1541. A fast and reliable numerical method for analyzing loaded rolling element bearing displacements and stiffness

Yu Zhang1, Guohua Sun2, Teik C. Lim3, Liyang Xie4

1, 4School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China

2, 3Department of Mechanical and Materials Engineering, University of Cincinnati,
Cincinnati, P.O. Box 210072, USA

1Corresponding Author

E-mail: 1yeahzhangyu@126.com, 2sungh@ucmail.uc.edu, 3limt@ucmail.uc.edu, 4lyxie@mail.neu.edu.cn

(Received 11 September 2014; received in revised form 8 November 2014; accepted 20 November 2014)

Abstract. The load-displacement relation for rolling element bearing is a system of nonlinear algebraic equations describing the relationship of bearing forces and displacements needed to compute the bearing stiffness. The computed bearing stiffness is typically employed to represent the bearing effect when modeling the whole geared rotor system to optimize the system parameters to minimize the unwanted vibrations. In this study, a robust numerical scheme called the energy method is developed and applied to solve for the bearing displacements from the potential energy of the bearing system instead of solving these nonlinear algebraic equations using the classical numerical integration. The proposed energy method is based on seeking the minimal potential energy derived from the theory of elasticity that describes the potential energy as a function of the displacements of inner ring of rolling bearing relative to the housing support structure. Therefore, solving the system of nonlinear algebraic equations is converted into solving a global optimization problem in which the potential energy term is the objective function. The global optimization algorithm produces the bearing displacements that make the potential energy function of bearing system minimum. Parameter studies for bearing stiffness as the explicit expressions of bearing displacements are conducted with the varying unloaded contact angles and the varying orbital positions of rolling elements. The analysis applying the energy method is shown to yield the correct solution efficiently and reliably.

Keywords: rolling element bearing, nonlinear algebraic equations, bearing stiffness, energy method, potential energy of the bearing system, global optimization.

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