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TECHNICAL PAPERS

An Investigation of Steady-State Dynamic Response of a Sphere-Plane Contact Interface With Contact Loss

[+] Author and Article Information
Q. L. Ma

Department of Mechanical Engineering, The Ohio State University, 650 Ackerman Road, Columbus, OH 43202

A. Kahraman1

Department of Mechanical Engineering, The Ohio State University, 650 Ackerman Road, Columbus, OH 43202kahraman.1@osu.edu

J. Perret-Liaudet, E. Rigaud

 Laboratoire de Tribologie et Dynamique des Systèmes, UMR 5513, 36 Ave. Guy de Collongue, F-69134 Ecully Cedex, France

1

Author to whom correspondence should be addressed.

J. Appl. Mech 74(2), 249-255 (Feb 01, 2006) (7 pages) doi:10.1115/1.2190230 History: Received April 12, 2005; Revised February 01, 2006

In this study, the dynamic behavior of an elastic sphere-plane contact interface is studied analytically and experimentally. The analytical model includes both a continuous nonlinearity associated with the Hertzian contact and a clearance-type nonlinearity due to contact loss. The dimensionless governing equation is solved analytically by using multi-term harmonic balance method in conjunction with discrete Fourier transforms. The accuracy of the dynamic model and solution methods is demonstrated through comparisons with experimental data and numerical solutions for both harmonic amplitudes of the acceleration response and the phase difference between the response and the force excitation. A single-term harmonic balance approximation is used to derive a criterion for contact loss to occur. The influence of harmonic external excitation f(τ) and damping ratio ζ on the steady state response is also demonstrated.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

The dynamic model of a single degree-of-freedom sphere-plane contact oscillator

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Figure 2

The test setup: (1) vibration exciter, (2) force transducer, (3) moving cylinder, (4) accelerometer, (5) ball, (6) tri-axial force transducer, and (7) rigid frame

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Figure 3

Comparison of the acceleration response predicted by HBM and the shooting method for ζ=0.008, f3=0.04. (a) H1 and (b) H2; (—) stable HBM, (---) unstable HBM, and (◇) shooting method.

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Figure 4

Comparison of measured acceleration response to HBM prediction for ζ=0.007, f3=0.018. (a) H1 and (b) H2; (—) stable HBM, (---) unstable HBM, and (◻) measurements.

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Figure 5

Comparison of measured acceleration response to HBM prediction for ζ=0.008, f3=0.04. (a) H1 and (b) H2; (—) stable HBM, (---) unstable HBM, and (◻) measurements.

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Figure 6

Comparison of the phase angle of measured acceleration response to the prediction by HBM and the shooting method. ζ=0.007 and f3=0.031.

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Figure 7

Comparison of power series approximations to exact G[u(τ)], (a) Eq. 1, (b) Eq. 11, and (c) Eq. 11

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Figure 8

H1 versus Λ for ζ=0.008 and f3=0.014, 0.0195, and 0.03

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Figure 9

H1 versus Λ for f3=0.03 and ζ=0.008, 0.0123, and 0.02

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