Decomposition-based Assembly Synthesis Based on Structural Stiffness Considerations

This paper presents a method for systematically decomposes product geometry into a set of components considering the structural stiffness of the end product. A structure is represented a graph of its topology, and the optimal decomposition is obtained by combining FEM analyses with a Genetic Algorithm. As a case study, the side frame of a passenger car is decomposed for the minimum distortion of the front door panel geometry, where spot-welded joints are modeled as torsional springs. First, the rates of the torsional springs are treated as constant values obtained in the literature. Second, they are treated as design variables within realistic bounds. By allowing the change in the joint rates, it is demonstrated that the optimal decomposition can achieve the smaller distortion with less amount of joint stiffness (hence less welding spots), than the optimal decomposition with the typical joint rates available in the literature. INTRODUCTION To design any structural product, engineers adopt one of the two design methods: top-down and bottom-up methods. As the end products become more complicated and highly integrated, the top-down method is preferred since it allows the easier design assessment of an entire product during the design process. Top-down methods typically start with the preliminary design of the overall end product structure and proceed with the detailed design of components and substructures. If geometries and desired functions are simple, the structure can be built in one piece. To build complex structures in one piece, however, engineers need sophisticated manufacturing methods that would likely result in the higher manufacturing cost. Also, one piece structure will suffer from the lack of modularity: it would require the change or replacement of the entire structure even for local design changes or failures. It would be often natural, therefore, to design a structural product as an assembly of components with simpler geometries. To design multi-component structural products in top-down fashion, an overall product geometry must be decomposed at some point during the design process. In industry, such decompositions are typically done prior to the detailed design of individual components, taking into account of geometry, functionality, and manufacturability issues. However, this process is usually non-systematic and hence might result in a decomposition overlooking the integrity of the end product. For instance, automotive industry utilizes a handful of basic decomposition schemes of a vehicle that have not been changed for decades. This is because the desired form, functionality, materials, joining methods, and weight distribution of massproduction vehicles have not changed much for decades. However, the conventional decomposition schemes may no longer be valid for the vehicles with new technologies such as space frame, lightweight materials, and fuel cell or battery powered motors, which would have dramatically different structural properties, weight distribution, and packaging requirements. This motivates the development of a systematic decomposition methodology presented in this paper. In our previous work (Saitou and Yetis, 2000; Yetis and Saitou, 2000; Cetin and Saitou, 2001), we have termed assembly synthesis as the decision of which component set can achieve a desired function of the end product when assembled together, and assembly synthesis is achieved by the decomposition of product geometry. Since assembly process generally accounts 1 Copyright © 2002 by ASME 1 While this is true for many joints such as spot welds, threaded fasteners, and rivets, some joints (eg., arc welds) can be stiffer than components themselves. for more than 50% of manufacturing costs and also affects the product quality (Lotter, 1989), assembly synthesis would have a large impact on the quality and cost of the end product. As an extension of our previous work, this paper introduces a method for decomposing a product geometry considering the structural stiffness of the end product. Because the decomposition will determine the location of the joints between components, the structural integrity (e.g., stiffness) of the endproduct will be heavily influenced by the choice of a particular decomposition. Designers can use this method to get feedback on the possible decompositions before the detailed design stage. Via the decomposition of a graph representing its topology, a product is decomposed into a candidate set of components with simpler geometries, where joints among components are modeled as torsional springs. By combining FEM analyses with Genetic Algorithms (Holland, 1975; Goldberg, 1989), the optimal decomposition that gives the desired structural property of the end product is obtained. The case study discusses the assembly synthesis of the automotive side door panels.