Master of Science (MS)
Axiomatic Design, Chromatic Number, Graph Theory
Mechanical engineering design practices are increasingly moving towards a
framework called axiomatic design (AD). A key tenet of AD is to decrease the
information content of a design in order to increase the chance of manufacturing success.
An important way to decrease information content is to fulfill multiple functional
requirements (FRs) by a single part: a process known as part consolidation. One possible
method for determining the minimum number of required parts is to represent a design by
a graph, where the vertices are the FRs and the edges represent the need to separate their
endpoint FRs into separate parts. The answer is then the chromatic number of such a
graph. This research investigates the suitability of using two existing algorithms and a
new algorithm for finding the chromatic number of a graph in a part consolidation tool
that can be used by designers. The runtime complexities and durations of the algorithms
are compared empirically using the results from a random graph analysis with binomial
edge probability. It was found that even though the algorithms are quite different, they all
execute in the same amount of time and are suitable for use in the desired design tool.
Cavallaro, Jeffery Anthony, "Determination of a Graph's Chromatic Number for Part Consolidation in Axiomatic Design" (2020). Master's Theses. 5088.