Tool Path Generation And Form Error Evaluation For Ultra-precision Turning Of Non-rotational Symmetric Microstructured Surfaces

Non-rotational symmetric microstructured surfaces have been widely applied inthe fields of imaging, illumination, precision measurement and laser beam reshaping.The fabrication technique of such surfaces has become a key to the advancedmanufacture technologies in the21th century. Diamond turning of these surfaces hasthe advantages of high form accuracy, excellent surface roughness and the flexiblegeometries. Thus, it attracts more and more attention. During the turning process,both the linear motion of the sliders and the rotated angle of the spindle need to betaken into account. This distinguishes the non-rotational symmetric turning from thetraditional turning in the principle of surface generation. To obtain qualified surfaces,not only the ultra-precision machine and the high quality diamond tools are needed,but also the key technologies like tool path generation, form error evaluation andmachining simulation should be further studied.The fabrication is on the foundation of tool path generation. According to theturning principle of non-rotational symmetric surfaces, the algorithms are providedto calculate the tool paths of the fomula represented surfaces, array distributedsurfaces and the discrete points represented surfaces. To satisfy the accuracyrequirements, the tool nose radius needs to be compensated with the compensationcomponents both in X and Z direction. Thus, a high frequency motion componentwould be added onto the X slider which should move in one direction with aconstant speed. This high frequency motion is disadvantageous to the fabricationprocess. To solve the above problem, two tool path generation algorithms arebrought out. One is based on the Hermite interpolation and the other is based on thescattered data interpolation, both of them can decompose the high frequency motionto the Z direction. The first tool path generation method is suited for the fomularepresented surfaces and the second one is appropriate for the array distributed anddiscrete points represented surfaces.The form error evaluation is an important part of the analyzation of themachined results. Methods for evaluating the2-D profiles and3-D geometries of thenon-rotational symmetric surfaces are proposed. When evaluating measured profiles,the cross correlation of arc length-curvature curves was adopted to obtain thecorresponding points on measured and designed profiles. Based on thesecorresponding points, a high effecient algorithm was developed to estimate therotation and the translation parameters for initial matching. The real coded geneticalgorithm was adopted to fine match the measured profile with the designedtemplate. Then, the profile error can be characterized. The local extreme curvature points are used as the feature points for initial matching the measured with thedesigned surface. After establishing the models of initial and fine matching, thematching models were both solved using the genetic algorithm. Then the form errorwas obtained and the robustness of the algorithm was discussed.Simulation is an effective way to predict the form error and to ensure themachining quality. During the turning process of non-rotational symmetric surfaces,the numerical control program is complicated, the machining parameters are variedand the results also are affected by the environment. Thus, it is highly needed toestablish a simulation system according to the real machining system. Thesimulation system includes not only the model of the cutting force, the motioncontrol system, the vibration of the sliders, the cutting tool geometry, the surfacegeneration, but also the kinematic and the simplified dynamic model of the machine.In the kinematic model, each moving part can be simplified as a rigid body with sixdegree of freedoms and the3-D cutting tool path can be obtained by the coordinatetransformation. Then the3-D geometry of the machined surface can be obtainedbased on a sampling mehtod. This simulation system can not only predict the surfaceroughness, but also can be used to analyze the influence of the spindle speed, thetool nose radius compensation and the tool alignment error on the form error whichwould be of instructive significance for the real machining process.To avoid the interference between the diamond tool and the surface to befabricated, diamond tools with proper geometry parameters are needed. Method fortool geometry selection including the tool nose radius, rake angle and clearanceangle was proposed. Many kinds of non-rotational symmetric surfaces werefabricated. The sinusoidual grid surface is a fomula represented surface which canbe used as the mold to fabricate the pertubated target for the inertially confinedfusion experiment. The array distributed surfaces are square and hexagonaldistributed aspherical micro lens array (MLA) which are widely used in opticalsystems. Based on the optical design, the molds of the MLA were fabricated with theform error was evaluated, the affect of the tool alignment error on the form error ofthe micro lens was discussed and the focal spots and the image character were tested.The tested results show that the ultra-precision turning menthod is an excellent wayfor the fabrication of MLA. As to the discrete points represented surfaces, a figuregenerated form a picture and two continuous diffractive surfaces were successfullyfabricated which further validate the tool path generation algorithm.