复杂曲面宽行数控加工理论及其应用研究
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摘要
数控技术是先进制造技术的基础和核心,已经成为衡量一个国家制造业发展水平的标志。作为数控技术的重要组成部分,数控加工编程技术一直是人们的研究重点和难点。随着航空航天、汽车、新能源、微电子等领域的发展,不断出现的复杂曲面零部件对数控加工编程技术提出了更高的挑战。目前,以实现宽行线接触为目标的宽行数控加工技术已经在加工效率方面体现出了比较明显的优势,但在理论及应用上尚有大量的研究工作亟待努力开展。为此,本文以圆环面刀具为基础,对复杂曲面宽行数控加工编程技术中的刀具定位、刀轨规划等基础理论进行了深入研究与实践。
对现有的多点切触加工理论和几种典型多点刀位算法进行了分析,以最大化加工带宽为目标,以保证刀具表面和工件曲面在两个切触点处满足绝对切触、避免局部过切及控制两个切触点之间的最大欠切误差为三个主要约束条件,建立了多点切触加工的通用数学模型,为后续的研究工作奠定了重要的理论基础。为了使用圆环面刀具加工复杂凸曲面,推导出了刀具底面中心和凸曲面之间没有干涉时凸曲面的最大曲率和刀具各相关参数之间的关系式。此外,基于圆环面刀具环心圆曲线,给出了刀位误差分布及加工带宽的一般性求取方法。
针对圆弧相交法的不足,提出了改进的圆弧相交法。首先将圆环面刀具和工件曲面之间的相对位置关系等效为圆环面刀具环心圆曲线和工件曲面等距面之间的位置关系,然后推导出了由刀具后跟角决定的环心圆曲线的参数方程,最后利用二分法对刀具后跟角实现了满足局部过切条件下的优化,由此确定所求刀位。同时,提出了改进的求圆环面刀具环心圆曲线到工件曲面的最小距离算法,以避免在刀位优化过程中发生局部过切。算例证明,改进的圆弧相交法不仅稳定、计算效率高,而且能够产生类似于多点刀位算法特有的“W”型误差分布,尽管不能使圆环面刀具和工件曲面之间获得两个切触点,但是在给定的加工误差下能够实现曲面的宽行线接触加工,因此是一种有效的宽行数控加工刀位算法。
在改进的圆弧相交法的基础上,进一步提出了基于两个切触点的宽行刀位算法——旋转切触法。首先推导出了由刀具后跟角和侧偏角决定的环心圆曲线的参数方程,然后在满足局部过切条件和两个切触点之间欠切条件的前提下,对刀具后跟角和侧偏角进行了优化,最终实现了圆环面刀具和工件曲面在最小主曲率方向两侧的两点切触,改善了复杂曲面的表面加工质量,算例对旋转切触法的正确性和有效性进行了验证。
为了使复杂曲面加工产生光顺规整的刀路并充分利用由宽行刀位算法带来的加工带宽的优势,定义了特征点、特征曲线、特征参数线及特征参数加工区域的概念,并在此基础上提出了特征参数线刀轨规划算法,其基本原理是使下一条刀路的左特征参数线对应的参数值等于当前刀路的右特征参数线对应的参数值,即使所有规划刀路对应的特征参数加工区域的集合恰好构成一张完整的工件曲面片。算例表明,特征参数线刀轨规划算法不仅可以产生光顺无干涉的刀路,而且相比于等参数线法能够有效减少曲面加工所需的刀路数量,提高实际加工效率。
以汽车顶盖凸曲面为例,对复杂开阔凸曲面的宽行数控加工进行了研究。首先给出了由散乱点云数据进行汽车顶盖凸曲面模型重建的过程,然后对不同走刀方向下的刀位误差分布进行了深入分析。结果表明：在多点切触加工凸曲面时,一般只有使刀具沿凸曲面的最大主曲率方向进给,圆环面刀具和工件凸曲面之间才有可能达到两点切触,这和模具凹曲面得出的结论是完全相反的。最后,分析了宽行刀位算法中的一些关键参数对刀位误差分布的影响,利用旋转切触刀位算法和特征参数线刀轨规划算法,生成了汽车顶盖凸曲面宽行数控加工的无干涉刀位轨迹。计算结果和加工实验则再次验证了本文提出的宽行刀位及刀轨优化算法的正确性。
Numerical control (NC) technology is the foundation and core of advanced manufacturing technology, and has become a symbol of the national manufacturing development level. As an important part of NC technology, the NC machining programming technology has been always the focus and difficulty of research. Along with the development of aerospace, automobile, new energy, microelectronics and other fields, increasing products with sculptured surface have led to higher challenges for the NC machining programming technology. At present, the wide strip NC machining, which aims to realize the line contact, has shown its obvious advantage in the processing efficiency. However, there is a great deal of research on the theory and application to be carried out. For this reason, based on the toroidal cutter, the research mainly on tool positioning and tool path planning of the wide strip NC machining programming technology for sculptured surface was deeply implemented.
After analyzing the existing theory of multi-point machining and classical multi-point tool positioning algorithms, the general mathematic model of the multi-point machining was established to provide an important theoretical basis for the subsequent research work. The optimization objective function was to maximize the machining strip width. And the three main constraint conditions were used to make tool and workpiece surface meet absolutely tangent in the two contact points, avoid the local gouge and control the maximum undercut error between the two contact points. For the convex sculptured surface machining with the toroidal cutter, the relational expression between the surface curvature and the tool's parameters without interference was deduced. In addition, the calculation method of tool position error distribution and machining strip width based on the circular curve of the toroidal cutter was also given.
According to the drawback of Arc-intersect Method (AIM), the improved Arc-intersect Method (IAIM) was put forward. The relative location relationship between the toroidal cutter and the workpiece surface was firstly translated into that between the circular curve of the toroidal cutter and the offset surface of the workpiece surface. Then the parametric equation of the circular curve of tool determined by the backwards angle of tool was deduced. The final too positions were gotten after that the backwards angle of tool was to be optimized by the bisection method. Meanwhile, the improved algorithm for calculating the minimum distance between the circular curve of tool and the workpiece surface was also presented in order to avoid the local gouge. An example showed that the IAIM could not only be stable and efficient, but also produce the "W" shaped tool position error distribution like those multi-point tool positioning algorithms. Though there was only one contact point between the toroidal cutter and the workpiece surface, the IAIM was also considered to be an effective wide strip NC machining algorithm because it made the line contact machining become true under the given machining precision.
Based on the IAIM, the Rotary Cntact Method (RCM) that contained two contact points and belonged to the wide strip NC machining algorithm was developed. The parametric equation of the circular curve of tool defined by the backwards and side tilt angle of tool was similarly deduced. As the optimization of the backwards and side tilt angle of tool was finished, there were two contact points between the toroidal cutter and the workpiece surface around the minimum direction of curvature without gouging. The RCM improved the workpiece surface quality and was verified by an example.
In order to obtain the smooth tool paths and take full of the advantages brought by the wide strip NC machining algorithm, the definition of characteristic point, characteristic curve, characteristic parameter curve and characteristic parameter machining field was respectively given. Furthermore, the characteristic parameter curve tool path planning method was presented here. The basic idea was to determine the optimal tool positions by the RCM, and then make the left characteristic parameter curve of the next path being collinear with the right characteristic parameter curve of the current path under the given machining precision by the iterative calculation. Finally, the tool paths were completely arranged. An example showed that the characteristic parameter curve tool path planning method could not only generate the smooth and interfere-free tool paths, but also improve the actual machining efficiency by contrast with the iso-parametric method.
The multi-point machining for the general convex sculptured surface was discussed through the example of cover car convex surface. The method to complete the model reconstruction of the cover car convex surface from the scattered points clouds was firstly described. Then the tool position error distribution for different path directions was deeply inspected. Results showed that the condition for multi-point contact was to make the tool feed along the maximum direction of curvature of the convex surface, which was completely opposite to the concave surface. At last, the relationship between the key parameters of the wide strip NC machining algorithm and the tool position error distribution was discussed. The non-interference tool paths for the cover car convex surface were gotten by the RCM and the characteristic parameter curve tool path planning method. Computational results and the machining experiment proved the proposed tool positioning and tool path planning method once again.
对现有的多点切触加工理论和几种典型多点刀位算法进行了分析,以最大化加工带宽为目标,以保证刀具表面和工件曲面在两个切触点处满足绝对切触、避免局部过切及控制两个切触点之间的最大欠切误差为三个主要约束条件,建立了多点切触加工的通用数学模型,为后续的研究工作奠定了重要的理论基础。为了使用圆环面刀具加工复杂凸曲面,推导出了刀具底面中心和凸曲面之间没有干涉时凸曲面的最大曲率和刀具各相关参数之间的关系式。此外,基于圆环面刀具环心圆曲线,给出了刀位误差分布及加工带宽的一般性求取方法。
针对圆弧相交法的不足,提出了改进的圆弧相交法。首先将圆环面刀具和工件曲面之间的相对位置关系等效为圆环面刀具环心圆曲线和工件曲面等距面之间的位置关系,然后推导出了由刀具后跟角决定的环心圆曲线的参数方程,最后利用二分法对刀具后跟角实现了满足局部过切条件下的优化,由此确定所求刀位。同时,提出了改进的求圆环面刀具环心圆曲线到工件曲面的最小距离算法,以避免在刀位优化过程中发生局部过切。算例证明,改进的圆弧相交法不仅稳定、计算效率高,而且能够产生类似于多点刀位算法特有的“W”型误差分布,尽管不能使圆环面刀具和工件曲面之间获得两个切触点,但是在给定的加工误差下能够实现曲面的宽行线接触加工,因此是一种有效的宽行数控加工刀位算法。
在改进的圆弧相交法的基础上,进一步提出了基于两个切触点的宽行刀位算法——旋转切触法。首先推导出了由刀具后跟角和侧偏角决定的环心圆曲线的参数方程,然后在满足局部过切条件和两个切触点之间欠切条件的前提下,对刀具后跟角和侧偏角进行了优化,最终实现了圆环面刀具和工件曲面在最小主曲率方向两侧的两点切触,改善了复杂曲面的表面加工质量,算例对旋转切触法的正确性和有效性进行了验证。
为了使复杂曲面加工产生光顺规整的刀路并充分利用由宽行刀位算法带来的加工带宽的优势,定义了特征点、特征曲线、特征参数线及特征参数加工区域的概念,并在此基础上提出了特征参数线刀轨规划算法,其基本原理是使下一条刀路的左特征参数线对应的参数值等于当前刀路的右特征参数线对应的参数值,即使所有规划刀路对应的特征参数加工区域的集合恰好构成一张完整的工件曲面片。算例表明,特征参数线刀轨规划算法不仅可以产生光顺无干涉的刀路,而且相比于等参数线法能够有效减少曲面加工所需的刀路数量,提高实际加工效率。
以汽车顶盖凸曲面为例,对复杂开阔凸曲面的宽行数控加工进行了研究。首先给出了由散乱点云数据进行汽车顶盖凸曲面模型重建的过程,然后对不同走刀方向下的刀位误差分布进行了深入分析。结果表明：在多点切触加工凸曲面时,一般只有使刀具沿凸曲面的最大主曲率方向进给,圆环面刀具和工件凸曲面之间才有可能达到两点切触,这和模具凹曲面得出的结论是完全相反的。最后,分析了宽行刀位算法中的一些关键参数对刀位误差分布的影响,利用旋转切触刀位算法和特征参数线刀轨规划算法,生成了汽车顶盖凸曲面宽行数控加工的无干涉刀位轨迹。计算结果和加工实验则再次验证了本文提出的宽行刀位及刀轨优化算法的正确性。
Numerical control (NC) technology is the foundation and core of advanced manufacturing technology, and has become a symbol of the national manufacturing development level. As an important part of NC technology, the NC machining programming technology has been always the focus and difficulty of research. Along with the development of aerospace, automobile, new energy, microelectronics and other fields, increasing products with sculptured surface have led to higher challenges for the NC machining programming technology. At present, the wide strip NC machining, which aims to realize the line contact, has shown its obvious advantage in the processing efficiency. However, there is a great deal of research on the theory and application to be carried out. For this reason, based on the toroidal cutter, the research mainly on tool positioning and tool path planning of the wide strip NC machining programming technology for sculptured surface was deeply implemented.
After analyzing the existing theory of multi-point machining and classical multi-point tool positioning algorithms, the general mathematic model of the multi-point machining was established to provide an important theoretical basis for the subsequent research work. The optimization objective function was to maximize the machining strip width. And the three main constraint conditions were used to make tool and workpiece surface meet absolutely tangent in the two contact points, avoid the local gouge and control the maximum undercut error between the two contact points. For the convex sculptured surface machining with the toroidal cutter, the relational expression between the surface curvature and the tool's parameters without interference was deduced. In addition, the calculation method of tool position error distribution and machining strip width based on the circular curve of the toroidal cutter was also given.
According to the drawback of Arc-intersect Method (AIM), the improved Arc-intersect Method (IAIM) was put forward. The relative location relationship between the toroidal cutter and the workpiece surface was firstly translated into that between the circular curve of the toroidal cutter and the offset surface of the workpiece surface. Then the parametric equation of the circular curve of tool determined by the backwards angle of tool was deduced. The final too positions were gotten after that the backwards angle of tool was to be optimized by the bisection method. Meanwhile, the improved algorithm for calculating the minimum distance between the circular curve of tool and the workpiece surface was also presented in order to avoid the local gouge. An example showed that the IAIM could not only be stable and efficient, but also produce the "W" shaped tool position error distribution like those multi-point tool positioning algorithms. Though there was only one contact point between the toroidal cutter and the workpiece surface, the IAIM was also considered to be an effective wide strip NC machining algorithm because it made the line contact machining become true under the given machining precision.
Based on the IAIM, the Rotary Cntact Method (RCM) that contained two contact points and belonged to the wide strip NC machining algorithm was developed. The parametric equation of the circular curve of tool defined by the backwards and side tilt angle of tool was similarly deduced. As the optimization of the backwards and side tilt angle of tool was finished, there were two contact points between the toroidal cutter and the workpiece surface around the minimum direction of curvature without gouging. The RCM improved the workpiece surface quality and was verified by an example.
In order to obtain the smooth tool paths and take full of the advantages brought by the wide strip NC machining algorithm, the definition of characteristic point, characteristic curve, characteristic parameter curve and characteristic parameter machining field was respectively given. Furthermore, the characteristic parameter curve tool path planning method was presented here. The basic idea was to determine the optimal tool positions by the RCM, and then make the left characteristic parameter curve of the next path being collinear with the right characteristic parameter curve of the current path under the given machining precision by the iterative calculation. Finally, the tool paths were completely arranged. An example showed that the characteristic parameter curve tool path planning method could not only generate the smooth and interfere-free tool paths, but also improve the actual machining efficiency by contrast with the iso-parametric method.
The multi-point machining for the general convex sculptured surface was discussed through the example of cover car convex surface. The method to complete the model reconstruction of the cover car convex surface from the scattered points clouds was firstly described. Then the tool position error distribution for different path directions was deeply inspected. Results showed that the condition for multi-point contact was to make the tool feed along the maximum direction of curvature of the convex surface, which was completely opposite to the concave surface. At last, the relationship between the key parameters of the wide strip NC machining algorithm and the tool position error distribution was discussed. The non-interference tool paths for the cover car convex surface were gotten by the RCM and the characteristic parameter curve tool path planning method. Computational results and the machining experiment proved the proposed tool positioning and tool path planning method once again.
引文
[1]江忠君.对我国数控技术发展的战略思考[J].中国现代教育装备,2010,7：165-167.
[2]曹丽萍.浅谈数控技术的发展[J].工业技术,2009,24：124.
[3]姚乐.我国数控技术的现状及发展方向[J].科技管理研究,2009,11：261-262.
[4]张承瑞.数控技术发展趋势[J].现代制造技术与装备,2007,2：3-6.
[5]机械工程学科发展战略报告(2011-2020).国家自然科学基金委员会工程与材料科学部,科学出版社,2010.
[6]国家中长期科学和技术发展规划纲要(2006-2020).中华人民共和国国务院,2006.
[7]张洪.从增大行距宽度减少波纹度的角度看型面加工发展的方向[C].北京航空学院庆祝建校三十周年论文集,北京：北京航空学院,1982.
[8]李志强.曲面的宽行数控加工理论研究及其在大型抛物面天线加工中的应用[D].北京：北京航空航天大学,2004.
[9]王丹.双角度约束刀轨优化理论及其在自由曲面加工中的应用[D].北京：北京航空航天大学.2009.
[10]王丹,徐汝锋,陈五一.基于UG二次开发的宽行加工算法实现[J].机床与液压,2008,36(12)：32-34.
[11]易红.数控技术[M].机械工业出版社,2005.
[12]Piegl, L., Tiller, W. Curve and surface construction using rational B-splines[J]. Computer-Aided Design,1987,19 (9):485-498.
[13]Piegl, L., Tiller, W. The NURBS book[M]. Berlin Heidelberg:Springer-Verlag, Section Edition,1997.
[14]Farin, G. Curve and surface for CAGD[M]. Morgan Kaufmann, The fifth edition:A practical guide,2001.
[15]ANSI, U. S. Product Data Association (US PRO), ANS US PRO/IPO-100-1996:The Initial Graphics Exchange Specification (IGES) Version 5.3, IGES/PDES,1996.
[16]ISO Secretariat, National Institute of Standards and Technology (NIST), Standard for The Exchange of Product model data (STEP), ISO 10303, A series of document, Part 42: Geometric and Topological Representation, ISO 10303-42. MD:Gaithersburg,1994.
[17]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001.
[18]Mason, F. Die and mold finishing-how fast?[J]. Manufacturing Engineering,1995,115 (33): 35-36.
[19]Kim, B. H. and Chu, C. N. Effect of cutter mark on surface roughness and scallop height in sculptured surface machining[J]. Computer-Aided Design,1994,26 (3):179-188.
[20]Kruth, J. P. and Klewais, P. Optimization and dynamic adaptation of cutter inclination during five-axis milling of sculptured surfaces[J]. Annals of CIRP,1994,43 (1):443-448.
[21]Dragomatz, D. and Mann, S. A classified bibliography of literature on NC milling path generation [J]. Computer-Aided Design,1997,29 (3):239-247.
[22]Vickers, G. W. and Bedi, S. The definition and manufacture of compound curvature surfaces using G-Surf[J]. Computers in Industry,1985,6:173-183.
[23]Vickers, G. W. and Quan, K. W. Ball-mills versus end-mills for curved surface machining[J]. Journal of Engineering for Industry,1989,111 (22):22-26.
[24]Warkentin, A. Multi-point machining of sculptured surfaces[D]. Waterloo, Ontario, Canada: University of Waterloo,1997.
[25]王小椿,吴序堂,李艳斌.密切曲率法一一种自由曲面加上的新概念[J].西安交通大学学报,1992,26(5)：51-58.
[26]Wang, X. C., Li, Y. B., Ghosh, S. K. and Wu, X. T. Curvature catering-a new approach in manufacturing of sculptured surface (part1.Theorem)[J]. Journal of Materials Processing Technology,1993,38 (1-2):159-176.
[27]Wang, X. C., Li, Y. B., Ghosh, S. K. and Wu, X. T. Curvature catering-a new approach in manufacturing of sculptured surface (part2.methodolody)[J]. Journal of Materials Processing Technology,1993,38 (1-2):177-194.
[28]Li, F., Wang, X. C., Ghosh, S. K. and Kong, D. Z. Gouge detection and tool position modification for five-axis NC machining of sculptured surfaces[J]. Journal of Materials Processing Technology,1995,48 (1-4):739-745.
[29]Li, F., Wang, X. C., Ghosh, S. K. and Kong, D. Z. Tool-path generation for machining sculptured surfaces[J]. Journal of Materials Processing Technology,1995,48 (1-4):811-816.
[30]张瑞乾,冯学斌,卜国磊,等.用密切曲率法加工边界受限制的曲面[J].机械科学与技术,1997,16(4)：674-677.
[31]张瑞乾,王小椿,吴序堂.用密切曲率法加工自由曲面及其刀位轨迹的排列[J].西安交通大学学报,1997,31(12)：55-60.
[32]张瑞乾,沈兵,王小椿,等.用二阶密切曲率法法加工自由曲面[J].机械工程学报,1998,34(2)：87-92.
[33]沈兵,高军,张瑞乾,等.用密切曲率法加上自由曲面[J].新技术新工艺,1998,4：19-21.
[34]Jensen, C. G. and Anderson, D. C. Accurate tool placement and orientation for finish surface machining[J]. Journal of Design and Manufacturing,1993,3 (4):251-261.
[35]Jensen, C. G., Anderson, D. C. and Mullins, S. H. Scallop elimination based on precise 5-axis tool placement, orientation, and step-over calculations[J]. Advances in Design Automation ASME,1993,65 (2):535-544.
[36]Rao, N., Bedi, S. and Buchal, R. Implementation of the principal-axis method for machining of complex surfaces[J]. International Journal of Advanced Manufacturing Technology,1996, 11:249-257.
[37]Rao, N., Ismail, F. and Bedi, S. Tool path planning for five-axis machining using the principal axis method[J]. International Journal of Machine Tools and Manufacture,1997,37 (7): 1025-1040.
[38]陈涛,钟毅芳,周济.自由曲面5轴数控加工刀位轨迹的生成算法[J].机械工程学报,2001,37(12)：100-103.
[39]杨德武,彭芳瑜,周云飞.基于主曲率匹配的五坐标刀位轨迹优化[J].华中科技大学学报,2001,29(12)：8-11.
[40]李志强,陈五一.复杂曲面五坐标加工中主曲率匹配法的刃形误差[J].机械工程学报,2006,42(2)：135-140.
[41]Warkentin, A., Bedi, S. and Ismail, F.5-axis milling of spherical surfaces[J]. International Journal of Machine Tools and Manufacture,1995,36 (2):229-243.
[42]Warkentin, A., Ismail, F. and Bedi, S. Intersection approach to multi-point machining of sculptured surfaces[J]. Computer Aided Geometric Design,1998,15 (6):567-584.
[43]Warkentin, A., Ismail, F. and Bedi, S. Multi-point tool positioning strategy for 5-axis machining of sculptured surfaces[J]. Computer Aided Geometric Design,2000,17 (1): 83-100.
[44]Warkentin, A. Multi-point machining with anti-gouging and scallop height control[J]. Transactions of the CSME/de la SCGM,2004,28 (1):25-42.
[45]Warkentin, A., Ismail, F. and Bedi, S. Comparison between multi-point and other 5-axis tool position strategies[J]. International Journal of Machine Tools and Manufacture,2000,40 (2): 185-208.
[46]倪炎榕,马登哲,张洪,等.圆环面刀具五坐标数控加工复杂曲面优化刀位算法[J].机械工程学报,2001,37(2)：87-91.
[47]倪炎榕,张洪,郭静萍.圆环面刀具五坐标数控加工复杂曲面刀位算法分析[J].机械科学与技术,2002,21(2)：188-190.
[48]吕雪丽,张洪.广域曲率吻合原则与复杂曲面数控加工的全面优化[J].机械设计与制造,2003.5：94-96.
[49]吕雪丽.圆环面刀具五坐标数控宽行线接触加工复杂曲面的研究[D].北京：北京航空航天大学.2003.
[50]李志强,陈五一,张洪.四坐标精密加工大型曲面中的刀位优化[J].中国机械工程,2005,16(4)：311-314.
[51]Engeli, M., Waldvogel, J. and Schnider, T. Method for processing work pieces by removing material[J]. United States Patent,2002, US 6 485 236[P].
[52]钟慧琴,金曼,肖俊,等Hermite五坐标数控加工刀位算法研究[J].新技术新工艺,2005,9：4-6.
[53]王瑞秋,边永梅,陈五一Hermite算法的收敛性分析及其改进[J].北京航空航天大学学报,2006,32(2)：239-243.
[54]王瑞秋,陈五一,金曼.多点切触加工中的局部干涉分析[J].航空航天大学学报,2006,32(5)：580-584.
[55]Gray, P., Bedi, S. and Ismail, F. Rolling ball method for 5-axis surface machining[J]. Computer-Aided Design,2003,35 (4):347-357.
[56]Gray, P., Ismail, F. and Bedi, S. Graphics-assisted rolling ball method for 5-axis surface mchining[J]. Computer-Aided Design,2004,36 (7):653-663.
[57]Gray, P., Bedi, S. and Ismail, F. Arc-intersect method for 5-axis tool positioning[J]. Computer-Aided Design,2005,37 (7):663-674.
[58]Gray, P., Ismail, F. and Bedi, S. Arc-intersect method for 311/22-axis tool paths on a 5-axis machine[J]. International Journal of Machine Tools and Manufacture,2007,47:182-190.
[59]金曼,张俐,陈志同.圆环面刀具五坐标加上端点误差控制刀位优化[J].北京航空航天大学学报,2006,32(9)：1125-1128.
[60]王瑞秋,金曼,陈五一,等.端点误差控制刀位算法的改进[J].航空学报,2007,28(2)：438-444.
[61]Cho, H. D., Jun, Y. T. and Yang, M. Y. Five-axis CNC milling for effective machining of sculptured surfaces[J]. International Journal of Production Research,1993,31 (11): 2559-2573.
[62]Li, S. X, Jerard, R. B.5-axis machining of sculptured surfaces with a flat-end cutter[J]. Computer-Aided Design,1994,26 (3):165-178.
[63]Liu, X. W. Five-axis NC cylindrical milling of sculptured surfaces[J]. Computer-Aided Design,1995,27 (12):887-894.
[64]Lee, Y. S. Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining[J]. Computer-Aided Design,1997,29 (7):507-521.
[65]Yoon, J. H., Pottmann, H. and Lee, Y. S. Locally optimal cutting positions for 5-axis sculptured surface machining[J]. Computer-Aided Design,2003,35 (1):69-81.
[66]Bedi, S., Mann, S. and Menzel, C. Flank milling with flat end cutters[J]. Computer-Aided Design,2003,35 (3):293-300.
[67]Menzel, C., Bedi, S. and Mann, S. Triple tangent flank milling of ruled surfaces[J]. Computer-Aided Design,2004,36 (3):289-296.
[68]Chiou, J. C. J. Accurate tool position for five-axis ruled surface machining by swept envelope approach[J]. Computer-Aided Design,2004,36 (10):967-974.
[69]蔡永林,席光,查建中.任意扭曲直纹面叶轮数控侧铣刀位计算与误差分析[J].西安交通大学学报,2004,38(5)：517-520.
[70]吴广宽,席光.自由曲面三元叶轮5轴数控粗加工刀位生成算法[J].西安交通大学学报,2005,39(7)：731-734.
[71]王瑞秋,陈五一.多点切触加工的割线法[J].机械上程学报,2006,42(7)：203-206.
[72]曹利新,祁少华.基于散乱数据点的数控加工刀位直接生成[J].中国机械工程,2006,17(11)：1101-1104.
[73]席光,吴广宽,郑健生.基于半径和角偏置的直纹面五坐标加工刀位生成算法[J].机械工程学报,2008,44(4)：92-96.
[74]Cao, L. X., Gong, H. and Liu, J. The offset approach of machining free form surface part 1: Cylindrical cutter in five-axis NC machine tools[J]. Journal of Materials Processing Technology,2006,174 (1-3):298-304.
[75]Cao, L. X., Gong, H. and Liu, J. The offset approach of machining free form surface part 2: Toroidal cutter in 5-axis NC machine tools[J]. Journal of Materials Processing Technology, 2007,184 (1-3):6-11.
[76]李正强,陈志同,肖俊.鼓形刀宽行刀位优化纬线分割算法[J].北京航空航天大学学报,2007,33(6)：731-735.
[77]孔马斌,胡自化,李慧,等.基于等距曲面的弧面凸轮单侧面数控加工刀位优化算法[J].机械工程学报,2008,44(11)：277-282.
[78]陈志同,张洪,张俐.采用经线分划刀具的多坐标端铣加工刀位优化方法[P].中国专利,200810106647.7,2008-05-14.
[79]Gong, H., Cao, L. X. and Liu, J. Second order approximation of tool envelope surface for 5-axis machining with single point contact[J]. Computer-Aided Design,2008,40 (5): 604-615.
[80]Gong, H., Fang, F. Z. and Hu, X. T. et al. Optimization of tool positions locally based on the BCELTP for 5-axis machining of free-form surfaces[J]. Computer-Aided Design,2010,42 (6): 558-570.
[81]樊文刚,王小椿.快速进给铣刀五坐标端铣加工刀位计算[J].北京交通大学学报,2010,34(1)：154-157.
[82]徐汝锋,陈五一,陈志同.基于经线划分的非圆截面环形刀具刀位优化算法[J].航空学报,2010,31(2)：410-417.
[83]Zhu, L. M., Ding, H. and Xiong, Y. L. Third Order Point Contact Approach for Five-Axis Sculptured Surface Machining Using Non-ball End Tolls-Part Ⅰ:Third Order Approximation of Tool Envelope Surface[J]. Sci China Ser E-Tech Sci,2010,53:1904-1912.
[84]Zhu, L. M., Ding, H. and Xiong, Y. L. Third order point contact approach for five-axis sculptured surface machining using non-ball end tools-Part Ⅱ:Tool positioning strategy [J]. Sci China Ser E-Tech Sci,2010,53:2190-2197.
[85]杨长棋.复杂曲面多轴加上的高精度、高效率数控编程系统研究[D].重庆：重庆大学,2004.
[86]丁汉,毕庆贞,朱利民,等.五轴数控加工的刀具路径规划与动力学仿真[J].科学通报,2010,55(25)：2510-2519.
[87]Wang, H., Chang, H., Wysk, R. A. and Chandawarkar, A. On the efficiency of NC tool path planning for face milling operations[J]. Journal of Engineering for Industry,1987,109 (4): 370-376.
[88]Chiou, C. J., Lee, Y. S. A machining potential field approach to tool path generation for multi-axis sculptured surface machining[J]. Computer-Aided Design,2002,34 (5):357-371.
[89]Broomhead, P. and Edkins, M. Generating NC data at the machine tool for the manufacture of free-form surfaces[J]. International Journal of Production Research,1986,24 (1):1-14.
[90]Loney, G. and Ozsoy, T. NC machining of free-form surfaces[J]. Computer-Aided Design, 1987,19 (2):85-90.
[91]Elber, G. and Cohen, E. Toolpath generation for freeform surface models[J]. Computer-Aided Design,1994,26 (6):490-496.
[92]Bobrow, J. E. NC machine tool path generation from OSG part representations[J]. Computer-Aided Design,1985,17 (2):69-72.
[93]Yong, S. S. and Lee, K. NC milling tool path generation for arbitrary pockets defined by sculptured surfaces[J]. Computer-Aided Design,1990,22 (5):273-284.
[94]Huang, Y. and Oliver, J. Non-constant parameter NC tool path generation of sculptured surfaces[J]. International Journal of Advanced Manufacturing Technology,1994,9 (5): 281-290.
[95]Suresh, K. and Yang, D. C. H. Constant scallop-height machining of free-form surfaces[J]. Journal of Engineering for Industry,1994,116 (2):253-259.
[96]Sarma, R. and Dutta, D. Geometry and generation of NC tool paths[J]. Journal of Mechanical Design, Transactions of the ASME,1997,119 (2):253-258.
[97]Lee, Y. S. Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining[J]. Computer-Aided Design,1998,30 (7):559-570.
[98]Feng, H. and Li, H. Constant scallop-height tool path generation for three-axis sculptured surface machining[J]. Computer-Aided Design,2002,34 (9):647-654.
[99]Tournier, C. and Duc, E. A surface based approach for constant scallop height tool-path generation[J]. The International Journal of Advanced Manufacturing Technology,2002,19 (5): 318-324.
[100]Tournier, C. and Duc, E. Iso-scallop height tool path generation in 5-axis milling[J]. The International Journal of Advanced Manufacturing Technology,2005,25 (9):867-875.
[101]Ding, S., Mannan, M. A., Poo, A. N. and et al. Adaptive iso-planar tool path generation for the machining of free-form surfaces[J]. Computer-Aided Design,2003,35 (2):141-153.
[102]Ding, S., Mannan, M. A., Poo, A. N. and et al. The implementation of adaptive isoplanar tool path generation for the machining of free-form surfaces[J]. International Journal of Advanced Manufacturing Technology,2005,26 (7-8):852-860.
[103]蔡永林,席光,樊宏周,等.任意曲面叶轮五坐标数控加工刀位轨迹生成[J].西安交通大学学报,2003,37(1)：77-80.
[104]孙玉文,束长林,刘健.基于矢量分析的数控加工轨迹设计方法研究[J].机械工程学报,2005,41(3)：160-164.
[105]王太勇,张志强,王涛,等.复杂参数曲面高精度刀位轨迹规划算法[J].机械工程学报,2007,43(12)：109-113.
[106]Lee, S. G., Kim, H. C. and Yang, M. Y. Mesh-based tool path generation for constant scallop-height machining[J]. The International Journal of Advanced Manufacturing Technology,2008,37 (1-2):15-22.
[107]陈晓兵,廖文和,吴海兵,等.三角网格表面等残留高度刀轨生成算法[J].计算机辅助设计与图形学学报,2009,21(12)：1800-1804.
[108]吴福忠.基于包络面构建的等残留高度刀具路径规划[J].农业机械学报,2009,40(1)：217-221.
[109]Xu, R. F., Chen, Z. T., Chen, W. Y. and et al. Dual drive curve tool path planning method for 5-axis NC machining of sculptured surfaces[J]. Chinese Journal of Aeronautics,2010,23 (4): 486-494.
[110]Lee, Y. S. and Chang, T. C.2-Phase approach to global tool interference avoidance in 5-axis machining[J]. Computer-Aided Design,1995,27 (10):715-729.
[111]张和明,张玉云,熊光楞.复杂曲面五坐标数控加工干涉检查与刀位修正[J].清华大学学报(自然科学版),1998,38(2)：65-68.
[112]蔡永林,席光,樊宏周,等.曲面5轴加工中全局十涉检查与刀位修正[J].机械工程学报,2002,38(9)：131-135.
[113]陈松,姜虹,李学艺,等.自由曲面五坐标数控加工十涉检查[J].工程图学学报,2003(3)：31-36.
[114]陈丽萍,陈燕,胡德金.非球头刀数控加工无干涉刀位的计算方法[J].上海交通大学学报,2004,38(7)：1130-1133.
[115]严思杰,周云飞,陈学东,等.五轴NC加工十涉检查与避免算法研究[J].中国机械工程,2006,17(17)：1822-1825.
[116]杨长祺,贾维,刘海江.多轴机床加上复杂自由曲面的刀底十涉避免[J].机械工程学报,2006,42(6)：174-178.
[117]李万军,赵东标,牛敏,等.五轴加工全局干涉检查及其避免[J].计算机集成制造系统,2011,17(5)：1011-1015.
[118]Hwang, Y. R. and Ho, M. T. Estimation of maximum allowable step length for five-axis cylindrical machining[J]. Journal of Manufacturing Processes,2000,2 (1):15-24.
[119]Hwang, Y. R. and Liang, C. S. Cutting error analysis for spindle-tilting type five-axis NC machines[J]. The International Journal of Advanced Manufacturing Technology,1998,14 (6): 399-405.
[120]陈金成,徐志明,钟廷修,等.机床沿曲线高速加上时的运动学与动力学特性分析[J].机械工程学报,2002,38(1)：31-34.
[121]蒋勇敏,许明恒.数控加工轨迹运动控制建模及仿真研究[J].中国机械工程,2006,17(21)：2220-2223.
[122]Ho, M. C., Hwang, Y. R. and Hu, C. H. Five-axis machining improvement via cutting error control and tool orientation smoothing[D]. Taoyuan:National Central University,2004.
[123]Jun, C. S., Cha, K. and Lee, Y. S. Optimizing tool orientation for 5-axis machining by configuration space search method[J]. Computer-Aided Design 2003,35 (6):549-566.
[124]王丹,陈志同,陈五一.五轴加工中非线性误差的检测和处理方法[J].北京航空航天大学学报,2008,34(9)：1003-1006.
[125]Wang N, Tang K. Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath[J]. Computer-Aided Design,2007,39 (10):841-852.
[126]罗明,吴宝海,李山,张定华.自由曲面五轴加工刀轴矢量的运动学优化方法[J].机械工程学报,2009,45(9)：158-163.
[127]段春辉.五轴联动数控机床通用后置处理系统研制[D].成都：西南交通大学,2004.
[128]唐清春,吴汉夫.CAM后置处理技术现状及发展趋势[J].计算机应用技术,2009,36(12)：43-45.
[129]韩向利,袁哲俊.五坐标机床后置处理方法的研究[J].组合机床与自动化加工技术,1995.3：34-37.
[130]张利波,周济.开放式数控编程通用后置处理器[J].机械电子,1996,4：3-4.
[131]刘日良,张承瑞,宋现春,等.5轴数控机床坐标系统的一个特例及其后置处理方法[J].机械设计与制造工程,2002,31(3)：61-62.
[132]刘雄伟,张定华等.数控加工理论与编程技术[M].北京：机械工业出版社,2003.
[133]陈涛,彭芳瑜,周云飞.基于结构误差补偿的多坐标机床后置变换[J].中国制造业信息化,2003,32(2)：88-90.
[134]赵云峰,程丽,杨彦东,等.面向并联机床的后置处理方法研究[J].机械设计,2009,26(8)：25-27.
[135]郑2默,林浒,盖荣丽.基于通用运动模型的五轴机床后置处理[J].计算机集成制造系统,2010,16(5)：1006-1011.
[136]陈维桓.微分几何[M].北京：北京大学出版社,2006.
[137]陈丽萍,陈燕,胡德金.一种快速完备的自由曲线和曲面间最短距离求取算法[J].上海交通大学学报,2003,37：41-44.
[138]龚堰珏,负敏,王小椿.自由曲线曲面距离迭代算法的研究及其可视化处理[J].小型微型计算机系统,2003,24(12)：2306-2308.
[139]Ma, Y. L. and Hewitt, W. T. Point inversion and projection for NURBS curve and surface: Control polygon approach[J]. Computer Aided Geometric Design,2003,20 (2):79-99.
[140]董明晓,郑康平,许伯彦,等.一种快速求取空间点到曲面最短距离的算法[J].组合机床与自动化加工技术,2004,9：11-12.
[141]Hu, S. M. and Wallner, J. A second order algorithm for orthogonal projection onto curves and surfaces[J]. Computer Aided Geometric Design,2005,22 (3),251-260.
[142]Selimovic, I. Improved algorithms for the projection of points on NURBS curves and surfaces[J]. Computer Aided Geometric Design,2006,23 (5):439-445.
[143]李淑萍,闫坤,李环,等.利用单纯形法优化点到曲面的最近距离[J].工程图学学报,2006.1：116-118.
[144]Chen, X. D., Yong, J. H., Wang, G. Z. and et al. Computing the minimum distance between a point and a NURBS curve[J]. Computer-Aided Design,2008,40 (10-11):1051-1054.
[145]Chen, X. D., Xu, G., Yong, J. H. and et al. Computing the minimum distance between a point and a clamped B-spline surface[J]. Graphical Models,2009,71 (3):107-112.
[146]Liu, X. M., Yang, L., Yong, J. H. and et al. A torus patch approximation approach for point projection on surfaces[J]. Computer Aided Geometric Design,2009,26 (5):593-598.
[147]徐汝锋,陈志同,陈五一.计算点到曲面最短距离的网格法[J].计算机集成制造系统, 2011,17(1)：95-100.
[148]黄慕欢,林茜.正交矩阵在空间坐标变换中的作用[J].高等数学研究,2009,12(2)：24-26.
[149]陈宏远.汽车覆盖件CAD模型重构及成形过程数值模拟[D].西安：西北工业大学,2006.
[150]金涛,陈建良,童水光.逆向工程技术研究进展[J].中国机械工程,2002,13(16)：1430-1437.
[151]王峰.汽车车身曲面反求中点云分块方法研究及应用[D].淄博：山东理工大学,2006.
[152]安晓超.汽车覆盖件逆向重构及拉延成形数值模拟[D].镇江：江苏大学,2008.
[153]谢斌.逆向工程在汽车覆盖件成形技术上的应用[D].合肥：合肥工业大学,2005.
[154]杨宪武.车身曲面重构中三维散乱点云的参数化及拟合[D].淄博：山东理工大学,2007.
[155]杨科彪.车身测量数据点云三角剖分方法的研究[D].淄博：山东理工大学,2008.
[2]曹丽萍.浅谈数控技术的发展[J].工业技术,2009,24：124.
[3]姚乐.我国数控技术的现状及发展方向[J].科技管理研究,2009,11：261-262.
[4]张承瑞.数控技术发展趋势[J].现代制造技术与装备,2007,2：3-6.
[5]机械工程学科发展战略报告(2011-2020).国家自然科学基金委员会工程与材料科学部,科学出版社,2010.
[6]国家中长期科学和技术发展规划纲要(2006-2020).中华人民共和国国务院,2006.
[7]张洪.从增大行距宽度减少波纹度的角度看型面加工发展的方向[C].北京航空学院庆祝建校三十周年论文集,北京：北京航空学院,1982.
[8]李志强.曲面的宽行数控加工理论研究及其在大型抛物面天线加工中的应用[D].北京：北京航空航天大学,2004.
[9]王丹.双角度约束刀轨优化理论及其在自由曲面加工中的应用[D].北京：北京航空航天大学.2009.
[10]王丹,徐汝锋,陈五一.基于UG二次开发的宽行加工算法实现[J].机床与液压,2008,36(12)：32-34.
[11]易红.数控技术[M].机械工业出版社,2005.
[12]Piegl, L., Tiller, W. Curve and surface construction using rational B-splines[J]. Computer-Aided Design,1987,19 (9):485-498.
[13]Piegl, L., Tiller, W. The NURBS book[M]. Berlin Heidelberg:Springer-Verlag, Section Edition,1997.
[14]Farin, G. Curve and surface for CAGD[M]. Morgan Kaufmann, The fifth edition:A practical guide,2001.
[15]ANSI, U. S. Product Data Association (US PRO), ANS US PRO/IPO-100-1996:The Initial Graphics Exchange Specification (IGES) Version 5.3, IGES/PDES,1996.
[16]ISO Secretariat, National Institute of Standards and Technology (NIST), Standard for The Exchange of Product model data (STEP), ISO 10303, A series of document, Part 42: Geometric and Topological Representation, ISO 10303-42. MD:Gaithersburg,1994.
[17]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001.
[18]Mason, F. Die and mold finishing-how fast?[J]. Manufacturing Engineering,1995,115 (33): 35-36.
[19]Kim, B. H. and Chu, C. N. Effect of cutter mark on surface roughness and scallop height in sculptured surface machining[J]. Computer-Aided Design,1994,26 (3):179-188.
[20]Kruth, J. P. and Klewais, P. Optimization and dynamic adaptation of cutter inclination during five-axis milling of sculptured surfaces[J]. Annals of CIRP,1994,43 (1):443-448.
[21]Dragomatz, D. and Mann, S. A classified bibliography of literature on NC milling path generation [J]. Computer-Aided Design,1997,29 (3):239-247.
[22]Vickers, G. W. and Bedi, S. The definition and manufacture of compound curvature surfaces using G-Surf[J]. Computers in Industry,1985,6:173-183.
[23]Vickers, G. W. and Quan, K. W. Ball-mills versus end-mills for curved surface machining[J]. Journal of Engineering for Industry,1989,111 (22):22-26.
[24]Warkentin, A. Multi-point machining of sculptured surfaces[D]. Waterloo, Ontario, Canada: University of Waterloo,1997.
[25]王小椿,吴序堂,李艳斌.密切曲率法一一种自由曲面加上的新概念[J].西安交通大学学报,1992,26(5)：51-58.
[26]Wang, X. C., Li, Y. B., Ghosh, S. K. and Wu, X. T. Curvature catering-a new approach in manufacturing of sculptured surface (part1.Theorem)[J]. Journal of Materials Processing Technology,1993,38 (1-2):159-176.
[27]Wang, X. C., Li, Y. B., Ghosh, S. K. and Wu, X. T. Curvature catering-a new approach in manufacturing of sculptured surface (part2.methodolody)[J]. Journal of Materials Processing Technology,1993,38 (1-2):177-194.
[28]Li, F., Wang, X. C., Ghosh, S. K. and Kong, D. Z. Gouge detection and tool position modification for five-axis NC machining of sculptured surfaces[J]. Journal of Materials Processing Technology,1995,48 (1-4):739-745.
[29]Li, F., Wang, X. C., Ghosh, S. K. and Kong, D. Z. Tool-path generation for machining sculptured surfaces[J]. Journal of Materials Processing Technology,1995,48 (1-4):811-816.
[30]张瑞乾,冯学斌,卜国磊,等.用密切曲率法加工边界受限制的曲面[J].机械科学与技术,1997,16(4)：674-677.
[31]张瑞乾,王小椿,吴序堂.用密切曲率法加工自由曲面及其刀位轨迹的排列[J].西安交通大学学报,1997,31(12)：55-60.
[32]张瑞乾,沈兵,王小椿,等.用二阶密切曲率法法加工自由曲面[J].机械工程学报,1998,34(2)：87-92.
[33]沈兵,高军,张瑞乾,等.用密切曲率法加上自由曲面[J].新技术新工艺,1998,4：19-21.
[34]Jensen, C. G. and Anderson, D. C. Accurate tool placement and orientation for finish surface machining[J]. Journal of Design and Manufacturing,1993,3 (4):251-261.
[35]Jensen, C. G., Anderson, D. C. and Mullins, S. H. Scallop elimination based on precise 5-axis tool placement, orientation, and step-over calculations[J]. Advances in Design Automation ASME,1993,65 (2):535-544.
[36]Rao, N., Bedi, S. and Buchal, R. Implementation of the principal-axis method for machining of complex surfaces[J]. International Journal of Advanced Manufacturing Technology,1996, 11:249-257.
[37]Rao, N., Ismail, F. and Bedi, S. Tool path planning for five-axis machining using the principal axis method[J]. International Journal of Machine Tools and Manufacture,1997,37 (7): 1025-1040.
[38]陈涛,钟毅芳,周济.自由曲面5轴数控加工刀位轨迹的生成算法[J].机械工程学报,2001,37(12)：100-103.
[39]杨德武,彭芳瑜,周云飞.基于主曲率匹配的五坐标刀位轨迹优化[J].华中科技大学学报,2001,29(12)：8-11.
[40]李志强,陈五一.复杂曲面五坐标加工中主曲率匹配法的刃形误差[J].机械工程学报,2006,42(2)：135-140.
[41]Warkentin, A., Bedi, S. and Ismail, F.5-axis milling of spherical surfaces[J]. International Journal of Machine Tools and Manufacture,1995,36 (2):229-243.
[42]Warkentin, A., Ismail, F. and Bedi, S. Intersection approach to multi-point machining of sculptured surfaces[J]. Computer Aided Geometric Design,1998,15 (6):567-584.
[43]Warkentin, A., Ismail, F. and Bedi, S. Multi-point tool positioning strategy for 5-axis machining of sculptured surfaces[J]. Computer Aided Geometric Design,2000,17 (1): 83-100.
[44]Warkentin, A. Multi-point machining with anti-gouging and scallop height control[J]. Transactions of the CSME/de la SCGM,2004,28 (1):25-42.
[45]Warkentin, A., Ismail, F. and Bedi, S. Comparison between multi-point and other 5-axis tool position strategies[J]. International Journal of Machine Tools and Manufacture,2000,40 (2): 185-208.
[46]倪炎榕,马登哲,张洪,等.圆环面刀具五坐标数控加工复杂曲面优化刀位算法[J].机械工程学报,2001,37(2)：87-91.
[47]倪炎榕,张洪,郭静萍.圆环面刀具五坐标数控加工复杂曲面刀位算法分析[J].机械科学与技术,2002,21(2)：188-190.
[48]吕雪丽,张洪.广域曲率吻合原则与复杂曲面数控加工的全面优化[J].机械设计与制造,2003.5：94-96.
[49]吕雪丽.圆环面刀具五坐标数控宽行线接触加工复杂曲面的研究[D].北京：北京航空航天大学.2003.
[50]李志强,陈五一,张洪.四坐标精密加工大型曲面中的刀位优化[J].中国机械工程,2005,16(4)：311-314.
[51]Engeli, M., Waldvogel, J. and Schnider, T. Method for processing work pieces by removing material[J]. United States Patent,2002, US 6 485 236[P].
[52]钟慧琴,金曼,肖俊,等Hermite五坐标数控加工刀位算法研究[J].新技术新工艺,2005,9：4-6.
[53]王瑞秋,边永梅,陈五一Hermite算法的收敛性分析及其改进[J].北京航空航天大学学报,2006,32(2)：239-243.
[54]王瑞秋,陈五一,金曼.多点切触加工中的局部干涉分析[J].航空航天大学学报,2006,32(5)：580-584.
[55]Gray, P., Bedi, S. and Ismail, F. Rolling ball method for 5-axis surface machining[J]. Computer-Aided Design,2003,35 (4):347-357.
[56]Gray, P., Ismail, F. and Bedi, S. Graphics-assisted rolling ball method for 5-axis surface mchining[J]. Computer-Aided Design,2004,36 (7):653-663.
[57]Gray, P., Bedi, S. and Ismail, F. Arc-intersect method for 5-axis tool positioning[J]. Computer-Aided Design,2005,37 (7):663-674.
[58]Gray, P., Ismail, F. and Bedi, S. Arc-intersect method for 311/22-axis tool paths on a 5-axis machine[J]. International Journal of Machine Tools and Manufacture,2007,47:182-190.
[59]金曼,张俐,陈志同.圆环面刀具五坐标加上端点误差控制刀位优化[J].北京航空航天大学学报,2006,32(9)：1125-1128.
[60]王瑞秋,金曼,陈五一,等.端点误差控制刀位算法的改进[J].航空学报,2007,28(2)：438-444.
[61]Cho, H. D., Jun, Y. T. and Yang, M. Y. Five-axis CNC milling for effective machining of sculptured surfaces[J]. International Journal of Production Research,1993,31 (11): 2559-2573.
[62]Li, S. X, Jerard, R. B.5-axis machining of sculptured surfaces with a flat-end cutter[J]. Computer-Aided Design,1994,26 (3):165-178.
[63]Liu, X. W. Five-axis NC cylindrical milling of sculptured surfaces[J]. Computer-Aided Design,1995,27 (12):887-894.
[64]Lee, Y. S. Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining[J]. Computer-Aided Design,1997,29 (7):507-521.
[65]Yoon, J. H., Pottmann, H. and Lee, Y. S. Locally optimal cutting positions for 5-axis sculptured surface machining[J]. Computer-Aided Design,2003,35 (1):69-81.
[66]Bedi, S., Mann, S. and Menzel, C. Flank milling with flat end cutters[J]. Computer-Aided Design,2003,35 (3):293-300.
[67]Menzel, C., Bedi, S. and Mann, S. Triple tangent flank milling of ruled surfaces[J]. Computer-Aided Design,2004,36 (3):289-296.
[68]Chiou, J. C. J. Accurate tool position for five-axis ruled surface machining by swept envelope approach[J]. Computer-Aided Design,2004,36 (10):967-974.
[69]蔡永林,席光,查建中.任意扭曲直纹面叶轮数控侧铣刀位计算与误差分析[J].西安交通大学学报,2004,38(5)：517-520.
[70]吴广宽,席光.自由曲面三元叶轮5轴数控粗加工刀位生成算法[J].西安交通大学学报,2005,39(7)：731-734.
[71]王瑞秋,陈五一.多点切触加工的割线法[J].机械上程学报,2006,42(7)：203-206.
[72]曹利新,祁少华.基于散乱数据点的数控加工刀位直接生成[J].中国机械工程,2006,17(11)：1101-1104.
[73]席光,吴广宽,郑健生.基于半径和角偏置的直纹面五坐标加工刀位生成算法[J].机械工程学报,2008,44(4)：92-96.
[74]Cao, L. X., Gong, H. and Liu, J. The offset approach of machining free form surface part 1: Cylindrical cutter in five-axis NC machine tools[J]. Journal of Materials Processing Technology,2006,174 (1-3):298-304.
[75]Cao, L. X., Gong, H. and Liu, J. The offset approach of machining free form surface part 2: Toroidal cutter in 5-axis NC machine tools[J]. Journal of Materials Processing Technology, 2007,184 (1-3):6-11.
[76]李正强,陈志同,肖俊.鼓形刀宽行刀位优化纬线分割算法[J].北京航空航天大学学报,2007,33(6)：731-735.
[77]孔马斌,胡自化,李慧,等.基于等距曲面的弧面凸轮单侧面数控加工刀位优化算法[J].机械工程学报,2008,44(11)：277-282.
[78]陈志同,张洪,张俐.采用经线分划刀具的多坐标端铣加工刀位优化方法[P].中国专利,200810106647.7,2008-05-14.
[79]Gong, H., Cao, L. X. and Liu, J. Second order approximation of tool envelope surface for 5-axis machining with single point contact[J]. Computer-Aided Design,2008,40 (5): 604-615.
[80]Gong, H., Fang, F. Z. and Hu, X. T. et al. Optimization of tool positions locally based on the BCELTP for 5-axis machining of free-form surfaces[J]. Computer-Aided Design,2010,42 (6): 558-570.
[81]樊文刚,王小椿.快速进给铣刀五坐标端铣加工刀位计算[J].北京交通大学学报,2010,34(1)：154-157.
[82]徐汝锋,陈五一,陈志同.基于经线划分的非圆截面环形刀具刀位优化算法[J].航空学报,2010,31(2)：410-417.
[83]Zhu, L. M., Ding, H. and Xiong, Y. L. Third Order Point Contact Approach for Five-Axis Sculptured Surface Machining Using Non-ball End Tolls-Part Ⅰ:Third Order Approximation of Tool Envelope Surface[J]. Sci China Ser E-Tech Sci,2010,53:1904-1912.
[84]Zhu, L. M., Ding, H. and Xiong, Y. L. Third order point contact approach for five-axis sculptured surface machining using non-ball end tools-Part Ⅱ:Tool positioning strategy [J]. Sci China Ser E-Tech Sci,2010,53:2190-2197.
[85]杨长棋.复杂曲面多轴加上的高精度、高效率数控编程系统研究[D].重庆：重庆大学,2004.
[86]丁汉,毕庆贞,朱利民,等.五轴数控加工的刀具路径规划与动力学仿真[J].科学通报,2010,55(25)：2510-2519.
[87]Wang, H., Chang, H., Wysk, R. A. and Chandawarkar, A. On the efficiency of NC tool path planning for face milling operations[J]. Journal of Engineering for Industry,1987,109 (4): 370-376.
[88]Chiou, C. J., Lee, Y. S. A machining potential field approach to tool path generation for multi-axis sculptured surface machining[J]. Computer-Aided Design,2002,34 (5):357-371.
[89]Broomhead, P. and Edkins, M. Generating NC data at the machine tool for the manufacture of free-form surfaces[J]. International Journal of Production Research,1986,24 (1):1-14.
[90]Loney, G. and Ozsoy, T. NC machining of free-form surfaces[J]. Computer-Aided Design, 1987,19 (2):85-90.
[91]Elber, G. and Cohen, E. Toolpath generation for freeform surface models[J]. Computer-Aided Design,1994,26 (6):490-496.
[92]Bobrow, J. E. NC machine tool path generation from OSG part representations[J]. Computer-Aided Design,1985,17 (2):69-72.
[93]Yong, S. S. and Lee, K. NC milling tool path generation for arbitrary pockets defined by sculptured surfaces[J]. Computer-Aided Design,1990,22 (5):273-284.
[94]Huang, Y. and Oliver, J. Non-constant parameter NC tool path generation of sculptured surfaces[J]. International Journal of Advanced Manufacturing Technology,1994,9 (5): 281-290.
[95]Suresh, K. and Yang, D. C. H. Constant scallop-height machining of free-form surfaces[J]. Journal of Engineering for Industry,1994,116 (2):253-259.
[96]Sarma, R. and Dutta, D. Geometry and generation of NC tool paths[J]. Journal of Mechanical Design, Transactions of the ASME,1997,119 (2):253-258.
[97]Lee, Y. S. Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining[J]. Computer-Aided Design,1998,30 (7):559-570.
[98]Feng, H. and Li, H. Constant scallop-height tool path generation for three-axis sculptured surface machining[J]. Computer-Aided Design,2002,34 (9):647-654.
[99]Tournier, C. and Duc, E. A surface based approach for constant scallop height tool-path generation[J]. The International Journal of Advanced Manufacturing Technology,2002,19 (5): 318-324.
[100]Tournier, C. and Duc, E. Iso-scallop height tool path generation in 5-axis milling[J]. The International Journal of Advanced Manufacturing Technology,2005,25 (9):867-875.
[101]Ding, S., Mannan, M. A., Poo, A. N. and et al. Adaptive iso-planar tool path generation for the machining of free-form surfaces[J]. Computer-Aided Design,2003,35 (2):141-153.
[102]Ding, S., Mannan, M. A., Poo, A. N. and et al. The implementation of adaptive isoplanar tool path generation for the machining of free-form surfaces[J]. International Journal of Advanced Manufacturing Technology,2005,26 (7-8):852-860.
[103]蔡永林,席光,樊宏周,等.任意曲面叶轮五坐标数控加工刀位轨迹生成[J].西安交通大学学报,2003,37(1)：77-80.
[104]孙玉文,束长林,刘健.基于矢量分析的数控加工轨迹设计方法研究[J].机械工程学报,2005,41(3)：160-164.
[105]王太勇,张志强,王涛,等.复杂参数曲面高精度刀位轨迹规划算法[J].机械工程学报,2007,43(12)：109-113.
[106]Lee, S. G., Kim, H. C. and Yang, M. Y. Mesh-based tool path generation for constant scallop-height machining[J]. The International Journal of Advanced Manufacturing Technology,2008,37 (1-2):15-22.
[107]陈晓兵,廖文和,吴海兵,等.三角网格表面等残留高度刀轨生成算法[J].计算机辅助设计与图形学学报,2009,21(12)：1800-1804.
[108]吴福忠.基于包络面构建的等残留高度刀具路径规划[J].农业机械学报,2009,40(1)：217-221.
[109]Xu, R. F., Chen, Z. T., Chen, W. Y. and et al. Dual drive curve tool path planning method for 5-axis NC machining of sculptured surfaces[J]. Chinese Journal of Aeronautics,2010,23 (4): 486-494.
[110]Lee, Y. S. and Chang, T. C.2-Phase approach to global tool interference avoidance in 5-axis machining[J]. Computer-Aided Design,1995,27 (10):715-729.
[111]张和明,张玉云,熊光楞.复杂曲面五坐标数控加工干涉检查与刀位修正[J].清华大学学报(自然科学版),1998,38(2)：65-68.
[112]蔡永林,席光,樊宏周,等.曲面5轴加工中全局十涉检查与刀位修正[J].机械工程学报,2002,38(9)：131-135.
[113]陈松,姜虹,李学艺,等.自由曲面五坐标数控加工十涉检查[J].工程图学学报,2003(3)：31-36.
[114]陈丽萍,陈燕,胡德金.非球头刀数控加工无干涉刀位的计算方法[J].上海交通大学学报,2004,38(7)：1130-1133.
[115]严思杰,周云飞,陈学东,等.五轴NC加工十涉检查与避免算法研究[J].中国机械工程,2006,17(17)：1822-1825.
[116]杨长祺,贾维,刘海江.多轴机床加上复杂自由曲面的刀底十涉避免[J].机械工程学报,2006,42(6)：174-178.
[117]李万军,赵东标,牛敏,等.五轴加工全局干涉检查及其避免[J].计算机集成制造系统,2011,17(5)：1011-1015.
[118]Hwang, Y. R. and Ho, M. T. Estimation of maximum allowable step length for five-axis cylindrical machining[J]. Journal of Manufacturing Processes,2000,2 (1):15-24.
[119]Hwang, Y. R. and Liang, C. S. Cutting error analysis for spindle-tilting type five-axis NC machines[J]. The International Journal of Advanced Manufacturing Technology,1998,14 (6): 399-405.
[120]陈金成,徐志明,钟廷修,等.机床沿曲线高速加上时的运动学与动力学特性分析[J].机械工程学报,2002,38(1)：31-34.
[121]蒋勇敏,许明恒.数控加工轨迹运动控制建模及仿真研究[J].中国机械工程,2006,17(21)：2220-2223.
[122]Ho, M. C., Hwang, Y. R. and Hu, C. H. Five-axis machining improvement via cutting error control and tool orientation smoothing[D]. Taoyuan:National Central University,2004.
[123]Jun, C. S., Cha, K. and Lee, Y. S. Optimizing tool orientation for 5-axis machining by configuration space search method[J]. Computer-Aided Design 2003,35 (6):549-566.
[124]王丹,陈志同,陈五一.五轴加工中非线性误差的检测和处理方法[J].北京航空航天大学学报,2008,34(9)：1003-1006.
[125]Wang N, Tang K. Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath[J]. Computer-Aided Design,2007,39 (10):841-852.
[126]罗明,吴宝海,李山,张定华.自由曲面五轴加工刀轴矢量的运动学优化方法[J].机械工程学报,2009,45(9)：158-163.
[127]段春辉.五轴联动数控机床通用后置处理系统研制[D].成都：西南交通大学,2004.
[128]唐清春,吴汉夫.CAM后置处理技术现状及发展趋势[J].计算机应用技术,2009,36(12)：43-45.
[129]韩向利,袁哲俊.五坐标机床后置处理方法的研究[J].组合机床与自动化加工技术,1995.3：34-37.
[130]张利波,周济.开放式数控编程通用后置处理器[J].机械电子,1996,4：3-4.
[131]刘日良,张承瑞,宋现春,等.5轴数控机床坐标系统的一个特例及其后置处理方法[J].机械设计与制造工程,2002,31(3)：61-62.
[132]刘雄伟,张定华等.数控加工理论与编程技术[M].北京：机械工业出版社,2003.
[133]陈涛,彭芳瑜,周云飞.基于结构误差补偿的多坐标机床后置变换[J].中国制造业信息化,2003,32(2)：88-90.
[134]赵云峰,程丽,杨彦东,等.面向并联机床的后置处理方法研究[J].机械设计,2009,26(8)：25-27.
[135]郑2默,林浒,盖荣丽.基于通用运动模型的五轴机床后置处理[J].计算机集成制造系统,2010,16(5)：1006-1011.
[136]陈维桓.微分几何[M].北京：北京大学出版社,2006.
[137]陈丽萍,陈燕,胡德金.一种快速完备的自由曲线和曲面间最短距离求取算法[J].上海交通大学学报,2003,37：41-44.
[138]龚堰珏,负敏,王小椿.自由曲线曲面距离迭代算法的研究及其可视化处理[J].小型微型计算机系统,2003,24(12)：2306-2308.
[139]Ma, Y. L. and Hewitt, W. T. Point inversion and projection for NURBS curve and surface: Control polygon approach[J]. Computer Aided Geometric Design,2003,20 (2):79-99.
[140]董明晓,郑康平,许伯彦,等.一种快速求取空间点到曲面最短距离的算法[J].组合机床与自动化加工技术,2004,9：11-12.
[141]Hu, S. M. and Wallner, J. A second order algorithm for orthogonal projection onto curves and surfaces[J]. Computer Aided Geometric Design,2005,22 (3),251-260.
[142]Selimovic, I. Improved algorithms for the projection of points on NURBS curves and surfaces[J]. Computer Aided Geometric Design,2006,23 (5):439-445.
[143]李淑萍,闫坤,李环,等.利用单纯形法优化点到曲面的最近距离[J].工程图学学报,2006.1：116-118.
[144]Chen, X. D., Yong, J. H., Wang, G. Z. and et al. Computing the minimum distance between a point and a NURBS curve[J]. Computer-Aided Design,2008,40 (10-11):1051-1054.
[145]Chen, X. D., Xu, G., Yong, J. H. and et al. Computing the minimum distance between a point and a clamped B-spline surface[J]. Graphical Models,2009,71 (3):107-112.
[146]Liu, X. M., Yang, L., Yong, J. H. and et al. A torus patch approximation approach for point projection on surfaces[J]. Computer Aided Geometric Design,2009,26 (5):593-598.
[147]徐汝锋,陈志同,陈五一.计算点到曲面最短距离的网格法[J].计算机集成制造系统, 2011,17(1)：95-100.
[148]黄慕欢,林茜.正交矩阵在空间坐标变换中的作用[J].高等数学研究,2009,12(2)：24-26.
[149]陈宏远.汽车覆盖件CAD模型重构及成形过程数值模拟[D].西安：西北工业大学,2006.
[150]金涛,陈建良,童水光.逆向工程技术研究进展[J].中国机械工程,2002,13(16)：1430-1437.
[151]王峰.汽车车身曲面反求中点云分块方法研究及应用[D].淄博：山东理工大学,2006.
[152]安晓超.汽车覆盖件逆向重构及拉延成形数值模拟[D].镇江：江苏大学,2008.
[153]谢斌.逆向工程在汽车覆盖件成形技术上的应用[D].合肥：合肥工业大学,2005.
[154]杨宪武.车身曲面重构中三维散乱点云的参数化及拟合[D].淄博：山东理工大学,2007.
[155]杨科彪.车身测量数据点云三角剖分方法的研究[D].淄博：山东理工大学,2008.