旋转机械转子-机匣系统碰摩的随机响应

Stochastic Response to Impact/Rub Acted on Rotor-Stator Box System in Rotary Machine

针对仅考虑具有质量偏心的旋转机械Jeffcott转子-机匣系统碰摩模型的动力学方程,进行了转子-机匣系统碰摩的随机响应研究·应用Kronecker代数、矩阵微分理论、向量值和矩阵值函数的二阶矩技术、矩阵摄动理论和概率统计方法系统地研究了转子-机匣系统碰摩的随机响应问题,推导出了一般的数学表达式,给出了数值分析解·分析了把转轴刚度和阻尼、定子刚度和阻尼、偏心距和定子径向刚度作为随机参数的随机系统的响应·分析表明,该转子系统在初始阶段振动强烈,响应幅值超过转子和定子之间的间隙,会发生碰摩现象·

Based on the impact/rub dynamic equation for Jeffcott rotor in a rotary machine with mass eccentricity, the stochastic response to the impact/rub acted on a rotor-stator box system is systematically investigated by way of Kronecker algebra, matrix calculus, second order moment analysis of vector-valued and matrix-valued functions, matrix perturbation theories and probability statistics methods. The generalized mathematical expressions of both first order and second order moments in the stochastic response are thus derived with numerical solutions given. Analyzes the stochastic responses to the random parameters of the rotor-stator box system, such as the shaft stiffness and damping, stator stiffness and damping, eccentricity and radial stiffness of stator. The results indicate that in the rotor system a strong vibration takes place initially, to which the response amplitude is greater than the radial clearance between rotor and stator, thus leading to impact/rub.