A Transformational Approach to Mechanical Design Using a Bond Graph Grammar by

During the design process, a designer transforms an abstract functional description for a device into a physical description that satisfies the functional requirements. In this sense, design is a transformation from the functional domain to the physical domain; however, this transformation process is not well characterized nor understood for mechanical systems. The difficulty arises, at least in pan, because mechanical designs are often composed of highlyintegrated, tightly-coupled components where the interactions among the components are essential to the behavior and economic execution of the design. This assertion runs counter to design methodologies in other engineering fields, such as software design and circuit design, that result in designs in which each component fulfills a single function with minimal interaction. Because of the geometry, weight, and cost of mechanical components, converting a single behavioral requirement into a single component is often both impractical and infeasible. Each component may contribute to several required behaviors, and a single required system behavior may involve many components. In fact, most mechanical • components perform not only the desired behavior, but also many additional, unintended behaviors. In good mechanical designs, these additional behaviors often are exploited. The long term goal of our research is to create a transformational strategy in which the design specifications for a mechanical system can be transformed into a description of a collection of mechanical components. To realize this goal requires formal representations for the behavioral and the physical specifications of mechanical systems as well as formal representations for the behaviors and the physical characteristics of mechanical components. Because the interactions of components are important in our synthesis strategy, the representation of the behaviors of mechanical components must be . linked to the representation of their physical characteristics; that is, we are concerned with modeling the relationship between form and function of components. Finally, we need a strategy that enables us to transform an abstract description of the desired behavior of a > device into a description that corresponds to a collection of available physical components. In this paper, we present a graph-based language to describe both the behavioral specifications of a design as well as the behavior of the available physical components. We also briefly discuss a graphbased grammar for the representation of the physical characteristics of the components that enables us to guide the translation from specifications to components [Pinilla 89]. The transformation strategy is discussed in a companion paper [Hoover 89]. Introduction During the design process, t designer transforms an abstract functional description for a device into a physical description that satisfies the functional requirements. In this sense, design is a transformation from the functional domain to the physical domain [Mostow 85, Rinderle 82]; however, the basis for selecting appropriate transformations and methods for accomplishing transformations are not well understood. The implicit basis for design transformations in circuits [Steinberg 86], software [Wirth 71], and some architectural applications [Fcnvcs 87] result in a degree and type of modularity not well suited to mechanical devices [Rinderle 86]. Good mechanical designs are often composed of highly-integrated, tightly-coupled components where the interactions among the components are essential to the behavior and economic execution of the design. This assertion runs counter to design methodologies in other engineering fields, such as software design and circuit design, that result in designs in which each component fulfills a single function with minimal interaction. Because of the geometry, weight, and cost of mechanical components, convening a single behavioral requirement into a single component is often both impractical and infeasible. Each component may contribute to several required behaviors, and a single required system behavior may involve many components. In fact, most mechanical components perform not only the desired behavior, but also many additional, unintended behaviors. In good mechanical designs, these additional behaviors often are exploited. 'Mechanical engineers tend to use the words function and behavior interchangeably. Qualitative physicists make a distinction between these »ords: that is, the design's function is what it is used for, while its behavior is *hai u does. For example, the function of a clock is to display the time, but its behavior might be the rotation of hands. Similarly, a motor may be designed to function as a prime mover, but can also function as a door stop because it has additional behaviors due to its mass. In this paper. Junction is used to indicate ihe subset of behaviors which are required for the device to perform satisfactorily. This statement does not contradict the design axioms put forth by Suh (Suh 80, Suh 88]. The design axioms state that good designs maintain independence of functional requirements and minimize the information content of the design Suh points out that by integrating functions into t single component, information content may be reduced without compromising the independence of functional requirements. UNIVERSITY LIBRARIES CARNEGIE MELLON UNIVERSITY PITTSBURGH, PA 15213-3890 The direct transformation of behavioral requirements into physical components may result in undesirable designs for two reasons. The first is that matching individual behaviors directly to components does not enable the integration of behaviors into more compact or more economical collections of physical components. The second reason is that physical components have not only the desired behavior and physical characteristics but also many additional, incidental behaviors and characteristics. The appropriate device configuration and selection of components depends to some extent on exploiting or compensating for these incidental behaviors. By creating a formal description of a limited set of behaviors for mechanical designs and a corresponding description of physical components, we can generate the description of a physical system that takes advantage of the multiple behaviors of its components. This paper focuses on the grammar that underlies the transformation from behavioral specifications to physical components. The transformation strategy is discussed in a companion paper [Hoover 89]. Overview of Our Approach The goal of our research is to create a transformational strategy by which the design specifications for a mechanical system can be transformed into a description of a collection of mechanical components. Both behavioral and physical requirements as well as behavioral and physical characteristics of the available mechanical components must be represented to execute such a transformational approach to design. We are investigating the use of representations based on formal grammars to facilitate the characterization of our approach with respect to completeness, complexity, etc. and to take advantage of the advances in formal language theory. Because the interactions of components are important in our synthesis strategy, the representation of the behaviors of mechanical components must be linked to the representation of their physical characteristics; that is, we are concerned with modeling the relationship between form and function of components. Finally, we need a strategy that enables us to transform an abstract description of the desired behavior of a device into a description that corresponds to a collection of physical components. This paper primarily addresses the first issue, that of formal representations of behavior. To realize the goal of formalizing the transformation from the behavioral to the physical domain, we have begun to explore a small domain within mechanical design, the domain of gear box design. Clearly, one reason for selecting this domain is that gear box design is a well-understood, highly-parameterized area of mechanical design. Nevertheless, we believe that our representation and transformation formalism will be applicable in other mechanical design domains, particularly to the class of design problems that we call configuration design. By configuration design, we mean designs composed from standard component families but for which allowable configurations are not specified a priori. Our approach is based on the following assertions: • The behavioral requirements of mechanical systems can be represented using a graph grammar based on bond graphs. • The behavioral characteristics of components can be represented using a graph grammar based on bond graphs. • The physical characteristics of designs and components can be represented using an augmented topology and geometry graph. • The behavioral and physical graphs of components can be linked parametrically. • The behavioral specifications graph can be transformed into a description of a physical system with associated behavioral and geometric representations. Representational issues will be discussed at greater length in subsequent sections; however, we note here that our underlying representation for behavior is based on bond graphs [Paynter 61]. Usin^ bond graphs, we can construct a formal grammar that rives us a general representation of classes of mechanical behavior. lit common practice, bond graphs are constructed to model the behavior of physical systems. We use bond graphs not only to model the behavior of physical systems, but also to represent behavior in the abstract, as with a design specification. Thus a device configuration can be generated by transforming a specification bond graph into a functionally equivalent graph which corresponds to a configuration of available components. The type of graph transformations used are those that decompose, aggregate, and redistribute graph primitives. A major advantage of using bond graphs to represent design requirements is that we can define transformation rules that alter the structure of the bond graph but that do not alter the dynamic behavior of the system represented by the graph. The implications of this statement are important Because we can transform the specifications graph to represent many different physical systems, we do not impose an initial structure or configuration on the physical design; that is, we do not require an a priori decomposition of the design specifications. To complete this methodology, we plan to represent the physical characteristics of designs and components using another graph grammar that is based on an augmented topology graph [Pinilla 89] and non-manifold geometry [Gursoz 89]. We plan to link parametrically the bond graph representation and the topology and geometry graph representation. With a geometric representation, characteristics such as the volume or mass can be modeled and computed, and from the bond graphs, the dynamic behavior of the final design can be modeled. In this paper, wfe do not discuss the geometric representation in detail because our work on linking the geometry and behavior is preliminary. A Brief Introduction to Bond Graphs Bond graphs, which were created by Paynter [Paynter 61], provide a convenient and uniform representation for the dynamic behavior of a broad class of physical systems, including those within the mechanical, electrical, hydraulic, thermal, and biological domains. Bond graphs have been used extensively in a wide variety of application areas including robotic manipulators [Margolis 79], torque conveners [Hrovat 85], and vacuum cleaners [Remmerswaal 85]. A brief introduction to bond graphs is given here. For a complete discussion, see Karnopp and Rosenberg [Kamopp 75]. Bond graphs enable mechanical and hydraulic systems to be represented in a manner equivalent to electric circuit diagrams. For example, a spring in a mechanical device acts like an electrical capacitor by storing and releasing energy. To illustrate the similarity, Figure 1 shows an RLC circuit with its equivalent bond graph and a mass-spring-damper system with its equivalent bond graph. While Figure 1 illustrates separate electrical and mechanical systems, one of the most powerful attributes of bond graphs is that they can be used to model integrated electrical, mechanical, and hydraulic systems. Using bond graphs, physical systems are represented as a graph of lumped-parameter, idealized elements. Power is the currency of bond graphs; power flows through the bonds (edges) in the graph, and power is dissipated, stored, supplied, and transformed at the ports (vertices) in the graph. The ports, or vertices, of bond graphs are divided into three categories: • 1-port elements dissipate power, store energy, and supply power. Dampers, springs, and masses arc the mechanical elements represented by the passive 1-port elements. Force (effort) and velocity (flow) sources are represented as active 1-ports. • 2-port elements transform power. Transformers axe 2port elements that represent an imposed proportionate relationship between similar quantities, e.g. a gear pair constrains rotational speeds. Gyrators are a 2-port