Rough Surface Contact
DOI:
https://doi.org/10.21152/1750-9548.11.2.197Abstract
This paper studies the contact of general rough curved surfaces having nearly identical geometries, assuming the contact at each differential area obeys the model proposed by Greenwood and Williamson. In order to account for the most general gross geometry, principles of differential geometry of surface are applied. This method while requires more rigorous mathematical manipulations, the fact that it preserves the original surface geometries thus makes the modeling procedure much more intuitive. For subsequent use, differential geometry of axis-symmetric surface is considered instead of general surface (although this “general case” can be done as well) in Chapter 3.1. The final formulas for contact area, load, and frictional torque are derived in Chapter 3.2.
References
Anton, H., 1999, Calculus: A New Horizon, sixth ed., Wiley, New York.
Bhushan, B., 2001, Surface Roughness Analysis and Measurement Techniques, in: Bhushan, B. (Ed.), Modern Tribology Handbook, CRC Press, Boca Raton.
Blau, P.J., 2001, The significance and use of friction coefficient, Tribology International, 34(9), 585-591. https://doi.org/10.1016/s0301-679x(01)00050-0
Gray, A., 1997, Surfaces of Revolution, Modern Differential Geometry of Curves and Surfaces with Mathematica, second ed., Boca Raton, CRC Press, Florida, 457-480.
Greenwood, J.A., Williamson, J.B.P. (1966) Contact of nominally flat surfaces, Proceedings of the Royal Society A, 295(1442), 300–319.
Grégory, A., 2014, On the Mechanical Friction Losses Occurring In Automotive Differential Gearboxes, The Scientific World Journal, 2014.
Jackson, R.L., et al., 2013, Contact mechanics, in: Menezes, P.L., Nosonovsky, S., Lovell, S., (Eds.), Tribology for Scientists and Engineers, Springer, New York.
Jackson, R. L., Green, I., 2011, On the Modeling of Elastic Contact between Rough Surface, Tribology Transactions, 54, 300-314. https://doi.org/10.1080/10402004.2010.542277
Liu, S.B., 2005, An extension of the Hertz theory for three-dimensional coated bodies, Tribology Letters, 18(3), 303–314. https://doi.org/10.1007/s11249-004-2757-4
Lu, W., 2014, Prediction of Surface Topography at the End of Sliding Running-In Wear Based on Areal Surface Parameters, Tribology Transactions, 57(3), 553-560. https://doi.org/10.1080/10402004.2014.887165
Menezes, P.L., et al., 2013, Fundamentals of Engineering Surfaces, in: Menezes, P.L., Nosonovsky, S., Lovell, S., (Eds.), Tribology for Scienties and Engineer, Springer, New York.
MuPAD, Symbolic Math in MATLAB, https://www.mathworks.com/discovery/mupad.html
Shampine, L.F., 2008, MATLAB Program for Quadrature in 2D, Applied Mathematics and Computation, 202(1), 266–274. https://doi.org/10.1016/j.amc.2008.02.012
Sneddon, I. N., 1965, The Relation between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile, International Journal of Engineering Science, 3(1), 47-57. https://doi.org/10.1016/0020-7225(65)90019-4
Yastrebov, V.A., Anciaux, G., Molinari, J.F., From Infinitesimal to Full Contact between Rough Surfaces: Evolution of the Contact Area, International Journal of Solids and Structures, 52, 83-102. https://doi.org/10.1016/j.ijsolstr.2014.09.019
Published
How to Cite
Issue
Section
Copyright (c) 2017 T Nguyen, B Alzahabi

This work is licensed under a Creative Commons Attribution 4.0 International License.