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Applied Mathematics and Mechanics

, Volume 39, Issue 3, pp 365–378 | Cite as

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

  • Yulin Jin
  • Zhenyong Lu
  • Rui Yang
  • Lei Hou
  • Yushu Chen
Article

Abstract

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then, the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is calculated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally, the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

Keywords

rolling element bearing Hertzian contact fractional index cubic polynomial rotor ball bearing system 

Chinese Library Classification

O32 

2010 Mathematics Subject Classification

74H45 

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Notes

Acknowledgements

The authors appreciate for the comments of the editors and reviewers. We appreciate for the support of the China Scholarship Council.

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yulin Jin
    • 1
  • Zhenyong Lu
    • 1
  • Rui Yang
    • 1
  • Lei Hou
    • 1
    • 2
  • Yushu Chen
    • 1
  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.School of Energy Science and EngineeringHarbin Institute of TechnologyHarbinChina

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