On Topological Approaches for Planning of Electro-Mechanical Assemblies

Abstract

Assembly planning pertains to the process of creating a complete plan for fabricating the product from its constituent parts, considering the final product geometry and resources available at the manufacturing facility. Complex electro-mechanical products constitute a large number of systems and sub-systems that employ electrical and mechanical processes to provide specific functionality to the user; they contain multiple equipment, which are connected by energy and fluid carriers such as wire harnesses and pipes. The assembly planning of electro-mechanical products, especially with the propagation of electric vehicles and more electric air-crafts, has increasingly become more and more significant and challenging. The methods in the literature fall short of a full-scale industry implementation as they are unable to handle complex, realistic products with a large number of parts. Consequently, the current industry practices predominantly rely on manual or interactive procedures that employ commercially available Computer-Aided Design (CAD) tools. These approaches are time-consuming, expensive, and error-prone due to the intricate nature of modern electro-mechanical systems. Considering the competitive nature of today’s market, automation in assembly planning is crucial for product development and manufacturing. With this motivation, we develop, in this thesis, a topological computational framework to deal efficiently and effectively with the practical requirements of automated planning of electro-mechanical assemblies. We classify the subassemblies making up an electro-mechanical product as (1) rigid and (2) flexible assemblies. Rigid assemblies refer to assemblies whose functionality is dependent on the shape of the constituent parts, and flexible assemblies refer to assemblies whose functionality is not affected by the shape of the parts in any significant manner. IC engine in an automobile is an instance of the former, whereas wire harnesses are an instance of the latter. Such classification of assemblies allows us to address the concerned challenges categorically.

Firstly, we address the problem of disassembly sequence planning of complex rigid assemblies with inspiration from the intuitive performance of humans, which relies on the accessibility of parts. However, accessibility analysis of parts in an assembly remains largely unexplored in the literature. In this thesis, we carry out a novel topological analysis of an assembly of parts that leads to the notion of shell structures associated with 3D CAD assemblies; the shell structures are then used for the accessibility analysis of parts in the assembly. The proposed approach classifies the surface domains of parts as mating or non-mating domains. Beyond this point, all the procedures are symbolic, which provides representational and computational efficiency and robustness. The non-mating domains are used to construct the shell structure, and the mating domains are used to generate the liaison information of the assembly. We present a graph-based representation of shells, which leads to efficient accessibility analysis. A part accessibility-based assembly partitioning scheme is proposed for disassembly sequencing. The method requires only a one-time computation of the shells. The accessibility information pertaining to parts is updated without any recomputation throughout the disassembly process. Further applications of shell structures, such as in subassembly identification and parallel disassembly, which are important for maintenance planning and end-of-life processing, are also demonstrated. The methods are equally applicable to assemblies of smooth or discreet objects. In this work, we propose a grid-based method for constructing the shell structure from the tessellated model of the assembly.

Secondly, we address the routing problem of flexible assemblies, where the determination of the shape of the paths connecting a pair of terminals is the requirement. In particular, we consider wire harness routing. We show that in order to automatically generate the desirable bundles of wires, we must consider all the non-homotopy classes of paths between a given pair of terminals. Thus, the traditional shortest-path schemes are inadequate. We present an approach for computing all non-homotopic paths associated with a pair of source–destination points using the non-trivial loops on a shell. We introduce the notion of routing graphs, which are generated from specific non-trivial loops in the first homology group associated with the surface of the product. The routing graph, which is constructed only once, encodes the homotopy of the routing environment and is, therefore, used to find all the non-homotopic paths between multiple source–destination pairs. Based on the path embedding requirements, we classify the routing process into (1) on-surface routing, when the paths are required to be on the surface of the product, and (2) in-air routing, when the paths are allowed to venture into the product ambiance space. In the former case, the routing graph is defined by both the handle and tunnel loops in the first homology group, whereas in the latter case, it is defined by only the handle loops. We propose a linking number-based strategy for computing the handle and tunnel loops for a given closed surface. The methods are extended for routing in assemblies using the shell structures associated with the assembly. We show that shell structures not only represent the appropriate solution space for routing but also provide a method to immediately verify the existence of a path between two specified terminals; this verification does not require exhaustive traversal of the entire solution space, as with earlier methods.

Thirdly, we address the problem of automatically generating wire harness designs. We developed a topological approach that yields all the possible electrically admissible but topologically distinct harness system layouts that can be used to connect the specified set of terminals. Each generated layout represents a possible harness design. For layout generation, the proposed method employs the routing graphs associated with the closed surfaces bounding the product. The developed methods can generate both – (1) on-surface and (2) in-air routings. For the final geometric embedding of the generated harnesses, we present an optimization-based methodology that determines the optimum lengths of the segments over which the wires should be bundled together.

Finally, we present a description of computer implementation details. We developed multiple software modules that handle different methods developed in this work. We also implemented a GUI-enabled software application that employs the developed modules and can be used for assembly planning. The software was used for assembly planning of multiple realistic products represented as tessellated models. The results demonstrate the efficiencies and efficacy of the developed methods.

To summarize, this thesis presents a generic computational topological framework for efficient automated assembly planning of electro-mechanical products. The methods developed are robust and efficient due to their topological nature.