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Modelling of a rotor-ball bearings system using Timoshenko beam and effects of rotating shaft on their dynamics

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Abstract

This study has focused on the influence of rotating shaft on the dynamics of rotor-ball bearings system. A mathematical modelling of the system has been carried out by considering shaft as rotating Timoshenko beam model. The radial force of rotor unbalance varied with rotating speed. The contact between balls and races is considered as nonlinear spring, whose stiffness is obtained by using Hertzian contact deformation theory. After the modelling for shaft, the governing equation of bearing are derived. The proposed mathematical model is validated experimentally. Moreover, the proposed model is also validated with previous published studies. The bifurcation diagram and Lyapunov exponent are presented to define the state of the system as a function of rotational speed. Fast Fourier transform (FFT) and phase trajectory are used to investigate the influence of the shaft under dynamics of the system.

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Authors and Affiliations

  1. Machine Dynamics and Vibration Lab., Mechanical Engineering Discipline, PDPM, Indian Institute of Information Technology Design & Manufacturing, Jabalpur, 482005, India

    J. Metsebo, N. Upadhyay & P. K. Kankar

  2. Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Sciences, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

    J. Metsebo & B. R. Nana Nbendjo

Authors
  1. J. Metsebo
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  2. N. Upadhyay
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  3. P. K. Kankar
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  4. B. R. Nana Nbendjo
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Corresponding author

Correspondence to N. Upadhyay.

Additional information

Recommended by Associate Editor Ohseop Song

Jules Metsebo received his B.S. and M.S. degrees in Physics from University of Yaoundé, Yaoundé, Cameroon. He is currently a Ph.D. student at the Physics Department of the Faculty of Science. His research interests include nonlinear dynamics and vibration control.

Nitin Upadhyay received Master of Technology (M.Tech.) in Industrial Engineering and Management from National Institute of Technology, Tiruchirappalli, India. Currently he is a Ph.D. student at the Mechanical Engineering Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur (MP) India. His current research areas are Non-linear dynamics, Fault diagnosis of rotor bearing system, condition monitoring and signal processing.

P. K. Kankar is an Assistant Professor in Mechanical Engineering, PDPMIndian Institute of Information Technology, Design and Manufacturing Jabalpur. He obtained his Ph.D. at Indian Institute of Technology Roorkee, India. His research interests include vibration, design, condition monitoring of mechanical components, nonlinear dynamics and soft computing.

Blaise Romeo Nana Nbendjo received his Ph.D. in Mechanics from University of Yaoundé I, Yaoundé, Cameroon. He is currently an Associate Professor at the Physics Department of the Faculty of Science of the same University. His research interests include nonlinear dynamics, chaos and vibration control.

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Metsebo, J., Upadhyay, N., Kankar, P.K. et al. Modelling of a rotor-ball bearings system using Timoshenko beam and effects of rotating shaft on their dynamics. J Mech Sci Technol 30, 5339–5350 (2016). https://doi.org/10.1007/s12206-016-1101-x

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  • DOI: https://doi.org/10.1007/s12206-016-1101-x

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