NORMAL LINE CONTACT OF FINITE-LENGTH CYLINDERS

Qiang Li, Valentin L. Popov

DOI Number
10.22190/FUME170222003L
First page
63
Last page
71

Abstract

In this paper, the normal contact problem between an elastic half-space and a cylindrical body with the axis parallel to the surface of the half-space is solved numerically by using the Boundary Element Method (BEM). The numerical solution is approximated with an analytical equation motivated by an existing asymptotic solution of the corresponding problem. The resulting empirical equation is validated by an extensive parameter study. Based on this solution, we calculate the equivalent MDR-profile, which reproduces the solution exactly in the framework of the Method of Dimensionality Reduction (MDR). This MDR-profile contains in a condensed and easy-to-use form all the necessary information about the found solution and can be exploited for the solution of other related problems (as contact with viscoelastic bodies, tangential contact problem, and adhesive contact problem.) The analytical approximation reproduces numerical results with high precision provided the ratio of length and radius of the cylinder are larger than 5. For thin disks (small length-to-radius ratio), the results are not exact but acceptable for engineering applications.

Keywords

Line Contact, Boundary Element Method, Finite-length Cylinder, Contact Stiffness, Method of Dimensionality Reduction

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References

Harris, T.A., 2001, Rolling bearing analysis, John Wiley and Sons, New York.

Norton, R., 2009, Cam Design and Manufacturing Handbook, Industrial Press.

Popov, V.L., 2010, Contact Mechanics and Friction: Physical Principles and Applications, Springer, Berlin.

Jonson, K.L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.

Landau, L.D., Lifshitz, E.M., 1970, Theory of Elasticity, Course of Theoretical Physics.

Venner, C.H., Lubrecht, A.A., 1994, Transient Analysis of Surface Features in an EHL Line Contact in the Case of Sliding, Journal of Tribology, 116(2), pp. 186–193.

Hamrock, B.J., Schmid, S.R., Jacobson, B.O., 2004, Fundamentals of Fluid Film Lubrication, Marcel Dekker, New York.

Prescott, J., 1946, Applied Elasticity, Dover Publications.

Thomas, H.R., Hoersch, V.A., 1930, Stresses Due to the Pressure of One Elastic Solid Upon Another: A Report of an Investigation Conducted by the Engineering Experiment Station, University of Illinois in Cooperation with the Utilities Research Commission.

Lundberg, G., 1939, Elastische Berührung zweier Halbräume, Forschung auf dem Gebiet des Ingenieurwesens A, 10(5), pp. 201–211.

Norden, B.N., 1973, On the compression of a cylinder in contact with a plane surface, National Bureau of Standards, Washington D.C.

Puttock, M.J., Thwaite, E.G., 1969, Elastic Compression of Spheres and Cylinders at Point and Line Contact, National Standards Laboratory.

Nakhatakyan, F.G., 2011, Precise solution of Hertz contact problem for circular cylinders with parallel axes, Russian Engineering Research, 31(3), pp. 193–196.

Kunz, J., de Maria, E., 2002, Die Abplattung im Kontaktproblem paralleler Zylinder, Forschung Im Ingenieurwesen, 67(4), pp. 146–156.

Thwaite, E.G., 1969, A precise measurement of the compression of a cylinder in contact with a flat surface, Journal of Physics E: Scientific Instruments, 2(1), pp. 79–82.

Glovnea, M., Diaconescu, E., 2004, New Investigations of Finite Length Line Contact, In ASME Proceedings, Special Symposia on Contact Mechanics, pp. 147–152.

Najjari, M., Guilbault, R., 2014, Modeling the edge contact effect of finite contact lines on subsurface stresses, Tribology International, 77, pp. 78–85.

Argatov, I., Heß, M., Pohrt, R., Popov, V.L., 2016, The extension of the method of dimensionality reduction to non-compact and non-axisymmetric contacts, ZAMM Journal of Applied Mathematics and Mechanics, 96(10), pp. 1144–1155.

Popov, V.L., Heß, M., 2015, Method of Dimensionality Reduction in Contact Mechanics and Friction, Springer, Berlin.

Popov, V.L., Pohrt, R., Heß, M., 2016, General procedure for solution of contact problems under dynamic normal and tangential loading based on the known solution of normal contact problem, The Journal of Strain Analysis for Engineering Design, 51(4), pp. 247–255.

Pohrt, R. Li, Q., 2014, Complete Boundary Element Formulation for Normal and Tangential Contact Problems, Physical Mesomechanics, 17(4), pp. 334–340.

Pohrt, R., Popov, V.L., 2015, Adhesive contact simulation of elastic solids using local mesh-dependent detachment criterion in boundary elements method, Facta Universitatis, Series: Mechanical Engineering, 13(1), pp. 3–10.

Li, Q., Popov, V.L., 2016, Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials, arXiv:1612.08395.




DOI: http://dx.doi.org/10.22190/FUME170222003L

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