Coupling parametric instability and resonance of a rotating flexible disk with unstressed initial runout under several parametrical excitations

Abstract

With an improved Hill’s method, which is suitable for harmonic balance processing and coupling of nodal circles and nodal diameters, a dynamics research of a rotating flexible disk is carried out by considering unstressed initial runout and several parametrical excitations. The partial differential equation of disk system is obtained by Galerkin’s method considering three different types of excitations, namely slider loading, speed fluctuation and electromagnetic attraction. The individual and coupling effects of parametrical excitations on system’s instability and resonance are studied via numerical simulation. The instability results are shown by different colors based on RGB color space, and the disk’s steady-state amplitudes under different parameter settings are calculated with different nodal circles and nodal diameters. The calculation results show that these excitations affect the disk system’s stability and resonance in their own way. Meanwhile, this method is universal for the flexible disk’s steady-state vibration problems in practical engineering analysis.