An Approach to Automate and Optimize Concept Generation of Sheet Metal Parts by Topological and Parametric Decoupling

This paper describes an approach to automate the design for sheet metal parts that satisfy multiple objective functions such as material cost and manufacturability. Unlike commercial software tools such as PRO/SHEETMETAL, which aids the user in finalizing and determining the sequence of manufacturing operations for a specified component, our approach starts with spatial constraints in order to create the component geometries and helps the designer design. While there is an infinite set of parts that can feasibly be generated with sheet metal, it is difficult to define this space systematically. To solve this problem, we have created 108 design rules that have been developed for five basic sheet metal operations: slitting, notching, shearing, bending, and punching. A recipe of the operations for a final optimal design is then presented to the manufacturing engineers thus saving them time and cost. The technique revealed in this paper represents candidate solutions as a graph of nodes and arcs where each node is a rectangular patch of sheet metal, and modifications are progressively made to the sheet to maintain the parts manufacturability. This paper also discusses a new topological optimization technique to solve graph-based engineering design problems by decoupling parameters and topology changes. This paper presents topological and parametric tune and prune ((TP) 2 ) as a topology optimization method that has been developed specifically for domains representable by a graph grammar schema. The method is stochastic and incorporates distinct phases for modifying the topologies and modifying parameters stored within topologies. Thus far, with abovementioned sheet metal problem, (TP) 2 had proven better than genetic algorithm in terms of the quality of solutions and time taken to acquire them.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[3]  James E. Campbell,et al.  An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment , 1981 .

[4]  Manfred Nagl.  Bibliography on graph-rewriting systems (graph grammars) , 1982, Graph-Grammars and Their Application to Computer Science.

[5]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[6]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[7]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[8]  Leonard Bolc,et al.  Search methods for artificial intelligence , 1992 .

[9]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series) , 1992 .

[10]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[11]  Robert H. Sturges,et al.  BendCad: a design system for concurrent multiple representations of parts , 1996, J. Intell. Manuf..

[12]  Moshe Shpitalni,et al.  Two-Stage Algorithm for Determination of the Bending Sequence in Sheet Metal Products , 1997 .

[13]  J. Cagan,et al.  A Shape Annealing Approach to Optimal Truss Design With Dynamic Grouping of Members , 1997 .

[14]  Kenneth N. Brown,et al.  Optimized process planning by generative simulated annealing , 1997, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[15]  Satyandra K. Gupta,et al.  Automated process planning for sheet metal bending operations , 1998 .

[16]  Jonathan Cagan,et al.  Optimal Configuration Design: An Integrated Approach Using Grammars , 1998 .

[17]  Jonathan Cagan,et al.  Agent-Based Synthesis of Electromechanical Design Configurations , 2000 .

[18]  Xin Li,et al.  Transformation of an EGT Grammar: New Grammar, New Designs , 2004 .

[19]  Matthew I. Campbell,et al.  A Grammar-Based Approach to Sheet Metal Design , 2002, DAC 2002.

[20]  Matthew I. Campbell,et al.  Toward an automated approach to the design of sheet metal components , 2003, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[21]  Matthew I. Campbell,et al.  Evaluation Method for the Topological Synthesis of Sheet Metal Components , 2004, DAC 2004.

[22]  Gregory S. Hornby,et al.  Functional Scalability through Generative Representations: The Evolution of Table Designs , 2004 .

[23]  Matthew I. Campbell,et al.  Automated Synthesis of Sheet Metal Parts by Optimizing a Fabrication Based Graph Topology , 2005 .

[24]  Hartmut Ehrig,et al.  Transformations of structures: An algebraic approach , 1981, Mathematical systems theory.

[25]  Jonathan Cagan,et al.  A Framework for Computational Design Synthesis: Model and Applications , 2005, J. Comput. Inf. Sci. Eng..

[26]  Tomas Akenine-Möller,et al.  Fast, Minimum Storage Ray-Triangle Intersection , 1997, J. Graphics, GPU, & Game Tools.

[27]  Matthew I. Campbell,et al.  A Graph Grammar Approach to Generate Neural Network Topologies , 2007, DAC 2007.

[28]  Matthew I. Campbell,et al.  A Unified Approach to Solving Graph Based Design Problems , 2007 .

[29]  A graph theory approach to the synthesis and optimization of a modified transportation network , 2007 .

[30]  I Campbell Matthew,et al.  A Graph Topology Optimization Method for the Synthesis of Robust and Efficient Routes , 2007 .

[31]  Matthew I. Campbell,et al.  An Approach to Automate Concept Generation of Sheet Metal Parts Based on Manufacturing Operations , 2008, DAC 2008.