## 1 Introduction
At the same time, the VLSGW has better workpiece surface topology and wear resistance than the USGW. Based on the principle of grinding kinematics and the topology of point sets, [PERSON] et al. [12] proposed a topological mapping grinding method for structured concave surfaces. In the study, a topological space consisting of a workpiece and grinding wheel was established, and the topological features of the structural pits and grinding wheel were extracted. The topological mapping equation of the grinding process was established, and the structural grinding wheel was designed according to the topological mapping equation. Finally, according to a grinding geometry simulation, the influence of grinding parameters on the surface topography of the pits was studied, and grinding experiments were carried out. [PERSON] et al. [13] studied the influence of the geometric parameters of a structured grinding wheel on the geometry of a structured surface during grinding. Firstly, the geometric parameters of the structured grinding wheel were determined. The synthetic geometric parameters of the structure surface were calculated, and the numerical and simulation models of the structured grinding wheel and grinding process were established according to the relevant working conditions. The results showed that the geometric parameters of each wheel affected the geometry of the structure surface at different rates. Grinding experiments were carried out, and the results showed that there was significant compatibility between the predicted surface and the machined surface, reflecting the accuracy of the proposed method for machining structured surfaces by grinding. [PERSON] et al. [14] proposed a grinding surface microstructure method based on structured grinding wheels. Wire Electrical Discharge Machining (WEDM) technology was used to carry out structured dressing on the surface of a grinding wheel. The microstructure of a sapphire surface was ground with the structured grinding wheel after dressing. The effects of grinding speed, grinding depth, and feed rate on the surface roughness at the bottom of the micro-grooves in sapphire under both up-grinding and down-grinding conditions using structured grinding wheels were investigated. The results showed that the surface morphology of the micro-grooves after grinding remained intact, and the surface quality from down-grinding is better than that of up-grinding. [PERSON] et al. [15] studied the law of the influence of the grinding force of an ordered grinding wheel on workpiece surface geometry. Firstly, according to the parameters of the ribbed drag-reducing surface, a misaligned grinding wheel that can realize the machining of the ribbed drag-reducing surface was designed. Secondly, a simplified model of the grinding process of the rib-reducing surface was established, and a mechanical simulation of the workpiece surface morphology was carried out based on the finite element method. Finally, the influence of grinding speed, grinding depth, grain angle, and layout parameters on the surface geometry of the rib was studied, and the relationship between grinding force and surface topography was comprehensively discussed. In order to analyze the influence of grinding process parameters on the reflection effect, [PERSON] et al. [16] carried out a theoretical exploration of the grinding process and workpiece surface topography of a grooved structured wheel with a large spiral angle. A macroscopic mathematical model and a microscopic particle random distribution model of the large spiral angle grooved grinding wheel were established, and the cutting process of the chip-cutting edge of the grinding wheel was deduced and calculated. Based on a model of the mechanism involved in grinding surface macro profile generation, the numerical mapping relationship between the spiral groove control parameters and process parameters and the reflection effect coefficient was calculated.