The Research On Tool Path Planning Of Diamond Turning Of Non-Rotationally Symmetric Optical Surface

The optical system designed by aspheric surface can correct many lens aberrations, and it can reduce the energy loss and get the high quality image at the same time, therefore it has been widely used. Due to the introduction of more design parameters, the non-rotationally symmetric (NRS) surface has a more broad application prospects than the symmetric surface. Because of the complexity and high precision requirement of NRS surface, how to manufacture it efficiently and precisely remains a difficult problem in the field of optical manufacturing. In recent years, the diamond turning technology based on fast tool servo (FTS) has been considered as a revolutionary technology to achieve this goal and become a hot spot of international research. The contradiction between the frequency and stroke of the existing FTS devices limits the scope of the FTS technology. This thesis studies on the tool path planning that based on surface decomposition for the FTS. By the surface decomposition, not only the processing of NRS surface of large gradient can be achieved, but also the designers can estimate the manufacturability of the product at the beginning and guide the design process, if the results of decomposition were integrated in the optical design software.In this thesis, the present processing methods of NRS optical surface were analyzed, and the processing principle and processing system of diamond turning technology based on FTS were introduced emphatically. The research status of FTS diamond turning technology based on FTS was reviewed in terms of the new FTS device, the tracking control of tool path, and the methods of path generation. Combined with live turning technology, the principle of planning FTS tool path based on surface decomposition was illustrated.Then the equations of the typical NRS surfaces under the workpiece coordinate system were derived, and the establishing method of freeform surface model was introduced. Combined with the principle of FTS machining system, and according to tool spiral path, the thesis derived the establishing method of NRS surface machining model, this model is a series discrete spots on the spindle angle under the workpiece coordinate. The influences of the feed of every rotation, spindle speed and pulse numbers of optoelectronic encoder on the surface processing model were analyzed. The surface roughness was directly affected by the size of every rotation feed, and both of the frequency of Z axis vector height of cutter-contact point that is relative to spindle angle and the maximum amplitude of reciprocating motion of FTS can be decreased by increasing the feed of every rotation. The increasing of pulse numbers can decrease output step lengths of FTS on circumferential direction, however, more pulse numbers could lead to the delay of digital analog conversion, even the pulse numbers would be lost. So the less pulse numbers should be chosen on the premise of meeting the requirements of interpolation error. On the premise of fixing the feed of every rotation and pulse numbers, increasing the spindle speed can enhance the output frequency of trigger pulse, and requests that the FTS device should have the bigger reciprocation frequency at the same time.The existing methods of surface decomposition were induced into the angle of practical machining (Fourier Series Expansion Method, Mean Method) and idea of surface approaching (Continuous Least Square Method). The amount of calculation of the Fourier Series Expansion Method was very large, which can introduce approximate error easily and couldn't get analytical expression. In contrast, the geometric meaning of Mean Method is more obvious, by introducing the concept of surface section line, the analytical expression and minimum blank of typical regular NRS surface which is decomposed by Mean Method can be deduced, but these above two kinds of methods were just used for regular NRS surface. The result got from continuous least square method is simple and can be used easily, but in this process, approximate error has been introduced, because of using the power series. So inspired by the continuous least square method, Fitting Decomposition Method has been developed, and the effects of sampling point, sampling mode and fitting function on the result of decomposition was also discussed in this thesis. The method takes the machining model as foundation of decomposition, so it can be used for any NRS surface and its decomposition effect is better than Continuous Least Square Method. By adopting the asymmetric amplitude as evaluation index, both of the decomposition effects of toric surface and off-axis surface were relative better by Mean Method and Fitting Decomposition Method, so the feasibility of Fitting Decomposition Method has been proved. Combined with new type FTS device with double frequencies, the decomposition program of frequency-dividing fitting has been proposed, and given full play to the advantage of devices of different driving modes. In addition, the program can meet the requirements of evaluating manufacturability quickly and diversity of designing NRS surface.According to the characteristics of FTS diamond turning, how to choose the tip shape and the geometric parameters of the diamond tool reasonably have been discussed by the thesis. Considering the tool setting and cutting materials for FTS, the rake angle of diamond tool should be 0o, and the clearance angle, nose radius and wrap angle should meet the non-interference conditions, which are respectively the circumferential, the circular arcs and the radial direction. Due to the tool path obtained by decomposition is just the tool contact trajectory, and in order to avoid the overcut of tool nose, a method of generating the cutter location data by calculating the offset has been proposed by the thesis.By studying on the method of surface decomposition and tool location data generation, this thesis extended the application scope of surface decomposition for any NRS surface, and combined with new type FTS device with double frequencies, the machining capacity of FTS by diamond turning could be expanded.