摘要
本文在分析了国内外计算机辅助公差设计技术、新一代GPS标准体系和误差评定方法的研究现状基础上，结合国家自然科学基金“基于产品几何技术规范的集成公差设计理论与方法”(50275136)、“基于GPS的三维公差建模方法与技术研究”(50505046)，研究了基于数学定义的三维公差建模方法和基于新一代GPS形状误差评定技术，开发了集成于Solidworks系统的公差建模和误差评定原型系统，并用实例验证了其正确性和有效性。本论文的主要研究内容如下：
第一章：分析了计算机辅助公差设计的研究现状，综述了新一代GPS标准体系、形位误差的评定方法以及不确定理论的研究与进展，讨论了本课题的研究背景和意义，给出了本论文的主要研究内容、总体框架及创新点。
第二章：首先分析了基于语义的公差分类方法，给出了基于SDT的公差数学建模理论，然后系统地研究了基于SDT的尺寸公差数学模型。根据约束条件将平面尺寸公差进行分类，分析了不同类型平面尺寸公差的约束关系，建立了相应尺寸公差的数学模型，并用实例进行了验证分析。
第三章：首先建立了形状公差的数学模型。然后基于公差原则研究了平行度、垂直度、倾斜度等定向公差数学模型，扩展并完善公差的数学定义，给出各公差语义的数学表达式。分析了尺寸和形位公差的复合公差数学模型，并给出了同时具有尺寸公差、平行度公差和平面度公差要求的复合公差数学模型。
第四章：系统地研究了基于最小实体要求(LMR)、最大实体要求(MMR)的圆柱特征同轴度、位置度不同约束条件，给出了基于公差原则的同轴度、位置度等定位公差数学模型。以孔中心轴线为研究对象，研究了满足独立原则和最大实体要求时中心要素解释和表面要素解释的对称度公差数学模型。
第五章：首先根据最小区域法，建立了形位误差评定的数学模型以及目标函数，利用粒子群算法(PSO)求解，得到形位误差评定的解。然后根据新一代GPS不确定度理论计算评定结果的不确定度。
第六章：以Solidworks为开发平台，应用VC++和Matlab等工具开了基于数学定义的三维公差建模和误差评定的原型系统，并用实例验证了前几章所提出的理论与方法。
第七章：概括了全文的主要研究内容；并对进一步开展研究进行探讨和展望。
On the basis of comprehensive analysis for recent research status of computer-aided tolerancing,the improved Geometrical Product Specification (GPS) system and error evaluation both in and out ofChina, binding State Natural Science Foundation of China ("Design theory of integration Tolerancebased on Geometrical Product Specifications" No. 50275136 and "Research on Tolerance Modelingbased on Geometrical Product Specification" No. 50505046), tolerance modeling based on themathematic definition and the techniques of error evaluation based on the improved GPS are studied inthis dissertation. The prototype system for tolerance modeling and error evaluation is developed basedon Solidworks and verified by examples.
In chapter 1, the important role of computer-aided tolerancing in modern manufacture and theimproved GPS system, error evaluation technique and uncertainty theory are summarized. The maincontents, general structure scheme and innovation points of this dissertation are given.
In chapter2, the basic theory of tolerance mathematical model is analyzed firstly. Then thetolerance model of size tolerance for plane based on Small Displacement Torsor (SDT) is studied. SDTis adopted for representing the tolerance zone. The planer surface is classified according to constraintcondition. Different dimension constraint models are detailed. A generic mathematical model of sizetolerance is deduced based on SDT systematically which can interpret the semantics of size toleranceexactly and completely. An example is given to illustrate the application of the model in toleranceanalysis.
In chapter 3, the model condition of orientation tolerance is analyzed deeply based on toleranceprinciple. The tolerance models of orientation tolerance such as parallelism, perpendicularity andangularity are developed, so as to extend the tolerance mathematical definition. By using toleranceprinciple, different limit for modeling geometric tolerances are analyzed systematically. Themathematical model with size tolerance, parallelism and flatness simultaneity is given.
In chapter 4, the mathematical models of coaxiliality, symmetry and position are developedsystematically. Firstly, the constraint conditions of coaxiliality and position are developed systematicallyunder Least Material Requirement (LMR) and Maximum Material Requirement (MMR). So themathematical models for cylindrical feature based on MMR and LMR are proposed for coaxiliality andposition tolerance. Then the constraint conditions of linear symmetry tolerance are discussedsystematically under independence principle and MMR. The corresponding mathematical models oflinear symmetry of surface feature and central feature are deduced based on independence principle andMMR.
In chapter 5, the method for the uncertainty evaluation of form errors based on the Particle Swarm Optimization (PSO) algorithm is studied. Under the condition of minimum zone, the mathematicalmodel of the form error and the optimal objective function are given. PSO algorithm is used to searchfor the optimal solution of form error. The coefficients of the line equation and propagation ofuncertainty are calculated so that the result of form error evaluation and the uncertainty of the result canbe obtained. The evaluation results are more accurate and accord with requirements of new generationGPS standard.
In chapter 6, the prototype system for tolerance modeling and error evaluation is developed basedon Solidworks, VC++ and Matlab. Some examples are studied to demonstrate the proposed theory andmethod.
In chapter 7, the important results and conclusions of the dissertation are summarized and thefuture research of compute-aided tolerancing and error evaluation 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：浙江大学出版社．1999
[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论文集．杭州．2000：6～14 ．
[3] 吴昭同．现代质量工程中几个重要的研究进展．全国首届计算机辅助公差设计专题学术会议论文集．杭州．2000：15～23
[4] Bjorke, O. Computer-Aided Tolerancing. 2nd ed. NewYork. ASME Press. 1989
[5] Tsai, J. C. Tolerance reasoning for concurrent CAD/CAM systems. [Ph.D. dissertation]. Stanford University, 1993
[6] Salomons, O. W. Computer support in the design of mechanical products, constraint specification and satisfaction in feature based design for manufacturing. [Ph.D. dissertation]. University of Twente, The Netherlands. 1995
[7] Yanyan Wu. Development of mathematical tools for modeling geometric dimensioning and tolerancing. [Ph.D. dissertation]. Arizona State University, 2002
[8] 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．2000
[9] 胡洁．基于变动几何约束网络的形位公差设计理论与方法的研究．[博士学位论文]．浙江大学，杭州．2001
[10] 蔡敏．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．[博士学位论文]．浙江大学，杭州．2002
[11] 曹衍龙．面向制造环境的公差稳健设计方法与技术的研究．[博士学位论文]．浙江大学，杭州．2003
[12] Hillyard C. Dimensions and Tolerances in Shape Design. University of Cambridge, UK: ph.D. Dissertation, 1978
[13] Requicha A A G. Toward a Theory of Geometric Tolerancing. Int. J. Rob. Res. 1983, 2(4): 45～49
[14] Weill R., Clement, A., Hocken, R., Farmer, L. E., Gladman, C. A., Wirtz, A., Bourdet, P., Freckleton, J.E., Kunzmann, H., Ham, I., Trumpold, H., Matthias, E. Tolerancing for function. Annals of the CIRP. 1988, 37(2): 603～610
[15] 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.
[16] 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
[17] 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
[18] Nassef, A. O., ElMaraghy, H. A. Probabilistic analysis of geometric tolerances. Proceedings of 4th CIRP Seminars on Computer Aided Tolerancing. 1995: 187～203
[19] Mathieu, L., Clement, A., Bourdet, P. Modeling, representation and processing of tolerances, tolerance inspection: a survey of current hypothesis. Proceedings of 5th CIRP Seminars on Computer Aided Tolerancing. 1997: 1～33
[20] 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
[21] 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
[22] 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
[23] 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
[24] Clement, A., Riviere, A., Serre, P. Global consistency of dimensioning and tolerancing. Proceedings of 6th. CIRP Seminars on Computer Aided Tolerancing. 1999: 1～26
[25] 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
[26] 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
[27] 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
[28] Glancy, 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
[29] Salomons, O. W., Van Der Zwaag, J. A., Zijistra, J., Van Houten, F. J. A. M. Dynamic tolerance analysis, part Ⅰ: a theoretical framework using bondgraphs. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 271～282
[30] Laperriere, L., Lafond, P. Tolerance analysis and synthesis using virtual joints. Proceedings of 6th CIRP Seminars on Computer Aided Tolerancing. 1999: 405～414
[31] 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
[32] Srinivasan, V., An integrated view of geometrical product specification and verification. Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing. France, 2001: 7～18
[33] 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
[34] Tsai, J, C., A STEP translator toward computer integrated tolerancing. Proceedings of 7th CIRP Seminars on Computer Aided Tolerancing. France, 2001, 255～264
[35] Mathieu L., Ballu A., GEOSPELLING: a common language for Specification and Verification to express method uncertainty. Proceedings of 8th CIRP Seminar on Computer Aided Tolerancing. USA, 2003
[36] ANSI Y 14.5 M. Dimensioning and tolerancing. ASME, New York, 1994
[37] ISO/TC 213. http://www.ds.dk/
[38] Jiang X Q. Review of the next generation GPS.2nd International Symposium on Instrumentation Science and Technology, Jinan China. 2002, (3): 9～16
[39] ISO/TS 14253—2. Geometrical Product Specification (GPS) Inspection by measurement of workpieces and measuring equipment—Part 2: Guide to the estimation of uncertainty in GPS measurement, in calibration of measuring equipment and in product verification, 1999
[40] ISO/TS 17450—2. Geometrical product specifications (GPS)—General concepts—Part 2: Basic tenets, specifications, operators and uncertainties, 2002
[41] ISO/TS 14253-1. Geometrical product specification (GPS)—Inspection by measurement of workpieces and measuring equipment—Part 1: Decision rules for proving conformance or non-conformance with specifications, 1998
[42] 张琳娜，赵凤霞，李晓沛等．现代产品几何技术规范(GPS)体系的理论基础及关键技术研究．机械强度．2004，26(5)：547～551
[43] 张琳娜，赵凤霞，李晓沛等．现代产品几何技术规范(GPS)体系及应用分析．机械强度，2004，26(4)；400～40
[44] 赵凤霞，张琳娜，常永昌等．现代产品几何技术规范(GPS)的数字化理论基础．机械强度，2004，26(6)：652～655
[45] 蒋向前．现代产品几何技术规范((GPS)国际标准体系．机械工程学报，2004，．40(12)：133～138
[46] 张琳娜，崔凤喜，李晓沛等．新一代GPS标准体系的构成及关键技术．中国标准化，2004．12：45～48
[47] 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
[48] 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
[49] 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
[50] 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
[51] 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
[52] 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
[53] 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
[54] 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
[55] 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
[56] 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
[57] 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
[58] Jayarman R, Srinivasan V. Geometric Tolerance: Ⅰ. Virtual Boundary Requirement. IBM J. RES. DEVELOP, 1989, 33(2): 90～104
[59] Srinivasan V, Jayarman R. Geometric Tolerance: Ⅱ. Conditional Tolerances. IBM J. RES. DEVELOP, 1989, 33(2): 105～125
[60] 张文祖．一种尺寸与公差的表达模式．中国机械工程．1993，4(1)：10～13
[61] Hillyard R C, Braid I C. Analysis of Dimensions and Tolerances in Computer-Aided Mechanical Design. CAD, 1978, 10(3): 161～166
[62] Light R A, Gossard D C. Modification of Geometric Models Through Variations Geometry. Computer Aided Design, 1982, 14(4): 209～214
[63] 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
[64] Hoffman P. Analysis of Tolerances and Process Inaccuracies in Discrete Part Manufacturing. Computer-Aided Design, 1982, 14(2): 83～88
[65] 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
[66] Zhang B C. Geometric modeling of dimensioning and tolerancing[Ph D Disseration]. Arizonas State University, 1992
[67] 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)
[68] A Desrochers. Modeling three dimensional tolerance zones using screw parameters. Proceedings DETC: 25th Design Automation Conference, las-Vegas, 1999: 1～12
[69] Roy U, Li B. Representation and interpretation of geometric tolerances for polyhedral objects Ⅰ. form tolerances. Computer Aided Design, 1998, 30 (2): 151～161
[70] Roy U, Li B. Representation and interpretation of geometric tolerances for polyhedral objects Ⅱ. size, orientation and position tolerances. Computer Aided Design, 1999(31): 273～285
[71] Davidson J K, Mujezinovic A, Shah J J. A New Mathematical Model for Geometric Tolerances as Applied to Round Faces. ASME Journal Mechanical Design, 2002, 124: 609～622
[72] Johnson R H et.al. Dimensioning and Tolerancing Final Report. Technical Report R-84-GM-02.2CAM-I, USA, 1985
[73] 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): 156～165
[74] 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
[75] Roy U. Tolerance Representation Scheme in Solid Modeling: Parrts Ⅰ&Ⅱ. Proceedings of the 15th ASME Design Automation Conference
[76] Gossard D C. Representing Dimensions, Tolerances, and Features in MCAE systems. IEEE Computer Graphics & Applications. 1988: 51～59
[77] A Descrocher, A Clement. A dimensioning and tolerancing assistatance model for CAD/CAM systems. Journal of Advanced Manufacturing Technology, 1994, 10(9): 352～362
[78] Guiford J. Representational Primitive for Geometric Tolerancinng. Computer Aided Design, 1993, 25(9): 577～586
[79] Willhelm. Computer Methods for Tolerancing Design. New Jersey: World Science Publishing Company, 1992
[80] 刘玉生，曹衍龙．TolRM：面向三维CAD的公差建模系统．计算机辅助设计与图形学学报．2006，18(8)：1179～1184．
[81] Hillyard R C, Braid I C. Characterizing Non-ideal Shapes in Terms of Dimensions and Tolerance. Comput. Graph., 1987, 12(3): 234～238
[82] Liu C R, Gossard D C, Light R A. Variational Geometry in Computer Aided Desing. Comput. Graph. 1981, 15(3)
[83] Light R A, Gossard D C. Modification of Geometric Models Through Variations Geometry. Computer Aided Design, 1982, 14(4): 209～214
[84] 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
[85] Turner J U. Tolerance in Computer-Aided Geometric Design. [Ph.D. dissertation]. Renssetaer Polytechnic Institutes, 1987
[86] Mitchell W, Siddall J N. The Primization Problem with Optimal Tolerance Assignment and Full Acceptance. ASME Journal of Mechanical Design, 1981, 103: 842～849
[87] Mitchell W, Siddall J N. The Optimal Tolerance Assignment With Less Than Full Acceptance. ASME Journal of Mechanical Design, 1981, 104: 855～860
[88] Parkson D B. Tolerancing of Component Dimensions in CAD. Computer Aided Design, 1984, 16(1): 25～32
[89] Roman S. Computer Tolerance Assignment. Computer Ind. Engineering. 1991, 21(1): 67～71
[90] Lee W J, Woo T C. Tolerance: Their Analysis and Synthesis. Journal of Engineering for Industry. 1990, 112: 113～121
[91] 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
[92] 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
[93] Daniel F, Weill R, Bourdet P, Computer Aided Tolerancing and Dimensioning in Process Planning. Manuf. Tech. CIRP Ann. 1986, 35(1): 381～386
[94] 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
[95] 曹衍龙．基于数学定义的公差建模方法与技术研究．浙江大学博士后出站报告．杭州，2005
[96] 李柱，徐振高，蒋向前．互换性与测量技术．北京：高等教育出版社，2004
[97] 汪恺．形状和位置公差标准应用指南．北京：中国标准出版社，2000
[98] 廖平．基于遗传算法的形状误差计算研究．[博士学位论文]．中南大学，长沙．2002
[99] 崔长彩．形位误差评定的进化遗传算法研究．[博士学位论文]．哈尔滨工业大学，哈尔滨．2003
[100] S.T.Huang, K.C.Fan, John H.Wu. A new minimum zone method for evaluating flatness errors. Precision Engineering 1993, 15(1): 25～32
[101] Tohrn Kanada, Soichiroh Suzuki. Evaluation of minimum zone flatness by means of nonlinear optimization techniques and its verification. Precision Engineering 1993, 15(2): 93～99
[102] 蒋庄德，赵卓贤．球度误差的几何判别标准．仪器仪表学报．1991．12(1)：35～39
[103] M.T. Traband, S. Joshi, R.A. Wysk, T.M. Cavalier, Evaluation straightuess and flatness tolerances using the minimum zone, Manufacturing Review. 1989, (2): 189～195
[104] Jyunping Huang. An Exact Minimum Zone Solution for Three-Dimensional Straightness Evaluation Problems. Precision Engineering. 1999, 23(3): 204～208
[105] Jyunping Huang. An Efficient Approach for Solving the Straightness and the Flatness Problems at a Large Number of Data Points. Computer Aided Design. 2003, 35(1): 15～25
[106] MJ Kaiser, KK Krishnan, Geometry of the minimum zone flatness functional: Planar and spatial case, Precision Engineering. 1998, 22 (3): 174～183
[107] Lee M. K. A new convex hull based approach to evaluating flatness tolerance. Computer Aided Design. 1997, (29): 861～868
[108] Hossein S. C., Huay SL, Saied M. Straightness and flatness tolerance evaluation: an optimization approach. Precision Engineering 1996, 18(1): 30～37
[109] G.L. Samuel, M.S.Shunmugam. Evaluation of straightness and flatness error using computational geometric techniques. Computer-Aided Design. 1999, (31): 829～843
[110] Zhu Xiangyang, Han Ding. Flatness tolerance evaluation: an approximate minimum zone solution. Computer-Aided Design. 2002, (34): 655～664
[111] 范裕健，赵卓贤．圆柱面形状误差评定的理论与方法．机械工程学报．1994，30(2)：19～25
[112] Novaski O., Barczak ALC. Utilization of Voronoi Diagrams for Circularity Algorithms. Precision Engineering. 1997, 20(3): 188～195
[113] S.H.Cheraghi, H.S.Lim, S.motavalli, Straightness and flatness tolerance evaluation: an optimization approach. Precision Engineering 1996; 18(1): 30～37
[114] Qing Zhang, K.C. Fan, Zhu Li. Evaluation method for spatial straightness errors based on minimum zone condition. Precision Engineering. 1999, (23): 264～272
[115] 张青，范光照，徐振高，李柱．按最小条件评定空间直线度误差的理论研究．计量学报．1998，19(4)：246～253
[116] Jyunping Huang. An exact solution for the roundness evaluation problems. Precision Engineering. 1999, 23: 2～8
[117] Lai J Y, Chen I H. Minimum zone evaluation of circles and cylinders. International Journal of Machine Tools & Manufacture. 1996, 36(4): 435～451
[118] Liu, W.W., Nie, H.J., A optimal algorithm used in roundness error evaluation. Chinese Journal of Scientific Instrument. 1998, 19(4): 430～433
[119] J. Huang, E. A. Lehtihet. Contribution to the minimax evaluation of circularity error. International Journal of production Research. 2001, 39(16): 3813～3826
[120] Carr K, Ferreira P. Verification of form tolerances Part Ⅰ: Basic Issues, Flatness, and Straightness. Precision Engineering. 1995, 17(2): 131～143
[121] Carr K, Ferreira P. Verification of form tolerances Part Ⅱ: Cylindricity and straightness of a median line. Precision Engineering. 1995, 17(2): 144～156
[122] Shuo-yan Chou, Chungwei Sun. Assessing cylindrieity for oblique cylindrical features. International Journal of Machine Tools & Manufacture. 2000, (40): 327～341
[123] Chen C K, Wu S C. A method for measuring and separating cylindrical and spindle errors in machine tool rotational parts. Measurement Science and Technology. 1999, 10: 76～83
[124] 刘永超，陈明．形位公差的进化算法．计量学报，2001，22(1)：18～22
[125] 李郝林．DNA计算模型在圆柱度误差评定中的应用．计量学报．2004，25(2)：107～110
[126] 廖平，喻寿益．基于遗传算法的空间直线度误差的求解．中南工业大学学报．1998，29(6)：586～588
[127] 廖平，喻寿益．基于遗传算法的圆的半径测量．计量学报．2001，22(2)：87～89
[128] Hsinyi Lai, Wenyuh Jywe. Precision modeling of form errors for cylindricity evaluation using genetic algorithms. Journal of the International Societies for Precision Engineering and Nanotechnology. 2000, (24) 310～319
[129] 王伯平，孙大刚，孔令德，王晓慧．基于遗传算法的直线度误差的测量．计量学报，2004，25(1)：16～18
[130] Cui Changcai, Che Rensheng, Ye Dong. Research on the minimum zone cylindricity evaluation based on genetic algorithms. Chinese journal of mechanical engineering. 2003, 16(2): 167～170
[131] Cui changeai, Ye Dong, Huang Qingcheng. Precise computation of planar straightness error using genetic algorithm. Optics and Precision Engineering. Aug. 2003, 11 (4): 374～378
[132] Cui Changcai, Che Rensheng, Huang Qingcheng. Genetic algorithm-based evaluation of spatial straightness error. Journal of Harbin Institute of Technology. 2003, 10(4): 418～421
[133] Cui Changcai, Che Rensheng, Li, Z.Y. Form error evaluation of circles based on a finely-designed genetic algorithm. Chinese journal of mechanical engineering. 2004, 17(1): 59～62
[134] 温秀兰，宋爱国．基于改进遗传算法评定圆柱度误差．计量学报．2004，25(2)：115～118
[135] Wen Xiulan, Song Aiguo. An improved genetic algorithm for planar and spatial straightness error evaluation. International Journal of Machine Tools & Manufacture. 2003 (43): 1157～1162
[136] 刘智敏．不确定度原理．中国计量出版社．北京，1993
[137] 李慎安．测量结果不确定度的估计与表达．中国计量出版社．北京，1997
[138] 费业泰．误差理论与数据处理．机械工业出版社．北京，2000
[139] 倪骁骅．形状误差测量结果不确定度的研究及应用．[博士学位论文]．合肥工业大学．2002
[140] 朱坚民．测量不确定度的非统计评定理论与方法．[博士学位论文]．华中科技大学，2001
[141] 谢少锋．测量系统分析与动态不确定度及其应用研究．[博士学位论文]．合肥工业大学．2003
[142] 王江，邹自强．测量点数对圆度测量不确定度的影响．计量技术，1988，12：15～18
[143] 刘景玉，宋芸．直线度误差测量不确定度分析．计量技术，1993，(4)：11～13
[144] 方福来．按节距法测量平面度误差时，测量结果不确定度的相关计算方法．计量技术，1997，(9)：8～9
[145] S. D. Phillips, B. Borchardt, W. T. Esteler, etal. The estimation of measurement uncertainty of small circular features measured by coordinate measuring machine. Precision Engineering, 1998, 22(2): 87～99
[146] Woncheol Choi, Thomas R Kurfess. Uncertainty of extreme fit evaluation for three-dimensional measurement data analysis. Computer Aided Design, 1998, 30 (7): 549～557
[147] Bjorn Karlsson. Fuzzy Handling of Uncertainty in Industrial Recycling. IEEE Instrumentation and Measurement Technology Conference. St. Paul, USA, 1998. 5: 832～836
[148] O. Artbaner. Application of Interval, Statistical, and Fuzzy Methods to the Evaluation of Measurements. Metrologia. 1998, 25(2): 81～86
[149] 国际标准化组织．肖明耀，康金玉译．测量不确定度表达指南．北京，中国计量出版社，1994
[150] S.D. Phillips, W.T. Estler, M.S.Levenson. Calculation of Measurement Uncertainty Using Pior Information. Journal of Research of the National Institute of Standards and Technology, 1998, 103(6): 625～63
[151] K.Weise, W. Woger. A Bayesian Theory of Measurement Uncertainty. Measurement Science Technology. 1993, 4: 1～11
[152] Jurgen Beyerer. The Value of additional Knowledge in Measurement-A Bayesian Approach. Measurement, 1999, 25: 1～7
[153] 刘智敏．不确定度评定的一种新方法—最大方差法．宇航计测技术 1996，18(1)：24～35
[154] 王中宇，夏新涛，朱坚民．测量不确定度的非统计理论．国防工业出版社，北京，2000
[155] 陈善勇，李圣怡．多特征的位形空间理论及其在定向公差建模与评定中的应用．机械工程学报．2005，41(9)：7～11
[156] CAO Yah-long, LIU Yu-sheng, MAO Jian, YANG Jiang-xin. 3DTS: A 3D tolerancing system based on mathematical definition. Journal of Zhejiang University SCIENCE A.2006, 7(11): 1810～1818
[157] 张博，李宗斌．采用多色集合理论的公差信息建模与推理技术．机械工程学报．2005，41(10)：111～116
[158] J. Kennedy, R. Eberhart. Particle swarm optimization. Proceedings of IEEE International Conference on Neutral Networks, Perth, Australia, 1995: 1942～1948
[159] A. Noorul Haq, K. Sivakurnar. Particle swarm optimization (PSO) algorithm for optimal machining allocation of clutch assembly. International Journal of Advanced Manufacturing Technology, 2005(27): 865～869
[160] Shi Y, Eberart R C. A Modified Particle Swarm Optimizer. IEEE World Congress on Computational Intelligence, Anchorage, USA, 1998
[161] Eberhart R C, Shi Y. Particle swarm optimization: developments, applications and resources. Proceedings of the IEEE Congress on Evolutionary Computation. Piscataway, NJ: IEEE Service Center, 2001. 81～86
[162] A.A.G.Requicha. Solid Modeling and Beyond. IEEE Computer Graphics&Applications. 1992, (9), 31～44
[163] A.A.G.Requicha. Solid Modeling: Current Status and Research Directions. IEEE Computer Graphics & Applications. 1983, (10), 25～37
[164] A.A.G.Requicha. Solid Modeling: A Historical Summary and Contemporary Assessment. IEEE Computer Graphics & Applications. 1982, (3), 9～24
[165] 刘玉生，杨将新，吴昭同，等．CAD系统中公差信息建模技术综述．计算机辅助设计与图形学报，2001，13(11)：1048～1054
[166] LIU Yu-sheng, YANG Jiang-xin, WU Zhao-tong, et al. A mathematical medol of symmetry based on mathematical definition[J]. Journal of Zhejiang University Scinece A, 2002, 3(1): 24～29
[167] CAI Min, YANG Jiang-xin, WU Zhao-tong. Mathematical model of cylindrical form tolerance. Journal of Zhejiang University Scinece A, 2004, 5(7): 890～895
[168] 刘玉生，高曙明，曹衍龙．三维CAD系统中变动孔特征通用生成方法．机械工程学报．2005，41(7)：112～118
[169] Liu Y S, Gao S M. Variational geometry based tolerance preevaluation for pattern of holes.International Journal of Production Research, 2004, 42(8): 1659～1675
[170] B. K. A. Ngoi and C. K. Tan. Geometrics in computer-aided tolerance charting. International Joumaiof Production Research, 1995, 33(3): 835～868
[171] 刘玉生，高曙明，吴昭同等．一种基于数学定义的三维公差语义表示方法．中国机械工程，2003，14(3)：241～245
[172] Bourdet, Mathew, et al, The concept of small displacement torsors in metrology, Advanced Mathematical Tools in Metrology Ⅱ in Series on advances in mathematics for applied science, World Scientific, 1996, vol. 40
[173] F Villeneuve, O Legoff, Y Landon. Tolerance for manufacturing: a three-dimensional model[J]. International Journal Production Research, 2001, 39(8): 1625～1648
[174] Y S Hong, T C Chang. Tolerancing algebra: a building block for handling tolerancing interactions in design and manufacturing[J]. International Journal Production Research, 2002, 40(18): 4633～4649
[175] H Wang, N Prarnanik, U Roy. A Scheme for Transformation of Tolerance Specifications to Generalized Deviation Space for Use in Tolerance Synthesis and Analysis. Proceedings of DETC 02. Montreal Canada, 2002: 1～9
[176] F Vignat, F Villeneuve. 3D Transfer of Tolerances Using a SDT Approach: Application to Turning Process. Journal of Computing and Information Science in Engineering. 2003, (3): 45～53
[177] F Villeneuve, F Vignat. Manufacturing process simulation for tolerance analysis and syntheis. Proceedings of IDMM. Bath, UK. April, 2004
[178] F Vignat, F Villeneuve. Simulation of the manufacturing process(1) generic resolution of the positioning problem. Procesdings of the 9th CIRPcomputer aided tolerancing semimear. Tempe, USA. April, 2005
[179] F Vignat, F Villeneuve. Simulation of the manufacturing process(2) analysis of its consequences on a functional tolerance. Procesdings of the 9th CIRPcomputer aided tolerancing semimear. Tempe, USA. April, 2005
[180] 孙家广，杨长贵．计算机图形学(新版)．北京：清华大学出版社．2003年
[181] 刘玉生．可视化公差分析方法的研究．工程设计．2001，4：168-172
[182] 国家技术监督局．GB／T4249-1996 公差原则．北京：中国标准出版社，1996
[183] 国家技术监督局．GB／T19671-1996形状和位置公差 最大实体要求 最小实体要求和可逆要求．北京：中国标准出版社，1996
[184] 茆诗松，王静龙．数理统计．上海：华东师范大学出版社．1990年
[185] 陈希孺．数理统计引论．北京：科学出版社．1981年
[186] 王启付，王战江，王书亭．一种动态改变惯性权重的粒子群优化算法．中国机械工程，2005，16(11)：945～948
[187] Shi Y, Eberart R C. A Modified Particle Swarm Optimizer. IEEE World Congress on Computational Intelligence, Anchorage, USA, 1998
[188] Eberhart R C, Shi Y. Particle swarm optimization: developments, applications and resources. Proceedings of the IEEE Congress on Evolutionary Computation. Piscataway, NJ: IEEE Service Center, 2001. 81～86
[189] 李明，宋成芳，周泽魁．二维不规则零件排样问题的粒子群算法求解．江南大学学报(自然科学版)，2005，4(3)：266～269
[190] 傅强，胡上序，赵胜颖．基于PSO算法的神经网络集成构造方法．浙江大学学报(工学版)，2004，38(12)：1596～1600
[191] 茅健，曹衍龙．基于粒子群算法的空间直线度误差评定．工程设计学报，2006，13(5)：291～294
[192] JerOme Bachmann, Jean marc Linares, Jean Michel Sprauel, et al. Aide in decision-making: contribution to uncertainties in three-dimensional measurement. Precision Engineering, 2004, 28(1): 78～88
[193] BIPM-IEC-IFCC-ISO-IUPAC-IUPAP-OIML. Guide to the Expression of Uncertainty in Measurement(GUM)
[194] 温秀兰，宋爱国．改进遗传算法及其在平面度误差评定中的应用．应用科学学报．2003，21(3)：221～224
[195] Wen, Y. J., Chien, H.L.. The min-max problem for evaluating the form error of a circle. Measurement. 1999, 26: 273～282
[196] CUI Changcai, CHE Rensheng, YE Dong. Circularity error evaluation using genetic algorithm. Optics and precision engineering. 2001, 9(6): 499～505
[197] Fan K C, Lee J C. Analysis of minimum zone sphericity error using minimum potential energy theory. Precision Engineering, 1999, 23: 65～72
[198] Cui C C, Che R S, Ye D, et al, Sphericity error evaluation using the genetic algorithm. Optics and Precision Engineering, 2002, 10(4): 333～339.
[199] 叶炜威，余才佳编著．SolidWorks 2006实体建模与二次开发教程．北京：国防工业出版社．2006
[200] 清源计算机工作室编著Visual C++6.0开发宝典．北京：机械工业出版社．1999
[201] 于涛，李勇，马维士编著．Visual C++6.0教程．北京：科学出版社．2003
[202] 孙样，徐流美，吴清．MATLAB 7.0基础教程．北京：清华大学出版社．2005
[203] 飞思科技产品研发中心编著．MATLAB 7基础与提高．北京：电子工业出版社．2005
[204] 曹衍龙，茅健，杨将新．基于数学定义的直线定向公差数学模型．农业机械学报(已录用)．
[205] 杨将新，茅健，曹衍龙，徐旭松．基于MMR和LMR的同轴度数学模型研究．浙江大学学报(工学版)(已录用)．
[206] 茅健，曹衍龙，杨将新，徐旭松．基于公差原则的直线对称度公差数学模型．中国机械工程(已录用)