The paper is focused on the stability computation of a rotating system affected by parametric excitation, by using a frequency based computational method. The test case is a Jeffcott rotor excited by the unbalance of the disk and by the parametric excitation due to varying compliance of the rolling bearing elements of the supports. The stability of a system is typically studied using Floquet's theory based on direct time integration, or less often using Harmonic Balance Method (HBM) and Hill's Method, based on computations in frequency domain. In this paper all these methods are applied and produce cross-confirming results. However, it should be noted that these methods require separate, computationally demanding analyses, which are usually not applied to systems with a large number of degrees of freedom. Standard analyses of rotating systems typically entail the computation of Frequency Response Curves using HBM. In the paper it will be shown that the standard application of HBM cannot track the presence of instability. This deficiency is especially dangerous as it may lead the designer to overlook potentially dangerous speed ranges. The paper proposes an alternative method to track the presence of instability while computing the frequency response of the system here named Jacobian Based Approach (JBA). Its results are validated against standard stability analysis techniques.

该论文的重点是通过使用基于频率的计算方法来计算受参数激励影响的旋转系统的稳定性。测试案例是一个 Jeffcott 转子，它由圆盘的不平衡和由于支撑的滚动轴承元件的不同柔量而引起的参数励磁励磁。通常使用基于直接时间积分的 Floquet 理论研究系统的稳定性，或者较少使用谐波平衡方法 (HBM) 和希尔方法，基于频域计算。在本文中，所有这些方法都被应用并产生了交叉确认的结果。然而，应该注意的是，这些方法需要单独的、计算要求高的分析，通常不适用于具有大量自由度的系统。旋转系统的标准分析通常需要计算频率响应曲线使用 HBM。在本文中，将表明 HBM 的标准应用无法跟踪不稳定性的存在。这种缺陷尤其危险，因为它可能导致设计人员忽略潜在危险的速度范围。本文提出了一种替代方法来跟踪不稳定性的存在，同时在此处计算系统的频率响应，称为雅可比方法 (JBA)。其结果已根据标准稳定性分析技术进行了验证。