基于CAD的公差分析与设计
|
摘要
近年来，随着计算机信息技术的迅猛发展，现代机械制造业依托计算机信息技术，取得了快速的进步。在这种背景下，计算机集成制造系统(CMIS)、计算机辅助设计与制造技术(CAD／CAM)的研究与应用取得了重大的突破和引人注目的成就，但是，计算机辅助公差设计技术(Computer Aided Tolerance，简称CAT)作为CAD／CAM集成的关键技术之一，其发展远远落后于CAD／CAM的发展。针对CAT技术发展的现状，本文在CAT技术的研究与应用方面主要做了如下工作：
1、介绍了计算机辅助公差设计研究的历史与现状；综述了国内外计算机辅助公差设计研究方面的阶段性成果；提出本文的主要研究内容和总体构架。
2、介绍尺寸链的相关基础知识；提出尺寸链数学模型，分析了以图论为基础的数学模型的建立；分析了以深度优先搜索法进行尺寸链自动生成的搜索过程。
3、传统公差分析方法是进行公差分析的基础，本文除对极值法和概率法进行分析外，还讨论了蒙特卡罗方法和数论方法，给出了运用数论方法进行公差分析的步骤，并对两种方法的统计特性进行比较研究。
4、介绍了运用传统的极值法和概率法进行公差综合的方法，基于零件公差与制造成本之间的关系，建立了公差成本模型，分析了最小成本法和线型规划法进行公差分配。
5、以前述计算机辅助公差设计关键技术理论研究为基础，综合公差与配合的查询及典型零件的公差设计，开发计算机辅助公差设计原型系统。
In recent years, along with the computer information technology swift and violent development, the modern mechanical manufacturing industry depended on the computer information technology, has made fast progress. Under this kind of background, significant breakthroughs and noticeable achievements have been obtained in the research and application of computer integrated manufacturing system (CMIS) and computer aided design and manufacturing (CAD/CAM). However, Computer Aided Tolerance (CAT) lags far behind CMIS and CAD/CAM. In view of the present situation in CAT technological development, the main work which has been done in this paper is as follows:
1、Introduce the history and present situation of research in Computer Aided Tolerance; Summarize the domestic and foreign gradual achievement in the research of CAT; Propose the main research contents and the skeleton of this paper.
2、Introduce the elementary knowledge related to dimension chain; Propose mathematical model of dimension chain, and analyze the process to build mathematical model; Analyze the search process to generate dimension chain using deep first search method.
3、Traditional methods in tolerance analysis including extreme value method and probability method are introduced. Besides Monte Carlo method and number theoretic method are discussed, and compared with their statistical characteristics. The approach using number theoretical method is describled.
4、Study Tolerance-Cost Model which is based on the relationship between tolerance and manufacturing cost. Minmum cost method and linear programming method are built to allocate tolerance, which are based on Tolerance-Cost model.
5、In the end, the prototype system is given out, which is developed on the theories studied before with VC6.0 and Access software.
1、介绍了计算机辅助公差设计研究的历史与现状；综述了国内外计算机辅助公差设计研究方面的阶段性成果；提出本文的主要研究内容和总体构架。
2、介绍尺寸链的相关基础知识；提出尺寸链数学模型，分析了以图论为基础的数学模型的建立；分析了以深度优先搜索法进行尺寸链自动生成的搜索过程。
3、传统公差分析方法是进行公差分析的基础，本文除对极值法和概率法进行分析外，还讨论了蒙特卡罗方法和数论方法，给出了运用数论方法进行公差分析的步骤，并对两种方法的统计特性进行比较研究。
4、介绍了运用传统的极值法和概率法进行公差综合的方法，基于零件公差与制造成本之间的关系，建立了公差成本模型，分析了最小成本法和线型规划法进行公差分配。
5、以前述计算机辅助公差设计关键技术理论研究为基础，综合公差与配合的查询及典型零件的公差设计，开发计算机辅助公差设计原型系统。
In recent years, along with the computer information technology swift and violent development, the modern mechanical manufacturing industry depended on the computer information technology, has made fast progress. Under this kind of background, significant breakthroughs and noticeable achievements have been obtained in the research and application of computer integrated manufacturing system (CMIS) and computer aided design and manufacturing (CAD/CAM). However, Computer Aided Tolerance (CAT) lags far behind CMIS and CAD/CAM. In view of the present situation in CAT technological development, the main work which has been done in this paper is as follows:
1、Introduce the history and present situation of research in Computer Aided Tolerance; Summarize the domestic and foreign gradual achievement in the research of CAT; Propose the main research contents and the skeleton of this paper.
2、Introduce the elementary knowledge related to dimension chain; Propose mathematical model of dimension chain, and analyze the process to build mathematical model; Analyze the search process to generate dimension chain using deep first search method.
3、Traditional methods in tolerance analysis including extreme value method and probability method are introduced. Besides Monte Carlo method and number theoretic method are discussed, and compared with their statistical characteristics. The approach using number theoretical method is describled.
4、Study Tolerance-Cost Model which is based on the relationship between tolerance and manufacturing cost. Minmum cost method and linear programming method are built to allocate tolerance, which are based on Tolerance-Cost model.
5、In the end, the prototype system is given out, which is developed on the theories studied before with VC6.0 and Access software.
引文
[1] 孙玉芹，孟兆新．机械精度设计基础[M]．北京：科学出版社，2003．225
[2] Bjorke O. Computer Aided Tolerancing[M].Tapir publishers: Norway,1978
[3] 张根保．计算机辅助公差综述[J]．中国机械工程，1996，7(5)：47-50
[4] 吴昭同，杨将新，等．计算机辅助公差优化设计[M]．杭州：浙江大学出版社，1999
[5] 张根宝．计算机辅助公差设计及其关键技术[A]．全国首届计算机辅助公差设计专题会议论文集[C]．杭州：浙江大学出版社，2000，6-14
[6] 吴昭同．现代质量工程中几个重要的研究进展[A]．全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000，15-23
[7] R. Weill. Tolerancing for Function[J]. CIRP Annals, 1988, 37(2): 1-8
[8] Hillyyard C. Dimensions and Tolerances in Shape Design[D]. UK: University of Cambridge, 1978
[9] Requicha A A G. Toward a Theory of Geometric Tolerancing[J]. International Journal Robotics Res, 1983, 2(4), 45-49
[10] Turner J U. Tolerance in Computer-Aided Geometric Design[D]. USA: Rensselaer Polytechnic Institute, 1978
[11] Jayarman R, Srimivasan V. Geometric Tolerance::I. Virtual Boundary Requirement[J]. IBM J. Res. Develop, 1989, 33(2): 90-104
[12] Clement A, Riviere A. Tolerancing versus nominal modeling in next gemeration CAD/CAM system[A]. Proceedings of 3rd CIRP Seminars on Aided Tolerancing[C]. London: Chapman & Hall, 1993, 97-114
[13] ANSI Standard Y14.5.1M-1994. Mathematical Definition of Dimensioning and Tolerancing Principles[S]. New York: American Society of Mechanical Engineers, 1994
[14] Martinsen, K. Statistical process control using vectorial tolerancing[A]. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing[C]. London: Chapman & Hall, 1995, 173-186
[15] ISO/TC213. http://www.ds.dk/
[16] Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing[C], Toronto, 1997
[17] Nassef A. Optimal allocation of types and magnitudes of geometric tolerances[D]. Canada: McMaster University, 1997
[18] Zhang H. C. Advanced tolerancing techniques[M].. John Wiley & Sons Inc. 1997
[19] Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing[C]. Netherlands, 1999
[20] Salomons O W. Computer support in the design of mechanical products, constraint specification and satisfaction in feature based design for manufacturing[D]. Netherlands: University of Twente, 1995
[21] 全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000
[22] Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing[C]. London: Chaman & Hall, 2001
[23] 杨将新．基于装配成功率的公差优化设计系统研究[D]．杭州：浙江大学，1996
[24] 方红芳．设计公差和工序公差并行设计的研究[D]．杭州：浙江大学，1997
[25] 刘玉生．基于数学定义的平面尺寸和形位公差建模与表示技术的研究[D]．杭州：浙江大学，1997
[26] 刘玉生，吴昭同，杨将新．基于成本模型的计算机辅助公差设计的研究[J]．浙江大学学报(自然科学版)，1995，29(6)：698-704
[27] 胡洁，基于变动几何约束网络的行为公差设计理论与方法研究[D]．杭州：浙江大学，2001
[28] 胡洁，吴昭同．面向装配的变动几何约束网络的生成方法研究[J]．计算机辅助设计与图形学报，2002，14(1)：79-82
[29] 李斌，张根保，徐宗俊．有向功能关系图OFRG功能实现的代数方法[J]．重庆大学学报，1999，22(1)：41-46
[30] 李斌，计算机辅助公差设计中有向功能关系图OFRG功能实现方法及应用[D]．重庆：重庆大学，1998
[31] 廖小云，刘延龄，程森林．柔薄型零件装配精度分析研究的现状与进展[A]．全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000，60-63
[32] 黄彤军．基于特征的公差分析和综合的研究．[D]，武汉：华中科技大学，1995．
[33] 孙绍民．CAD环境中公差分析与综合的研究[D]．哈尔滨：哈尔滨工业大学，1997
[34] 姬舒平．虚拟装配环境下公差并行设计方法的研究[D]．哈尔滨：哈尔滨工业大学，2000
[35] 闫艳，宁汝新．并行工程中的公差设计研究与开发[J]．计算机集成制造系统，2000，6(5)：43-47
[36] 闫艳，宁汝新，刘文丰．公差设计特征专家系统[A]．全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000，112-116
[37] 周志革，黄文振，张利．数论方法在统计公差分析中的应用[J]．机械工程学报，2000，36(3)：69-72
[38] 范秀敏．装配系统的公差建模与优化[D]．上海交通大学，1998
[39] Requicha A A G. Tolerances a theory of geometric tolerancing[J]. International Journal Robotics Res, 1983, 2(3): 437-464
[40] Srinivasan V, Jayarman R. Geometric tolerance: Ⅱ. conditional tolerances[J]. IBM J. Res. Develop, 1989, 33(2): 105-125
[41] Etesmi F A. Mathematical Model for Geometric Tolerancing. [J]. Journal of Mechanical Design, 1993, 115(3): 81-86
[42] Chase K W, Green W H. Design issues in mechanical tolerance analysis[J]. Manufacturing Review, 1988, 1:50-59
[43] Parimal Kopardekar. Tolerance allocation using neural networks[J]. Int. J. Adv. Manuf. Technol., 1995(10): 269-276
[44] Michael W, Siddall J N. Optimization Problem with Tolerance Assignment and Full Acceptance[J]. ASME Journal of Mechanical Design, 1981, 103(12): 842-848
[45] Patdison D B. The Application of Reliability Methods to Tolerancing[J]. ASME Journal of Mechanical Design, 1982, 104(7): 612-618
[46] Patdison D B. Tolerancing of Component Dimension in CAD[J]. Computer-Aided Design, 1984, 16(1): 25-32
[47] Patdison D B. Assessment and Optionzation of Dimensional Tolerances[J]. Computer-Aided Design, 1985, 17(4): 191-199
[48] Ting K L, Long Y F. Performance Quality and Tolerance Sensitivity of Mechanisms[J]. Journal of Mechanical Design, 1996, 118(3): 144-150
[49] Dong Z, Soom A. Automatic optimal tolerance design for related dimension chains[J]. ASME Manufacturing Review, 1990, 3(4): 262-271
[50] Lee W J, Woo T C. Tolerances: Their Analysis and Synthesis[J]. ASME Journal of Engineering for Industry, 1990, 110(5): 113-121
[51] Hoffmann P. Analysis of Tolerances and Process Inaccuracies in Discrete Part Manufacturing[J]. Computer-Aided Design, 1982, 14(2): 83-88
[52] Daniel F,Weill R, Bourdet P. Computer Aided Tolerancing and dimensioning in Process Planning[J]. Manuf. Tech. CIRP Ann.,1986, 35(1): 381-386
[53] Daniel F. Development of a Computer Program for the Optimation of Tolerance Transformation from Design to Manufacturing[D]. Haifa: Technion-Israel Institute of Technology, 1986
[54] 张荣瑞．尺寸链原理及其应用[M]．北京：机械工业出版社，1986．1-5
[55] 方开泰，王元．数论方法在统计中的应用[M]．北京：科学出版社，1996．19-30
[56] 周志革，黄文振，张利．一种计算随机变量函数均值和标准差的方法[J]．机械强度，2001，23(1)：107-110
[57] 方开泰，王元．数论方法在统计中的应用[M]．北京：科学出版社，1996．ⅰ-ⅲ
[58] 周志革，黄文振，张利．统计公差分析与综合的数论序贯优化方法[J]．上海交通大学学报，2000，34(3)：374-377
[59] 张永祥，古力，郭景富，景士伟，桑海峰，刘林茂．基于Visual C++的伪随机数发生器及其在离子输运模拟中的应用[J]．东北师大学报(自然科学版)，2002，34(2)：36-40
[60] 赵颖．球极投影变换在统计中的应用[J]．北京工业大学学报，2004，30(1)：120-123
[61] 周恺．面向装配的计算机辅助公差设计及选择装配[D]．北京理工大学，2003
[2] Bjorke O. Computer Aided Tolerancing[M].Tapir publishers: Norway,1978
[3] 张根保．计算机辅助公差综述[J]．中国机械工程，1996，7(5)：47-50
[4] 吴昭同，杨将新，等．计算机辅助公差优化设计[M]．杭州：浙江大学出版社，1999
[5] 张根宝．计算机辅助公差设计及其关键技术[A]．全国首届计算机辅助公差设计专题会议论文集[C]．杭州：浙江大学出版社，2000，6-14
[6] 吴昭同．现代质量工程中几个重要的研究进展[A]．全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000，15-23
[7] R. Weill. Tolerancing for Function[J]. CIRP Annals, 1988, 37(2): 1-8
[8] Hillyyard C. Dimensions and Tolerances in Shape Design[D]. UK: University of Cambridge, 1978
[9] Requicha A A G. Toward a Theory of Geometric Tolerancing[J]. International Journal Robotics Res, 1983, 2(4), 45-49
[10] Turner J U. Tolerance in Computer-Aided Geometric Design[D]. USA: Rensselaer Polytechnic Institute, 1978
[11] Jayarman R, Srimivasan V. Geometric Tolerance::I. Virtual Boundary Requirement[J]. IBM J. Res. Develop, 1989, 33(2): 90-104
[12] Clement A, Riviere A. Tolerancing versus nominal modeling in next gemeration CAD/CAM system[A]. Proceedings of 3rd CIRP Seminars on Aided Tolerancing[C]. London: Chapman & Hall, 1993, 97-114
[13] ANSI Standard Y14.5.1M-1994. Mathematical Definition of Dimensioning and Tolerancing Principles[S]. New York: American Society of Mechanical Engineers, 1994
[14] Martinsen, K. Statistical process control using vectorial tolerancing[A]. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing[C]. London: Chapman & Hall, 1995, 173-186
[15] ISO/TC213. http://www.ds.dk/
[16] Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing[C], Toronto, 1997
[17] Nassef A. Optimal allocation of types and magnitudes of geometric tolerances[D]. Canada: McMaster University, 1997
[18] Zhang H. C. Advanced tolerancing techniques[M].. John Wiley & Sons Inc. 1997
[19] Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing[C]. Netherlands, 1999
[20] Salomons O W. Computer support in the design of mechanical products, constraint specification and satisfaction in feature based design for manufacturing[D]. Netherlands: University of Twente, 1995
[21] 全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000
[22] Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing[C]. London: Chaman & Hall, 2001
[23] 杨将新．基于装配成功率的公差优化设计系统研究[D]．杭州：浙江大学，1996
[24] 方红芳．设计公差和工序公差并行设计的研究[D]．杭州：浙江大学，1997
[25] 刘玉生．基于数学定义的平面尺寸和形位公差建模与表示技术的研究[D]．杭州：浙江大学，1997
[26] 刘玉生，吴昭同，杨将新．基于成本模型的计算机辅助公差设计的研究[J]．浙江大学学报(自然科学版)，1995，29(6)：698-704
[27] 胡洁，基于变动几何约束网络的行为公差设计理论与方法研究[D]．杭州：浙江大学，2001
[28] 胡洁，吴昭同．面向装配的变动几何约束网络的生成方法研究[J]．计算机辅助设计与图形学报，2002，14(1)：79-82
[29] 李斌，张根保，徐宗俊．有向功能关系图OFRG功能实现的代数方法[J]．重庆大学学报，1999，22(1)：41-46
[30] 李斌，计算机辅助公差设计中有向功能关系图OFRG功能实现方法及应用[D]．重庆：重庆大学，1998
[31] 廖小云，刘延龄，程森林．柔薄型零件装配精度分析研究的现状与进展[A]．全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000，60-63
[32] 黄彤军．基于特征的公差分析和综合的研究．[D]，武汉：华中科技大学，1995．
[33] 孙绍民．CAD环境中公差分析与综合的研究[D]．哈尔滨：哈尔滨工业大学，1997
[34] 姬舒平．虚拟装配环境下公差并行设计方法的研究[D]．哈尔滨：哈尔滨工业大学，2000
[35] 闫艳，宁汝新．并行工程中的公差设计研究与开发[J]．计算机集成制造系统，2000，6(5)：43-47
[36] 闫艳，宁汝新，刘文丰．公差设计特征专家系统[A]．全国首届计算机辅助公差设计专题学术会议论文集[C]．杭州：浙江大学出版社，2000，112-116
[37] 周志革，黄文振，张利．数论方法在统计公差分析中的应用[J]．机械工程学报，2000，36(3)：69-72
[38] 范秀敏．装配系统的公差建模与优化[D]．上海交通大学，1998
[39] Requicha A A G. Tolerances a theory of geometric tolerancing[J]. International Journal Robotics Res, 1983, 2(3): 437-464
[40] Srinivasan V, Jayarman R. Geometric tolerance: Ⅱ. conditional tolerances[J]. IBM J. Res. Develop, 1989, 33(2): 105-125
[41] Etesmi F A. Mathematical Model for Geometric Tolerancing. [J]. Journal of Mechanical Design, 1993, 115(3): 81-86
[42] Chase K W, Green W H. Design issues in mechanical tolerance analysis[J]. Manufacturing Review, 1988, 1:50-59
[43] Parimal Kopardekar. Tolerance allocation using neural networks[J]. Int. J. Adv. Manuf. Technol., 1995(10): 269-276
[44] Michael W, Siddall J N. Optimization Problem with Tolerance Assignment and Full Acceptance[J]. ASME Journal of Mechanical Design, 1981, 103(12): 842-848
[45] Patdison D B. The Application of Reliability Methods to Tolerancing[J]. ASME Journal of Mechanical Design, 1982, 104(7): 612-618
[46] Patdison D B. Tolerancing of Component Dimension in CAD[J]. Computer-Aided Design, 1984, 16(1): 25-32
[47] Patdison D B. Assessment and Optionzation of Dimensional Tolerances[J]. Computer-Aided Design, 1985, 17(4): 191-199
[48] Ting K L, Long Y F. Performance Quality and Tolerance Sensitivity of Mechanisms[J]. Journal of Mechanical Design, 1996, 118(3): 144-150
[49] Dong Z, Soom A. Automatic optimal tolerance design for related dimension chains[J]. ASME Manufacturing Review, 1990, 3(4): 262-271
[50] Lee W J, Woo T C. Tolerances: Their Analysis and Synthesis[J]. ASME Journal of Engineering for Industry, 1990, 110(5): 113-121
[51] Hoffmann P. Analysis of Tolerances and Process Inaccuracies in Discrete Part Manufacturing[J]. Computer-Aided Design, 1982, 14(2): 83-88
[52] Daniel F,Weill R, Bourdet P. Computer Aided Tolerancing and dimensioning in Process Planning[J]. Manuf. Tech. CIRP Ann.,1986, 35(1): 381-386
[53] Daniel F. Development of a Computer Program for the Optimation of Tolerance Transformation from Design to Manufacturing[D]. Haifa: Technion-Israel Institute of Technology, 1986
[54] 张荣瑞．尺寸链原理及其应用[M]．北京：机械工业出版社，1986．1-5
[55] 方开泰，王元．数论方法在统计中的应用[M]．北京：科学出版社，1996．19-30
[56] 周志革，黄文振，张利．一种计算随机变量函数均值和标准差的方法[J]．机械强度，2001，23(1)：107-110
[57] 方开泰，王元．数论方法在统计中的应用[M]．北京：科学出版社，1996．ⅰ-ⅲ
[58] 周志革，黄文振，张利．统计公差分析与综合的数论序贯优化方法[J]．上海交通大学学报，2000，34(3)：374-377
[59] 张永祥，古力，郭景富，景士伟，桑海峰，刘林茂．基于Visual C++的伪随机数发生器及其在离子输运模拟中的应用[J]．东北师大学报(自然科学版)，2002，34(2)：36-40
[60] 赵颖．球极投影变换在统计中的应用[J]．北京工业大学学报，2004，30(1)：120-123
[61] 周恺．面向装配的计算机辅助公差设计及选择装配[D]．北京理工大学，2003