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

Yu Zhang, Guohua Sun, Teik C. Lim, Liyang Xie

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)620-642
Number of pages23
JournalJournal of Vibroengineering
Issue number2
StatePublished - 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Mechanical Engineering


  • Bearing stiffness
  • Energy method
  • Global optimization
  • Nonlinear algebraic equations
  • Potential energy of the bearing system
  • Rolling element bearing


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