Theoretical And Technological Research Of SPDT Machining For Freeform Surfaces Under Precision Constraints

Free surface is a collective name for asymmetric and irregular surfaces.Because of the irregularity of the freeform surface,it brings great convenience to the designer.In the field of shape design,free-form surfaces can give full play to the imagination of designers.In the field of optics,free-form mirrors can greatly improve optical utilization and reduce the structural size of optical systems.With the increasing importance of free-form surfaces in the field of optics,ultra-precision machining of free-form surfaces has become one of the hot topics for domestic scholars.In recent years,single-point diamond turning has become a common method for machining freeform surfaces,because it does not require subsequent processing steps to enable the surface to achieve nanometer-level surface roughness and sub-micron-level contour accuracy.However,most of the research on single-point diamond turning of free-form surfaces is based on parametric surface models.With the triangular mesh surface model becoming the main description of free-form surfaces,it is important to study the method of single-point diamond turning free-form surfaces based on the triangular mesh surface model.In this paper,a precision-driven method of ultra-precision SPDT for machining free-form surfaces with triangular mesh surface as the theoretical model is presented.The aim is to improve the machining efficiency while ensuring the machining accuracy.The data structure of the triangular mesh surface model is analyzed.The topological reconstruction of the data of the triangular mesh surface is completed by programming.In addition,the method of solving the normal vector of each region on the triangular mesh surface is studied,and the normal vectors of vertex are calculated in advance and stored in the topological structure.The spiral trajectory with the best machining effect is selected as the original turning trajectory in this paper,and combined with the method of finding points on the triangular mesh surface,the plane spiral trajectory is projected onto the triangular mesh surface.Based on the principle of single-point diamond turning,three kinds of errors caused by turning trajectory,radial feed error,turning trajectory interpolation error and radius compensation error were analyzed and studied.The theoretical calculation formula of radial feed error and the feasibility of precision driven turning method are verified by plane turning experiments.Combined with NURBS interpolation and interpolation theory,a precision-driven turning trajectory planning method is proposed.The NURBS interpolation method is used in the radial direction to solve the parametric expression of the cross-sectional profile curve of the free-form surface,and the program loop iteration is used to obtain the feed that meets the accuracy requirements to achieve the optimization of radial distribution.In the cutting feed direction,the NURBS interpolation method and bow height error control principle are used to optimize the interpolation point distribution of the turning trajectory.In the tool feed direction,the NURBS interpolation method and bow height error control principle are combined to optimize the interpolation point distribution of the turning trajectory.Finally,radius compensation was performed according to the normal vector of each trajectory point at the triangular grid surface,and the turning trajectory planning was completed.On the NanoForm250 ultra-precision lathe,according to the precision-driven single-point diamond turning free-form surface method proposed in this paper,two free-form surfaces represented by triangular mesh surfaces were turned.The surface roughness of the processed surface was measured by a Talysurf PGI 1240 profiler,and the surface profile of the curved surface was measured by a vhx5000?Among them,the surface roughness of the processed curved surface A is 102.6nm,the PV value is 10.4?m,the RMS is 2.8?m;the surface roughness of the processed curved surface B is 132.4nm,the PV value is 9.9?m,and the RMS is 2.7?m.Taking into account system errors,temperature and other factors,the measured values are more in line with expectations.