摘要
本论文在分析国内外计算机辅助公差设计技术的发展历史和研究现状的基础上，结合国家自然科学基金“设计和制造(工序)公差并行优化设计的研究”(59575076)及“综合公差计算机辅助设计系统的研究”(59705022)，以圆柱要素为研究对象对公差的数学建模与分析技术进行研究。论文的主要研究内容包括轴孔要素的公差数学建模、装配可行性分析及装配质量分析。
第一章：阐述了计算机辅助公差设计的发展历史和研究现状，讨论了本课题的研究背景和意义，结合国家自然科学基金提出了本论文的主要研究内容，给出了本文的总体框架和创新点。
第二章：建立公差数学建模基本理论。对国外几种主要的公差数学定义方法进行剖析，指出各自的优缺点。给出基于综合GPS标准ISO14660的公差数学定义中的一些基本概念与基本理论，如几何要素、公差带、点的空间运动、公差变换矩阵等。当同一要素存在多个形位公差要求时，建立各公差带之间的约束关系。
第三章：建立圆柱要素尺寸公差、形状公差、定向公差和定位公差的数学模型。首先，在ASME Y14.5.1M-1994公差数学定义的基础上，采用点集的形式用矢量方程严格定义国标中各形位公差带；然后，在公差数学定义理论的基础，基于要素的自由度分析，采用不等式约束方程的形式建立各公差带的数学模型。
第四章：建立轴孔要素装配可行性分析方法。首先建立圆柱要素的相符性分析技术，基于漂移带的尺寸公差语义，结合当前国标，对于LMC条件以及采用独立原则的MMC条件，给出相符性验证的充要条件；对于采用独立原则与最大实体原则的MMC条件，给出相符性验证的充分条件。然后，在漂移模型、虚拟边界要求、条件公差理论以及ISO和国家标准的公差原则基础上，给出可用于单轴孔要素、双轴孔要素、复合位置度公差、多轴孔等复杂情况下装配可行性分析的软件量规数学等效式。研究加工与检测过程的模拟仿真，实现设计阶段的加工模拟、检测仿真与装配成功率预算。
第五章：研究装配体的装配质量分析方法。研究装配体中的变动来源，建立二维与三维中的变动传播模型。在装配体尺寸变动分析模型的基础，进一步建立形位公差分析模型；采用矩阵分析的方法实现装配体的装配质量分析。
第六章：开发基于MDT的装配尺寸链生成与公差分析原型系统，以三个实例分别演示了公差的数学建模，装配可行性分析与装配质量分析理论在工程实践中的应用，验证文中所提出的理论与方法。
浙江大学博士学位论文:基于数学定义的圆柱要素公差数学建模与分析技术的研究
第七章:对基于数学定义的圆柱要素公差数学建模与分析技术的研究工作进行了总
结;对计算机辅助公差设计系统应该进一步开展的工作进行探讨和展望。
Based on the "Study on Simultaneous Design of Blueprint Tolerance and Process Tolerance" (National Nature Science Fund Project, No: 59575076) and the "Study on Computer Aided Tolerancing System" (National Nature Science Fund Project, No: 59705022), the theories of tolerance mathematically modelling and tolerance analysis was studied. The main contents comprise mathematically modelling of tolerance and analysis of assemble feasibility and assembly quality
In the first chapter, the development and State-of-the-arts of computer aided tolerancing system at home and abroad are summarized. Based on those, the background and meaning of CAT system are proposed. At last, National Nature Science Fund Projects are combined and the main contents, general structure scheme and innovation points of this dissertation are present.
In the second chapter, the basic theory of tolerance mathematically modeling was build. The main method of tolerance mathematically definition abroad was analyzed and the advantage and disadvantage was pointed. Based on new definition defined by General GPS Standard, the essence definition and theory was presented, such as geometry feature, tolerance zone, point movement and tolerance transformation matrix. When there are several tolerance on one feature, the constrain relationship between each tolerance zone was established.
In the third chapter, mathematical model of size tolerance, form tolerance, orientation tolerance and location tolerance of cylindrical feature was established. First, based on the tolerance mathematical definition of ASME Y14.5.1M-1994, each tolerance in national standard was established by vector equation. Then in the foundation of tolerance mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature.
In the fourth chapter, the method of assembly feasibility analysis for shaft and hole feature was established. First, conformance analysis technique was build. As for LMC and MMC of RFS principle, sufficient and necessary condition was given. As for RPS principle and MMC of MMC principle, sufficient condition was given. Then, based on offset model, virtual boundary demand, condition tolerance ,ISO standard and national standard, soft gauge for single cylindrical feature, two cylindrical feature, compound location tolerance and several
cylindrical feature were given. Simulate machining and measure process to realize process and measure simulation and assembly feasibility rate evaluation.
In the fifth chapter, assembly quality was studied. The source of variation in assembly was studied. The variation transmit in two and three dimension was established. Based on the dimension variation analysis model, analysis model for form tolerance and location tolerance was established. Matrix analysis model was adopted to realize assembly quality analysis.
In the sixth chapter, assembly dimension chain and tolerance analysis system was build on MDT. Three examples are studied to demonstrate that the tolerance mathematical model, assembly feasibility and assembly quality analysis theory can be used in practice and the theory and method presented in this thesis is in effect.
In the seventh chapter, all of the work in this dissertation is summed up, and the future research of computer-aided tolerancing is prospected.
引文
[1] 吴昭同，杨将新等．计算机辅助公差优化设计．杭州：浙江大学，1999．10
[2] 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，全国高校互换性与测量技术研究会二000年年会”论文集，浙江大学，6-14，2000．8
[3] 杨将新．基于装配成功率的公差优化设计系统研究．[博士学位论文]．浙江大学，杭州．1996
[4] 方红芳．设计公差和工序公差并行设计的研究．[博士学位论文]．浙江大学，杭州．1997
[5] 刘玉生．基于数学定义的平面尺寸和行为公差建模与表示技术的研究．[博士学位论文]．浙江大学，杭州．1997
[6] 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．重庆大学学报．1999，22(1)：41～46
[7] 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．全国首届计算机辅助公差设计专题学术会议论文集．杭州．2000：60～63
[8] 黄彤军．基于特征的公差分析和综合的研究．[博士学位论文]．华中科技大学，武汉．1995
[9] 孙绍民．CAD环境中公差分析与综合的研究．[博士学位论文]．哈尔滨工业大学，哈尔滨．1997
[10] 姬舒平．虚拟装配环境下公差并行设计方法的研究．[博士学位论文]．哈尔滨工业大学，哈尔滨．2000
[11] 闫艳，宁汝新．并行工程中的公差设计研究与开发．计算机集成制造系统．2000，6(5)：43-47
[12] 闫艳，宁汝新，刘文丰．公差设计特征专家系统．全国首届计算机辅助公差设计专题学术会议论文集．杭州．2000：112～116
[13] 周志革，黄文振，张利．数论方法在统计公差分析中的应用．机械工程学报．2000，36(3)：69～72
[14] 范秀敏．装配系统的公差建模与优化．[博士学位论文]．上海交通大学，上海．1998
[15] Hillyard C. Dimensions and Tolerances in Shape Design. University of Cambridge, UK: ph D. Dissertation, 1978
[16] Bjorke O. Computer-Aided Tolerancing, Tapir publishers, Norway, 1978
[17] Requicha A A G Toward a Theory of Geometric Tolerancing. Int. J. Rob. Res. 1983,2(4) :45～49
[18] Turner J U. Tolerance in Computer-Aided Geometric Design. Ph.D. Thesis, Renssetaer Polytechnic Institutes, 1987
[19] Weil R. Tolerancing for Function. CIRP Annals, 1988, 37(2): 1～8
[20] Clement, A., Riviere, A. Tolerancing versus nominal modeling in next generation CAD/CAM system. Proceedings of 3rd CIRP Seminars on Computer Aided Tolerancing. 1993:97～114
[21] ElMaraghy, H. A., ElMaraghy, W. H. A System for modeling geometric tolerances for mechanical design.
Proceedings of 3rd CIRP Seminars on Computer Aided Tolerancing. 1993: 11-24
[22] Nassef, A. O., ElMaraghy, H. A. Allocation of tolerance types and values using genetic algorithms. Proceedings of 3rd CIRP Seminars on Computer Aided Tolerancing. 1993: 147-156
[23] Clement, A., Riviere, A., Serre, P. A declarative information model for functional requirements. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 1-15
[24] Desrochers, A., Maranzana, R. Constrained dimensioning and tolerancing assistance for mechanisms. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 19~30
[25] Ballu, A., Mathieu, L. Univocal expression of functional and geometrical tolerances for design. manufacturing and inspection. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 31-46
[26] Salomons, O. W., Jonge Poerink, H. J., Van Slooten, F., Van Houten, F. J. A. M., Kals, H. J. J. A Tolerancing tool based on kinematic analogies. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995:47-70
[27] Portman, V. T., Weill, R. D. Modeling spatial dimensional chains for CAD/CAM applications. Proceedings of4th CIRP Seminars on Computer Aided Tolerancing. 1995: 71-85
[28] Maeda, T, Tokuoka, N. Toleranced feature modeling by constraint of degree of freedom for assignment of tolerance. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 89-103
[29] Tonshoff, H. K., Ehrmann, M. Quality features in CAD and CAPP systems. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 104-116
[30] Srinivasan, V., O'Connor, M. A. Towards an ISO standard for statistical tolerancing. Proceedings of 4lh CIRP Seminars on Computer Aided Tolerancing. 1995: 159-172
[31] Martinsen, K. Statistical process control using vectorial tolerancing. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 173-186
[32] Nassef, A. O., ElMaraghy, H. A. Probabilistic analysis of geometric tolerances. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 187-203
[33] Robert G W, Lu C Y. Tolerance Synthesis to Support Concurrent Engineering. Annals of the CIRP. 1992． 41(1) :197-200
[34] Srinivasan R S. Geometric Tolerancing in Mechanical Design Using Fractal-based Parameters. Journal of Mechanical Design, 1995, 117(3) : 203-206
[35] Ting K L, Long Y F. Performance Quality and Tolerance Sensitivity of Mechanisms. Journal of Mechanical Design, 1996, 118(3) : 144-150
[36] Feng C X. Kusiak A. Robust Tolerance Design With the Integer Programming Approach. Journal of Manufacturing Science and Engineering. 1997, 119(11) : 603-610
[37] Nassef A O, Elmaraghy H A. Allocation of Geometric Tolerance : New Criterion and Methodology. Annals of CIRP, 1997, 46(1)
[38] Park S H, Lee K W. Verification of Assemblability between Toleranced parts. CAD, 1998, 30(2) : 95-104
[39] Willi
[40] 张根保．计算机辅助公差设计综述．中国机械工程，1996，7(5) ：47-50
[41] Zhang G B, Porcher M. An Investigation into a Mathematical Model of Optimal Tolerancing Surpporting Concurrent Engineering. The 13-th ASME Annual International Computer in Engineering Conference and Exposition, SanDiego, C. A., USA, 1993
[42] ASME Standard Y14． 5． 1M-1994． Mathematical Definition of Dimensioning and Tolerancing Principles. American Society of Mechanical Engineers. New York
[43] ISC/TC 213． http://www.ds.dk/.
[44] Jayarman R, Srinivasan V. Geometric Tolerance : Ⅰ. Virtual Boundary Requirement. IBM J. RES. DEVELOP, 1989, 33(2) : 90-104
[45] Srinivasan V, Jayarman R. Geometric Tolerance : Ⅱ. Conditional Tolerances. IBM J. RES. DEVELOP, 1989, 33(2) : 105-125
[46] Etesmi F A. Mathematical Model for Geometric Tolerancing. Journal of Mechanical Design, 1993, 115(3) : 81-86
[47] Hillyard R C.Braid I C. Analysis of Dimensions and Tolerances in Computer-Aided Mechanical Design. CAD, 1978, 10(3) :161~166
[48] Liu C R, Gossard D C, Light R A. Variational Geometry in Computer Aided Desing. Comput. Graph 1981,15(3:)
[49] Light R A, Gossard D C. Modification of Geometric Models Through Variations Geometry. Computer Aided Design, 1982, 14(4) : 209-214
[50] Gossard D C, Zuffante R P, Sakurai H. Representing Dimensions Tolerances and Features in MCAE systems. IEEE Comput. Graph. &Appli., 1988, 8(2) :51~59
[51] Hoffman P. Analysis of Tolerances and Process Inaccuracies in Discrete Part Manufacturing. Computer-Aided Design, 1982, 14(2) : 83-88
[52] Turner J U, Wozny M J, Hoh D D. Tolerance Analysis in a Solid Modeling Envirement. ASME Proc. Of Comput. In Engin. Conf. 1989, 169-175
[53] Salamons O W et.al. A Computer Aided Tolerancing Tool I : Tolerance Specification, Computers in Industry, 1996,31 : 161-174
[54] Salamons 0 W et.al. A Computer Aided Tolerancing Tool II : Tolerance Analysis, Computers in Industry. 1996,31 : 175-186
[55] Alvin. What the New Standard Means for Manufacturing. Manufacturing Engineering. 1995 : 47-52
[56] U. Roy, B. Li. Representation and interpretation of geometric tolerances for polyhedral objects-Ⅰ. Form tolerances. Computer-Aided Design. 30(2) :151-161, 1998
[57] U. Roy, B. Li. Representation and interpretation of geometric tolerances for polyhedral objects. Ⅱ. Size, orientation and position tolerances. Computer-Aided Design. 31:273-285, 1999
[58] Shan J J. Dimension and Tolerance Modeling and Transformations in Feature based Design and Manufacturing. Journal of Intelligent Manufacturing. 1998, 9 : 475-488
[59] 黄灿明，梁天培等．基于特征的几何公差实体模型的研究(1) (2) ．机械设计与研究1997，13(1) (2)
[60] Johnson R H et.al. Dimensioning and Tolerancing Final Report. Technical Report R-84-GM-02． 2CAM-I.USA, 1985
[61] Repuicha A A G, Chan S. Representation of Geometric Features, Tolerances and Attributes in Solid Modelers Based on Constructive Solid Geometry. IEEE J. Robor. &Automat., 1986: RA-2(3) :1 56-165
[62] Roy U, Liu C R. Feature-based Representational Scheme of a Solid Modeler for Providing Dimension and Tolerancing Information. Robotics and Computer Integrated Manufacturing, 1988, 4(3) : 335-345
[63] Roy U. Tolerance Representation Scheme in Solid Modeling: Pants Ⅰ&Ⅱ. Proceedings of the 15th ASME Design Automation Conference.
[64] Gossard D C. Representing Dimensions, Tolerances, and Features in MCAE systems. IEEE Computer Graphics & Applications. 1988 : 51-59
[65] Guiford J. Representational Primitive for Geometric Tolerancinng. Computer Aided Design. 1993, 25(9) : 577-586
[66] Salamons O W. Computer Support in the Design of Mechanical Products, constraint specifiction and satisfaction in feature based design for manufacturing. Ph. D. Thesis, University of Tweme, 1995
[67] 何俊民．基于综合方程式的计算机辅助公差设计．杭州：浙江大学硕士学位论文，1996． 2
[68] The VSAS(Variaitional Simulation Analysis Software). Applied Computer Solutions : St. Clair Shore. Michigan. USA. 1984
[69] Hillyard R C,Braid I C. Characterizing Non-ideal Shapes in Terms of Dimensions and Tolerance. Comput. Graph., 1987, 12(3) :234~238
[70] Trescy P. Automated Tolerance Analysis for Mechanical Assemblies Modeled With Geometric Features and Relational data structure. Computer Aided Design, 1991, 23(6)
[71] Mitchell W, Siddall J N. The Primization Problem with Optimal Tolerance Assignment and Full Acceptance. ASME Journal of Mechanical Design, 103:842-849
[72] Mitchell W, Siddall J N. The Optimal Tolerance Assignment With Less Than Full Acceptance. ASME Journal of Mechanical Design, 104:855-860
[73] Parkson D B. Tolerancing of Component Dimensions in CAD. Computer Aided Design, 1984, 16(1) : 25-32
[74] Roman S. Computer Tolerance Assignment. Computer Ind. Engineering, 21(1) : 67-71
[75] Dong Z, Soom. Automatic tolerance analysis from a CAD database, asme 86-det-36 Eng.Tech.Conf.Colubus, Ohio, USA, 1986
[76] Lee W J, Woo T C. Tolerance : Their Analysis and Synthesis. Journal of Engineering for Industry
[77] Lee W J, Woo T C. Optimum selection of discrete tolerance. Technical Report 87-94 Dep. Industrial and Operations Engineering. University of Michigan USA, 1987,12
[78] Chase K W, Green W H. Design Issues in Mechanical Tolerance Analysis. ASME Ann. Winter Meet Advanced Topics in Manufacturing Technology Boston MA/USA, 1987, 13-18
[79] Daniel F, Weill R, Bourdet P, Computer Aided Tolerancing and Dimensioning in Process Planning. Manuf. Tech.CIRP Ann. 1986, 35(1) :381~386
[80] Daniel F. Development of a Computer Program for the Optimation of Tolerance Transformation from Design to Manufacturing. MS Thesis Technion Isonel Institute of Technology Haifa Isarael, 1986,3
[81] U. Roy, B. Li. Representation and interpretation of geometric tolerances for polyhedral objects-Ⅰ. Form tolerances. Computer-Aided Design. 30(2) :151-161, 1998
[82] U. Roy, B. Li. Representation and interpretation of geometric tolerances for polyhedral objects. Ⅱ. Size, orientation and position tolerances. Computer-Aided Design. 31:273-285, 1999
[83] Turner J U. A Feasibility Space Approach for Automated Tolerancing. ASME Journal of Engineering for Industry, 115:341-345
[84] Wirtz A Vectorial Tolerancing a Basic element for quality control. Proceeding, 3rd CIRP seminar on Computer Aided Tolerancing, Cachan(F), 115-128
[85] Clement A, Riviere A, tolerancing Versus Nominal Modeling in Next Generation CAD/CAM System. Proceedings, CIRP seminar on Computer aided tolerancing, Penn State University, USA
[86] Salomans O W. A Tolerance Tool Based on Kinematic Analogies. Computer Aided Tolerancing, 1996． 47-69
[87] Srinivasan, V., An integrated view of geometrical product specification and verification. Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing. France, 2001: 7-18．
[88] 王伯平．互换性与技术测量．北京：机械工业出版社，2000． 2
[89] 郑叔芳，吴晓琳．机械工程测量学.北京：科学出版社，1999． 9
[90] 蒋寿伟等．新编形状和位置公差标注注解．北京：中国标准出版社，2000． 4
[91] Srinivasan V. Role of Sweeps in Tolerance Semantics. Manufacturing Review, 1993,6(4) :275-281
[92] Voelcker B. A Current Perspective on Tolerancing and Metrology, Manufacturing Review. 1993,
6(4)：258～268
[93] 六项互换性基础标准汇编，北京：中国标准出版社，1987，127～154．
[94] 花国樑，互换性与测量技术基础．北京理工大学出版社，1986，104～107
[95] Srinivasan V. Recent Efforts in Mathematization of ASME/ANSI Y14.SM Standard. Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, ENS de Cachan. Paris, France, 1993, 97～113
[96] 汪恺等译，形位公差在设计、制造及检验中的应用，北京：中国计量出版社，1997，89～97
[97] Srinivasan V. Role of Sweeps in Tolerance Semantics. Manufacturing Review, 1993,6(4):275～281
[98] Suresh K , Voeleker H B. New Challenges in Dimensional Metrology:A Case Study Based on "Size", Manufacture Review, 1994, 7(4): 291～303
[99] 朱从贵、黄明强．公差数学定义及评价．上海计量测试，1996，1：40～42，48
[100] 石玉珍．六项互换性基础标准汇编．北京：中国标准出版社出版，1987
[101] Robert G. Wilhelm, Stephen G. -Y. Lu , Computer Methods For Tolerance Design. World Scientific Publishing Co. Pte. Ltd, Singapore, 1992
[102] Nassef A, EIMaraghy H. Probabilistic Analysis of Geometric Tolerances. Proceedings of the 4th CIRP Seminars on Computer Aided Tolerancing: 187-203.
[103] 王东泉．计算机图形学与CAD技术．上海：上海交通大学出版社．1992．11
[104] 郭建平．三坐标测量机上质量保证技术与软件量规的研究．杭州：浙江大学硕士学位论文，1996．2
[105] 高惠璇．统计计算．北京：北京大学出版社，1995．7
[106] 奥野忠一，芳贺敏郎．试验设计方法．北京：机械工业出版社，1985．12
[107] 孙荣恒，伊亨云，刘群荪．数理统计．重庆：重庆大学出版社，2000．2
[108] Kenneth W, Chase, Alan R. Parkinson. A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies. Research in Engineering Design, 3:23-37, 1991
[109] Kenneth W. Chase, Jinsong Gao etc. Including geometric feature variations in tolerance analysis of mechanical assemblies, ⅡE Transactions, 28:795-807,1996
[110] Jinsong Gao, Kenneth W. Chase and Spencer P. Magleby, Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments, ⅡE Transactions, 30:367-377, 1998
[111] 全国首届计算机辅助公差设计专题学术会议论文集．杭州．2000
[112] Srinivasan, V. A Geometrical product specification language based on a classification of symmetry groups. Computer Aided Design. 1999, 31 : 659～668
[113] Wu, Y. G., Gao, S. M., Chen, Z. C. Automatic setup planning and operation sequencing for satisfying tolerance requirements. Proceeding of ASME Design Engineering Technical Conferences, 2001
[114] Tsai, J. C,, Tsai, W. A knowledge base approach for tolerancing in computer-aided process planning. Proceeding of ASME Design Engineering Technical Conference. 1999
[115] Tang, X. Q., Davies, B. J. Computer aided dimensional planning. International Journal of Production Research. 1988, 26(2) : 283-297
[116] Farmer, L. E., Harris, A. Q Change of datum of the dimensions on engineering design drawings. International Journal of Machining Tool Design Research. 1984, 24(4) : 267-275
[117] Ngoi, B. K. A., Ong, C. T. A complete tolerance charting system. International Journal of Production Research. 1993, 31(2) : 453-469
[118] Ngoi, B. K. A., Ong, C. T. Computer aided process dimensioning. The International Journal of Advanced Manufacturing Technology. 1993, 8: 371-376
[119] Sfantsikopoulos, M. M. A cost-tolerance analytical approach for design and manufacturing. The International Journal of Advanced Manufacturing Technology. 1990, 5: 126-134
[120] Mittal, R. O., Irani, S. A., Lehtihet, E. A. Tolerance control in the machining of discrete components. Journal of Manufacturing Systems. 1990, 9(3) : 233-246
[121] Ngoi, B. K. A., Fang, S. L. Computer aided tolerance charting. International Journal of Production Research. 1994, 32(8) : 1939-1954
[122] Cogun, C. A correlation between deviations in form and size tolerances. International Journal of Production Research. 1991,29(5) : 1017-1023
[123] Lee, J., Johnson, G E. Optimal tolerance allotment using a genetic algorithm and truncated monte carlo simulation. Computer Aided Design. 1993, 25(9) : 601-611
[124] Sports. M. F. Allocation of tolerances to minimize cost of assembly. Journal of Engineering for Industry. 1973:762-764
[125] Srinivasan, V. ISO deliberates statistical tolerancing. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 25-35
[126] Varghese, P., Braswell, R. N., Wang, B., Zhang, C., Statistical tolerance analysis using FRPDF and numerical convolution. Computer Aided Design. 1996, 28: 723-732
[127] Pabon, J., Young. Keirouz, W. Integrating parametric geometric geometry, features, and variational modeling for conceptual design. International Journal of Systems Automation: Research and Applications. 1992,2: 17-36
[128] Wang. N., Ozsoy, T. M. Automatic generation of tolerance chains from mating relations represented in assembly models. ASEM Journal of Mechanical Design. 1993, 115(4) : 757-761
[129] Wirtz, A. Vectorial tolerancing a basic element for quality control. Proceedings of 3rd CIRP seminar on Computer Aided Tolerancing. 1993: 115-128
[130] Shah, J. J., Van, Y, Zhang, B. C. Dimension and tolerance modeling and transformations in feature based design and manufacturing. Journal of Intelligent Manufacturing. 1998, 9: 475-488
[131] Wang, N., Ozsoy, T. M. A scheme to represent features, dimensions, and tolerances in geometric modeling. Journal of Manufacturing Systems. 1991, 10(3) : 233~240
[132] Faux, I. D. Modelling of components and assemblies in terms of shape primitives based on standard dimensioning and tolerancing surface features. In Geometric Modeling for Product Engineering. Elsevier Science, Amsterdam, North-Holland. 1990
[133] Yu, Y. C., Liu, C. R., Kashyap, R. L. A variational solid model for mechanical parts. Proceedings of the USA-Japan Symp. Advances in Flexible Automation and Robotics. 1988: 237-244
[134] Roy, U., Banerjee, P., Liu, C. R. Design of an automated assembly environment. Computer Aided Design. 1989, 21(9) : 567-569
[135] Requicha, A. A. Mathematical definition of tolerance specifications. Manufact. Rev. 1993, 6(4) : 269-275
[136] Requicha, A. A., Chan, S. C. Representation of geometric features, tolerances, and attributes in solid modelers based on constructive geometry. J. Robotics and Automation. 1986, 2(3) : 156-166
[137] Mathieu, L., Clement, A., Bourdet, P. Modeling, representation and processing of tolerances, tolerance inspection: a survey of current hypothesis. Proceedings of 5th C1RP Seminars on Computer Aided Tolerancing. 1997: 1-33
[138] Bennich, P. International standards for design tolerancing review and future perspective. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 37-51
[139] Braun, P. R. Research in statistical tolerancing: examples of intrinsic non-normalities, and their effects. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 52-63
[140] Bialas, S., Kiszka, K. Relations between ISO 1101 geometrical tolerances and vectorial tolerances-conversion problems. Proceedings of 5Ih CIRP Seminars on Computer Aided Tolerancing. 1997: 88-99
[141] Clement, A., Riviere, A., Serre, P., Valade, C. The TTRSs: 13 constraints for dimensioning and tolerancing. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 122-131
[142] Laperriere, L. Identifying and quantifying functional elements dispersions during functional analysis. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 157-170
[143] Desrochers, A., Delbart, O. Determination of part position uncertainty within mechanical assembly using screw parameters. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 185-196
[144] Morse, E. P. More on the effects of non-normal statistics in geometric tolerancing. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 254-261
[145] Dong, Z., Wang, G G Automated cost modeling for tolerance synthesis using manufacturing process data, knowledge reasoning and optimization. Proceedings of 5th CIRP Seminars on Computer Aided
Tolerancing. 1997: 282-293
[146] Chase, K.. W., Magleby, S. P. A comprehensive system for computer aided tolerance analysis of 2-D and 3-D mechanical assemblies. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 294-307
[147] Salomons, O. W., Van Houten, F. J. A. M, Kals, H. J. J. Current status of CAT systems. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 438-452
[148] Nassef, A. Optimal allocation of types and magnitudes of geometric tolerances. [Ph.D. dissertation]. McMaster University, Canada. 1997
[149] Zhang. H. C. Advanced tolerancing techniques. John Wiley & Sons, Inc. 1997
[150] Zhang, G B. Simultaneous tolerancing for design and manufacturing. Advanced tolerancing techniques. John Wiley & Sons, Inc. 1997: 207-232
[151] Clement, A., Riviere, A., Serre, P. Global consistency of dimensioning and tolerancing. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 1-26
[152] Chen, M. S., Young, K. W. Optimising tolerance allocation for mechanical assemblies considering geometric tolerances based on a simplified algorithm. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 27-36
[153] Tsai, J. C., Wang, W. W. Development of a computer aided tolerancing system in CAD environment. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 47-54
[154] Desrochers. A.. Verheul, S. A three dimensional tolerance transfer methodology. Proceedings of 6Ih CIRP Seminars on Computer Aided Tolerancing. 1999: 83-92
[155] Britten. W.. Weber, C. Transforming ISO 1101 tolerances into vectorial tolerance representations-a CAD-based approach. Proceedings of 6'h CIRP Seminars on Computer Aided Tolerancing. 1999: 93-100
[156] Ha, S.. Hwang. I.. Lee. K.,Rho, H. M. Tolerance representation scheme for integrated cutting process &. inspection planning. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 131-138
[157] Pairel, E.. Giordano, M.. Samper, S. Towards easier and more functional semantics for geometrical tolerancing. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 139-147
[158] Bley, H.. Oltermann. R., Thome. 0． , Weber, C. A tolerance system to interface design and manufacturing. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 149-156
[159] Ballot, E., Bourded. P., Thiebaut. F. Contribution of a mathematical model of specifications of a part to their coherence analysis. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999． 157-166
[160] Linares. J. M., Boukebbab. S., Sprauel. J. M. Parametric tolerancing. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 167-176
[161] Clancy, C. G, Bogard, T. V. Innovations in integrating tolerance analysis technologies for a computer aided tolerancing system. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 215-222
[162] Soderberg, R., Lindkvist, L. Two step procedure for robust design using CAT technology. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 231-240
[163] Salomons, O. W., Begelinger, R. E., Post, E., Van Houten, F. J. A. M. Application of TTRS method in industrial practice tolerance specification for industrial cooling water pumps. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 251-260
[164] Salomons, O. W., Van Der Zwaag, J. A., Zijlstra, J., Van Houten, F. J. A. M. Dynamic tolerance analysis. pan I: a theoretical framework using bondgraphs. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999:271-282
[165] Salomons, O. W., Van Der Zwaag. J. A., Zijlstra, J., Van Houten, F. J. A. M. Dynamic tolerance analysis. pan 11: issues to be resolved when applying bondgraphs. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999:283-292
[166] Gerth, R. J. Cost tolerance sensitivity analysis for concurrent engineering design support. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 313-324
[167] Laperriere, L., Lafond, P. Tolerance analysis and synthesis using virtual joints. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 405-414
[168] Srinivasan, V, An integrated view of geometrical product specification and verification. Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing. France, 2001: 7-18
[169] Hu, J., Wu, Z. T, Yang, J. X., Variational geometric constraints network for computer aided tolerancing. Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing. France, 2001: 213-222
[170] Tsai, J. C., A STEP translator toward computer integrated tolerancing. Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing. France, 2001,255-264
[171] Chase, K. W., Gao, 3． , Magleby, S. P., Sorensen, C. D. Including geometric feature variation in tolerance analysis of mechanical assemblies. HE Transactions. 1996, 28: 795-807
[172] Chase, K.. W., Gao, J., Magleby, S. P., Gao, J., Tolerance analysis of two and three dimensional mechanical assemblies with small kinematic adjustments. Advanced tolerancing techniques. John Wiley & Sons, Inc. 1997: 103-138