In practice, even the tiny relative reciprocating motion generated by external load or environmental vibration can cause interface wear. In this work, three-dimensional (3D) finite element analysis (FEA) is used to investigate the fretting wear between deformable crossed parabolic cylinders. Fretting is achieved by the application of a periodic displacement-controlled load, while the contact pair is defined as the same material, i.e., Carbon Steel/Carbon Steel, Copper Alloy/Copper Alloy, and Aluminum Alloy/Aluminum Alloy. Meanwhile, three different axis crossing angles are also studied, i.e., 45°, 60°, and 90°. Originally, a wide range of coefficients of friction (COFs) are applied to the interface without considering the damage. The results show that, when the COF is sufficiently large (µ = 1), the junction growth and the tangential load increase significantly in the first loading cycle, but then become gradually stable. Subsequently, the Archard wear model is applied to the frictional interface. Empirical equations for the initial gross slip distance and the wear volume at the end of the partial slip are established in turn. Furthermore, an empirical equation for the wear volume of a single fretting cycle is established, which is in good agreement with the FEA results. Lastly, the effect of relevant parameters on the wear volume for a single fretting cycle under elastic condition is discussed, but also the evolution of wear volume in the early stage of cyclic fretting. All the results are normalized, enabling their application to the 3D fretting wear of other material pairs.

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