GRANT
journal
ISSN 1805-062X, 1805-0638 (online), ETTN 072-11-00002-09-4
EUROPEAN GRANT PROJECTS | RESULTS | RESEARCH & DEVELOPMENT | SCIENCE
sequences of runs with constant conditions of the experiment, where
random influences are reduced by the scheduling of runs.
Phases of Design of Experiment method are. Choice of factors with
an influence on the outcome. Choice of lower and upper values for
each factor. Crafting the plan of the experiment. The experiment
itself – a measurement of all runs. Finding of significant factors.
Generating of the regression model. Application of results into a real
problem.
The outcome from the DOE is a level of significance of the factor’s
effect on system output. This is calculated by statistical hypothesis
testing. The next outcome is the regression function. Regression
function describes the system and its calculated from the correlation
between factors, significance, and response [8], [9], and [3].
2.3
Minimizing the number of setup attempts on
kilnforming process with DOE method
Glass manufacturing is a complex process with many variables.
When there is a need to lower the number of setup attempts, DOE is
a good tool [4]. As a result of DOE, an equation (1) describing the
kilnforming process appears.
4
1
7
3
1
6
2
1
5
4
4
3
3
2
2
1
1
0
x
x
b
x
x
b
x
x
b
x
b
x
b
x
b
x
b
b
Y
⋅
⋅
+
⋅
⋅
+
⋅
⋅
+
+
⋅
+
⋅
+
⋅
+
⋅
+
=
(1)
Where Y is measured outcome (response), b0 – b7 are coefficients of
regression, and x1 – x4 are factors.
From equation (1), there is easily
possible to calculate demanded values for parameters to set up the
process and get the requested result on the first attempt. When a
description of the whole kilnforming process is needed, the DOE
must be done for all types of forms and glass.
3.
THEORETICAL BASIS
After the Design of Experiment for glass, kilnforming is made.
Setup attempts are reduced to a minimum. Problems can occur when
a request for more and more accurate results appears. There is a
need to know the kilnforming process better. If the accuracy of the
setting is not known, even that DOE was used defect could be made.
That is why this paper is focused on the accuracy of the regression
function. From this equation, we are able to determine a degree of
accuracy whit which setting for parts can be made on a minimal
number of attempts. This is more described in a case study below.
4.
CASE STUDY
The case study was made on the same process and the same
experiment as in [4]. It is a glass slumping process in a Czech
company where custom glass parts are produced. Final products are
glass-metal assemblies, that is why good accuracy of slumped parts
is needed. The experiment was done on a circle dropout form, where
before glass a separator was applied as can be seen in Figure 1.
Figure. 1: Dropout form with separator.
To minimize setup attempts by DOE, several process parameters are
defined as constants. Type of glass, kiln, shape of dropout form,
position in the kiln, and orientation of tin layer. The experiment runs
followed the temperature curve where forming temperature and
forming time were parameters for change, as other parameters for
change glass thickness and diameters of a hole in form were chosen.
The outcome of the process is the depth of glass dropout.
Lower, upper and middle points for the experiment were set based
on experiences from previous work with the kiln. See Table 1
below.
Table 1: Lower, upper and middle points for the experiment.
Factor
Lower
point
Upper
point
Middle
point
Forming temperature
620 °C
720 °C
670 °C
Forming time
300 s
2700 s
1500 s
Glass thickness
4 mm
12 mm
8 mm
Diameter of hole in form
150 mm
500 mm
325 mm
Based on table 1, the experiment was created. Runs were generated
by statistical software Minitab. For each run, a depth of dropout was
measured and written into the software. After all runs were made,
the software calculated a regression equation. The whole experiment
with the outcome is summed in Table 2.
Table 2: Complete Design of Experiment plan with a response and regression values
Run order
Forming
temperature (A)
Forming time
(B)
Glass thickness
(C)
Diameter of
hole in form (D)
Depth of
dropout (Y)
Regression
value
[°C]
[s]
[mm]
[mm]
[mm]
[mm]
1
620
300
4
150
1.1
1.0064
2
720
2700
4
150
14.0
15.1564
3
720
2700
12
500
115.2
114.5522
4
620
300
12
500
20.8
19.5582
5
670
1500
8
325
28.1
33.1283
6
620
2700
12
150
1.4
1.4672
7
670
1500
8
325
30.3
33.1283
8
720
300
12
150
13.5
13.7052
9
720
300
4
500
70.0
69.1074
10
620
2700
4
500
30.0
30.4735
11
620
2700
12
150
1.1
1.4672
12
720
2700
4
150
15.8
15.1564
13
620
300
4
150
0.9
1.0064
14
620
300
12
500
18.4
19.5582
15
720
300
12
150
13.9
13.7052
Vol. 9, Issue 1
115