Vibration analysis of ball bearings with a localized defect applying piecewise response function

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The amplitude and time duration of the impulse generated by a ball bearing passing over a local defect on the race are determined by the shape and size of the local defect. To identify the operation status of the bearing an accurate relationship between the impulse response and the size and shape of the local defect is necessary. In this paper, a dynamic simulation method is proposed to study ball bearing with local defect based on the coupling of the piecewise function and the Hertzian contact mechanism at the edge of the local defect. The ball bearing is modeled as a two-degree of freedom system. The impulse force is determined by the ratio of the ball size to the defect size and the contact deformation at the edge of the local defect is included. The contact mechanical characteristics between the ball and the race with different defect sizes are studied and compared with available results in the literature. It is shown that the proposed method can provide a more close to real impulse for the contact between the ball and the race with different defect sizes compared to the assumed rectangular or half-sine impulse function. It is also shown that the proposed method provides a new method for dynamic simulation of ball with a localized defect.