Study On Mathematical Modeling And Analysis Of Cylindrical Feature Based On Mathematic Definition

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 qualityIn 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 severalcylindrical 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.