机械装配建模及零件尺寸标注自动化技术研究
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摘要
计算机科学的飞速发展、先进制造技术的广泛应用，正在促使传统的机械制造业发生根本性的变化。目前， CAD 、CAPP、CAM已取得了重大的突破和辉煌的成就。但是，机械产品公差设计的发展却远远地滞后于它们。公差设计的现状无法与目前CAD/CAPP/CAM集成发展的要求相适应，已成为制约它们进一步发展的瓶颈，迫切需要人们集中力量对计算机辅助尺寸和公差设计(CADT)进行深入的研究。利用计算机来辅助确定零件合适的尺寸标注模式、完成零件尺寸的自动化标注，是计算机辅助尺寸和公差设计研究领域中的一个重要部分，具有重大的工程意义。
本文就是在这样的一个大背景下，通过对“装配建模”、“尺寸链技术的应用”、 “尺寸标注模式的研究”等关键技术进行深入的研究，灵活应用图论中的相关数学工具，利用现代CAD环境所提供的比较方便的ActiveX技术，开发出相应的系统，确定出零件的功能尺寸和标注模式，实现零件尺寸标注的自动化。
在本文中完成了以下的工作：
(1) 通过分析装配体中零部件之间的约束关系，建立装配体的有向功能关系图(OFRG)装配模型。
(2) 运用图论中的最短路径搜索算法从装配模型中自动搜索出功能约束尺寸链，确定零件的功能尺寸。
(3) 根据尺寸标注所要求的正确性、完整性、清晰性及合理性等原则，用改进了的图论中的生成树算法，确定出零件的非功能尺寸，完成零件尺寸标注模式的分析。
(4) 自动对待标注的尺寸按方向进行分组、完成尺寸的优先级设定、在CAD环境下实现尺寸标注在零件图上的优化布置。
(5) 结合实例，详细地介绍了机械装配建模和零件尺寸标注自动化技术的完整的实现过程。
Rapid development of computer science and extensive application of Advanced Manufacturing Technology are bringing radical changes to traditional manufacturing. At present, great breakthrough and resplendent achievement have been made in CAD 、CAPP 、CAM. But the development of tolerancing design in mechanical product has lagged behind them greatly. The actuality of tolerancing design can't adapt to the requirement of CAD/CAPP/CAM integrated developing and has become the bottleneck of their further development, which makes it necessary to do in-depth research on Computer Aided Dimensioning and Tolerancing(CADT). It is an important part in CADT field and of great significance in engineering to utilize computer to aid engineers to ascertain the suitable dimensioning mode, complete the automatic dimensioning of parts.
In such a background, with the in-depth research on key techniques such as "assembly modeling"、 "application of dimension chain technique"、"research on dimensioning mode", the flexible application of correlative mathematical tools in Graph Theory, the utilization of relatively convenient ActiveX technique provided by CAD, the corresponding system has been developed to ascertain the functional dimensions and dimensioning mode, complete the automatic dimensioning of parts.
In this paper, the following tasks have been accomplished:
(1) Analyzing the constraint relation of parts to accomplish Oriented Functional Relationship Graph (OFRG) assembly modeling.
(2) Utilizing the shortest path algorithm in Graph Theory to search functional dimension chains automatically in the assembly model and ascertain the functional dimensions of the part.
(3) On the basis of the dimensioning principle of correctness, integrality, clearness and rationality, utilizing the modified spanning tree algorithm in Graph Theory to ascertain the non-functional dimensions, accomplish the dimensioning mode analysis of the part.
(4) Automatically grouping dimensions by their directions, accomplishing the priority level enactment of dimensions and implementing the optimal lay of dimensions on the part drawing under the CAD environment.
(5) Use the example to introducing the entire implementing process of the mechanical assembly modeling & automatic dimensioning technique on parts in detail.
本文就是在这样的一个大背景下，通过对“装配建模”、“尺寸链技术的应用”、 “尺寸标注模式的研究”等关键技术进行深入的研究，灵活应用图论中的相关数学工具，利用现代CAD环境所提供的比较方便的ActiveX技术，开发出相应的系统，确定出零件的功能尺寸和标注模式，实现零件尺寸标注的自动化。
在本文中完成了以下的工作：
(1) 通过分析装配体中零部件之间的约束关系，建立装配体的有向功能关系图(OFRG)装配模型。
(2) 运用图论中的最短路径搜索算法从装配模型中自动搜索出功能约束尺寸链，确定零件的功能尺寸。
(3) 根据尺寸标注所要求的正确性、完整性、清晰性及合理性等原则，用改进了的图论中的生成树算法，确定出零件的非功能尺寸，完成零件尺寸标注模式的分析。
(4) 自动对待标注的尺寸按方向进行分组、完成尺寸的优先级设定、在CAD环境下实现尺寸标注在零件图上的优化布置。
(5) 结合实例，详细地介绍了机械装配建模和零件尺寸标注自动化技术的完整的实现过程。
Rapid development of computer science and extensive application of Advanced Manufacturing Technology are bringing radical changes to traditional manufacturing. At present, great breakthrough and resplendent achievement have been made in CAD 、CAPP 、CAM. But the development of tolerancing design in mechanical product has lagged behind them greatly. The actuality of tolerancing design can't adapt to the requirement of CAD/CAPP/CAM integrated developing and has become the bottleneck of their further development, which makes it necessary to do in-depth research on Computer Aided Dimensioning and Tolerancing(CADT). It is an important part in CADT field and of great significance in engineering to utilize computer to aid engineers to ascertain the suitable dimensioning mode, complete the automatic dimensioning of parts.
In such a background, with the in-depth research on key techniques such as "assembly modeling"、 "application of dimension chain technique"、"research on dimensioning mode", the flexible application of correlative mathematical tools in Graph Theory, the utilization of relatively convenient ActiveX technique provided by CAD, the corresponding system has been developed to ascertain the functional dimensions and dimensioning mode, complete the automatic dimensioning of parts.
In this paper, the following tasks have been accomplished:
(1) Analyzing the constraint relation of parts to accomplish Oriented Functional Relationship Graph (OFRG) assembly modeling.
(2) Utilizing the shortest path algorithm in Graph Theory to search functional dimension chains automatically in the assembly model and ascertain the functional dimensions of the part.
(3) On the basis of the dimensioning principle of correctness, integrality, clearness and rationality, utilizing the modified spanning tree algorithm in Graph Theory to ascertain the non-functional dimensions, accomplish the dimensioning mode analysis of the part.
(4) Automatically grouping dimensions by their directions, accomplishing the priority level enactment of dimensions and implementing the optimal lay of dimensions on the part drawing under the CAD environment.
(5) Use the example to introducing the entire implementing process of the mechanical assembly modeling & automatic dimensioning technique on parts in detail.
引文
[1] 张根保等.先进制造技术.重庆.重庆大学出版社.1996: 85-90
[2] 张根保.自动化制造系统.北京.机械工业出版社.1999:220-226
[3] 白英彩等.计算机集成制造系统-CIMS概论.北京.清华大学出版社.1997:18-60
[4] 童秉枢等.机械CAD技术基础.北京.清华大学出版社.1996:1-30,223-240
[5] 童秉枢.现代CAD技术.北京.清华大学出版社. 2000: 1-10
[6] 殷国富等.计算机辅助设计技术与应用.北京.科学出版社.2000:1-10
[7] 宁汝新等.CAD/CAM技术. 北京.机械工业出版社.1999:65-95
[8] 吴昭同等.计算机辅助公差优化设计.杭州.浙江大学出版社.1999:28-39
[9] 张根保.计算机辅助公差设计及其关键技术.全国首届计算机辅助公差设计专题学术会议论文集.浙江杭州.2000.浙江大学出版社.2000.8: 6-14
[10] 龚劬.图论与网络最优化算法.重庆.重庆大学应用数学系.2000.1:1-80
[11] 王朝瑞. 图论. 北京. 北京理工大学出版社. 1997:1-50
[12] 徐俊明.图论及其应用.合肥.中国科技大学出版社.1998:1-35
[13] 廖念钊等.互换性与技术测量.北京.中国计量出版社.1991:1-32
[14] 刘之生.尺寸链理论及应用.北京.兵器工业出版社.1990:1-50
[15] 张荣瑞.尺寸链理论及其应用.北京.机械工业出版社. 1986:1-85
[16] 王钰. 用VBA开发AutoCAD 2000应用程序.北京.人民邮电出版社. 1999:301-310
[17] 张国宝. AutoCAD Visual Basic开发技术. 北京. 科学出版社. 2000:4-36
[18] 胡荣等.AutoCAD2000开发工具——VBA及ActiveX开发指南.北京.人民邮电出版社.1999:22-36,125-133
[19] 张苏苹等.AutoCAD2000中文版标准培训教程.北京.电子工业出版社.2000:1-50,226-258
[20] 姜勇等.AutoCAD2000三维造型高级培训教程. 北京.人民邮电出版社.2000:2-43
[21] 刘嘉敏. 机械装配图建模方法及应用研究.硕士学位论文. 重庆.重庆大学.1998:5-7，23-40
[22] 纪丰伟. 快速绘图方法在机械CAD中的应用研究.硕士学位论文. 重庆.重庆大学.1999: 46-55
[23] 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. 博士学位论文.杭州.浙江大学.2000: 3-10,66-77
[24] 张国宝. AutoCAD 2000 VBA开发技术.北京.清华大学出版社. 2000:1-38
[25] 王洋 ,王春河等.基于特征的装配尺寸链自动生成及分析的研究.计算机辅助设计与图形学学报.1998(3): 138-144
[26] 王石刚 ，邹慧君等.面向装配特征的CAD系统建模的信息模型.机械设计与研究.1998(3): 21-23
[27] 胡健 ,郭钢.产品零部件相关修改的建模与实现方法. 机械设计与研究.1999(4): 29-31
[28] 刘嘉敏 ,张根保.机械装配建模及其在自动尺寸标注和公差设计中的应用. 机械设计. 1998(8): 40-43
[29] 吴永健.机械图的尺寸注法.机械工业出版社.1981：1-95
[30] 江思敏，刘向锋等.基于配合特征的配合零件链自动生成.机械设计.2000(11):28-30
[31] 龚石钰等.机械制图.成都科技大学出版社.1989:141-154
[32] 孙先虎.机械制图及微机绘图.机械工业出版社.1998:190-216
[33] 罗述洁等.机械设计课程设计.贵州科技出版社.1993:144,178
[34] 何小柏等.机械设计课程设计.高等教育出版社.1995:36
[35] Evangelos Petroutsos. Visual Basic 6从入门到精通.电子工业出版社.1999:1-562
[36] Eric Brierley, Anthony Prince, David Rinaldi. Visual Basic 6开发人员指南.北京：机械工业出版社.1999:117-149
[37] 国家技术监督局.GB/T16675.1～16675.2-1996技术制图简化表示法.北京：中国标准出版社.1997:29-45
[38] 国家技术监督局.技术制图与机械制图.北京：中国标准出版社.1996:1-10
[39] Alain Desrochers. A CAD/CAM Representation Model Applied to Tolerance Transfer Methods .In Proc. of Design Engineering Technical Conferences: 24th Design Automation Conference: 352-362
[40] S.Gupta. Variational Solid Modeling for Tolerance Analysis.IEEE Computer Graphics & Applications. 1993(5): 64-74
[41] 丁晓东.零件尺寸设计应遵循的工艺准则.机械制造.2001（8）：39-40
[42] 刘胡瑶，仲梁维.基于MDT的参数化产品设计.机械设计与制造工程.2000（6）：5-6
[43] 高志，江思敏等.二维图形的特征分析与特征建模.机械设计与研究.1999（4）：23-25
[44] R.Soderberg. Tolerance Chain Detection by Geometrical Constraint Based Coupling Analysis. Journal of Engineering Design.10(1):5-24
[45] 孙正兴，张福炎等.基于特征参数化设计中的尺寸约束及其表示.机械设计.1998（5）：1-4
[46] K.M.Yu. A Review of Automatic Dimensioning and Tolerancing Scheme .Engineering with Computers.1994(10):63-80
[47] 李健，唐忠民等.基于特征的产品装配建模系统.制造业自动化.2000（12）：70-75
[48] F.Etesami. Tolerance Verification through Manufactured Part Modeling. Journal of Manufacturing System.1998(8):223-232
[49] 高剑峰，张申生等.二维几何约束求解器. 计算机辅助设计与图形学学报，2000（2）：110-115.
[50] 庄晓，周雄辉等.三维装配约束求解的解析方法. 计算机辅助设计与图形学学报.1999（11）：497-499
[51] 李晓棠，张满仓.CAD二次开发应用中应注意的问题.机械研究与应用,1998(1)：22-23
[52] 纪丰伟，陈恳，张根保.二维参数化技术的发展现状及趋势分析.机械设计与制造工程,2000（7）：38-40
[53] 于海燕，秦鹏飞.等隐含约束的识别与归整方法.计算机应用.2000(1): 34-36
[54] 戴国洪，倪前富等.基于特征的轴类零件信息生成系统.机械设计与制造工程.1999(11)：37-39
[55] 李彦涛,胡事民等.一个几何约束系统分解的新算法.计算机辅助设计与图形学学报,2000(12)：926-930
[56] 李文锋，陈定方.基于图形和图像融合的产品特征建模.机械设计.2001(4)：1-3
[57] 薛丽霞，唐忠民等.基于约束的几何造型系统.工程设计.2001(1)：21-24
[58] 陆国栋，黄长林等.基于分治思想的尺寸自动标注方法的研究与实现. 计算机辅助设计与图形学学报.2001（6）：521-526
[59] John Derosa and Joel McGrath.3D Solid Modeling for Assembly Design. IEEE/SEMI Advanced Semiconductor Manufacturing Coference.1991: 128-130
[60] U Roy and C R Liu. "Establishment of functional relationships between product components in assembly database", Computer-aided design, Vol.20 NO.10, December, 1988: 570-580
[61] 黎华，苏铁明等.基于约束的机械产品零件参数化特征建模技术研究及实现.组合机床及自动化加工技术.2001（4）：13-16
[62] 孙东光，邓家禔.CAD系统智能化尺寸标注沉浸环境的研究与实现. 计算机辅助设计与图形学学报.2001（9）：805-811
[63] Jami J.Shah and Bing-Chun Zhang. Attributed Graph Model for Geometric Tolerancing. DE-Vol.44-2, Advances in Design Automation-Volume 2.ASME 1992:133-140
[64] B.K.A.Ngoi and Ong Jon Min. Optimum Tolerance Allocation in Assembly. Int J Adv Manuf Technol.1999(15):660-665
[65] A.Desrochers and A.Clement. A Dimensioning and Tolerancing Assistance Model for CAD/CAM Systems. Int J Adv Manuf Technol.1994(9):352-361
[66] B.RAMANI,S.CHERAGHI and J.M.TWOMEY.CAD based integrated tolerancing system. Vol.36, IJPR 1998:2891-2910
[67] V.S.KULKARNI and S.S.PANDE. Representation of feature relationship tolerances in solid models . Vol.34,IJPR 1996:1975-1994
[68] JAMI J.SHAH. Dimension and tolerance modeling and transformations in feature based design and manufacturing .Journal of Intelligent Manufacturing 1998(9):475-488
[69] Kamrani A K.An integrated knowledge-based system for product design feasibility and manufacturability analysis [J]. Computers Ind.Eng, 1996,31(1/2): 83-86
[70] Shankat S R,Jansson D G. A generalized methodology for evaluating manufacturability. In: Parsaei H R,Sullivan W G,eds. Concurrent Engineering. London: Chapman & Hall, 1993.248-263
[71] G.A.Britton, K.Whybrew and S.B.Tor. An Industrial Implementation of Computer-Aided Tolerance Charting . Int J Adv Manuf Technol.1996(12):123-131
[72] M.Nusswald. Minimizing Manufacturing Costs of Tolerance Chains .Manufacturing System Vol29.1999(5):403-406
[73] A.D.Marshall and R.R.Martin. Automatic Inspection of Three-Dimensional Geometric Features.PED-Vol.59,Concurrent Engineering ,ASME 1992:53-67
[74] N.P.Juster and P.M.Dew .Automating Linear Tolerance Analysis Across Asseblies. Journal of Mechanical Design.1992(3):174-179
[75] Rikard Soderberg. CATI: A Computer Aided Tolerancing Interface.DE-Vol.44-2,Advances in Design Automation-Volume 2 ASME 1992:157-164
[76] KAUSHAL Panchal, Shivakumar Raman and P.Simin . Computer-aided tolerance assignment procedure for design dimensioning. INT.J.PROD.RES,1992(3):599-610
[77] Etesami F.A. Mathematical Model for Geometric Tolerances. Journal of Mechanical Design.115(2):81-86
[78] Jormaz D N,Khoshnevis B. Process Planning Knowledge Representation Using an Object-Oriented Data Model. International Journal of Computer Integrated Manufacturing, 1997,10(1-4):92-104
[79] FM.N.Latif, R.G.Hannam. Feature-based Design and the Object-oriented Approach. Journal of Engineering Design, 1996:83-88
[80] Krause F L, et al. Product modeling[J] .Annals of the CIRP, 1993, 42(2): 695-706
[81] Bronsvoort W F, Jansen F W. Feature modeling and conversion-key to concepts to concurrent engineering[J] .Computers in Industry, 1993,21:61-86
[82] Usher J M, Bowden R O. The application of genetic algorithms to operation sequencing for use in computer aided process planning [J]. Computers Industry Engineering.1996, 30(4): 999-1013
[83]Guilford J. Representational Primitives for Geometric Tolerancing.CAD.25(9):577-586, 1997
[84] Roy U. Tolerance representation scheme in solid Modeling: Parts Ⅰ& Ⅱ.Proceedings of the 15th ASME Design Automation Coference.Montreal.1989:1-17
[85] H.A.Elmaraghy. A System for Modeling Geometric Tolerances for Mechanical Design. CIRP 3rd Seminar on Computer Aided Tolerancing .1995:11-24
[86] 胡洁,吴昭同等.面向功能的三维装配公差链的自动生成.工程设计.2001(3)：131-134
[87] 张树有，谭建荣等.基于装配层的配合尺寸继承与检验.计算机辅助设计与图形学学报.2001（6）：509-513
[88] 严蔚敏等.数据结构（C语言版）.清华大学出版社.1997:1-12,156-190
[2] 张根保.自动化制造系统.北京.机械工业出版社.1999:220-226
[3] 白英彩等.计算机集成制造系统-CIMS概论.北京.清华大学出版社.1997:18-60
[4] 童秉枢等.机械CAD技术基础.北京.清华大学出版社.1996:1-30,223-240
[5] 童秉枢.现代CAD技术.北京.清华大学出版社. 2000: 1-10
[6] 殷国富等.计算机辅助设计技术与应用.北京.科学出版社.2000:1-10
[7] 宁汝新等.CAD/CAM技术. 北京.机械工业出版社.1999:65-95
[8] 吴昭同等.计算机辅助公差优化设计.杭州.浙江大学出版社.1999:28-39
[9] 张根保.计算机辅助公差设计及其关键技术.全国首届计算机辅助公差设计专题学术会议论文集.浙江杭州.2000.浙江大学出版社.2000.8: 6-14
[10] 龚劬.图论与网络最优化算法.重庆.重庆大学应用数学系.2000.1:1-80
[11] 王朝瑞. 图论. 北京. 北京理工大学出版社. 1997:1-50
[12] 徐俊明.图论及其应用.合肥.中国科技大学出版社.1998:1-35
[13] 廖念钊等.互换性与技术测量.北京.中国计量出版社.1991:1-32
[14] 刘之生.尺寸链理论及应用.北京.兵器工业出版社.1990:1-50
[15] 张荣瑞.尺寸链理论及其应用.北京.机械工业出版社. 1986:1-85
[16] 王钰. 用VBA开发AutoCAD 2000应用程序.北京.人民邮电出版社. 1999:301-310
[17] 张国宝. AutoCAD Visual Basic开发技术. 北京. 科学出版社. 2000:4-36
[18] 胡荣等.AutoCAD2000开发工具——VBA及ActiveX开发指南.北京.人民邮电出版社.1999:22-36,125-133
[19] 张苏苹等.AutoCAD2000中文版标准培训教程.北京.电子工业出版社.2000:1-50,226-258
[20] 姜勇等.AutoCAD2000三维造型高级培训教程. 北京.人民邮电出版社.2000:2-43
[21] 刘嘉敏. 机械装配图建模方法及应用研究.硕士学位论文. 重庆.重庆大学.1998:5-7，23-40
[22] 纪丰伟. 快速绘图方法在机械CAD中的应用研究.硕士学位论文. 重庆.重庆大学.1999: 46-55
[23] 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. 博士学位论文.杭州.浙江大学.2000: 3-10,66-77
[24] 张国宝. AutoCAD 2000 VBA开发技术.北京.清华大学出版社. 2000:1-38
[25] 王洋 ,王春河等.基于特征的装配尺寸链自动生成及分析的研究.计算机辅助设计与图形学学报.1998(3): 138-144
[26] 王石刚 ，邹慧君等.面向装配特征的CAD系统建模的信息模型.机械设计与研究.1998(3): 21-23
[27] 胡健 ,郭钢.产品零部件相关修改的建模与实现方法. 机械设计与研究.1999(4): 29-31
[28] 刘嘉敏 ,张根保.机械装配建模及其在自动尺寸标注和公差设计中的应用. 机械设计. 1998(8): 40-43
[29] 吴永健.机械图的尺寸注法.机械工业出版社.1981：1-95
[30] 江思敏，刘向锋等.基于配合特征的配合零件链自动生成.机械设计.2000(11):28-30
[31] 龚石钰等.机械制图.成都科技大学出版社.1989:141-154
[32] 孙先虎.机械制图及微机绘图.机械工业出版社.1998:190-216
[33] 罗述洁等.机械设计课程设计.贵州科技出版社.1993:144,178
[34] 何小柏等.机械设计课程设计.高等教育出版社.1995:36
[35] Evangelos Petroutsos. Visual Basic 6从入门到精通.电子工业出版社.1999:1-562
[36] Eric Brierley, Anthony Prince, David Rinaldi. Visual Basic 6开发人员指南.北京：机械工业出版社.1999:117-149
[37] 国家技术监督局.GB/T16675.1～16675.2-1996技术制图简化表示法.北京：中国标准出版社.1997:29-45
[38] 国家技术监督局.技术制图与机械制图.北京：中国标准出版社.1996:1-10
[39] Alain Desrochers. A CAD/CAM Representation Model Applied to Tolerance Transfer Methods .In Proc. of Design Engineering Technical Conferences: 24th Design Automation Conference: 352-362
[40] S.Gupta. Variational Solid Modeling for Tolerance Analysis.IEEE Computer Graphics & Applications. 1993(5): 64-74
[41] 丁晓东.零件尺寸设计应遵循的工艺准则.机械制造.2001（8）：39-40
[42] 刘胡瑶，仲梁维.基于MDT的参数化产品设计.机械设计与制造工程.2000（6）：5-6
[43] 高志，江思敏等.二维图形的特征分析与特征建模.机械设计与研究.1999（4）：23-25
[44] R.Soderberg. Tolerance Chain Detection by Geometrical Constraint Based Coupling Analysis. Journal of Engineering Design.10(1):5-24
[45] 孙正兴，张福炎等.基于特征参数化设计中的尺寸约束及其表示.机械设计.1998（5）：1-4
[46] K.M.Yu. A Review of Automatic Dimensioning and Tolerancing Scheme .Engineering with Computers.1994(10):63-80
[47] 李健，唐忠民等.基于特征的产品装配建模系统.制造业自动化.2000（12）：70-75
[48] F.Etesami. Tolerance Verification through Manufactured Part Modeling. Journal of Manufacturing System.1998(8):223-232
[49] 高剑峰，张申生等.二维几何约束求解器. 计算机辅助设计与图形学学报，2000（2）：110-115.
[50] 庄晓，周雄辉等.三维装配约束求解的解析方法. 计算机辅助设计与图形学学报.1999（11）：497-499
[51] 李晓棠，张满仓.CAD二次开发应用中应注意的问题.机械研究与应用,1998(1)：22-23
[52] 纪丰伟，陈恳，张根保.二维参数化技术的发展现状及趋势分析.机械设计与制造工程,2000（7）：38-40
[53] 于海燕，秦鹏飞.等隐含约束的识别与归整方法.计算机应用.2000(1): 34-36
[54] 戴国洪，倪前富等.基于特征的轴类零件信息生成系统.机械设计与制造工程.1999(11)：37-39
[55] 李彦涛,胡事民等.一个几何约束系统分解的新算法.计算机辅助设计与图形学学报,2000(12)：926-930
[56] 李文锋，陈定方.基于图形和图像融合的产品特征建模.机械设计.2001(4)：1-3
[57] 薛丽霞，唐忠民等.基于约束的几何造型系统.工程设计.2001(1)：21-24
[58] 陆国栋，黄长林等.基于分治思想的尺寸自动标注方法的研究与实现. 计算机辅助设计与图形学学报.2001（6）：521-526
[59] John Derosa and Joel McGrath.3D Solid Modeling for Assembly Design. IEEE/SEMI Advanced Semiconductor Manufacturing Coference.1991: 128-130
[60] U Roy and C R Liu. "Establishment of functional relationships between product components in assembly database", Computer-aided design, Vol.20 NO.10, December, 1988: 570-580
[61] 黎华，苏铁明等.基于约束的机械产品零件参数化特征建模技术研究及实现.组合机床及自动化加工技术.2001（4）：13-16
[62] 孙东光，邓家禔.CAD系统智能化尺寸标注沉浸环境的研究与实现. 计算机辅助设计与图形学学报.2001（9）：805-811
[63] Jami J.Shah and Bing-Chun Zhang. Attributed Graph Model for Geometric Tolerancing. DE-Vol.44-2, Advances in Design Automation-Volume 2.ASME 1992:133-140
[64] B.K.A.Ngoi and Ong Jon Min. Optimum Tolerance Allocation in Assembly. Int J Adv Manuf Technol.1999(15):660-665
[65] A.Desrochers and A.Clement. A Dimensioning and Tolerancing Assistance Model for CAD/CAM Systems. Int J Adv Manuf Technol.1994(9):352-361
[66] B.RAMANI,S.CHERAGHI and J.M.TWOMEY.CAD based integrated tolerancing system. Vol.36, IJPR 1998:2891-2910
[67] V.S.KULKARNI and S.S.PANDE. Representation of feature relationship tolerances in solid models . Vol.34,IJPR 1996:1975-1994
[68] JAMI J.SHAH. Dimension and tolerance modeling and transformations in feature based design and manufacturing .Journal of Intelligent Manufacturing 1998(9):475-488
[69] Kamrani A K.An integrated knowledge-based system for product design feasibility and manufacturability analysis [J]. Computers Ind.Eng, 1996,31(1/2): 83-86
[70] Shankat S R,Jansson D G. A generalized methodology for evaluating manufacturability. In: Parsaei H R,Sullivan W G,eds. Concurrent Engineering. London: Chapman & Hall, 1993.248-263
[71] G.A.Britton, K.Whybrew and S.B.Tor. An Industrial Implementation of Computer-Aided Tolerance Charting . Int J Adv Manuf Technol.1996(12):123-131
[72] M.Nusswald. Minimizing Manufacturing Costs of Tolerance Chains .Manufacturing System Vol29.1999(5):403-406
[73] A.D.Marshall and R.R.Martin. Automatic Inspection of Three-Dimensional Geometric Features.PED-Vol.59,Concurrent Engineering ,ASME 1992:53-67
[74] N.P.Juster and P.M.Dew .Automating Linear Tolerance Analysis Across Asseblies. Journal of Mechanical Design.1992(3):174-179
[75] Rikard Soderberg. CATI: A Computer Aided Tolerancing Interface.DE-Vol.44-2,Advances in Design Automation-Volume 2 ASME 1992:157-164
[76] KAUSHAL Panchal, Shivakumar Raman and P.Simin . Computer-aided tolerance assignment procedure for design dimensioning. INT.J.PROD.RES,1992(3):599-610
[77] Etesami F.A. Mathematical Model for Geometric Tolerances. Journal of Mechanical Design.115(2):81-86
[78] Jormaz D N,Khoshnevis B. Process Planning Knowledge Representation Using an Object-Oriented Data Model. International Journal of Computer Integrated Manufacturing, 1997,10(1-4):92-104
[79] FM.N.Latif, R.G.Hannam. Feature-based Design and the Object-oriented Approach. Journal of Engineering Design, 1996:83-88
[80] Krause F L, et al. Product modeling[J] .Annals of the CIRP, 1993, 42(2): 695-706
[81] Bronsvoort W F, Jansen F W. Feature modeling and conversion-key to concepts to concurrent engineering[J] .Computers in Industry, 1993,21:61-86
[82] Usher J M, Bowden R O. The application of genetic algorithms to operation sequencing for use in computer aided process planning [J]. Computers Industry Engineering.1996, 30(4): 999-1013
[83]Guilford J. Representational Primitives for Geometric Tolerancing.CAD.25(9):577-586, 1997
[84] Roy U. Tolerance representation scheme in solid Modeling: Parts Ⅰ& Ⅱ.Proceedings of the 15th ASME Design Automation Coference.Montreal.1989:1-17
[85] H.A.Elmaraghy. A System for Modeling Geometric Tolerances for Mechanical Design. CIRP 3rd Seminar on Computer Aided Tolerancing .1995:11-24
[86] 胡洁,吴昭同等.面向功能的三维装配公差链的自动生成.工程设计.2001(3)：131-134
[87] 张树有，谭建荣等.基于装配层的配合尺寸继承与检验.计算机辅助设计与图形学学报.2001（6）：509-513
[88] 严蔚敏等.数据结构（C语言版）.清华大学出版社.1997:1-12,156-190