Matrix Computational Solving Method Basedon Functional Chain For Mechanical And Electrical Product Design

Conceptual design is the most important phase in the product development process, and it is also the weakest link of the computer aided design. Along with the development of the computer technology, network technology, collaborative conceptual design technology and the intelligent conceptual design technology, the conceptual design will be moving in the network, intelligent and digital direction. Considering the importance of the conceptual design, under the support of the national natural science fund project(No. 50505017, 50505017), the formal and intelligent design methods of the mechanical and electrical products are proposed in this paper. By means of matrix computation, many methods in the conceptual design are proposed, such as the function analysis method of the mechanical and electronic product, the functional modeling method, the functional decomposition method, the aggregation method of the design solution, etc. The aim of this paper is to develop the automatic design methods of the conceptual design, and to provide decision-making solution for the development of new products.The main content of this paper is as follows:(1) The expression methods of the product functional information and the acquisition methods of the functional chain are proposed in this paper. Functional information expression is the basis of the product conceptual design. In order to analize the product functional information, the definition and decomposition method of the product function, the meta-function and function ontology are introduced firstly. Then the definition, type and aggreation method of the functional chain are introduced too. Secondly, the matrix-based expression method of the functional chain is proposed, and some functional or component matrixes are defined. Finally, the functions of a few cases are analized, and the information matrixes of the cases are defined.(2) The matrix-based design method of the single-functional chain is proposed. The relationship between functions and components can be clearly expressed by matrix, and then the matrix is used to solve the functional chain design in the method. First the decomposition method of the functional chain is proposed, and then the function- component matrix, the function correlation matrix, the design structure matrix and the design solution matrix are defined. Second the design process of a transmission mechanism is used to illustrate the proposed method. In the method, the relevances, constraints and conflicts between functions and components are expressed, computed and transferd by various matrixes. The design solutions in the design solution matrix both can meet the demand of the product function and can meet the requirements of design structure.(3) The optimization method of the functional chain design solution is proposed. First the principle of ant colony algorithm, the similarity theory, the definition of the generalized distance and the structure method of the similarity matrix are introduced in the paper. And then the design solution evaluation model, the ant colony algorithm based optimization model, the evaluation criterion, weightings and the calculation method of the evaluation value are proposed, and the pheromone matrix and the probability matrix are defined. Second the design solution matrix containing similarity information is acquired by the calculation of the similarity matrix and the design solution matrix, and then the initiale pheromone matrix and the initial probability matrix are obtained from the design solution matrix. Finally, the product design problem is transformed into the optimal path problem in the ant colony algorithm, and the optimal solution can be obtained by the calculation of the ant colony algorithm and the design solution matrix.(4) The aggregation method of multiple functional chains is proposed. First the similarities of the input/output flow and the meta-function in the two functional chains are analyzed, and the input flow similarity matrix, the output flow similarity matrix, the function similarity matrix and the general function similarity matrix are constructed. And then the calculation method of the component correlation matrix and the analysis method of the component correlation are proposed, and the functional similarities are mapped to the components’ relevance by the matrix calculation, and the aggregation solution of two functional chains is acquired by analizing the component correlation. Finally, the solving process of the aggregation solution is detailed throuth the aggregation of a shaver and a vacuum cleaner.(5) The prototype system for the mechanical and electrical product design is developed. First the product design knowledge database and the matrix information database are developed on the basis of the proposed methods. Second the mechanical and electrical product design prototype system is developed, and the proposed calculation methods are used to facilitate product design through the prototype system. Finally, the design solutions of a transmission mechanism and a three-axis servo drive mechanism are obtained under the help of the prototype system.