Study On The Modeling Of Tolerance Based On Mathematical Definition And Form Errors Evaluation

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.