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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Analytical Maximum Response of a Rigid Spindle-Angular Contact Ball Bearings Assembly Subject to Rotating Unbalance and Base Harmonic Excitations

Journal of Applied Nonlinear Dynamics 2(1) (2012) 1--32 | DOI:10.5890/JAND.2012.09.004

F.M.A. El-Saeidy

Faculty of Engineering and Information Technology, University of Technology Sydney, Po Box 123, Broadway, NSW 2007, Australia

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Analytical vibration of a rigid machine spindle-angular contact ball bearings assembly subject to base harmonic excitations plus mass imbalance is investigated. Equations of motion for a complicated ball bearing assembly system are derived using Lagrange’s equations. For time-invariant bearing stiffness and damping matrices, analytical solutions are obtained for the maximum and minimum radii of disk orbit/bearing orbit (i.e., orbit maximum and minimum amplitudes). Analytical and numerical results are in excellent agreement. With increasing bearing number of balls and/or axial preload, response amplitude and shifts resonance peaks decrease in high frequency regions. For time-varying bearing stiffness and damping matrices, numerical results are obtained from Runge-Kutta method, and such numerical results are discussed with regard to time domain and fast Fourier transform (FFT).With increasing base excitation frequency, nonlinear spindle-bearings assembly becomes much stiffer and decreases the corresponding response amplitude. In addition, chaotic motions of axial vibration are observed.


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