A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system
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.
Keywordsrolling element bearing Hertzian contact fractional index cubic polynomial rotor ball bearing system
Chinese Library ClassificationO32
2010 Mathematics Subject Classification74H45
Unable to display preview. Download preview PDF.
The authors appreciate for the comments of the editors and reviewers. We appreciate for the support of the China Scholarship Council.
- Harris, T. A. and Kotzalas, M. N. Advanced Concepts of Bearing Technology: Rolling Bearing Analysis, 5th ed., Taylor & Francis, London (2006)Google Scholar
- Zhang, Z. Y. Bifurcations and Hysteresis of Varying Compliance Vibrations of a Ball Bearing-Rotor System, Ph. D. dissertation, Harbin Institute of Technology (2015)Google Scholar
- Zhang, Z. Y. and Chen, Y. S. Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential. Applied Mathematics and Mechanics (English Edition), 35(4), 423–436 (2014) https://doi.org/10.1007/s10483-014-1802-9MathSciNetCrossRefGoogle Scholar
- Fu, C. G. Aeroengine Design Manual, Rotor Dynamics and Engine Body Vibration, Vol. 19, Aviation Industry Press, Beijing (1999)Google Scholar
- Lazovic, T., Ristivojevic, M., and Mitrovic, R. Mathematical model of load distribution in rolling bearing. FME Transactions, 36, 189–196 (2008)Google Scholar