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Research Papers: Applications

Multi-Event Excitation Force Model for Inner Race Defect in a Rolling Element Bearing

[+] Author and Article Information
Sidra Khanam

Industrial Tribology, Machine Dynamics,
and Maintenance Engineering Centre (ITMMEC),
Indian Institute of Technology Delhi,
New Delhi 110 016, India
e-mail: sidra.khanam10@gmail.com

N. Tandon

Industrial Tribology, Machine Dynamics,
and Maintenance Engineering Centre (ITMMEC),
Indian Institute of Technology Delhi,
New Delhi 110 016, India
e-mail: ntandon@itmmec.iitd.ernet.in

J. K. Dutt

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110 016, India
e-mail: jkrdutt@yahoo.co.in

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received November 11, 2014; final manuscript received June 20, 2015; published online October 1, 2015. Assoc. Editor: Zhong Min Jin.

J. Tribol 138(1), 011106 (Oct 01, 2015) (15 pages) Paper No: TRIB-14-1276; doi: 10.1115/1.4031394 History: Received November 11, 2014; Revised June 20, 2015

This paper presents a theoretical model for the forcing function generated on the structure as a rolling element negotiates a spall-like defect on the inner race, considered to be a moving race. The negotiation of defect has been seen as a sequence of events for the purpose of understanding the physics behind this negotiation. Such an analysis has not been attempted in the literature and thus forms the basic contribution in this work. Defects are assumed to generate two events; one at the leading edge and other at the trailing edge. The entry event at the leading edge is modeled using contact mechanics and is a function of load, speed, and curvature of defect edge whereas impact event, modeled using the principles of mechanics, is a function of load, speed, size of defect, and curvature of defect edge. The vibratory response of the nonlinear rotor bearing system subject to such excitation is simulated numerically using fourth-order Runge Kutta method and analyzed in both time and frequency domains. The modeling results provide insight into the physical mechanism which is not measured in practice and highlight the weakness of entry pulse in comparison to the impact pulse, also observed by several other researchers in their experimental tests. Defects of varying severity were simulated and tested to validate the proposed model and the acceptable correlation of amplitudes at the characteristic defect frequency provides a preliminary multi-event theoretical model. The developed model has therefore laid a theoretical platform to monitor the size of the defect on inner race which may be considered not only to identify but also to quantify the defect.

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Figures

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Fig. 1

Bearing geometry with defect on inner race and load distribution under radial load

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Fig. 2

(a) Motion of the ball around a defect located at the line of maximum load zone on the inner race and (b) eventwise description of ball’s motion around the defect—(i) ball entering into the defect, (ii) ball hitting the trailing edge of the defect along with the contact between the ball and defect edge approximated by a restoring element, and (iii) ball leaving the defect

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Fig. 3

Illustration of excitation force pulses: (a) periodic couple of forces representing excitation due to defect on inner race, (b) periodic function to represent time-varying load at a point on inner race, and (c) total forcing function

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Fig. 4

Experimental setup under study: (a) photographic view, (b) schematic view of the system encircled in (a), and (c) vibration model of the ball bearing

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Fig. 5

Flowchart for numerical computation

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Fig. 6

Simulated excitation force and the acceleration response for defect size 0.5 mm: (a) force time variation for 1 s, (b) enlarged view of the encircled zone of (a) to highlight the entry and impact events, (c) acceleration response of housing for 1 s, and (d) enlarged view of the encircled zone of (c) to observe entry and impact events

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Fig. 7

Simulated excitation force and the acceleration response for defect size 1.5 mm: (a) force time variation for 1 s, (b) enlarged view of the encircled zone of (a) to highlight the entry and impact events, (c) acceleration response of housing for 1 s, and (d) enlarged view of the encircled zone of (c) to observe entry and impact events

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Fig. 8

Explicit enlarged view of the simulated acceleration response due to entry and impact for (a) defect size = 0.5 mm and (b) defect size = 1.5 mm

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Fig. 9

Relationship between the defect size and TTI and duration between entry and impact force peaks (TD)

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Fig. 10

Spectra of excitation forces for (a) defect size = 0.5 mm and (b) defect size = 1.5 mm

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Fig. 11

Velocity spectra of vibration response of housing for (a) defect size = 0.5 mm and (b) defect size = 1.5 mm

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Fig. 12

Experimental vibration spectrum of housing for defects of different sizes

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Fig. 13

Variation of amplitude at characteristic defect frequency with defect size

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