# Effect of Wheel Path in Raster Grinding on Surface Accuracy of an Off-Axis Parabolic Mirror
###### Abstract
[22] reduced the influence of the geometric error of a grinding wheel on the accuracy of the aspheric profile by setting the initial grinding cycle. A new compensation approach was also developed to achieve wheel path optimization by modifying the NC wheel path for the next grinding cycle, with the grinding profile measured using a Talysurf profiler. [PERSON] et al. [23] built a theoretical scallop height model, and proposed a method to control the generation of an equal-scallow-height wheel path, which led to the uniform distribution of the scallop height of the freeform surface. The scallop height has an important influence on the surface roughness and surface morphology after surface grinding. Therefore, [PERSON] et al. [24] studied a mathematical model of the scallop height in rotary surface grinding. According to the corresponding relationship between the scallop height and the surface roughness, combined with the microscopic observation of the surface morphology, the influence of process parameters on the surface roughness and surface morphology upon precision grinding of a silicon nitride ceramic rotary surface workpiece was described. [PERSON] et al. [18] carried out ultra-precision grinding of non-rotational asymmetric biconical free-form optical elements using different raster wheel paths. The effects of grinding strategy, wheel path, and scallop height on the grinding contour accuracy and surface quality of biconical free-form optical devices were discussed. [PERSON] et al. [8] proposed a new method to calculate the surface scallop height of nano-ziro2 ceramics during ultra-precision grinding. This method can obtain a surface scallop height that conforms to the three-dimensional roughness sampling characteristics, and realize the prediction of the three-dimensional roughness following ultra-precision grinding. [PERSON] et al. [25] proposed a multi-scale model that uses different wheel paths for grinding and predicts the surface topography of micro-aspheric-cylindrical structural array (MACSA) mold ground. In summary, the method of controlling the wheel path to complete the entire process of free-form surface processing is widely used. And the grinding process of the off-axis parabolic surface of monocrystalline silicon can be planned and optimized based on the principle of scallop height generation. The off-axis parabolic surface is a non-rotating asymmetric surface, and is more suitable for raster path grinding. And the off-axis parabolic surface has the geometric characteristics of double curvature (the curvature in the meridian direction is different from that in the arc vector direction), and a raster path that can be divided into two wheel paths: stepping along the meridian direction and stepping along the arc vector direction [26]. There are few studies on the influence of different wheel paths on the surface shape error of a workpiece. Therefore, two different wheel paths of off-axis paraboloid grinding are compared in this paper. The scallop height, surface roughness, and surface shape error distribution of the machined surface are measured. Based on the scallop height model and the mapping relationship between the scallop height and the surface shape error, the calculation of the scallop height value and the analysis of the distribution of the surface error are realized. The influence of different raster paths on the scallop height and shape error is explained, and the wheel path suitable for off-axis paraboloid grinding is optimized.