基于NURBS非回转对称光学曲面金刚石车削轨迹的研究
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摘要
高精度非回转对称(NRS)光学曲面元件的特殊优越性使其在现代光学系统中有着无法替代的重要用途。随着需求量与日俱增,传统的研磨、抛光等机械加工方法已无法满足其对加工质量与数量的要求。因此,开发新的复杂型面光学曲面超精密成形加工方法,实现高效率、更经济的生产以满足其对精密度、数量和种类的要求成为我国光学制造领域迫切需要解决的难题。
本课题采用快速刀具伺服车削NRS曲面,创新的提出了基于NURBS曲面分解的方法研究刀具轨迹的形成机理。
1.研究NURBS曲面的数学模型和表达形式,分析其中各参数的数学与几何意义;介绍其它NRS光学曲面的基本方程与形貌,为刀具轨迹的生成算法提供理论基础。
2.研究快速刀具伺服车削成型的运动数学模型,将机床的直角坐标系形式转化为极坐标函数表达形式,进而将NURBS曲面与机床、刀具的复合运动相联系,建立了NURBS空间与柱面坐标空间的转化模型。在推导刀位坐标向量变换的基础上,模拟仿真了车削加工NRS曲面的螺旋线刀具轨迹计算方法,并进一步研究刀位坐标在柱面坐标系中时域空间的转换关系,对其基本原理与计算公式进行分析与推导。
3.对NURBS曲面进行分解,即分解为回转对称与非回转对称NURBS曲面两部分。将数值运算与实际加工成型模型相联系,分别建立了基于直线型和回转型快速刀具伺服机构的车削轨迹算法。包括对在分解中方程参数形式的变换,以及两类车削复合运动刀尖姿态不同的函数关系等问题进行探讨。
4.在MATLAB和Maple的环境下进行NURBS曲面对球面的拟合,并对拟合精度进行谐波分析。
5.在VERICUT软件环境下,对计算所得NRS曲面所得的回转对称部分加工轨迹进行了数控仿真。对其进行了数控车削实验,以验证NURBS曲面分解与拟合方法的合理性与正确性。
With modern science and technology to develop, more and more areas of cutting-edge optical components for the growing demand and have an accuracy of nano-scale processing of the target.At the same time, to improve the image quality, reduce processing costs, improve manufacturing efficiency, non-rotary symmetric optical surface of the diamond turning method has become the focus of attention in today's world. In order to improve the optical component manufacturing precision and accuracy to meet the needs of people living in the 21st century higher production needs, in recent years, the global manufacturing industry are actively exploring and developing new, precision, small components of the manufacturing process and methods, of which domestic outside researchers began to more and more concerned about the non-rotating surface of the turning symmetry. This is a concept of the traditional shape of the de-sac turning abandoned, will be hard to imagine the past applied to the machining process to meet the actual needs of production, and its shape is close to the concept of a major innovation in the manufacturing sector. However, non-rotation symmetrical surface technology at the same time, the turning is a knowledge-intensive technology, it is of modern mathematics, physics and other basic science and technology with today's digital manufacturing technology mechanical product of the combination. It broke the tradition of turning many of the technical concept of turning the course of the past to solve the existing problems, abandoned its fixed tool the concept of exercise using the tool servo drive has greatly enhanced the quality of turning parts, as well as the expansion of the turning types of processing components and the continuous improvement of application performance so that more and more widely. It can be said that the non-rotation symmetrical surface-precision turning technology is considered today a major breakthrough in the manufacturing sector, on behalf of the 21st century machinery development.
However, the non-rotary symmetric shape of optical surfaces turning many problems still exist. The traditional ultra-precision 2-axis rotary lathe can only satisfy the symmetry of the surface form, and who want access to parts the surface of a size, shape accuracy and surface roughness of the non-rotation symmetrical form of free-form surfaces, which is very difficult to meet the turning requirements. Therefore, the complexity of surface shape of precision components on the need for rapid tool and machine tool servo motor complex to be completed together. In the CNC,the tool path generation algorithm has become the focus of the study and one of the difficulties.
This issue from the perspective of applied research to the world of optical surfaces used in processing the fast tool servo based on a non-rotary symmetric optical surface of the NURBS surface object for the study, carried out by decomposition of the surface approach to generate tool trajectory for the target of non-rotation-symmetric optical surface diamond turning technology trajectory. In view of the current way of forming such a turning in the rapid development of the world, ahead of China's machinery manufacturing industry, as well as in theory, could make a significant contribution in the spline curve, surface model and the rational model in the precision turning process of solving the calculation to improve the trajectory the efficiency of planning to expand the type of CNC machining in the processing of research and reality can better promote the national defense, aerospace, medical and industrial fields, such as guidance, the process of research and has great application value. At present, though foreign scholars in this direction has been an in-depth research, and the 20th century, accompanied by the rapid development of optical manufacturing industry, in particular the optical surface has been formed on the calculation and analysis, manufacturing, testing assessment system, but For free-form NURBS forming the turning, there are still many problems calling for urgent solutions to study such a complex analysis of surface needs to be further in-depth, understanding, planning.
In this paper, the study of non-rotation-symmetric optical surface means there is no axis of symmetry of the optical surface. NURBS surface for today's world in the production of a wide range of application of life of a surface, but because of the complexity of its mathematical expression and the response is different from the conventional meaning of the mathematical equation, which in the mathematical processing, computer programming, processing, production control with to a lot of trouble, many problems have emerged at the same time. To this end, the core issue in the research paper before the NURBS surface of each parameter described in detail, starting from the NURBS curve, and gradually are given a variety of surface expression of the form of equations in order to facilitate the following specific issues in the study and in the computer software in an intuitive mapping of its geometry, that the necessary papers. In addition, other forms of non-rotation symmetrical surface, such as: off-axis surface, Zernike surfaces, such as ring surface model of the mathematics and geometry, papers have also been briefed for the surface to decompose and the trajectory planning to provide a mathematical basis.
Non-rotating Symmetric diamond turning of optical surfaces is a fast tool servo machine together with the formation of complex achieved through the establishment of spindle rotation and the displacement function of the tool to achieve a specific processing model. This paper introduces a fast tool servo design concept of the basic structure, as shown in Figure 1. As chart, similar to the slow machine tool servo platform rail, conventional rotary surface of the turning trajectory symmetry; fast tool servo surface to achieve non-slewing the turning symmetry. Paper analyzes the rapid movement of the servo tool, made from such a molding process and the shape of turning conventional features, that is, the tool itself can feed two servo movement. Pointed out that the processing of movement should be reflected in the work itself for the spiral form of the traditional surface for turning the form of concentric circles that are different. At the same time in the rotating spindle, the tool back and forth movement at all times, including a straight line back and forth and back and forth two types of rotary and high frequency is a relative axis movement.
Based on the NURBS surface is characterized by the vector space, the need to establish processes and tool spindle displacement angle between the function of these two requirements, thesis about the use of cylindrical coordinate system to create a vector space associated with the processing space of thinking, and space coordinates of the basic principles of the conversion process and algorithm are analyzed and deduced. The establishment of a NURBS surface space and machine space cylindrical coordinates of the correspondence between points. On the basis of further processing of the relevant parameters required for an analysis function is derived, the parameters of the transformation locus knife mechanism, the vector method of solving problems in depth. For the next rotation will be curved into symmetric and asymmetric non-rotating two parts to provide the ideological basis and the specific parameters, so that we can track in-depth study of the generation algorithm turning.
In the CNC machining processes and numerical analysis on the basis of the paper presents the design decomposition of NURBS surface program will be divided into surface: symmetric NURBS surface part of Rotary and non-rotating part of symmetric NURBS surface and the mathematical model through the establishment of two parts inter-relationship. Respectively by solving the extremal surface rotationally symmetric surface structure of the geometric equation of Fourier-based methods and surface integral equation can be divided into two parts to complete the mathematical methods suitable for different processing systems, respectively, the surface decomposition of the work surface.
Decomposition in the surface on the basis of further research papers NURBS curve curvature of the plane problem, the formula gives the curves of curvature. Further to a point on the curve radius of the value of linking with the coordinates. Tool path planning for the establishment of equations of motion, position coordinates corresponding to the groundwork done. Derived, respectively, based on the linear fast tool servo and rotary-based fast tool servo trajectory of the two types of turning the process of algorithm. Based on the linear fast tool servo applications the solution of differential, the slope of the ways to build on the geometric relationship between the equation, content and meaning easier to understand, but the drawback is that the complex equation, to be used in rotation, respectively, symmetric and non-rotary symmetric equation. Based on the rotary fast tool servo for solving the main manifestation of the specific points of the polar coordinate value, before the papers based on the curvature and the coordinates given by the relationship between the specific points set up one-step equations of motion, the continuous iterative process.
Paper based on the decomposition of surface applied mathematics MATLAB and Maple software platform, a NURBS surface fitting studies, aimed at reducing the surface morphology of the amplitude asymmetry, and strive to achieve the smallest amplitude asymmetry requirements. Least square method, the Newton interpolation surfaces, NURBS surfaces by scanning process to establish fitting curve, the NURBS surface expression analysis of a large number of data points, control points, given the accuracy of fitting, to be used on surfaces together. For more effective and intuitive assessment of the merits of precision, paper used the principle of harmonic analysis. By fitting the discrete points used to construct the harmonic Fourier integral, after more than right, by solving the amplitude, phase and cycle to analyze the accuracy of the volume difference, and is given from the surface fitting to the harmonic wave analysis of the flow diagram, as shown in Figure 2.
Since this issue is still in the early exploratory stage, the majority of laboratory equipment is also not perfect, but the lack of the experiment is not perfect, so papers in the surface decomposition, tool path computing, data fitting and the basis of harmonic analysis, only
After fitting a rotation symmetrical curved surface analysis, simulation and experimental work, that the future of non-rotary symmetric Turning to provide a reference. Analysis through the study opposite, the processing of data points to establish the feasibility of trajectory, the application of VERICUT software platform, a rotary-symmetric NURBS surface machining simulation study to verify the equation before the derivation of the principle of turning the course of the track as well as surface fitting surface morphology of the processability. NC subsequent experiment, as shown in Figure 3, the true realization of the NC machine tool in the tool trajectory curve. And in the turning process by setting the parameters of CNC machine tools turning strongly increased the surface quality of parts. Improve the initial preparatory work for this project. At present, non-rotary symmetric NURBS-based surface diamond turning optical track technology, there are still many problems, as well as its less than full-depth study. The subject of a series of studies of this process not only for expanded research in the field of ideas and also provided the basis for in-depth study is in line with the needs of practical application. In this paper, the direction of the research for the practical application of the initial phase, due to surface decomposition method and tool path generation algorithm and uniqueness of the optimal can not verify, so in future research studies are extremely broad space, and gradually complement, strengthen, simplify and improve in order to improve our country in the field of optical manufacturing technology.
本课题采用快速刀具伺服车削NRS曲面,创新的提出了基于NURBS曲面分解的方法研究刀具轨迹的形成机理。
1.研究NURBS曲面的数学模型和表达形式,分析其中各参数的数学与几何意义;介绍其它NRS光学曲面的基本方程与形貌,为刀具轨迹的生成算法提供理论基础。
2.研究快速刀具伺服车削成型的运动数学模型,将机床的直角坐标系形式转化为极坐标函数表达形式,进而将NURBS曲面与机床、刀具的复合运动相联系,建立了NURBS空间与柱面坐标空间的转化模型。在推导刀位坐标向量变换的基础上,模拟仿真了车削加工NRS曲面的螺旋线刀具轨迹计算方法,并进一步研究刀位坐标在柱面坐标系中时域空间的转换关系,对其基本原理与计算公式进行分析与推导。
3.对NURBS曲面进行分解,即分解为回转对称与非回转对称NURBS曲面两部分。将数值运算与实际加工成型模型相联系,分别建立了基于直线型和回转型快速刀具伺服机构的车削轨迹算法。包括对在分解中方程参数形式的变换,以及两类车削复合运动刀尖姿态不同的函数关系等问题进行探讨。
4.在MATLAB和Maple的环境下进行NURBS曲面对球面的拟合,并对拟合精度进行谐波分析。
5.在VERICUT软件环境下,对计算所得NRS曲面所得的回转对称部分加工轨迹进行了数控仿真。对其进行了数控车削实验,以验证NURBS曲面分解与拟合方法的合理性与正确性。
With modern science and technology to develop, more and more areas of cutting-edge optical components for the growing demand and have an accuracy of nano-scale processing of the target.At the same time, to improve the image quality, reduce processing costs, improve manufacturing efficiency, non-rotary symmetric optical surface of the diamond turning method has become the focus of attention in today's world. In order to improve the optical component manufacturing precision and accuracy to meet the needs of people living in the 21st century higher production needs, in recent years, the global manufacturing industry are actively exploring and developing new, precision, small components of the manufacturing process and methods, of which domestic outside researchers began to more and more concerned about the non-rotating surface of the turning symmetry. This is a concept of the traditional shape of the de-sac turning abandoned, will be hard to imagine the past applied to the machining process to meet the actual needs of production, and its shape is close to the concept of a major innovation in the manufacturing sector. However, non-rotation symmetrical surface technology at the same time, the turning is a knowledge-intensive technology, it is of modern mathematics, physics and other basic science and technology with today's digital manufacturing technology mechanical product of the combination. It broke the tradition of turning many of the technical concept of turning the course of the past to solve the existing problems, abandoned its fixed tool the concept of exercise using the tool servo drive has greatly enhanced the quality of turning parts, as well as the expansion of the turning types of processing components and the continuous improvement of application performance so that more and more widely. It can be said that the non-rotation symmetrical surface-precision turning technology is considered today a major breakthrough in the manufacturing sector, on behalf of the 21st century machinery development.
However, the non-rotary symmetric shape of optical surfaces turning many problems still exist. The traditional ultra-precision 2-axis rotary lathe can only satisfy the symmetry of the surface form, and who want access to parts the surface of a size, shape accuracy and surface roughness of the non-rotation symmetrical form of free-form surfaces, which is very difficult to meet the turning requirements. Therefore, the complexity of surface shape of precision components on the need for rapid tool and machine tool servo motor complex to be completed together. In the CNC,the tool path generation algorithm has become the focus of the study and one of the difficulties.
This issue from the perspective of applied research to the world of optical surfaces used in processing the fast tool servo based on a non-rotary symmetric optical surface of the NURBS surface object for the study, carried out by decomposition of the surface approach to generate tool trajectory for the target of non-rotation-symmetric optical surface diamond turning technology trajectory. In view of the current way of forming such a turning in the rapid development of the world, ahead of China's machinery manufacturing industry, as well as in theory, could make a significant contribution in the spline curve, surface model and the rational model in the precision turning process of solving the calculation to improve the trajectory the efficiency of planning to expand the type of CNC machining in the processing of research and reality can better promote the national defense, aerospace, medical and industrial fields, such as guidance, the process of research and has great application value. At present, though foreign scholars in this direction has been an in-depth research, and the 20th century, accompanied by the rapid development of optical manufacturing industry, in particular the optical surface has been formed on the calculation and analysis, manufacturing, testing assessment system, but For free-form NURBS forming the turning, there are still many problems calling for urgent solutions to study such a complex analysis of surface needs to be further in-depth, understanding, planning.
In this paper, the study of non-rotation-symmetric optical surface means there is no axis of symmetry of the optical surface. NURBS surface for today's world in the production of a wide range of application of life of a surface, but because of the complexity of its mathematical expression and the response is different from the conventional meaning of the mathematical equation, which in the mathematical processing, computer programming, processing, production control with to a lot of trouble, many problems have emerged at the same time. To this end, the core issue in the research paper before the NURBS surface of each parameter described in detail, starting from the NURBS curve, and gradually are given a variety of surface expression of the form of equations in order to facilitate the following specific issues in the study and in the computer software in an intuitive mapping of its geometry, that the necessary papers. In addition, other forms of non-rotation symmetrical surface, such as: off-axis surface, Zernike surfaces, such as ring surface model of the mathematics and geometry, papers have also been briefed for the surface to decompose and the trajectory planning to provide a mathematical basis.
Non-rotating Symmetric diamond turning of optical surfaces is a fast tool servo machine together with the formation of complex achieved through the establishment of spindle rotation and the displacement function of the tool to achieve a specific processing model. This paper introduces a fast tool servo design concept of the basic structure, as shown in Figure 1. As chart, similar to the slow machine tool servo platform rail, conventional rotary surface of the turning trajectory symmetry; fast tool servo surface to achieve non-slewing the turning symmetry. Paper analyzes the rapid movement of the servo tool, made from such a molding process and the shape of turning conventional features, that is, the tool itself can feed two servo movement. Pointed out that the processing of movement should be reflected in the work itself for the spiral form of the traditional surface for turning the form of concentric circles that are different. At the same time in the rotating spindle, the tool back and forth movement at all times, including a straight line back and forth and back and forth two types of rotary and high frequency is a relative axis movement.
Based on the NURBS surface is characterized by the vector space, the need to establish processes and tool spindle displacement angle between the function of these two requirements, thesis about the use of cylindrical coordinate system to create a vector space associated with the processing space of thinking, and space coordinates of the basic principles of the conversion process and algorithm are analyzed and deduced. The establishment of a NURBS surface space and machine space cylindrical coordinates of the correspondence between points. On the basis of further processing of the relevant parameters required for an analysis function is derived, the parameters of the transformation locus knife mechanism, the vector method of solving problems in depth. For the next rotation will be curved into symmetric and asymmetric non-rotating two parts to provide the ideological basis and the specific parameters, so that we can track in-depth study of the generation algorithm turning.
In the CNC machining processes and numerical analysis on the basis of the paper presents the design decomposition of NURBS surface program will be divided into surface: symmetric NURBS surface part of Rotary and non-rotating part of symmetric NURBS surface and the mathematical model through the establishment of two parts inter-relationship. Respectively by solving the extremal surface rotationally symmetric surface structure of the geometric equation of Fourier-based methods and surface integral equation can be divided into two parts to complete the mathematical methods suitable for different processing systems, respectively, the surface decomposition of the work surface.
Decomposition in the surface on the basis of further research papers NURBS curve curvature of the plane problem, the formula gives the curves of curvature. Further to a point on the curve radius of the value of linking with the coordinates. Tool path planning for the establishment of equations of motion, position coordinates corresponding to the groundwork done. Derived, respectively, based on the linear fast tool servo and rotary-based fast tool servo trajectory of the two types of turning the process of algorithm. Based on the linear fast tool servo applications the solution of differential, the slope of the ways to build on the geometric relationship between the equation, content and meaning easier to understand, but the drawback is that the complex equation, to be used in rotation, respectively, symmetric and non-rotary symmetric equation. Based on the rotary fast tool servo for solving the main manifestation of the specific points of the polar coordinate value, before the papers based on the curvature and the coordinates given by the relationship between the specific points set up one-step equations of motion, the continuous iterative process.
Paper based on the decomposition of surface applied mathematics MATLAB and Maple software platform, a NURBS surface fitting studies, aimed at reducing the surface morphology of the amplitude asymmetry, and strive to achieve the smallest amplitude asymmetry requirements. Least square method, the Newton interpolation surfaces, NURBS surfaces by scanning process to establish fitting curve, the NURBS surface expression analysis of a large number of data points, control points, given the accuracy of fitting, to be used on surfaces together. For more effective and intuitive assessment of the merits of precision, paper used the principle of harmonic analysis. By fitting the discrete points used to construct the harmonic Fourier integral, after more than right, by solving the amplitude, phase and cycle to analyze the accuracy of the volume difference, and is given from the surface fitting to the harmonic wave analysis of the flow diagram, as shown in Figure 2.
Since this issue is still in the early exploratory stage, the majority of laboratory equipment is also not perfect, but the lack of the experiment is not perfect, so papers in the surface decomposition, tool path computing, data fitting and the basis of harmonic analysis, only
After fitting a rotation symmetrical curved surface analysis, simulation and experimental work, that the future of non-rotary symmetric Turning to provide a reference. Analysis through the study opposite, the processing of data points to establish the feasibility of trajectory, the application of VERICUT software platform, a rotary-symmetric NURBS surface machining simulation study to verify the equation before the derivation of the principle of turning the course of the track as well as surface fitting surface morphology of the processability. NC subsequent experiment, as shown in Figure 3, the true realization of the NC machine tool in the tool trajectory curve. And in the turning process by setting the parameters of CNC machine tools turning strongly increased the surface quality of parts. Improve the initial preparatory work for this project. At present, non-rotary symmetric NURBS-based surface diamond turning optical track technology, there are still many problems, as well as its less than full-depth study. The subject of a series of studies of this process not only for expanded research in the field of ideas and also provided the basis for in-depth study is in line with the needs of practical application. In this paper, the direction of the research for the practical application of the initial phase, due to surface decomposition method and tool path generation algorithm and uniqueness of the optimal can not verify, so in future research studies are extremely broad space, and gradually complement, strengthen, simplify and improve in order to improve our country in the field of optical manufacturing technology.
引文
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