Trained Harmonic Balance Method for Parametrically Excited Jeffcott Rotor Analysis

Being able to identify instability regions is an important task for the designers of rotating machines. It allows discarding, since the early design stages, those configurations which may lead to catastrophic failures. Instability can be induced by different occurrences such as an unbalanced disk, torsional, and axial forces on the shaft or periodic variation of system parameters known as "parametric excitation." In this paper, the stability of a Jeffcott rotor, parametrically excited by the time-varying stiffness of the rolling bearings, is studied. The harmonic balance method (HBM) is here applied as an approximate procedure to obtain the well-known "transition curves (TCs)" which separate the stable from the unstable regions of the design parameter space. One major challenge in the HBM application is identifying an adequate harmonic support (i.e., number of harmonics in the Fourier formulation), necessary to produce trustworthy results. A procedure to overcome this issue is here proposed and termed "trained HBM" (THBM). The results obtained by THBM are compared to those computed by Floquet theory, here used as a reference. The THBM proves to be able to produce reliable TCs in a timely manner, compatible with the design process.