A theoretical justification of the slip index concept in fretting analysis

Abstract

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