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
All Rights Reserved
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
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 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