【作者】 茅健；

【导师】 杨将新； 曹衍龙；

【作者基本信息】 浙江大学 ， 机械制造及其自动化， 2007， 博士

【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。更多还原

【Abstract】 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.更多还原