vibration responses of this system to model uncertainties and parametric uncertainties in different speed ranges was studied. Thus, the modeling errors that cannot be considered by parametric methods were taken into account. The results showed that: the effects of model and parametric uncertainties on system natural frequency fluctuation were different. For variation coefficient 0.04 of elastic modulus of rotating shaft, the first-order natural frequency had 1.19% and 3.58% fluctuation, and the second-order natural frequency fluctuated by 1.82% and 3.64%; for variation coefficient 0.04 of support stiffness, the first-order natural frequency had 0.01% and 6.17% fluctuations, and the second-order natural frequency fluctuated by 0.68% and 6.18%, respectively. The sensitivity of vibration responses of the rotor system to the two kinds of uncertainties was related to speed ranges: within the range of lower than 120 rad/s and upper than 430 rad/s, the system responses were not sensitive to the two kinds of uncertainties; within the range of 120-200 rad/s and 270-430 rad/s, the effects of model uncertainties on the response fluctuation were greater than those of parametric uncertainties. The research results can provide a theoretical reference for the prediction of random responses of complex rotor systems.