Analysis of a Rocking and Walking Punch—Part II: General Numerical Solution Using Quadratic Programming

[+] Author and Article Information
D. Nowell

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

J. Appl. Mech 71(2), 234-239 (May 05, 2004) (6 pages) doi:10.1115/1.1641062 History: Received November 18, 2002; Revised July 24, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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Mugadu,  A., Sackfield,  A., and Hills,  D. A., 2004, “Analysis of a Rocking and Walking Punch—Part I: Initial Transient and Steady State,” ASME J. Appl. Mech., 71, 225–233.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Sackfield,  A., Truman,  C. E., and Hills,  D. A., 2001, “The Tilted Punch Under Normal and Shear Load (With Application to Fretting Tests),” Int. J. Mech. Sci., 43(8), pp. 1881–1892.
Nowell,  D., and Dai,  D. N., 1998, “Analysis of Surface Tractions in Complex Fretting Fatigue Cycles Using Quadratic Programming,” ASME J. Tribol., 120, pp. 744–749.
Kalker,  J. J., 1971, “A Minimum Principle for the Law of Dry Friction With Application to Elastic Cylinders in Rolling Contact,” ASME J. Appl. Mech., 38, pp. 875–880.
Gill, P. E., Murray, W., and Wright, M. H., 1981, Practical Optimization, Academic Press, London.


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Geometry of the problem
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Auxiliary coordinates used for |s/a|>0.5
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Discretization of the shear tractions by overlapping triangular elements
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Alternative positions for the last collocation point (a) distance h from the contact edge, (b) coincident with the contact edge, and (c) between (a) and (b)
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Effect of the position of the last collocation point: difference between position of the stick/slip interface in numerical and analytical solutions plotted as a function of collocation point position, Q/fP=0.75
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Comparison of numerical predictions of the shear tractions and analytical values, 1, for the first quarter cycle of loading, Q/fP=0.75,−0.5<s/a<0
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Comparison of numerical predictions of slip and analytical values, 1, for the first quarter-cycle of loading Q/fP=0.75,−0.5<s/a<0
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Evolution of cumulative slip at the center of the punch with loading cycle for the first few cycles of loading as s/a varies between −0.5 and 0.5. Vertical lines show when the direction of travel of the normal load is reversed
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Comparison between numerical values for steady-state slip per cycle and those obtained by an integral equation approach, 1
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Normalized shear tractions as s/a is cycled between −0.5 and 0.5, Q/fP=0.75




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