非球面轨迹包络磨削加工机理研究
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摘要
随着微电子、光电子、太阳能光伏技术的发展以及光学与电子学的融合及国内外市场竞争的日趋激烈,以非球面光学元件为代表的先进技术日益成为一个国家制造实力的重要体现,发展新的非球面加工技术,提高加工精度和效率,降低加工成本是不懈追求的目标。非球面轨迹包络磨削法可减少对设备精度要求,从理论上大幅减少了砂轮磨损,可以实现非球面光学元件的超精密加工。发展非球面轨迹包络磨削法,深入进行相关加工工艺研究,符合我国发展需求,能迅速提高我国非球面超精密加工水平。但是目前的非球面轨迹包络磨削法仍然存在砂轮磨损不均匀、加工表面粗糙度不均匀等问题,限制了其应用。本文针对轨迹包络磨削过程中存在的问题,对轨迹包络磨削机理进行了深入研究。主要内容如下：
根据非球面轨迹包络磨削成形原理,分析了圆弧回转面砂轮的结构、磨削过程中磨削点顺次移动提高磨粒有效利用过程,研究了轴对称非球面、非轴对称非球面加工中磨削方式、砂轮直径、砂轮宽度、砂轮端部圆弧半径等因素对轨迹包络磨削过程的影响。
建立了非球面轨迹包络磨削中磨削点的运动模型,通过建立圆弧回转面砂轮磨削点与加工曲面位置关系数学方程,提出了非球面磨削点绕砂轮端部圆弧圆心运动的角速度概念,得出了圆弧轨迹包络磨削加工中磨削点的运动角速度方程,并推导出非球面轨迹包络磨削点的线速度方程式,分析了非球面曲率半径、砂轮端部圆弧半径、非球面二次曲线形状参数等磨削点线速度的影响,为优化砂轮磨削加工参数,实现砂轮均匀磨损提供理论基础。基于非球面磨削点速度计算,建立了描述单位时间内轴对称非球面磨削量的数学模型,通过分段进给,控制砂轮进给速度,实现轴对称非球面恒去除量磨削。实验证明恒去除量磨削可以基本实现砂轮的均匀磨损。提出单位时间砂轮去除量和参与磨削的砂轮的面积之比λ,它可以作为影响圆弧回转面砂轮均匀磨损的特征值。理论分析表明：λ与砂轮端部圆弧半径、非球面二次曲线顶点曲率半径、非球面二次曲线的形状参数以及磨削的坐标等有关,磨削实验结果与理论分析一致。
建立圆弧回转面砂轮形状误差数学模型,分析了砂轮修整过程中砂轮对刀误差、砂轮半径、砂轮端部圆弧半径对砂轮修整误差的影响。建立轴对称非球面砂轮磨削对刀误差数学模型,得到存在对刀误差时的轴对称非球面子午截面磨削曲线方程,分析不同方向对刀误差对轴对称非球面形状精度的影响,结果表明,砂轮对刀出现误差影响轴对称轴对称非球面的母线形状和位置。
分析圆弧回转面砂轮与被加工非球面接触弧长的基础上研究非球面零件轨迹包络磨削过程中磨削力的规律,结果表明非球面轨迹包络磨削过程中磨削力数值较小磨削力随磨削点位置变化幅度有限,砂轮的种类、性能等因素对磨削力有较大影响。
通过对非球面轨迹包络磨削表面形成过程的分析,建立了轴对称、非轴对称非球面表面残留高度数学模型,分析了非球面曲率半径、砂轮端部圆弧半径、砂轮进给速度对非球面残留高度的影响。结果表明通过改变砂轮进给速度,控制砂轮移动间隔,可以改变磨削表面粗糙度,改善非球面磨削表面粗糙度均匀性。
通过对非球面轨迹包络磨削机理的研究,提出了兼顾表面粗糙度和面形精度的非球面轨迹包络磨削加工新工艺。在轴对称非球面磨削中可以采用恒去除量磨削粗磨,等残留高度和等λ值精磨；在非轴对称非球面磨削中,可以采用等残留高度磨削,等λ值磨削。
With the development of microelectronics, optoelectronics, solar photovoltaic technology and continuous integration of optics and electronics and increasingly fierce competition in the domestic market, advanced manufacturing technology of aspheric optical components is increasingly becoming an important manifestation of a country's manufacturing strength. It is the constant pursuit of the goal to improve the aspheric machining accuracy, efficiency and reduce the aspheric machining costs. Arc trajectory envelope grinding method (AEGM) is not high on the equipment precision requirement, and greatly reduces the grinding wheel wear, which can realize ultra-precision machining of aspheric optical element. However, there are some problems in grinding with AEGM, such as uneven grinding wheel wear, surface roughness of uneven, which limits its application. Development of aspheric arc trajectory envelope grinding method can rapidly improve our aspheric level of ultra-precision machining, which are in line with our development needs. Aimed at the existing problems in the process of arc trajectory envelope grinding, this paper makes in-depth research on the mechanism of AEGM, the main contents are as follows:
According to aspheric grinding principle with AEGM, structure of the arc revolving surface wheel has been analyzed and the law of grinding point sequentially mobile has been studied in grinding, which can improve effective utilization of abrasive grains. And some factors affecting arc trajectory envelope grinding have been studied, such as grinding methods of axisymmetric aspheric surface and non-axisymmetric, maximum diameter of the wheel, width of the wheel, the wheel end arc radius and others.
Firstly, the motion model of grinding point has been established in grinding aspheric surface with AEGM in this paper,. Then the concept of the angular velocity of grinding points around the arc center of the wheel end has been put forward by relationship between arc wheel grinding point and the processing curve position, and the angular velocity of grinding point has been obtained in grinding with AEGM. On this basis, the linear velocity equation of grinding point is deduced, and some factors, which affect the linear velocity, have been studied, such as the radius of the arc of the wheel end, the aspherical conic shape parameters, etc. Secondly, mathematical model of axis-symmetrical aspheric surface grinding volume within unit time has been established by velocity calculation formula of grinding point in grinding aspheric surface, and axisymmetric aspheric constant removal grinding has been realized through the sub-feed control wheel feed rate. Experiments show that constant removal grinding can basically achieve uniform wear of the wheel. Finally, the ratio (λ) of the area of the wheel in grinding and aspheric removal within a unit time has been proposed, which will affect uniform wear of the wheel. Theoretical analysis shows that the value of λ has nothing to do with the feeding speed of the wheel,but is associated with the arc radius of the wheel end, aspheric quadratic curve vertex radius of curvature, aspherical shape parameters of the quadratic curve, and a grinding coordinates, etc. The results are in accordance with the theoretic analysis.
Based on the Mathematical model of shape error in dressing arc revolving surface wheel, some influencing factors are analyzed in dressing the wheel, such as wheel setting error, radius of the wheel and arc radius of the wheel end. At the same time, by means of establishing mathematical model of tool setting errors in grinding axisymmetric aspheric surface, meridional cross curve equation of axisymmetric aspheric surface is deduced when tool setting errors exist. And influence of tool setting error in different directions on shape accuracy of axisymmetric aspheric surface is analyzed. The results show that tool setting errors affect the generatrix shape and position of axisymmetric aspheric surface.
Based on analyzing the contact are length between arc revolving surface wheel and aspheric surface, the rule of grinding force in grinding aspheric surface with AEGM is studied. Experiments show that the grinding force is small in grinding with AEGM, wheel types and performance and other factors have a greater impact on the grinding force.
Through surface forming analysis in grinding aspheric surface with AEGM, residual height mathematical model of aspheric surface is established, and the influence of aspherical radius of curvature, radius of the wheel ends and wheel feed rate on residual height is analyzed. The results show that grinding surface roughness can be adjusted by changing the feeding speed of the wheel and grinding walking control interval, which is an effective means to improve uniform roughness of aspheric in grinding.
According to study on machining mechanism of trajectory envelope grinding method for aspheric surface, a new technology is proposed in grinding aspheric surface with AEGM which compromises roughness and surface precision surface. That is coarse grinding with the constant removal grinding firstly and fine grinding with constant scallop-height grinding and constant value of λ in grinding axisymmetric aspheric surface. For non-axisymmetric aspheric surface, constant scallop-height grinding and constant value of A are adopted in grinding.
根据非球面轨迹包络磨削成形原理,分析了圆弧回转面砂轮的结构、磨削过程中磨削点顺次移动提高磨粒有效利用过程,研究了轴对称非球面、非轴对称非球面加工中磨削方式、砂轮直径、砂轮宽度、砂轮端部圆弧半径等因素对轨迹包络磨削过程的影响。
建立了非球面轨迹包络磨削中磨削点的运动模型,通过建立圆弧回转面砂轮磨削点与加工曲面位置关系数学方程,提出了非球面磨削点绕砂轮端部圆弧圆心运动的角速度概念,得出了圆弧轨迹包络磨削加工中磨削点的运动角速度方程,并推导出非球面轨迹包络磨削点的线速度方程式,分析了非球面曲率半径、砂轮端部圆弧半径、非球面二次曲线形状参数等磨削点线速度的影响,为优化砂轮磨削加工参数,实现砂轮均匀磨损提供理论基础。基于非球面磨削点速度计算,建立了描述单位时间内轴对称非球面磨削量的数学模型,通过分段进给,控制砂轮进给速度,实现轴对称非球面恒去除量磨削。实验证明恒去除量磨削可以基本实现砂轮的均匀磨损。提出单位时间砂轮去除量和参与磨削的砂轮的面积之比λ,它可以作为影响圆弧回转面砂轮均匀磨损的特征值。理论分析表明：λ与砂轮端部圆弧半径、非球面二次曲线顶点曲率半径、非球面二次曲线的形状参数以及磨削的坐标等有关,磨削实验结果与理论分析一致。
建立圆弧回转面砂轮形状误差数学模型,分析了砂轮修整过程中砂轮对刀误差、砂轮半径、砂轮端部圆弧半径对砂轮修整误差的影响。建立轴对称非球面砂轮磨削对刀误差数学模型,得到存在对刀误差时的轴对称非球面子午截面磨削曲线方程,分析不同方向对刀误差对轴对称非球面形状精度的影响,结果表明,砂轮对刀出现误差影响轴对称轴对称非球面的母线形状和位置。
分析圆弧回转面砂轮与被加工非球面接触弧长的基础上研究非球面零件轨迹包络磨削过程中磨削力的规律,结果表明非球面轨迹包络磨削过程中磨削力数值较小磨削力随磨削点位置变化幅度有限,砂轮的种类、性能等因素对磨削力有较大影响。
通过对非球面轨迹包络磨削表面形成过程的分析,建立了轴对称、非轴对称非球面表面残留高度数学模型,分析了非球面曲率半径、砂轮端部圆弧半径、砂轮进给速度对非球面残留高度的影响。结果表明通过改变砂轮进给速度,控制砂轮移动间隔,可以改变磨削表面粗糙度,改善非球面磨削表面粗糙度均匀性。
通过对非球面轨迹包络磨削机理的研究,提出了兼顾表面粗糙度和面形精度的非球面轨迹包络磨削加工新工艺。在轴对称非球面磨削中可以采用恒去除量磨削粗磨,等残留高度和等λ值精磨；在非轴对称非球面磨削中,可以采用等残留高度磨削,等λ值磨削。
With the development of microelectronics, optoelectronics, solar photovoltaic technology and continuous integration of optics and electronics and increasingly fierce competition in the domestic market, advanced manufacturing technology of aspheric optical components is increasingly becoming an important manifestation of a country's manufacturing strength. It is the constant pursuit of the goal to improve the aspheric machining accuracy, efficiency and reduce the aspheric machining costs. Arc trajectory envelope grinding method (AEGM) is not high on the equipment precision requirement, and greatly reduces the grinding wheel wear, which can realize ultra-precision machining of aspheric optical element. However, there are some problems in grinding with AEGM, such as uneven grinding wheel wear, surface roughness of uneven, which limits its application. Development of aspheric arc trajectory envelope grinding method can rapidly improve our aspheric level of ultra-precision machining, which are in line with our development needs. Aimed at the existing problems in the process of arc trajectory envelope grinding, this paper makes in-depth research on the mechanism of AEGM, the main contents are as follows:
According to aspheric grinding principle with AEGM, structure of the arc revolving surface wheel has been analyzed and the law of grinding point sequentially mobile has been studied in grinding, which can improve effective utilization of abrasive grains. And some factors affecting arc trajectory envelope grinding have been studied, such as grinding methods of axisymmetric aspheric surface and non-axisymmetric, maximum diameter of the wheel, width of the wheel, the wheel end arc radius and others.
Firstly, the motion model of grinding point has been established in grinding aspheric surface with AEGM in this paper,. Then the concept of the angular velocity of grinding points around the arc center of the wheel end has been put forward by relationship between arc wheel grinding point and the processing curve position, and the angular velocity of grinding point has been obtained in grinding with AEGM. On this basis, the linear velocity equation of grinding point is deduced, and some factors, which affect the linear velocity, have been studied, such as the radius of the arc of the wheel end, the aspherical conic shape parameters, etc. Secondly, mathematical model of axis-symmetrical aspheric surface grinding volume within unit time has been established by velocity calculation formula of grinding point in grinding aspheric surface, and axisymmetric aspheric constant removal grinding has been realized through the sub-feed control wheel feed rate. Experiments show that constant removal grinding can basically achieve uniform wear of the wheel. Finally, the ratio (λ) of the area of the wheel in grinding and aspheric removal within a unit time has been proposed, which will affect uniform wear of the wheel. Theoretical analysis shows that the value of λ has nothing to do with the feeding speed of the wheel,but is associated with the arc radius of the wheel end, aspheric quadratic curve vertex radius of curvature, aspherical shape parameters of the quadratic curve, and a grinding coordinates, etc. The results are in accordance with the theoretic analysis.
Based on the Mathematical model of shape error in dressing arc revolving surface wheel, some influencing factors are analyzed in dressing the wheel, such as wheel setting error, radius of the wheel and arc radius of the wheel end. At the same time, by means of establishing mathematical model of tool setting errors in grinding axisymmetric aspheric surface, meridional cross curve equation of axisymmetric aspheric surface is deduced when tool setting errors exist. And influence of tool setting error in different directions on shape accuracy of axisymmetric aspheric surface is analyzed. The results show that tool setting errors affect the generatrix shape and position of axisymmetric aspheric surface.
Based on analyzing the contact are length between arc revolving surface wheel and aspheric surface, the rule of grinding force in grinding aspheric surface with AEGM is studied. Experiments show that the grinding force is small in grinding with AEGM, wheel types and performance and other factors have a greater impact on the grinding force.
Through surface forming analysis in grinding aspheric surface with AEGM, residual height mathematical model of aspheric surface is established, and the influence of aspherical radius of curvature, radius of the wheel ends and wheel feed rate on residual height is analyzed. The results show that grinding surface roughness can be adjusted by changing the feeding speed of the wheel and grinding walking control interval, which is an effective means to improve uniform roughness of aspheric in grinding.
According to study on machining mechanism of trajectory envelope grinding method for aspheric surface, a new technology is proposed in grinding aspheric surface with AEGM which compromises roughness and surface precision surface. That is coarse grinding with the constant removal grinding firstly and fine grinding with constant scallop-height grinding and constant value of λ in grinding axisymmetric aspheric surface. For non-axisymmetric aspheric surface, constant scallop-height grinding and constant value of A are adopted in grinding.
引文
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