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Research Papers

Rapid Sliding Contact in Three-Dimensional by an Ellipsoidal Die on Transversely Isotropic Half-Spaces With Surfaces on Different Principal Planes

[+] Author and Article Information
L. M. Brock

Fellow ASME
Department of Mechanical Engineering,
University of Kentucky,
265 RGAN,
Lexington, KY 40506-0503
e-mail: louis.brock@uky.edu

Manuscript received February 24, 2013; final manuscript received May 9, 2013; accepted manuscript posted May 30, 2013; published online September 18, 2013. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(3), 031005 (Sep 18, 2013) (9 pages) Paper No: JAM-13-1091; doi: 10.1115/1.4024697 History: Received February 24, 2013; Revised May 09, 2013; Accepted May 30, 2013

A rigid ellipsoidal die slides on the surfaces of transversely isotropic half-spaces. In one case the material symmetry axis coincides with the half-space surface normal. In the other, the axis lies in the plane of the surface. In both cases sliding proceeds with constant sub-critical speed along a straight path at an arbitrary angle to the principal material axes. A three-dimensional dynamic steady state is considered, i.e., the contact zone surface must conform to the die profile and contact zone traction remains constant in the frame of the die. Exact solutions for contact zone traction are derived in analytic form, as well as formulas for contact zone geometry. Symmetry need not be assumed in the solution process. Anisotropy is found to largely determine zone shape at low sliding speed, but the direction of sliding can become a major influence at higher sliding speeds. Cartesian coordinates are used in the analysis, but introduction of quasi-polar coordinates allows problem reduction to a Cauchy singular integral equation.

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References

Barwell, F. T., 1979, Bearing Systems, Principles and Practice, Oxford University, Oxford, London.
Bayer, R. G., 1994, Mechanical Wear Prediction and Prevention, Marcel Dekker, New York.
Blau, P. J., 1996, Friction Science and Technology, Marcel Dekker, New York.
Ahmadi, N., Keer, L. M., and Mura, T., 1983, “Non-Hertzian Contact Stress Analysis for an Elastic Half-Space—Normal and Sliding Contact,” Int. J. Solids Struct., 19, pp. 357–373. [CrossRef]
Barber, J. R., 1983, “The Solution of Elasticity Problems for the Half-Space By the Method of Green and Collins,” Appl. Sci. Res., 40, pp. 135–157. [CrossRef]
Barber, J. R., 1992, Elasticity, Kluwer, Dordrecht, The Netherlands.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University, Cambridge, UK.
Hills, D. A., Nowell, D., and Sackfield, A., 1993, Mechanics of Elastic Contacts, Butterworth-Heinemann, Oxford, UK.
Kalker, J. J., 1990, Three-Dimensional Bodies in Elastic Constant, Kluwer, Dordrecht, The Netherlands.
Craggs, J. W., and Roberts, A. M., 1967, “On the Motion of a Heavy Cylinder Over the Surface of an Elastic Half-Space,” ASME J. Appl. Mech., 34, pp. 207–209. [CrossRef]
Churilov, V. A., 1978, “Action of an Elliptical Stamp Moving at a Constant Speed on an Elastic Half-Space,” J. Appl. Math. Mech., 42, pp. 1176–1182. [CrossRef]
Rahman, M., 1996, “Hertz Problem for a Rigid Punch Moving Across the Surface of a Semi-Infinite Elastic Solid,” Z. Angew. Math. Mech., 47, pp. 601–615. [CrossRef]
Brock, L. M., 2012, “Two Cases of Rapid Contact on an Elastic Half-Space: Sliding Ellipsoidal Die, Rolling Sphere,” J. Mech. Mater. Struct., 7, pp. 469–483. [CrossRef]
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University, New York.
Brock, L. M., 2002, “Exact Analysis of Dynamic Sliding Indentation at Any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space,” ASME J. Appl. Mech., 69, pp. 340–345. [CrossRef]
Hohn, F. E., 1965, Elementary Matrix Algebra, Macmillan, New York.
Jones, R. M., 1999, Mechanics of Composite Materials, 2nd ed., Brunner-Routledge, New York.
Sneddon, I. N., 1972, The Use of Integral Transforms, McGraw-Hill, New York.
Erdogan, F., 1985, “Mixed Boundary Value Problems in Mechanics,” Mechanics Today, Vol. 4, S.Nemat-Nasser, ed., S. Pergamon, New York, pp. 1–86.
Georgiadis, H. G., and Barber, J. R., 1993, “On the Super-Rayleigh/Subseismic Elastodynamic Indentation Problem,” J. Elasticity, 31, pp. 141–161. [CrossRef]
Brock, L. M., 2013, “Rapid Contact on a Pre-Stressed Highly Elastic Half-Space: The Sliding Ellipsoid and Rolling Sphere,” ASME J. Appl. Mech., 80, p. 021023. [CrossRef]
Peirce, B. O., and Foster, R. M., 1956, A Short Table of Integrals, 4th ed., Ginn, New York.
Stakgold, I. S., 1967, Boundary Value Problems in Mathematical Physics, Vol. 1, Macmillan, New York.

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