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Research Article | Open Access

A theoretical justification of the slip index concept in fretting analysis

Ivan I. ARGATOV^¹, Young S. CHAI^²()

1 Institut für Mechanik, Technische Universität Berlin, 10623 Berlin, Germany

2 School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea

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Abstract

Fretting in the partial-slip and gross-slip regimes under a constant normal load is considered. The tangential force–displacement relations for the forward and backward motions are described based the generalized Cattaneo–Mindlin theory of tangential contact and Masing’s hypothesis on modelling the force–displacement hysteretic loop. Besides the critical force and displacement parameters (characterizing the triggering of sliding), the model includes one dimensionless fitting parameter that tunes the tangential contact stiffness of the friction–contact interface. Explicit expressions are derived for the main tribological parameters of the fretting loop, including the slip index and the signal index. The presented phenomenological modelling approach has been applied to the analysis of two sets of experimental data taken from the literature. It has been shown that the experimentally observed simple relation of a rational type between the slip index and the slip ratio corresponds to the gross-slip asymptotics of the corresponding model-based predicted relation. The known quantitative criteria for the transition from the partial slip regime to the gross slip regime are expressed in terms of the stiffness parameter, and a novel geometric transition criterion is formulated.

Keywords

fretting wear slip index signal index partial slip energy ratio

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Volume 11 Issue 7,
July 2023

Pages 1265-1275

DOI: 10.1007/s40544-022-0662-1

Cite this article:

ARGATOV II, CHAI YS. A theoretical justification of the slip index concept in fretting analysis. Friction, 2023, 11(7): 1265-1275. https://doi.org/10.1007/s40544-022-0662-1

10.1007/s40544-022-0662-1.F001 Fig. 1Backbone curve for the Masing model of the tangential reaction of a fretting contact interface.
10.1007/s40544-022-0662-1.F002 Fig. 2Schematic diagram for a hysteresis loop of the Masing model in partial slip. (A hysteresis curve, which enters the gross slip stage, has been shown in Fig. 3.)
10.1007/s40544-022-0662-1.F003 Fig. 3A characteristic friction loop in the gross slip regime, when $x_{0} > x_{*}$ .
10.1007/s40544-022-0662-1.F004 Fig. 4Transition criteria.
10.1007/s40544-022-0662-1.F005 Fig. 5Variation of the dimensionless parameters s, $η,$ and $χ$ as functions of $ξ .$
10.1007/s40544-022-0662-1.F006 Fig. 6Variation of the slip ratio s vs. the modified slip index $δ / μ$ . Experimental data is according to Refs. [ 11 , 16 ].
10.1007/s40544-022-0662-1.F007 Fig. 7Effect of the stiffness parameter m on the variation of the backbone curve for $x_{0} < x_{*}$ . Effect of the different static and kinetic coefficients of friction ( $μ_{s} > μ_{k}$ ) on the variation of the backbone curve for $x_{0} > x_{*}$ .
10.1007/s40544-022-0662-1.F008 Fig. 8Variation of the energy ratio $η$ vs. the displacement amplitude $x_{0}$ . Experimental data is according to Ref. [ 21 ]. Curve 1 is drawn based on the constant friction coefficient model; curve 2 takes into account a drop of the friction coefficient from 0.9 to 0.85 in the transition to sliding.

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