The traveling wave surface is an important surface in the structured surface,which has excellent reduction friction performance.In order to grind the traveling wave dimple surface with array pattern,a method of planar topological mapping for grinding structured surfaces was proposed.Based on the theory of point set topology,the topological feature of the traveling wave unit and arrangement was analyzed,and the feature parameters were extracted.Combined with the generating mechanism of dimple surface during grinding,the topological space mapping relationship between the grinding wheel and the workpiece during grinding was established,and the structured abrasive cluster grinding wheel was designed.MATLAB software was used to simulate and analyze the grinding process of the traveling wave surface,the influence law of the relevant parameters was obtained,and the grinding of the structured surface was realized by grinding experiments.The results show that the structured grinding wheel designed based on the topology theory can realize the grinding of the dimple surface with an array traveling wave structure,and the topological properties of the traveling wave dimple surface remain unchanged after grinding.The topological feature parameters change correspondingly with the change of grinding parameters.