CHAPTER 3
INTEGRATION OF THE FINITE ELEMENT METHOD AND THE TAGUCHI METHOD

3.1 Simulating the real experiment

The traditional way of conducting the Taguchi method of design of experiments is to set the level combinations of various influencing factors and conduct the real time experiment and study the results. However, there are many cases where it is not possible to conduct a real experiment. One of the basic requirements of the Taguchi method is that all the experiments shall be conducted without altering the level combinations of the input design variables for each experiment. This may not be always feasible in a real experiment due to many practical difficulties in conducting the experiment such as a very high temperature / pressure study, hazardous conditions, cost, time etc., Instead the real experiment could be simulated by using various analytical tools or numerical techniques. For example, in order to study the residual stress behavior due to injection molding processes, one could conduct the experiment by simulating the injection molding process as shown in Figure 3.1, using the flow simulation software which is based on the numerical techniques [11]

Figure 3.1 Simulating real time experiment using numerical tools

The following are the potential advantage of simulating the real experiment .

  1. Easy to vary the range of input parameter values. In case of a real experiment, the extreme values are limited by the practical constraints.
  2. Any level combination of the independent variables is possible.
  3. The repeatability of the computer simulated experimental results is very high.
  4. The time and cost required to simulate the experiment is, in many cases, less.
  5. Easy access to results which are normally not possible.

The following section will cover how the finite element analysis can be effectively used as an experimental tool and the Taguchi method as a tool for designing the layout of the experiment.

3.2 The Finite element method and the Taguchi method as a design tool

The finite element method is one of the powerful numerical techniques to solve the complex physical phenomenon that are governed by the differential equations. Many of the practical engineering problems such as structural, thermal, magnetic, acoustic, etc., can be solved by the finite element method. Moreover, the finite element method is an increasingly common tool for engineering design. Every design is defined by a number of design variables which affect the performance of design.

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

In order to improve the performance of the design, it is essential to arrive the proper level combinations of the input parameters that affect the performance of the design. At the same time, it may not be necessary to consider the design variables which do not contribute significantly. Many of the standard finite element softwares / packages do not have facilities to check the contribution or significance of a design variable on the performance parameter. One way to solve this problem is to use design of experiments for varying the input design parameter values and predict the significance of each variable by studying the change in the objective function (performance parameter).

The Taguchi method is one such tool for conducting experiments using a statistical approach to understand the significance of independent factors and levels. The main advantage of Taguchi method is that the number of experiments conducted in most of the cases is lesser than that of any other experiment using a statistical approach.

By integrating the Taguchi method and the finite element method [7], an efficient design methodology can be developed. This integrated approach has the merits of both the finite element method and the Taguchi design of experiments. Using this approach, it is possible to obtain the percent contribution, significance and appropriate level value of each design variable. The concept of integrating Taguchi's design of experiments and finite element method is illustrated in Figure 3.2.

3.3 Optimization using integrated approach

The Taguchi method can be used for obtaining near optimal solution [8] to the analytical engineering problems. Instead of using the standard mathematical optimization procedure with all the design variables, one can conduct the experiments based on the Taguchi method and eliminate the insignificant design variables which does not contribute much to the objective function. After eliminating the insignificant variables, the standard mathematical optimization procedure could be used. The initial / starting value of the standard optimization problem is the near optimum level values obtained based on the Taguchi method of design of experiments. This results in significant saving of computational time. This is explained in the Figure 3.3

In case of optimization using the finite element method, the optimization program conducts the finite element analysis till the solution converges. After each iteration the response surface is drawn between the independent variables and the objective function, and then the near optimal solution is calculated based on relationship between the independent variable and the objective function.

Figure 3.3 Flowchart showing use of Taguchi method for near optimal solution

The following chapter explains the distributive co-operative problem solving approach used to integrate the Taguchi method and the finite element method and the implementation of this approach for developing a software.