The Research On Geometric Features Mathematical Modeling And 3D Tolerance Analysis Method Based On GPS

The quality of product designing has a decisive impact on the advantages and disadvanta ges of the final product. Tolerance design is an important technology to ensure the product qu ality, and it is also a key factor determines the product processing costs. However, the synergi stic effect of dimensional tolerance, geometric tolerance and load hasn’t got enough attention i n the traditional tolerance design theory.This paper researches the mathematical modeling of the 3D deviation by using a digital analysis method based on the new generation Geometrical Product Specification (GPS) standard system. It puts forward a 3D tolerance analysis method by the Homogeneous Transformation Matrix Method, which comprehensively considers the dimensional tolerance, the geometric tolerance and the parts’load. The main contents are as follows:(1) The position and pose of space objects are described by the vector coordinates. The expressions of the positional and postural variation quantity are also deduced. The formulas of the 3D deviation space transfer model are established by a method that describes the position and pose of the space objects with a 4D column vector.(2) The geometrical constant degrees of the new generation GPS is treated as an entry point. The 3D tolerance mathematical model of plane and cylinder dimensional is established by the Small Displacement Torsor (SDT) theory and the constraint condition between the tolerance boundaries and the mathematical relationship of the position and pose torsor. According to the definition of geometric tolerance in ASME, the mathematical model of flatness, parallelism etc geometric tolerances is established.(3) The node data of the deformed surfaces on the parts is extracted by finite element method, based on the certificated surface model of the new generation GPS standard system. Deformation information is fitted by specific mathematical principles, and then the elements of the fitted deformation of the parts are obtained. Finally, the 3D deviation mathematic model of the parts’deformation is established.(4) The manufacturing and deformation error of parts is implanted into the coupling and accumulating model of the 3D deviation by Homogeneous Coordinate Transformation Method. In product’s design phase, it researched the 3D tolerance analysis method under the parts’rigid and flexible assumptions.(5) The main purpose of tolerance analysis is to decrease the manufacturing costs and improve the product quality. In this paper, the orthogonal table of Taguchi Method serves as the basis of group for parts manufacturing deviation. Then by the matching and controlling experiment of the parts deviation, the most optimal matching and combining scheme is selected, and the purpose of improving product quality is realized.