| The freeform optical surfaces can improve the optical performance and opticalutilization. One or several optical elements can replace a large number of spherical andaspherical lenses which will simplify the optical system and make it light weight. Thistype lenses have a widely applications requirement in aerospace, national defense, andmany consumer-oriented industries, and showing an increasing trend. Therefore, thedesign and manufacture of freeform optics is one of the most popular and researchprospect directions. To improve the machining quality of freeform optics is the primarytarget of the manufacturing industry, including the machining accuracy and surfaceroughness.Because of the advantage of high efficiency and high precision, the single pointdiamond turning assisted by fast tool servo (FTS) have received attention from researchinstitutions and scholars of the world, such as MIT and Moore nanotechnology ofAmerica, Tohoku University of Japan, Fraunhofer Institute of Germany. Significantachievement has been achieved. Combined the research of home and board, and someprevious research experience, this dissertation mainly do some research on the twodegree freedom FTS.Most of the existing FTS can only do the linear movement, and the machinedfreeform surfaces are not homogeneous. Otherwise, in the tool path generation methods,the author has not read pertinent literature to talk about how to determine the number ofsampling points, namely the cutting points of per revolution. The both can be consideredas the limitations of the tool path generation method. A new method is taken out to helpdetermine the sampling points. This method is based on the interpolation principle whichcan calculate minimum cutting points. And, a constant scallop height tool pathgeneration method is described which can generate a homogenous free-form surface. Inorder to control the tool marks scallop height, the X-axis tool position must be adjustedin real time. The displacement of arbitrarily adjacent tool contact points are the same. Therefore, the scallop heights are the same which is the homogeneous surface.FTS system and CNC machine tools are two independent systems; the toolmovement is synthesized by the both. Therefore, the synchronized motion of the twosystems is the first problem to fabricate freeform surfaces. At present, most FTSs workat angle-synchronization working mode. FTSs bring the diamond tool to move in and outof the work-piece according to the spindle angle. But, the spindle speed drift will makethe X-axis displacement non-synchronize with the spindle angle which brings machiningerror to work-piece. A two-axis angle-synchronization working mode is described toeliminate the effect of the spindle speed.In order to adjust the tool positions both in X and Z direction realtime, a two-axisFTS is designed which consists of two voice coil motors and four flexure hinges. Thereis on cross talk between two direction movements. This FTS can obtain 0.5mm stroke inboth directions. Experimental tests under open loop conditions are taken out to test thestiffness, damping resonance frequency and the cross talk. The damping ratio is smallerthan 0.04, and there is still micro-size cross talk which may be caused by manufacturingand assembling of the FTS mechanism. The cross talk is reduced to 0.2μm byclosed-loop control. The FTS theoretical model is established and the model parametersare identified by experiments. Several methods are taken out to adjust the PIDparameters. FTS closed-loop controlled performances are tested and the performances inthe two directions are almost the same. The tracking error of a sinusoidal signal is about0.5%, and the movement resolution is 0.05μm.Based on the two-axis FTS and two-axis angle-synchronization working mode, abackpitch machining method is described. After the tool cutting from the excircle to thecenter, the diamond turning machine keeps working, and X direction slide feeding in theopposite direction, then, the tool cuts from center to excircle. The spiral direction of thetwo machining processes is opposite. This process needs the movement of FTS andmachine tools high synchronized; else machining errors will be brought to the workpieceeven destroy the finished surface. The cutting parameters of the second machiningprocess can be set to ultra-precision cutting standard which is propitious to improve the processing quality. The cutting experiments show that the form error and surfaceroughness are improved by 20%.A LVDT is used to achieve the in-situ measurement of freeform surfaces. Severalmeasurement methods of LVDT are described. Zernike Polynomials are used for thesurface fitting, and measuring head's radius compensation is proposed. A tilted flat ismeasured by the LVDT, and the error distribution is obtained. The PV error is about2.5μm while the height difference of the tilted flat is 0.1mm. Error compensation cuttingprocess is implemented by the two-axis FTS. The form error is reduced by 20%, andsurface roughness is improved, too.This dissertation summarized the method to choose diamond tool, and obtained thespecific method to calculate the tool parameters. The effect of tool center error tosinusoidal surface is described. A new method to adjust the tool center position isproposed which is to score two lines on the flat surface, and half of the distance is thetool center height error. If the second line is higher than the first line, the tool is higherthan the spindle center, else the tool is lower. Two height adjustment mechanisms aredesigned to adjust the tool height which can obtain sub-micro adjustable resolution. But,the stiffness of the mechanism is not high enough.The cutting parameters are detailed analyzed and summarized. Based on thefreeform surface property and FTS processing capacity, a method is proposed to definethe cutting parameters. The motion error of the diamond turning machine is measured.The new tool paths and machining methods are certified by cutting stairs surface,sinusoidal surface and tilted flat. The experiments results show that the machining resultdid not obtain the ideal value because of the bad material and machine tool errors. But,to a certain degree, the feasibility and superiority of these new methods are approved.
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