A two-dimensional wear contact problem with a stick zone is considered for a Hertzian cylindrical contact configuration and Archard’s equation of wear. A one-free-parameter simple model for the wear volume accumulation during the reciprocating wear process, which occurs in two symmetric variable slip zones, is developed and validated against numerical solutions available in the literature. The developed model takes into account the observed effect of non-monotonic evolution of the friction dissipated energy. The presented analytical modeling framework does not make use of any fitting parameters to be evaluated from experiments. The only free dimensionless parameter is suggested to be fixed based on numerical simulations for the maximum of the frictional damage that is proportional to the cumulative wear rate.

中文翻译：

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偏滑赫兹接触中磨损累积的简单模型

对于 Hertzian 圆柱接触配置和 Archard 磨损方程，考虑了具有粘性区的二维磨损接触问题。针对往复磨损过程中磨损体积累积的单自由参数简单模型，该模型发生在两个对称的可变滑移区中，并针对文献中可用的数值解进行了验证。所开发的模型考虑了观察到的摩擦耗散能量的非单调演化的影响。所提出的分析建模框架不使用任何从实验中评估的拟合参数。建议根据与累积磨损率成比例的最大摩擦损伤的数值模拟来固定唯一的自由无量纲参数。