Contact mechanics of solids of revolution is characterised by their deformation behaviour under load. This is strongly influenced by their geometry and elastic properties. These parameters and the applied load determine the deformation of the contiguous solids, giving rise to contact pressure distribution and sub-surface stress fields, which are necessary to determine fatigue spalling performance. Load bearing surfaces are usually lubricated and the deformation of contiguous solids is often crucial in providing a gap for lubricant film formation and avoidance of asperity interactions on adjacent surfaces and the ensuing wear. Therefore, determination of contact deformation is essential in prediction of contact conditions. This usually requires the solution of the elasticity integral in the form of elliptic functions, which are discretised and achieved through time intensive numerical methods. In lubricated counterformal contacts under high loads and with materials of high elastic moduli, this amounts for the major computing resource requirement within any form of analysis, such as the usual elastohydrodynamic lubrication. The paper shows that any arbitrary pressure distribution over a given contact area may be represented by a harmonic series. The response of the elastic solids to the application of such a harmonic series leads to the evaluation of their contact deformation and sub-surface stress field of also a harmonic nature. The repercussion of this approach is that for a given applied contact load, harmonic analysis may be employed in order to analytically obtain the same predictions as those with much more time consuming numerical analysis. The paper proves the analytical approach by comparison with the case of an infinite line contact, or a one-dimensional contact, for which analytic solution based on the Hertzian theory exists as a classical case. Then, the conformance of the methodology to deviations of surface friction. An advantage of the method over those reported in literature is the simultaneous evaluation of the local contact deformation, as well as the sub-surface stress field. This approach can be extended to the case of rough surfaces, where the harmonic analysis may be used as an approximation.
Harmonic Analysis to Determine Contact Characteristics of Concentrated Counterformal Contacts
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Teodorescu, M, Rahnejat, H, & Gohar, R. "Harmonic Analysis to Determine Contact Characteristics of Concentrated Counterformal Contacts." Proceedings of the ASME 7th Biennial Conference on Engineering Systems Design and Analysis. Volume 1. Manchester, England. July 19–22, 2004. pp. 663-668. ASME. https://doi.org/10.1115/ESDA2004-58544
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