The Research Of 3D Variation Modeling And Analysis Based On Deterministic Analysis In Auto-Body Assembly

The dimensional variation of auto-body has a direct effect on appearance, wind noise, shutdown of door and so on. The dimensional variation of auto-body not only depend on manufacturing process control, but also on the the process design. So it has great significance about the research of the variation analsysi of auto-body assembly. However, the characteristics that the multiple constraints and sequences in the auto-body assembly make the error stack-up very complex and it is difficult to search dimension-loop by utilizing the traditional dimension loop model in the 3-D variation analysis and synthesis in auto-body. Meanwhile, for the auto-body composed by great mounts of parts, the traditional Monte Carlo Simulation is time-consuming. So, the 3-D variation modeling and analysis is developed for auto-body assembly to raise the tolerance design of auto-body in this paper.According to the characteristic of multiple constraits and sequence, a 3-D assembly variation model based on deterministic locating is presented firstly; then the linearized and quadratic analysis method of the 3-D variation model is developed; finally based on the variation model and analysis method, a software prototype of 3-D variation analysis in auto-body is developed. The main research work and method are as follows:(1) The auto-body assembly has the characteristics of the multiple constraints and sequences, it is difficult to search dimension-loop by utilizing the traditional dimension loop model for the 3-D variation analysis。The deformation of auto-body assembly is very small and it can be consider as rigid body. A new 3-D variation model is presented in this paper, the hierarchical assembly process is decomposed to a series of deterministic locating of single part in this model. Firstly, the multiple constraints is transferred to deterministic locating; then the part variation and jig variation is taken as input to develop the model of deterministic locating by considering the quadratic geometry of constraints.(2) The linearized method of 3-D variation model Because the traditional Monte Carlo simulation is time-consuming, and can not be applied to tolerance synthesis, a linearized method is presented in this paper. At first, for nonlinear assembly function, the implicit differentiation and multi-variables Tayler Series Expansion are used to obtain the linear relationship between input and output. Then the stability and computational complexity are investigated to determint is application range. Finally this method is applied in case study to compare to Monte Carlo simulation. The presented method is efficient by avoiding resolving nonlinear equations, and in general applications, the relationship between input and output of assembly function is linear and closely linear, the linearized method can obtain enough accuracy.(3) The quadratic method of 3-D variation modelIn case that the assembly function is nonlinear, or the part dimension is not follow Gaussion distribution (for example, the position tolerance of hole can be consider as Rayley distribution), the application of Method of Moments in the nonlinear implicit assembly function is presented.Firstly the nonlinear implicit function is expanded by 2nd Taylor Series Expansion, and the finite differential method and Newton-Raphson method are utilized to obtain the 1st order, 2nd order and 2nd order mixed sensitivity matrix, then the mean, variance, skewness and kurtosis of part dimension are take as input to obtain the mean and variance of assembly diemension; and then the accuracy and computational complexity are investigated; finally it is compared to linearized method and Monte Carlo Simulation. The application of Method of Moments in the nolinear implicit function is a general method, and can be further extended to other fields, such as finite element analysis.(4) The development of 3D tolerance analysis softwareBased on the presented variation model and analysis method, by using C++, a 3D tolerance analysis software for auto-body assembly, AVAS, is developed and this software has applied for registration. The system adopts a functional 3-hierarchical structure: the data layer, algorithm layer and user layer. The Headlamp assembly and Auto-door assembly are utilized to validate the AVAS system and the core algorithm, the results is compared to the meament data and 3DCS software. It has the followed merits: independent with other exist CAD software; AVAS can choose linearized method in tolerance analysis to obtain higher efficiency as compared to the Monte Carlo Simulation; AVAS can deal with two or more assembly sequence in one model.