非回转对称微结构表面超精车削轨迹生成及形状误差评价
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摘要
非回转对称微结构表面在成像、照明、精密测量、激光光束整形等领域中得到了越来越广泛的应用，此类表面的超精密加工已经成为了21世纪先进制造技术中的一项关键技术。采用金刚石车削方法实现非回转对称微结构表面加工，具有形状精度高、表面粗糙度好、加工形状可灵活控制等优点，得到了越来越多的重视。车削加工此类表面时，需要同时考虑机床工作台的直线位移和主轴转动的角度，这决定了非回转对称表面车削与传统回转对称表面车削加工在表面成形原理上的差异。车削加工满足要求的非回转对称微结构表面，不仅需要相应的超精密加工设备、良好质量的金刚石刀具，还需要对刀具轨迹生成、形状误差评价、加工仿真等关键技术进行研究。
刀具轨迹是实现加工的基础。根据非回转对称微结构表面车削加工表面成形原理，分别给出了公式描述表面、阵列类表面和离散点描述表面的刀具轨迹计算方法。为保证所加工表面的形状精度，需对刀尖圆弧半径进行补偿，而刀具补偿量通常既有X坐标轴运动分量，又有Z坐标轴运动分量。刀尖圆弧半径补偿后，就使原本单向、匀速进给的X向工作台叠加了一个高频往复运动分量，不利于微结构表面的车削加工。针对上述问题，提出了基于Hermite插值和散乱点插值的两种刀具轨迹生成方法，可将刀尖圆弧半径补偿后的高频的运动分量都分解到Z坐标方向上。其中，基于Hermite插值的刀具轨迹生成算法适用于公式描述的表面，而基于散乱点插值的刀具轨迹生成算法则更适用于阵列类和离散点表示的表面。
形状误差评价是分析加工结果的重要部分。分别给出了非回转对称微结构表面加工结果二维轮廓误差及三维面形误差的评价方法。在进行轮廓误差计算时，采用弧长曲率曲线互相关方法得到测量轮廓与设计轮廓的对应点，根据这些对应点推导了实现轮廓粗匹配时对测量轮廓进行的的旋转、平移参数的快速计算方法，进而采用实数编码遗传算法实现测量轮廓与设计轮廓的精确匹配，得到了轮廓的轮廓误差。在面形误差评价时，采用曲率极值点作为粗匹配的特征点，建立了表面粗匹配和精匹配模型，采用遗传算法依次实现了对上述匹配模型的求解，得到了表面面形误差的评价结果，并对算法的可靠性进行了讨论。
加工仿真是预测形状误差，保证加工质量的有效手段。采用超精密车削加工非回转对称微结构表面时，加工程序复杂、加工参数各异、加工结果易受环境影响。因此，需要参照真实加工系统建立相应的仿真系统，仿真系统不仅包括切削力、运动控制系统、工作台振动、切削刀具轮廓、加工表面三维形貌等模型，并且还包括机床运动和简化的动力学模型，上述所有模型的综合决定了工件的最终加工质量。在机床运动模型中，将机床各运动部件均抽象为具有六个自由度的刚体，并通过坐标变换得到金刚石刀具相对于工件的三维切削轨迹，进而通过采样法建立了加工表面的三维形貌。此仿真系统不仅可以预测加工结果的表面粗糙度，还可以分析主轴转速、刀尖圆弧半径补偿、对刀误差等加工参数对表面形状误差的影响，对实际加工具有指导意义。
加工非回转对称微结构表面时需选择具有合适刀尖几何参数的金刚石刀具，以避免刀具与所加工的表面发生干涉。本文给出了金刚石刀具刀尖圆弧半径、前角、后角等几何参数的选择方法，并加工了多种非回转对称微结构表面。加工的公式描述表面为正弦网格表面，它可作为制作激光核聚变调制靶的模板。加工的阵列类表面为四边形和六边形排布的非球面微透镜阵列，它们在光学系统中具有广泛的应用。在对非球面形状参数进行光学性能优化的基础上，分别设计并加工得到了四边形和六边形排布微透镜阵列模板，对加工结果的形状精度进行了分析，对刀具对心误差对透镜形状误差的影响进行了讨论，并对热压印后非球面微透镜阵列的焦斑和成像性能进行了测试，表明超精密车削方法是加工微透镜阵列元件的一种有效手段。对于离散点描述的表面，成功实现了用图片表示的头像以及用于激光光束整形的连续衍射表面的加工，对刀具轨迹生成算法进行了验证。
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.
刀具轨迹是实现加工的基础。根据非回转对称微结构表面车削加工表面成形原理，分别给出了公式描述表面、阵列类表面和离散点描述表面的刀具轨迹计算方法。为保证所加工表面的形状精度，需对刀尖圆弧半径进行补偿，而刀具补偿量通常既有X坐标轴运动分量，又有Z坐标轴运动分量。刀尖圆弧半径补偿后，就使原本单向、匀速进给的X向工作台叠加了一个高频往复运动分量，不利于微结构表面的车削加工。针对上述问题，提出了基于Hermite插值和散乱点插值的两种刀具轨迹生成方法，可将刀尖圆弧半径补偿后的高频的运动分量都分解到Z坐标方向上。其中，基于Hermite插值的刀具轨迹生成算法适用于公式描述的表面，而基于散乱点插值的刀具轨迹生成算法则更适用于阵列类和离散点表示的表面。
形状误差评价是分析加工结果的重要部分。分别给出了非回转对称微结构表面加工结果二维轮廓误差及三维面形误差的评价方法。在进行轮廓误差计算时，采用弧长曲率曲线互相关方法得到测量轮廓与设计轮廓的对应点，根据这些对应点推导了实现轮廓粗匹配时对测量轮廓进行的的旋转、平移参数的快速计算方法，进而采用实数编码遗传算法实现测量轮廓与设计轮廓的精确匹配，得到了轮廓的轮廓误差。在面形误差评价时，采用曲率极值点作为粗匹配的特征点，建立了表面粗匹配和精匹配模型，采用遗传算法依次实现了对上述匹配模型的求解，得到了表面面形误差的评价结果，并对算法的可靠性进行了讨论。
加工仿真是预测形状误差，保证加工质量的有效手段。采用超精密车削加工非回转对称微结构表面时，加工程序复杂、加工参数各异、加工结果易受环境影响。因此，需要参照真实加工系统建立相应的仿真系统，仿真系统不仅包括切削力、运动控制系统、工作台振动、切削刀具轮廓、加工表面三维形貌等模型，并且还包括机床运动和简化的动力学模型，上述所有模型的综合决定了工件的最终加工质量。在机床运动模型中，将机床各运动部件均抽象为具有六个自由度的刚体，并通过坐标变换得到金刚石刀具相对于工件的三维切削轨迹，进而通过采样法建立了加工表面的三维形貌。此仿真系统不仅可以预测加工结果的表面粗糙度，还可以分析主轴转速、刀尖圆弧半径补偿、对刀误差等加工参数对表面形状误差的影响，对实际加工具有指导意义。
加工非回转对称微结构表面时需选择具有合适刀尖几何参数的金刚石刀具，以避免刀具与所加工的表面发生干涉。本文给出了金刚石刀具刀尖圆弧半径、前角、后角等几何参数的选择方法，并加工了多种非回转对称微结构表面。加工的公式描述表面为正弦网格表面，它可作为制作激光核聚变调制靶的模板。加工的阵列类表面为四边形和六边形排布的非球面微透镜阵列，它们在光学系统中具有广泛的应用。在对非球面形状参数进行光学性能优化的基础上，分别设计并加工得到了四边形和六边形排布微透镜阵列模板，对加工结果的形状精度进行了分析，对刀具对心误差对透镜形状误差的影响进行了讨论，并对热压印后非球面微透镜阵列的焦斑和成像性能进行了测试，表明超精密车削方法是加工微透镜阵列元件的一种有效手段。对于离散点描述的表面，成功实现了用图片表示的头像以及用于激光光束整形的连续衍射表面的加工，对刀具轨迹生成算法进行了验证。
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.
引文
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