A ball bearing in the presence of a spall on the inner race was studied. Based on Hertzian elastic contact theory

a research on non-linear excitation mechanism excited by the spall fault was carried out

and the internal excitation mechanism of double-impulse phenomenon was studied. As a result

a novel coupled non-linear dynamic model for double-impulse behavior of the ball bearing with a spall on the inner race was proposed

by considering the contact characteristics between the rolling elements and the bearing races and the excitation mechanism of time-varying displacement and contact force. The coupled solution to the second order non-linear differential equations was obtained by applying the Runge-Kutta numerical integral method

the relationship of double-impulse time spacings extracted from the simulated vibration signal was investigated. By comparison of the simulated

experimental and theoretical double-impulse time spacings under diverse shaft rotating speeds and inner race spall sizes of the ball bearing

all the relative errors between the simulated and theoretical double-impulse time spacings were less than 2 percent

and that between the simulated and the experimental double-impulse time spacings were less than 12 percent. In addition

the simulated signal agreed well with the experimental signal. Consequently

it was concluded that the effectiveness of the proposed nonlinear dynamic model in predicting the double-impulse time separation and vibration characteristics of the ball bearing was well validated.