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CHAPTER 5
TAGUCHI EXPERIMENTAL DESIGN
5.1 INTRODUCTION
The Taguchi method involves reducing the variation in a process through robust design of experiments. The overall objective of the method is to produce high quality product at low cost to the manufacturer. The Taguchi method was developed by Genichi Taguchi. He developed a method for designing experiments to investigate how different parameters affect the mean and variance of a process performance characteristic that defines how well the process is functioning. The experimental design proposed by Taguchi involves using orthogonal arrays to organize the parameters affecting the process and the levels at which they should be varied. Instead of having to test all possible combinations like the factorial design, the Taguchi method tests pairs of combinations. This allows for the collection of the necessary data to determine which factors most affect the product quality with a minimum amount of experimentation, thus saving time and resources. The Taguchi method is best used when there is an intermediate number of variables (3 to 50), few interactions between variables, and when only a few variables contribute significantly.
5.2 DESIGN OF EXPERIMENT
Classical experimental design methods are too complex and are not easy to use. A large number of experiments have to be carried out when the
number of process parameters increase. To solve this problem, the Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with only a small number of experiments. Three superplastic forming parameters are considered as controlling factors. They are Pressure, Temperature and Time. Each parameter has three levels – namely low, medium and high, denoted by 1, 2 and 3 respectively. According to the Taguchi method, if three parameters and 3 levels for each parameters L orthogonal array should be employed for the experimentation. Table 5. shows the Superplastic forming parameters and their levels considered for the experimentation. Table 5.1 Process parameters and levels
Process parameters
Levels
Level 1 Level 2 Level 3
Pressure (MPa) – A 0.2 0.4 0.
Temperature (^0 C) - B 560 580 600 Time (minutes) - C 15 30 45 Orthogonal arrays are special standard experimental design that requires only a small number of experimental trials to find the main factors effects on output. Before selecting an orthogonal array, the minimum number of experiments to be conducted is to be fixed based on the formula below N Taguchi = 1+ NV (L – 1) N Taguchi = Number of experiments to be conducted NV = Number of parameters L = Number of levels In this work NV = 3 and L = 3, Hence N Taguchi = 1+ 4 (3-1) = 9
that is, the lower-the-better, the higher-the-better, and the nominal-the-better. The S/N ratio for each response is computed differently based on the category of the performance characteristics and hence regardless of the category the larger S/N ratio corresponds to a better performance characteristic. In the present study the dome height and thinning factor are the-higher-the-better performance characteristics. Once all of the S/N ratios have been computed for each run of an experiment, Taguchi advocates a graphical approach to analyze the data. In the graphical approach, the S/N ratios and average responses are plotted for each factor against each of its levels. From the graphs, higher the better the values were selected and the confirmation tests were conducted. 5.4 PROCESS PARAMETERS
Figure 5.1 Process parameters and Responses
SUPERPLASTIC FORMING
PROCESS
PARAMETERS
PRESSURE
(0.2 MPa, 0.4 MPa &0.6 MPa) TEMPERATURE (560 C, 580 C & 600 C) TIME (15 Min, 30 Min & 45 Min)
RESPONSES
DOME HEIGHT
THINNING FACTOR
The different process parameters and the responses for the
superplastic forming was shown in Figure 5.1. The effect of process
parameters were discussed below.
5.4.1 Effect of Temperature Tong et al conducted superplastic forming in Al-4.4Cu-1.5Mg/SiCw composites. Maximum elongation of 440% was obtained at 523 °C. Further increase in temperature causes the ductility drop rapidly because of the presence of liquid phase at grain /interface boundaries. The literatures show that the composites were decrease in strength during superplastic forming. During superplastic forming, liquid phase forms from the second phase in elevated temperature. The liquid phase forms in grain boundaries and Al/SiCp inter phases. The occurrence of liquid phase on composites reduces the strength of Al6063/SiC composites during superplastic deformation and enhances their ability to achieve large elongation to failure. The requirement of high temperature is related to the accommodation process. Higher the temperature the faster the accommodation process and this leads to an increase in ductility with temperature. A small amount of liquid is likely to be beneficial for sliding process and related accommodation as suggested by Mabuchi and Higashi. At higher temperature too much liquid leads to premature fracture. This is attributed to intergranular decohesion at thick liquid boundaries. There fore, a liquid phase is required to be very thin both in order to relax the stress concentrations and to limit decohesion at liquid boundaries. To obtain thin liquid layer optimum temperature should be selected. 5.4.2 Effect of Pressure In this research work pressure has been maintained constant through out the process. Initially the strain rate was high and strain rates were
Figure 5.2 Procedure for Taguchi Analysis
Confirmation experiment to
check whether there is
improvement
Set performance
characteristics (Dome Height,
Thinning Factor)
Select control factors and their
levels
Choose orthogonal array as
per number of factor and
levels
Conduct experiments as per
orthogonal array and observe the
change in critical properties
Data Analysis - S/N Ratio
Arrive at optimal level of
process parameters
Analysis of
variance
Influence of
parameters
END
Yes
No
This statistical significance of the factors can be evaluated through the analysis of variance (ANOVA). A statistical ANOVA is performed to find the contribution of each factor for attaining the process outcome. Three process parameters considered for optimization of the study are A. Temperature B. Gas blow pressure, C. Forming Time Taguchi Orthogonal Array Design - L9 (33)*
Table 5.1 shows the taguchi orthogonal array selector which
shows the orthogonal array for the parameters and levels. For three
parameters and three levels L9 orthogonal array was selected from the
array selector.
Table 5.1 Array Selector PARAMETERS L E V E L S
2 L4 L4 L8 L8 L8 L8 L12 L12 L12 L12 L
3 L9 L9 L9 L18 L18 L18 L18 L27 L27 L27 L
4 L16 L16 L16 L16 L32 L32 L32 L32 L
5 L25 L25 L25 L25 L25 L50 L50 L50 L50 L50 L
The specimens were formed in an open die in accordance with Table 5.2 and height of the formed component was measured. Experimental data hence measured is as a shown in table 5.3. Taguchi method of optimization involves finding out Signal-to-Noise ratio (S/N) in order to minimize quality characteristic variation due to uncontrollable parameter. Dome height belongs to “larger the better” quality characteristics. 5.6 SUMMARY Design of Experiments was done by Taguchi’s technique. For three parameters and three levels L9 orthogonal array was selected. Through pilot study experiments the levels of parameters were selected. These experiments were conducted between 520 C and 600 C temperature and 0.2 MPa to 0. MPa pressure. From the pilot study the selected levels of temperature were 560 C, 580 C and 600 C.The pressures were 0.2 MPa, 0.4 MPa and 0.6 MPa. Dome height and thinning factor were the two response variables. Totally
nine experiments were conducted and S/N ratios for dome height and
thinning factor were plotted. Confirmation tests were conducted using
the higher the better values for dome height and thinning factor. The
influence of parameters was found by ANOVA technique.
