Dynamic modeling and quantitative diagnosis for dual-impulse behavior of rolling element bearing with a spall on inner race

The dual-impulse behavior, which is produced by the spall located on the surface of the bearing raceway, is closely related to the size of the spall zone. This allows to establish an accurate mechanism of quantitative fault diagnosis and spall size estimation. However, dynamic model of dual-impulse behavior, which couples the nonlinear excitation force and the impact force induced by the interaction between the rolling element and the spall zone, have not been proposed before, especially under the elastohydrodynamic lubrication (EHL) condition. To address this issue, the corresponding dual-impulse excitation mechanism is investigated and explained, and the force produced by the collision of the rolling element with the trailing edge of the spall zone is derived. A coupled nonlinear dynamic model of the rolling element bearing (REB) with a spall on the inner race is proposed in this paper, in which the displacement and excitation force originating from the passing process of the rolling element over the spall zone are modeled as a piecewise function. The transient collision force excited by the strike of the rolling element on the trailing edge of the spall area is introduced, and the contact between the rolling elements and both the bearing races under EHL condition is modeled. To validate the proposed model, the dual-impulse time spacing (DITS) is analysed, and the vibration responses and its corresponding envelope spectra under simulation and experimental conditions are studied theoretically and experimentally. The simulated results agree well with the experimental results.