一种基于频响因子的转子系统基础冲击响应计算方法

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (9) : 221-226.

论文

一种基于频响因子的转子系统基础冲击响应计算方法

谢最伟;贺少华; 吴新跃

作者信息 +

Shock response computation for rotor-bearing systems by a “frequency response coefficient” method

Xie Zui-wei;He Shao-hua1; Wu Xin-yue2

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文章历史 +

摘要

考查地震或水下非接触爆炸冲击下旋转机械的动态响应特性，一般从研究转子系统基础冲击响应出发。由于陀螺效应和转子-轴承的交互效应，转子系统运动方程系数矩阵呈非对称性，不能在模态坐标下解耦，无法利用常规模态叠加法求解，所以以往的研究一般采用数值积分如Newmark法等进行迭代求解，但数值积分法相对模态叠加法要耗费较多的计算资源。提出了一种复数域内转子系统冲击响应计算方法，无需坐标解耦但仍可以利用线性叠加法进行响应求解。首先将激励和响应傅立叶展开成复数形式，包括正向旋转项和反向旋转项，根据方程左右两边相同频率前系数相等的事实得到特征方程，将特征方程写成简单矩阵束的本征方程形式，求得矩阵束的本征值和本征向量，将本征向量正规化，进一步得到矩阵束的逆阵，将逆阵元素取名为“频响因子”，将逆阵与激励相乘即可得到频率响应幅值，将所有频率响应成分叠加即可得到系统响应。通过一个工程实例，比较了所提方法与数值积分方法的结果，比较分析表明，所提方法满足工程要求，可以作为转子系统基础冲击响应和瞬态响应计算的一种普适方法。

Abstract

To investigate dynamic response behaviors of rotating machinery subjected to seismic or non-contact underwater explosion shock, we always start from the study of rotor-bearing systems representing those machines under base motion. Due to the gyroscopic effect and the interaction between rotor and bearing, system matrixes are nonsymmetric, so, conventional mode-superposition method cannot be applied to solve the system motion equations. Numerical direct time-integration methods are now used commonly obtaining a transient response of rotor-bearing systems, but compared to linear superposition method, they require more computing resources. For the above reason, a superposition method in complex domain was proposed. With no need to decouple equations, linear superposition computation of responses can still be performed just like that in the conventional mode-superposition method. Firstly, shock excitation and response were both expanded into a complex form of Fourier series, including forward and backward rotating items. Characteristic equations were obtained by the fact that coefficient matrixs of same rotating frequency are equal. Characteristic equations were then rewritten into simple pencil of matrix’ latent value equations. Inverse matrix of which elements are called “ Frequency Response Coefficient” of the pencil of matrix was calculated out by using its right and left latent vectors which were normalized. Responses in each frequency were obtained by the product of the inverse matrix and shock excitation, and then synthesized into overall responses of the system. An engineering example is to compare the proposed method and the results of numerical integration methods, comparative analysis shows that the proposed method to meet the engineering requirements, and can be used as a universal method of shock response and transient response computation of rotor systems.

导出引用

谢最伟;贺少华;吴新跃. 一种基于频响因子的转子系统基础冲击响应计算方法[J]. 振动与冲击, 2011, 30(9): 221-226

Xie Zui-wei;He Shao-hua;Wu Xin-yue. Shock response computation for rotor-bearing systems by a “frequency response coefficient” method [J]. Journal of Vibration and Shock, 2011, 30(9): 221-226