GRANT
journal
ISSN 1805-062X, 1805-0638 (online), ETTN 072-11-00002-09-4
EUROPEAN GRANT PROJECTS | RESULTS | RESEARCH & DEVELOPMENT | SCIENCE
16
620
2700
4
500
30.6
30.4734
17
670
1500
8
325
30.7
33.1283
18
720
2700
12
500
113.5
114.5522
19
670
1500
8
325
29.5
33.1283
20
720
300
4
500
68.3
69.1074
All parameters of the experiment are significant, a review of
regression coefficients is summed in the Table 3.
Table 3: Values of regression coefficients
Coefficient
Value of coefficient [-]
b0
291
b1
-0.4811
b2
-0.04351
b3
-21.752
b4
-0.8819
b5
0.000074
b6
0.03403
b7
0.001532
When regression coefficients from Table 3 are put into an equation
(1), a final regression equation (2) appears.
D
A
C
A
B
A
D
C
B
A
Y
⋅
⋅
+
⋅
⋅
+
⋅
⋅
+
+
⋅
−
⋅
−
⋅
−
⋅
−
=
001532
.
0
03403
.
0
000074
.
0
8819
.
0
752
.
21
04351
.
0
4811
.
0
291
(2)
In equation (2) Y is a depth of glass dropout in millimeters, A is
forming temperature in [°C], B is forming time in seconds, C is the
thickness of glass plate in millimeters, and D is the diameter of the
hole in the form in millimeters.
5.
RESULTS AND DISCUSSION
For setting accuracy, real measured output values and regression
values must be compared. The difference between measured depths
and depths calculated from the regression equation are residuals.
Distribution and other plots of residual are seen in Figure 2.
From plots in Figure 1, there is seen that residual distribution is
symmetric around the regression function, which means the
equation describes the system well. A sit is seen biggest residual
values are up to 2 millimeters, which is quite good for custom glass
production. For verification several other runs were made, where
different values of parameters were set. These runs are summed in
Table 4
Figure 2:
Residual plots for the depth of glass dropout
Table 4: Verification runs
Forming
temperature (A)
Forming time
(B)
Glass thickness
(C)
Diameter of
hole in form (D)
Position of form
in kiln
Depth of
dropout (Y)
Regression
value
[°C]
[s]
[mm]
[mm]
[mm]
[mm]
695
450
8
225
Center
17.7
16.5293
625
1200
4
325
Center
16
16.2375
625
1500
8
225
Center
7.2
7.5665
625
1500
8
225
Side
7.5
7.5665
From Table 4 there is clear that the Regression function works well,
and the difference between real depth and calculated values is 1.2
millimeters on maximal. These measurements verify the equation
but also show us that accuracy of setting works too. After DOE
verification measurement should be done to verify the functionality
of the equation.
6.
CONCLUSION
DOE (Design of Experiment) is a powerful tool, and it can be very
useful for minimizing or optimizing process settings. As was seen
before the use of DOE is beneficial even for Glass manufacturing
processes as glass kilnforming. Sometimes just do DOE itself is not
enough, several verification runs should be made to ensure the
regression equation works well. During verification and experiment
itself, we should focus also on the accuracy of process outcomes in
comparison with demanded values. When request on very accurate
production appears even DOE is sometimes not enough and first the
accuracy of process setting should be considered.
Vol. 9, Issue 1
116