CHAPTER 6
CASE STUDY

6.1 The Description of problem

The example considered here is the simulation of a machining process [9] using the integrated approach of the Taguchi method and the finite element method. During the metal removing process, a large amount of heat is generated and some of the heat generated is dissipated to the surrounding and the remaining heat flows into the workpiece. The heat which flows into the workpiece results in thermal distortion of the workpiece. In order to machine the workpiece to a close tolerance, it is essential that the heat flow into the workpiece should be minimized. With this objective in mind, the following experiments are conducted to study the influence of various factors that minimizes the heat flow into the workpiece.

While the above experiment could have been done using a real experiment, there are many practical difficulties of machining at high speed and other constraints. With the computer simulated experiment, the design of experiments has become much easier.

6.2 Input Data

The various factors that affect the heat flow into the workpiece are as follows. The schematic diagram of the metal removing operation is shown in Figure 6.1.

  1. Depth of cut
  2. Cutting Speed
  3. Width of cut
  4. Shear angle
  5. Rake angle
  6. Flank angle
  7. Cutting Force
  8. Thrust Force
  9. Convection coefficient of coolant
  10. Convection coefficient of air
  11. Ambient temperature
  12. Thickness of tool coating
  13. Material


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

6.3 The finite element model

The finite element model of the above machining process consists of 2-D thermal solid elements (Stiff 55 of ANSYS Software). This element type is used for conducting the steady state thermal analysis with conduction capability. In addition to this the heat generation within the body and convection along the edges can be simulated. From the heat flux calculations, it is possible to find out the total heat flow into the workpiece. The partial listing of ANSYS parametric input file for the above model, called metcut.log, has been given in the Appendix B. The meshed model of the machining process is shown in Figure 6.2. Every time the experiment is conducted, the geometry automatically gets changed depending on the level settings of the design variables.


Figure 6.2 Finite element model of the machining process

6.4 Conducting the experiments

The following are the steps involved in the experimental design of machining process.

6.4.1 Reading the input file

The first step is reading the ANSYS parametric file. The listing of the input file is given in Appendix B. Once the ANSYS file is read, the program retrieves the complete set of design variables from the ANSYS file. These variables are stored in the blackboard database. The typical blackboard database information stored for the above case is shown in Figure 6.3.


Figure 6.3 Object oriented black board database

6.4.2 Selection of the independent variables

There are totally 85 assigned variables which are defined in the input file. Though only 13 design variables are identified for the above problem, the remaining variables are meant for node and element generation and other purposes. Hence one shall not choose the modeling variables as a design variable.


Figure 6.4 Selection of independent design variables

From the set of possible design variables, the following seven variables are considered for experimental study: 1) Depth of cut 2) Width of cut 3) Shear angle 4) Rake angle 5) Cutting Force 6) Tangential force and 7) Ambient temperature. For each design variable selected, the user inputs 3 different level values. This allows nonlinear effects of the design variables on the response to be represented. If all the level values of a particular design variable are same, then the variable is not considered for the design of experiment.

6.4.3 Selection of the Objective function

The objective function is the post-processing item of ANSYS software. In case the objective function is not directly expressible by a single equation, a set of ANSYS command may be necessary to obtain the objective function value. For the present case, the heat flow into the workpiece calculated separately and is stored in a separate file. The file, post.ans has been used for this purpose which is listed in Appendix C.

6.4.4 Conducting the Taguchi Experiment

Once the design variables are selected, the program automatically selects the L18 orthogonal array. The L18 orthogonal array is meant for conducting the experiments with maximum of 7 independent design variables, each having 3 levels.

After the selection of the orthogonal array, the ANSYS input file is modified with different level combinations of design variables. For each experiment, a new ANSYS parametric file is created. Since the geometry of the problem is changed in each experiment, ANSYS program calculates the stiffness matrix for every experiment and solves the problem. At the end of each experiment, the process parameter values are appended to a file. This is used for post processing process.

6.5 Post processing

Once the experiments are over, the program calculates the mean value of each level of all the variables, the sum of squares, the percent contribution and the near optimum level of each design variable. Based on the near optimum level of each variable, a new experiment is conducted with each design variable set to the near optimum level value. The program also calculates the F-value for each design variable. The summary of experimental results are shown in Table 6.1. The detailed output listing is given in Appendix D.

Variable Name
Level Settings
Optimum Level
Percent Contribution
ANOVA TEST
Level 1
Level 2
Level 3
F-Value F(2,15,.90)Whether Significant ?
1. To (degree)
25
30
35
2
0.17
0.001
2.69
No
2. T_force (N)
30
35
40
3
0.72
0.005
2.69
No
3. Cut_Force (N)
50
60
70
1
15.9
1.40
2.69
No
4. Rake_ang(deg)
0
2
4
1
0.03
0.0002
2.69
No
5. Shearang(deg)
20
30
40
3
14.43
1.26
2.69
No
6. C_width(inch)
0.08
0.11
0.13
1
0.66
0.005
2.69
No
7. D_cut (inch)
0.001
0.002
0.003
3
67.13
15.3
2.69
Yes

Table 6.1 Summary of experimental results

It can be observed from the analysis results that the most significant factor which dominates the heat flow into the workpiece is the depth of cut. The other two factors viz. cutting force and shear angle contribute to a limited extend. Though the percent contribution of these two variables are significant, the ANOVA test conducted at 90% confidence level rejects the significance of these design variables.

6.5.1 Sensitivity analysis

The sensitivity analysis of the machining operation shows that most of the design variables vary linearly except ambient temperature. In addition to this, the results shown in Figure 6.5 suggests that depth of cut, cutting force, and shear angle influences more than any other variables. Both rake angle and ambient temperature does not have a significant impact on the objective function.


Figure 6.5 Effect of different level values on the objective function


6.5.2 Percent contribution

The plot of percent contribution shown in Figure 6.6 confirms the results of the sensitivity analysis. As expected the contribution of depth of cut is significantly higher than any other variables. The other two variables viz. shear angle and cutting force contribute to a limited extend. The plot also shows that the percent contribution of combined interaction effect is negligible.

From the output results, the following insignificant factors can be removed from further optimization, viz. rake angle, tangential force and the ambient temperature.


Figure 6.6 Percent contribution of each design variable

6.5.3 Near optimum solution

The following plot shown in Figure 6.7 compares the performance parameter values for each experiment conducted along with the orthogonal array selected. At the end of all the experimental results, the results of the experiment for optimum level case is also shown. It shall be noted that the optimum heat flow into the workpiece is the lowest of all the experiments conducted.


Figure 6.7 Experimental results and optimum level values

6.6 Comparison of local optimum results

The summary of the experimental results given is Table 6.1 is based on the initial results of experiments based on Taguchi method. This results can be used for further mathematical optimization techniques.

From the Table 6.2, it is evident that the computational time can be considerably reduced by using Taguchi method as an initial step before conducting the standard optimization procedure than directly conducting optimization based on the standard optimization procedure.
Experiment TypeCPU time

(Seconds)

Optimum level values Optimum performance Remarks
1. Based on Taguchi method
--
1.Cut_force = 50

2.D_cut = .003

3.C_width=.08

4.Rake_ang=2

5.Shearang=40

6.T_force=40

7.To = 30

20.07
For near optimum

solution only

2. Standard optimization

technique

3,587
1.cut_force = 50

2.D_cut = .003

3.C_width=.078

4.Rake_ang=4

5.Shearang=40

6.T_force=31.399

7.To = 25

20.83
Conduct the standard optimization without conducting the design of experiments
3. Taguchi method +

Standard optimization technique

239.8
1.Cut_forc = 50

2.Shearangle=40

3.D_cut = 0.003

21.14
Use design of experiments results as an initial step. (use only significant design parameters)

Table 6.2 Comparison of locat optimization techniques

Since the significant design parameters exhibits a linear behavior, the optimum values take the extreme limits and hence the optimum performance parameter value based on the Taguchi method alone is better than the remaining two methods using standard optimization technique.

The standard optimization technique is based on the first order step descend method. The iterations of the optimization loop converges when the difference between two subsequent objective function value is less than 0.1.

6.7 Conclusion

The experimental results obtained by using the integrated approach confirms the common expectation that the depth of cut, cutting force and shear angle are more predominant parameters compared to other factors. If the final aim of the experimental study is to optimize the performance parameter, then the designer can conduct further experiments by keeping the near optimum level values as the starting value for the new experiment. Moreover the ambient temperature, rake angle, tangential force and width of cut can be removed form the further study provided the operating range of the above factors do not change from the conducted experiment.