A Formal Representation of Conjugate Verbs for Function Modeling

Abstract

Modern design problems often require multi-modal, reconfigurable solutions. Function modeling is a common tool used to explore solutions in early mechanical design. Currently, function modeling formalisms minimally support the modeling of multi-modal systems in a formal manner. There is a need in function modeling to capture multi-modal system and analyze the effects of control signals and status signals on their operating modes. This paper presents the concept of functional conjugacy, where two function verbs or functional subgraphs are topological opposites of each other. The paper presents a formal representation of these conjugate verbs that formally captures the transition from one mode of operation to its topological opposite based on the existence of, or the value of, signal flows. Additionally, this paper extends functional conjugacy to functional features, which supports conjugacy-based reasoning at a higher level of abstraction. Through the example of a system-level function model of a geothermal heat pump (GHP)operating in its heating and cooling modes, this paper demonstrates the ability to support modal reasoning on function models using functional conjugacy and illustrates the modeling efficacy of the extended representation.