INTEGRATION OF TAGUCHI DESIGN OF EXPERIMENTS
AND FINITE ELEMENT METHOD
FOR ROBUST DESIGN

A Masters Project Presented

by

SANKAR NELLIAN

DIRECTED BY : PROFESSOR IAN R GROSSE

Submitted to the Graduate School of the

University of Massachusetts Amherst in partial fulfillment

of the requirements for the degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

February 1996

Department of Mechanical Engineering

INTEGRATION OF TAGUCHI DESIGN OF EXPERIMENTS

AND FINITE ELEMENT METHOD

FOR ROBUST DESIGN

A Masters Project Presented

by

SANKAR NELLIAN

Approved as to style and content by:

Ian Grosse, Chair

Laurence Murch, Member

David Kazmer, Member

Corrado Poli, Department Head

Department of Mechanical Engineering

© Copyright by Sankar Nellian 1996

All Rights Reserved

Acknowledgments

ABSTRACT

The Taguchi method of design of experiments is a statistical tool based on the systematic approach of conducting minimal number of experiments using orthogonal arrays. Traditionally, this method has been used to predict the significant contribution of each design variables and the optimum combination of the design variables by conducting a real time experiment.

In this project, instead of the real time experiment, the finite element analysis is used as an analytical tool for conducting experiments. However the layout of the experimental design is still based on the Taguchi method of design of experiments. By integrating the Taguchi method with the finite element method, a new design tool has been evolved to study the effect of design variables on the performance of the design. This concept has been implemented in a common-lisp environment using blackboard approach of problem solving.

The major advantage of the technique is that it is not problem specific and can be extended to any design which can be represented by means of a finite element model. A typical case study is conducted to test the approach which confirms the effectiveness of the integration of Taguchi method and finite element method.

TABLE OF CONTENTS

ACKNOWLEDGMENTS.....................................................................................

ABSTRACT ......................................................................................................

LIST OF TABLES ...............................................................................................

LIST OF FIGURES .............................................................................................

Chapter Page

1.0 INTRODUCTION.......................................................................... 1

1.1 Introduction to design of experiments ........................................... 1

1.2 Comparison of various methods ....................................................... 2

1.3 Areas of application .................................................................... 4

1.4 Scope of the project .................................................................... 5

2.0 INTRODUCTION TO TAGUCHI METHOD ................................ 7

2.1 Background ............................................................................... 8

2.2 Basic concepts ............................................................................... 8

2.3 Assumptions of Taguchi method ........................................................ 11

2.4 Designing an experiment .................................................................... 11

2.5 Robust design ................................................................................. 15

3.0 INTEGRATION OF FINITE ELEMENT METHOD

AND TAGUCHI METHOD ........................................................ 17

3.1 Simulating real time experiment ........................................................ 17

3.2 Finite element method and Taguchi method as design tool .......... 18

3.3 Optimization using integrated approach ...................... 20

4.0 BLACKBOARD APPROACH FOR PROBLEM SOLVING ........... 22

4.1 Distributive cooperative problem solving ................................ 22

4.2 Blackboard approach ................................................................ 23

4.3 Implementation of blackboard approach ........................................ 24

5.0 IMPLEMENTATION OF INTEGRATED APPROACH FOR

THE DEVELOPMENT OF INFINITE SOFTWARE ....................... 29

5.1 Assumptions ............................................................................... 29

5.2 Basic algorithm ................................................................................ 29

6.0 CASE STUDY ................................................................................ 45

6.1 The Description of problem ......................................................... 45

6.2 Input Data ............................................................................... 46

6.3 The finite element model ................................................................. 47

6.4 Conducting the experiments ...................................................... 48

6.5 Post-processing ................................................................. 51

6.6 Conclusion ........................................................................ 55

7.0 CONCLUSION AND FURTHER SCOPE ............................. 56

7.1 Conclusion .................................................................... 56

7.2. Further Scope ............................................................... 56

APPENDICES

A. Knowledge sources developed for INFINITE software ................ 58

B. ANSYS parametric input file ................................................... 61

C. ANSYS post processing file .................................................... 64

D. Output results of design of experiment ............................................ 65

BIBLIOGRAPHY .................................................................. 69

LIST OF TABLES

Table Page

Table 2.1 Layout of L9 orthogonal array ...................... ....... 9

Table 4.1 The object unit classes and slot variables .............................. 26

Table 6.1 Summary of experimental results ............................ 51

Table A.1 List of knowledge sources developed ................................. 58

LIST OF FIGURES

Figure Page

Figure 3.1 Simulating real time experiment using numerical tools ........ 18

Figure 3.2 Finite element method and Taguchi method as a design tool ..... 19

Figure 3.3 Flowchart showing the use of Taguchi method for near

optimal solution ................................................................... 20

Figure 4.1 The basic concept of blackboard approach for problem solving ..... 24

Figure 4.2 Implementation of blackboard approach for the development

of INFINITE software .............................................. 25

Figure 5.1 Opening menu of the INFINITE software .................................. 30

Figure 5.2 Selection of independent variables ............................................. 33

Figure 5.3 Flowchart for the selection of independent variables ..................... 34

Figure 5.4 Selection of objective function variables ............................... 36

Figure 5.5 Mean level value of design variables .......................................... 39

Figure 6.1 Design variables that affect the heat flow into the workpiece ......... 46

Figure 6.2 Finite element model of the machining process ..................... 47

Figure 6.3 Object oriented blackboard database .......................................... 48

Figure 6.4 Selection of independent design variables ....................... 49

Figure 6.5 Effect of different level values on the objective function .......... 52

Figure 6.6 Percent contribution of each design variable .......... 53

Figure 6.7 Experimental results and optimum level values .......... 54