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# Mathematical Model for Rotor Bearing System by Considering the Effect of Shaft Dynamics and Localized Bearing Defects

[+] Author Affiliations
N. Upadhyay, P. K. Kankar

PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, Madhya Pradesh, India

M. Jules, B. R. Nana Nbendjo

University of Yaoundé, Yaoundé, Cameroon

Paper No. DETC2016-59313, pp. V008T10A024; 9 pages
doi:10.1115/DETC2016-59313
From:
• ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
• Volume 8: 28th Conference on Mechanical Vibration and Noise
• Charlotte, North Carolina, USA, August 21–24, 2016
• Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
• ISBN: 978-0-7918-5020-6

## abstract

This work is focused on development of model for unbalanced rotor bearing system to predict system behaviour in dynamic environment. In this model, nonlinearity is introduced due to two factors, namely, clearance of bearing and localized bearing races defects. The contact between the races and balls is considered as Hertzian contact which results in nonlinear restoring force due to elastic deformation in contact zone. In the mathematical formulation, the shaft is considered as rotating Timoshenko beam, supported on two ball bearings. After modelling of shaft corresponding equations representing the system behaviour has been formulated. The governing equations of motion are solved by Sixth order Runge-Kutta method. Bifurcation plots have been plotted to understand the state of the system in healthy condition and due to localized defects on races of the bearings. The Frequency spectrum and phase trajectory diagrams are also plotted for better understanding of the system response.

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