A dynamic model of an overhung rotor with ball bearings

Abstract

A ball bearing comprising rolling elements, inner and outer rings, and a cage structure can be described as a multi-body system (MBS). In order to predict the dynamic behaviour and resonance characteristics of a rotor-ball bearing system, it can be modelled and analysed as a MBS with flexible and rigid parts. In this study, a ball bearing is modelled with MBS approach using MSC ADAMS commercial software. The Hertzian theory is used for modelling the contact dynamics between the balls and the rings. The ball bearing model is then assembled with the rotor model which comprised a shaft and a disc positioned at the free end of the shaft. The ball bearing model is used with both flexible and rigid shaft assumptions in order to highlight the differences between the two cases. For the flexible shaft case, the MBS model also included a finite element model of the shaft. As expected, it is necessary to include the flexibility of the shaft in the model in order to to predict the changes in the modal characteristics of the system as a function of the rotor speed. Furthermore, including the gyroscopic effects leads to observe the forward and backward travelling modes with different natural frequencies. The effects of the bearing diametral clearance and localized defects on the inner and outer rings are modelled and analysed using the model developed. Also, the effects of the rotor unbalance on the vibration level of the whole system are examined. A test rig - consisting of two ball bearings, a shaft, and a disc - is also designed and developed so as to validate the theoretical model using experimental data. Order tracking and modal analyses are carried out and Campbell diagrams are obtained. Finally, the theoretical and the experimental results are compared and a refined MBS model is obtained for further analyses.