The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model
The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model
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DOI：
10.1016/j.ymssp.2019.04.018
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发表时间：
2019-08
影响因子：
8.4
通讯作者：
P. Bonello
中科院分区：
文献类型：
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作者：
P. Bonello
坎贝尔图描述了转子动力学系统关于其静态平衡条件的低振幅（线性）自由振动模式随速度的变化，并且是辅助解释非线性响应的重要工具。然而，坎贝尔图箔片空气轴承（FAB）转子系统目前推导出使用线性力系数（FC）的方法和个别模式还没有得到验证的瞬态非线性动力学分析（TNDA）在低振幅。事实上，FC和TNDA预测的领先（即最小阻尼）模式的稳定性之间的显着差异已被报道。本文首次建立了一种求解一般FAB转子模型的坎贝尔图的方法，避免了FC法。它是基于动力系统的雅可比矩阵的特征值分析。通过适当的缩放和应用适当的标准，可以过滤雅可比矩阵的多个特征向量以提取相关模式。每个模式进行了验证，使用TNDA与模式特定的初始条件来自坎贝尔图分析。该方法在文献中的三种情况下，分别说明其适用于复杂的轴承类型（3-垫），复杂的箔片模型，和柔性转子成功地进行了测试。
Campbell diagrams describe the variation with speed of the modes of low amplitude (linear) free vibration of a rotordynamic system about its static equilibrium condition, and are an important tool that aids the interpretation of the nonlinear response. However, Campbell diagrams for foil-air bearing (FAB) rotor systems are currently derived using the linear force coefficients (FC) method and individual modes have not been verified by transient nonlinear dynamic analysis (TNDA) at low amplitudes. In fact, significant discrepancies between FC and TNDA predictions for the stability of the leading (i.e. least damped) mode have been reported. This paper establishes for the first time a method for deriving Campbell diagrams of a generic FAB-rotor model that avoids the FC method. It is based on an eigenvalue analysis of the Jacobian matrix of the dynamical system. Through suitable scaling and the application of appropriate criteria, the multitude of eigenvectors of the Jacobian can be filtered to extract the relevant modes. Each mode is verified using TNDA with mode-specific initial conditions derived from the Campbell diagram analysis. The methodology is successfully tested on three cases in the literature, which respectively illustrate its applicability to complex bearing types (3-pad), complex foil models, and flexible rotors.