Multi-Event Excitation Force Model for Inner Race Defect in a Rolling Element Bearing

This paper presents a theoretical model for the forcing function generated on the structure as a rolling element negotiates a spall-like defect on the inner race, considered to be a moving race. The negotiation of defect has been seen as a sequence of events for the purpose of understanding the physics behind this negotiation. Such an analysis has not been attempted in the literature and thus forms the basic contribution in this work. Defects are assumed to generate two events; one at the leading edge and other at the trailing edge. The entry event at the leading edge is modeled using contact mechanics and is a function of load, speed, and curvature of defect edge whereas impact event, modeled using the principles of mechanics, is a function of load, speed, size of defect, and curvature of defect edge. The vibratory response of the nonlinear rotor bearing system subject to such excitation is simulated numerically using fourth-order Runge Kutta method and analyzed in both time and frequency domains. The modeling results provide insight into the physical mechanism which is not measured in practice and highlight the weakness of entry pulse in comparison to the impact pulse, also observed by several other researchers in their experimental tests. Defects of varying severity were simulated and tested to validate the proposed model and the acceptable correlation of amplitudes at the characteristic defect frequency provides a preliminary multi-event theoretical model. The developed model has therefore laid a theoretical platform to monitor the size of the defect on inner race which may be considered not only to identify but also to quantify the defect.