MTRL 460 Project 2 Design and Analysis of Experiments for Process Modeling and Optimization

2011

University of British Columbia

Group 10

Andy Wen

Calvina Martin

Kyle Huang

Hans Saputra

Introduction Advanced AIN ceramic is one of the primary candidates for replacement of Alumina in environments

requiring high-thermal conductivity ceramics. In order for the ceramic to be applicable as the substrate

material, it must have low porosity and high strength. In addition, AIN has a very hi gh thermal

conductivity. For most of these applications, the properties are listed as follows:

R1 : Maximum thermal conductivity Target: 215 W/mK

R2 : Maximum porosity Target: 0.52%

R3 : Maximum strength Target: 320 MPa

Note: The target values were altered to fit the data since the original target values falls outside the range of the obtained value. This may be

caused by the updated variables values given by Tom Troczynski.

Seven process variables, X1 to X7, were proposed to control the required properties R1, R2 and R3.

X1 : Annealing time at 1900°C (3.5 to 5 hr)

X2 : Heating rate (10 to 20 °C/min)

X3 : Powder milling time (1 to 10 hours)

X4 : Oxygen impurity content in AIN powder (1 to 4 wt%)

X5 : Sintering temperature (1650 - 1800°C)

X6 : Sintering time (2 to 6 hr)

X7 : Amount of Yttria additive to AIN powder (5 to 10 wt%)

With these data, we are able to use the DX program to explore the models and identify the significant

variables that would simultaneously result in the desirable levels of responses.

Step 2. Using the DX8 program, we designed the screening experiments with 27-3 fractional factorials to identify

the 4 significant variables out of the pool of the tentative 7 variables.

Figure 1. Data-entry for all the variables

Then with the data above, we generate the data-entry table for the 3 responses and continue to step 3.

Step 3. Using the LAB10 simulation program, the designed experiments were run by entering the values of

variables for each of the run (listed in Step 2 – Figure 1).

Figure 2. Data entry for Run #1

This will result in the values for R1, R2 and R3 in each run which will then be recorded in the DX8 data

entry table.

Figure 3. Data-entry table for 3 responses

Step 4. Using the DX8 program, we are able to analyze the results through the normal probability plots for

maximum thermal conductivity, minimum porosity and maximum strength.

Figure 4. Normal Probability Plots for Maximum Thermal Conductivity

Figure 5. Normal Probability Plots for Minimum Porosity

Figure 6. Normal Probability Plots for Maximum Strength

From figure 4, 5 and 6, we are able to identify the same four outliers which will be variables the

significant for all three responses. These variables are:

A: Annealing time at 1900°C

D: Oxygen impurity content in AIN powder

E: Sintering temperature

G: Yttria additive content in AIN powder

Step 5. With the 4 significant variables from step 4, we are able to run the DX8 program to generate the data-

entry table for the experiments. We use the Central Composite Design (CCD) to model the process in

terms of the 4 variables.

Figure 7. Data-entry table using 4 significant variables

Step 6. Using the LAB10 simulation program, the designed experiments were run again by entering the values of the four significant variables for each of the run (listed in Step 5 – Figure 7) whereas the values for the

rest of the variables are kept constant at mid-level of their allowed range.

Figure 8. Data entry for Run #1

The returned values of R1, R2 and R3 will then be recorded in the table.

Figure 9. Data-entry table with the 3 responses

Step 7. Three different empirical models for response 1, 2 and 3 were obtained using CCD module of DX8. These

models were assessed under ANOVA module. The acceptable conditions are:

Correlation coefficient r2 is larger than approximately 0.9

F-ratio is larger than approximately 20

Figure 10. ANOVA module for R1 (maximum thermal conductivity)

Figure 11.ANOVA module for R2 (minimum porosity)

Figure 12. ANOVA module for R3 (maximum strength)

As observed from the ANOVA module in figure 10, 11 and 12, all the response follows the acceptable

conditions of r2 > 0.9 and F-ratio > 20. Therefore, we can conclude that all the responses have a good

quality according to the acceptable conditions.

Figure 13. Empirical Model for R1 (maximum thermal conductivity)

Figure 14. Empirical Model for R2 (minimum porosity)

Figure 15. Empirical Model for R3 (maximum strength)

Step 8.

Figure 16. Cube plot for R1 (maximum thermal conductivity)

Figure 17. Cube plot for R2 (minimum porosity)

Figure 18. Cube plot for R3 (maximum strength)

Figure 19. Overlay Plot of Annealing time vs. Oxygen impurity

Figure 20. Overlay Plot of Annealing time vs. Sintering temperature

Figure 21. Overlay Plot of Annealing time vs. Amount of Yttria

As seen in figure 16, 17 and 18, the cubes identify the levels of the significant variables that would

simultaneously result in the desirable (target) levels of the responses. Thus, we can plot the response

surfaces for different combinations of the 4 variables such as figure 19, 20 and 21.

By doing so, the figures analyze the optimum conditions of the process that would result in a

combination of the responses R1, R2 and R3 closest to the target values R1T, R2T and R3T.

Step 9. In order to verify the model predictions, we use LAB10 program at the optimum level obtained from

“numerical solutions” in DX8.

Figure 22. Data entry for model verification

Figure 23. LAB10 simulation results

Figure 24. CCD-model predicted results

As seen from figure 23 and figure 24, the simulation values closely resembles those values from CCD-

model predicted results. Therefore, we can conclude that the simulations prove that the model is

successful and accurate.

Conclusion In conclusion, the results observed from the steps show that the simulation model is correct and

successful. From the project, with these data, we are able to use the DX program to explore the models

and identify the significant variables that would simultaneously result in the desirable levels of

responses.