A forced response-based method to track instability of rotating systems

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.