Parametric studies on dynamic stiffness of ball bearings supporting a flexible rotor

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Abstract
Most of the researchers in the field of dynamics of the rolling element bearing have considered bearing stiffness as time invariant and/or not related to dynamics of the bearing. In the present paper, the bearing stiffness has been taken as function of dynamic response at every time step of numerical simulation and a detailed parametric study is performed to investigate the effect of flexibility of the rotor shaft, rotational speed, and internal radial clearance on the instantaneous and average value of dynamic stiffness of the ball bearing. The mathematical formulation is based on the Timoshenko beam finite element theory. Gravity and bearing forces are considered as external forces acting on a free-free flexible shaft. A stable Newmark-β numerical integration scheme coupled with Newton–Raphson method is used for numerical integration and for convergence to an accurate value of bearing stiffness. The results showing the variation of different components of bearing stiffness as a function of time-invariant parameters has improved the understanding of the dynamic behavior of the bearing during motion. The variation pattern of bearing stiffness coefficients is observed to be sensitive to direction of rotation. The amplitude of periodic change of these coefficients increases with the increase of the stiffness ratio of shaft and the decrease of radial clearance.

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