Vibration transmission through rolling element bearings, part II: System studies

This paper extends the proposed bearing stiffness formulation of Part I and demonstrates its superiority over existing models in vibration transmission analyses for a generic single shaft-bearing-plate-mount system. The bearing stiffness matrix [K]_bm is incorporated in discrete system models involving lumped parameter and finite element modeling techniques. Shaft, plate and mount flexibilities are also included in such models. The stability issue associated with the proposed bearing model is addressed analytically by using Liapunov's stability method, and the system is found to be dynamically stable provided the preloads are sufficiently high. Eigensolution and forced harmonic response to the following rolling element bearing system example cases are obtained by using our formulation and results are compared with the predictions yielded by the current vibration models: (i) rigid shaft and plate system freely suspended; (ii) rigid shaft and plate supported on flexible mounts; (iii) an experimental set-up consisting of a flexible shaft, two ball bearings, a rectangular plate and the supporting structure. Analytical results indicate that our proposed model is indeed capable of predicting plate rigid-body angular motion or plate flexural motion as excited by shaft motion. Such predictions are not observed in existing vibration models. Also, models with lower degrees of freedom, developed by several previous investigators, tend to underestimate the resonant frequencies and force or moment transmissibilities as compared with our multi-degree-of-freedom models. Finally, comparisons between our model and experiment have been found to be reasonably good.