Quasi-Static Analysis Of A Ball Bearing Having Geometrical Imperfection (Waviness)

T. Hentati, M. Maatar, F. Dammak, T. Fakhfakh, M. Haddar

Professor Mohamed Haddar Director of the Mechanics Modelling and Production Research Unit. National School of Engineers of Sfax (ENIS) BP. W. 3038 Sfax TUNISIA E-mail mohamed.haddar@enis.rnu.tn

The wide range and large scale usage of rolling bearings indicates their necessity and vital contribution to the performance of modern industries. The influence of rolling bearings on the static and dynamic behavior of rotor-bearing systems has been recognized for many years. Global models predicting mechanical behavior of the loaded roller bearings have been developed. This work proposes a quasi-static model of bearing deflection. This work proposes a model of a rotating contact bearing having inner race, outer race and ball waviness. The non-linear deflection and the load distribution on each rolling element are determined. The global stiffness of rolling bearing and the exerted force applied by active balls on the inner race are deduced. A Newton-Raphson Method is used to solve the non-linear equilibrium equations. The equilibrium is reached when the residual vector becomes zero. The study is quasi static. The position of each rolling element changes when the inner race rotates. The time varying rolling bearing stiffnesses and the instantaneous position of inner race centre (shaft centre) are determined from the study of the instantaneous equilibrium of the different components of the rotating contact bearing.

KEYWORDS: Rotating contact bearing, quasi-static analysis, and waviness.

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