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Research Papers

Nonlinear Vibration Signature Analysis of a High Speed Rotor Bearing System Due to Race Imperfection

[+] Author and Article Information
P. K. Kankar

Mechanical Engineering Department,  PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur-482005, Indiapavankankar@gmail.com

Satish C. Sharma

Vibration & Noise Control Laboratory,  Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee-247667, Indiasshmefme@iitr.ernet.in

S. P. Harsha

Vibration & Noise Control Laboratory,  Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee-247667, Indiaspharsha@gmail.com

J. Comput. Nonlinear Dynam 7(1), 011014 (Nov 10, 2011) (16 pages) doi:10.1115/1.4004962 History: Received September 01, 2010; Revised August 20, 2011; Published November 10, 2011; Online November 10, 2011

In this paper the nonlinear dynamic responses of a rigid rotor supported by ball bearings due to surface waviness of bearing races are analyzed. A mathematical formulation has been derived with consideration of the nonlinear springs and nonlinear damping at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components for each order of waviness at the inner and outer races, also the excited frequency and waviness order relationships have been set up to prognosis the race defect on these bearing components. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of a rolling element bearing

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Figure 2

Waviness at inner race and outer race

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Figure 3

Geometry of contacting bodies

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Figure 4

Response plot for outer race waviness with γ = 1 μm and W = 19.3 N

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Figure 5

The vibration responses of bearing due to outer race waviness at different wave numbers. (a) Wave number Nw  = 5. (b) Wave number Nw  = 6. (c) Wave number Nw  = 7. (d) Wave number Nw  = 9. (e) Wave number Nw  = 11. (f) Wave number Nw  = 13. (g) Wave number Nw  = 15. (h) Wave number Nw  = 18. (i) Wave number Nw  = 21. (j) Wave number Nw  = 31.

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Figure 6

Response plot for inner race waviness with γ = 1 μm and W = 19.3 N

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Figure 7

The vibration responses of bearing due to inner race waviness at different wave numbers. (a) Wave number Nw  = 5. (b) Wave number Nw  = 6. (c) Wave number Nw  = 7. (d) Wave number Nw  = 8. (e) Wave number Nw  = 9. (f) Wave number Nw  = 11. (g) Wave number Nw  = 15. (h) Wave number Nw  = 16. (i) Wave number Nw  = 18. (j) Wave number Nw  = 21. (k) Wave number Nw  = 31.

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