Publication Date

Spring 2020

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Advisor

Sogol Jahanbekam

Keywords

Axiomatic Design, Chromatic Number, Graph Theory

Subject Areas

Mathematics

Abstract

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.

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