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.

考虑了在恒定法向载荷下部分滑动和总滑动状态下的微动磨损。基于切向接触的广义Cattaneo-Mindlin理论和Masing关于力-位移滞后环建模的假设，描述了前向和后向运动的切向力-位移关系。除了临界力和位移参数（表征滑动的触发）之外，该模型还包括一个无量纲拟合参数，用于调整摩擦接触界面的切向接触刚度。推导了微动环主要摩擦学参数的显式表达式，包括滑移指数和信号指数。所提出的现象学建模方法已应用于分析从文献中获取的两组实验数据。已经表明，实验观察到的滑移指数和滑移率之间的有理类型的简单关系对应于相应的基于模型的预测关系的总滑移渐近。从部分滑移状态到总滑移状态过渡的已知定量标准以刚度参数表示，并制定了一种新的几何过渡标准。