Analytic solution for the limiting shape of profiles due to fretting wear

Abstract

We consider fretting wear due to tangential oscillations of two contacting bodies. For small oscillation amplitudes, the wear occurs only in a circular slip zone at the border of the contact area. With increasing number of cycles, the wear profile tends to a limiting form, in which no further wear occurs. Under assumption of a constant coefficient of friction, the limiting form of the wear profile does not depend on the particular wear criterion and can be calculated analytically. An explicit analytic solution is presented for arbitrary initial shape and illustrated for the cases of parabolic and conical shapes.

Wear Analysis of a Heterogeneous Annular Cylinder

“…The MDR was proposed by Popov and Heß for the fast calculation of various contact problems [9]. Note that it provides not approximation but exact solutions for axisymmetric contacts by mapping of three-dimensional contacts onto one-dimensional contacts, and has been applied to studying on different wear problems, e.g., fretting wear [10] and gross slip wear [11], which were also validated by experiment [12] or by the finite element method [13]. The advantage of the MDR is very fast calculation; the disadvantage is that (for wear problems) it can only be applied to axially-symmetric contact problems.…”

Limiting shape of profile due to dual-mode fretting wear in contact with an elastomer

“…For the cases of pure tangential oscillations and elastic contact, the shakedown profiles have been calculated analytically in the paper. 26 In the paper, 30 the wear process has been simulated and it was confirmed that with increasing number of oscillation cycles the shape of worn profile tends to the limiting form found in Popov. 26 The same procedure as used in Dimaki et al 27 was additionally validated by comparison with finite element simulations in Dimaki et al 28 Thus, the approach of the paper 26 can be considered as validated by at least two independent simulation methods.…”

“…26 The same procedure as used in Dimaki et al 27 was additionally validated by comparison with finite element simulations in Dimaki et al 28 Thus, the approach of the paper 26 can be considered as validated by at least two independent simulation methods. In the present paper, we will generalize the treatment suggested in the paper 26 to the dual-mode wear (superposition of normal and tangential oscillations) and the case of visco-elastic contact.…”

Method of Dimensionality Reduction in Contact Mechanics and Friction: A User's Handbook. Ii. Power-Law Graded Materials

“…These include tribology, nanotechnology, biostructure mechanics and medicine. Completely analogous to the calculation of wear profiles between homogeneous materials [19,20], the investigation of fretting between elastically inhomogeneous materials should no longer constitute a barrier.…”

“…(18), (19) as well as Eqs. (22), (23) in the particular case k  0 the solutions of the Hertzian contact exactly follow.…”