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Final Report of Design
of Experiment A Study on the Relationship between the Factors
and Glue Viscosity
Ning Wenxin 宁温馨
Gao Eryang 高尔扬
Lin Yuxin 林雨馨
Yan Yan 颜 妍
Wan Mingchao 万明超
Contents
1. Background ................................................................................................................................... 1
2. Objective ....................................................................................................................................... 1
3. Literature Review .......................................................................................................................... 1
3.1 Glue invention and history .................................................................................................. 1
3.2 Component analysis ............................................................................................................ 2
3.3 Standard of office glue ........................................................................................................ 2
4. Analysis of Variables ..................................................................................................................... 3
4.1 Basic analysis ...................................................................................................................... 3
4.2 List of response variables .................................................................................................... 3
5. Design of Experiment ................................................................................................................... 5
5.1 Factor design ....................................................................................................................... 5
5.2 Experimental equipment ..................................................................................................... 6
5.3 Experimental procedure ...................................................................................................... 6
6. Data Analysis ................................................................................................................................ 7
6.1 Raw data .............................................................................................................................. 7
6.2 Main effect .......................................................................................................................... 7
6.3 Interactive effect.................................................................................................................. 8
6.4 Contour plot & Response surface plot ................................................................................ 9
6.5 Key factors ........................................................................................................................ 10
6.6 ANOVA ............................................................................................................................. 11
6.7 Response optimization ...................................................................................................... 14
7. Conclusion .................................................................................................................................. 15
References ....................................................................................................................................... 16
1
1. Background
Figure 1 Common kinds of office glue
An adhesive is any substance that, when applied to the surfaces of materials,
binds the surfaces together and resists separation. [1]
As a major form of adhesive, glue
plays an important role in daily life. It is not to exaggerate that without glue, one will
not work efficiently.
Office glue is a marvelous helper. People use it for adhesion when dealing with
papers, bills, and almost all kinds of files. However, whether office glue is effective in
this task is still in doubt. Perhaps the viscosity of glue derives from various factors,
which will influence the ultimate effect of adherence.
2. Objective
The experiment aims at figuring out the impact of different factors to viscosity of
office glue.
3. Literature Review
3.1 Glue invention and history
In 507 B.C, Chinese carpenter Lu Ban discovered the earliest glue, made of
swimming bladder. Then in the eighteenth century, the first formal adhesive, animal
glue, was born in Great Britain. However, modern glue, which relies more on
chemical synthesis, starts from 1942 and time has witnessed a rapid development of
2
technology. [2]
Nowadays, the most common kind of glue in our life is modern glue. Lower cost,
faster production, and better properties lead to its popularity.
Since the objective is related to office glue, common office glue is chosen for
experiments.
3.2 Component analysis
According to component comparison, polyvinyl acetate (PVA) acts as the most
crucial part of office glue.
Figure 2 Structure of PVA
PVA is a rubbery synthetic polymer with the formula (C4H6O2)n. It belongs to
the polyvinyl esters family with the general formula -[RCOOCHCH2]-. It is a type of
thermoplastic.[3]
It is soluble in water, and indispensable to achieve satisfactory
viscosity.
However, due to its chemical structure, the effect of PVA is influenced by
temperature, time, humidity, etc. As a result, all these factors are supposed to be
considered in measurement of viscosity.
3.3 Standard of office glue
Nowadays, the viscosity criterion of standardized glue is as below.
“ 4.5 粘接性
将 70g/m2~80g/m
2的 A4复印纸裁成(105±3)mm×(37±2)mm的试样,在试样的 90mm×37mm
部分均匀地涂一薄层胶,粘合,用手轻轻压平,然后在(30±10)℃、湿度(60±15)%的环境下
静置 1h,用手在未涂胶的两端均匀地加剥离力直至纸破,粘合处不应脱开。
——《中华人民共和国轻工行业标准. 2011》”
From above standard, temperature, humidity, contact surface, time, concentration of
glue will all affect the viscosity of glue.
3
4. Analysis of Variables
4.1 Basic analysis
Based on above fundamentals, we consider the experiment process as well. Here
we design a cause-effect plot as below.
Figure 3 Cause-effect plot
1) Environment and people are hard to control precisely, so blocking such factors
will lead to a better result.
2) In the equipment part, as surface roughness of wall and coated plank are
obviously distinct, choose them to be two contrastive conditions.
3) As for raw material selection and process control, quantitative criteria are able to
be utilized. Thus, accuracy of experiment is warranted.
However, there are still too many factors to control. To screen those variables, we
do some preliminary experiments at first. Set one variable at a fixed level, then we
gradually change the value of other factors.
1) As for concentration, 66.6% is the critical point, which means that further diluting
of glue is impossible to paste.
2) Viscous force doubles when processing time increases from 4min to 7min. So
does the surface area, when changing from 0.5 to 1.
According to the above data, we select variables and corresponding levels in the
experiment.
4.2 List of response variables
Response
variable (units)
Normal operating
level & range
Meas. precision,
accuracy
Relationship of response
variable to objective
4
Viscous force (0, 500)g Spring
dynamometer Estimate effect of each factor
Table 1 Response varaibles
List of control variables
Control
variable
(units)
Normal
level &
range
Meas. precision &
setting error
Proposed settings,
based on predicted
effects
Predicted effects
(for various
responses)
Time (0, 10)
min Stopwatch(0.01s)
Set two levels. Lower
one is between 2 to 4
minutes, while higher
one is between 6 to 9
minutes.
The longer the
time, the larger the
force.
Roughness
Rough
and
smooth
Experience
Set two levels. Rough
one is wall, while
smooth one is coated
plank.
The smoother the
surface, the larger
the force.
Concentration (66.6%,
100%) Experience
Set two levels. Lower
one is 60%, while
higher one is 100%.
The higher the
concentration, the
larger the force.
Surface area 25*34
mm2 Ruler
Set two levels. Lower
one is 20*17mm2,
while higher one is
25*34mm2.
The larger the area,
the larger the
force.
Table 2 Control variables
List of constant variables
Factor
(units)
Desired
experimental level
& allowable range
Meas.
precision
How to control (in
experiment)
Anticipated
effects
Temperature 25℃ Thermometer
To ensure the
effectiveness, control
experiment in the same
temperature.
Slight effect
in the result.
Humidity 40%-60% Hygrometer Control the experiment in
the same humidity.
Slight effect
in the result.
Wind power 0 Experience Do experiment indoors. No impact.
Sort of glue Same Experience Use a same bottle of glue. No impact.
Sort of
water Same Experience
Use a same bottle of water
to dilute the glue. No impact.
Table 3 Constant variables
List of nuisance factor
5
Nuisance
factor (units)
Measurement
precision
Strategy (e.g.,
randomization, blocking,
etc.)
Anticipated effects
Pressure Experience
A same and skilled operator
with relative small force to
press the hook.
After practice, the operator
will master the technique
and control pressure.
Uniformity Experience A same and skilled operator
plasters glue uniformly.
After practice, the operator
will plaster the glue
uniformly.
Table 4 Nuisance factors
5. Design of Experiment
5.1 Factor design
We have chosen four factors including time, roughness, concentration and surface
area. We design the factor levels as bellow.
Factors Low level (-) High level (+)
Time 2min~4min 6min~8min
Surface area 17mm*20mm
25mm*34mm
Concentration 60% 100%
Roughness Smooth (Coated plank) Rough (Wall)
Table 5 Factor levels
We design a full factorial experiment. The design matrix is shown below.
Run Factor
Time Surface area Concentration Roughness
1 - - - -
2 + - - -
3 - + - -
4 + + - -
5 - - + -
6 + - + -
7 - + + -
8 + + + -
9 - - - +
10 + - - +
11 - + - +
12 + + - +
13 - - + +
14 + - + +
6
15 - + + +
16 + + + +
Table 6 Design matrix
5.2 Experimental equipment
We use glue, spring dynamometer, hook codes and hook to help us accomplish
the experiment. They are listed as bellow:
Equipment Amount
Glue 1
Spring dynamometer 1
Hook codes 4*(200g+50g+20g+10g)
Hook(without original glue) 1
Table 7 List of the equipment
Figure 4 Experimental equipment
5.3 Experimental procedure
The experimental steps are list as below:
1. Clean the surface.
2. Apply the glue evenly.
3. Position the hook.
4. Wait for some time.
5. Add weight until the hook fall down, and get the viscous force.
6. Change the parameters and repeat above steps.
7
Figure 5 Experimental procedure
6. Data Analysis
6.1 Raw data
After constructing the experiment design, we carry out the experiment and get
the results in the table below
标准序 运行序 time area concentration roughness replication1 replication2
1 1 -1 -1 -1 -1 160 g 140 g
2 2 1 -1 -1 -1 400 g 360 g
3 3 -1 1 -1 -1 410 g 400 g
4 4 1 1 -1 -1 470 g 480 g
5 5 -1 -1 1 -1 400 g 180 g
6 6 1 -1 1 -1 240 g 360 g
7 7 -1 1 1 -1 300 g 340 g
8 8 1 1 1 -1 440 g 480 g
9 9 -1 -1 -1 1 160 g 120 g
10 10 1 -1 -1 1 140 g 180 g
11 11 -1 1 -1 1 200 g 220 g
12 12 1 1 -1 1 140 g 280 g
13 13 -1 -1 1 1 120 g 120 g
14 14 1 -1 1 1 140 g 180 g
15 15 -1 1 1 1 200 g 200 g
16 16 1 1 1 1 320 g 300 g
Table 8 Raw data
Next we perform data analysis on these results to explore the relationship
between those factors and the response.
6.2 Main effect
First of all, we want to have a grasp of the main effects of these four factors. The
result is shown below
8
1-1
360
320
280
240
200
1-1
1-1
360
320
280
240
200
1-1
time
均值
area
concentration roughness
force 主效应图数据均值
Figure 6 Main effect plot
We can learn from this plot that time, area and roughness have a significant influence
on the viscous force of glue, where the effect of time and area is positive and that of
roughness is negative. Besides, we can also find that concentration has a very weak
effect on the force.
6.3 Interactive effect
The interaction plot of the four factors is shown below
1-1 1-1 1-1
400
300
200
400
300
200
400
300
200
time
area
concentration
roughness
-1
1
time
-1
1
area
-1
1
concentration
force 交互作用图数据均值
9
Figure 7 Interaction plot
From the result we can find that the interactions between time and roughness, area
and roughness, area and concentration are relatively significant, which needs to be
further checked.
6.4 Contour plot & Response surface plot
The contour plot is shown below
area*time
10-1
1.0
0.5
0.0
-0.5
-1.0
concentration*time
10-1
1.0
0.5
0.0
-0.5
-1.0
roughness*time
10-1
1.0
0.5
0.0
-0.5
-1.0
concentration*area
10-1
1.0
0.5
0.0
-0.5
-1.0
roughness*area
10-1
1.0
0.5
0.0
-0.5
-1.0
roughness*concentration
10-1
1.0
0.5
0.0
-0.5
-1.0
time -1
area -1
concentration -1
roughness -1
保持值
>
–
–
–
–
–
–
< 100
100 150
150 200
200 250
250 300
300 350
350 400
400
force
force 的等值线图
Figure 8 Contour plot
As well as the response surface plot
1250
0
300350400
-10 -11
force
area
time
12500
300
-1
350
0 -11
force
concentration
time
1100
0
200
300
-10 -11
force
roughness
time
1250
0
300350
-1
400
0 -11
force
concentration
area
1100
0
200300
-1
400
0 -11
force
roughness
area
1100
0
150200250
-10 -11
force
roughness
concentration
time -1
area -1
concentration -1
roughness -1
保持值
force 的曲面图
10
Figure 9 Response surface plot
From the result we can find that the response surfaces of time & area, time &
concentration and area & concentration are not planes, which indicates that there
should be some interactions in the three factors. Besides, the rest surfaces, roughness
& time, roughness & area and roughness & concentration, can be regarded as planes,
so there are no interactions between roughness and other factors.
6.5 Key factors
In order to find the key factors, we draw the normal plot of effects
5.02.50.0-2.5-5.0-7.5-10.0
99
95
90
80
70
60
50
40
30
20
10
5
1
标准化效应
百分
比
A time
B area
C concentration
D roughness
因子 名称
不显著
显著
效应类型
ABC
D
B
A
标准化效应的正态图(响应为 force,Alpha = 0.05)
Figure 10 Normal plot of effects
And the Pareto plot
11
AC
AB
C
BC
ABD
CD
BD
ABCD
BCD
ACD
AD
ABC
A
B
D
9876543210
项
标准化效应
2.120
A time
B area
C concentration
D roughness
因子 名称
标准化效应的 Pareto 图(响应为 force,Alpha = 0.05)
Figure 11 Pareto plot of effects
From the result we can learn that the items of roughness, area, time and
time*area*concentration have significant effects on the viscosity of glue.
6.6 ANOVA
Firstly we take all combinations of the four factors into consideration and have
the following results
拟合因子: force 与 time, area, concentration, roughness
force 的估计效应和系数(已编码单位)
系数标
项 效应 系数 准误 T P
常量 268.13 9.550 28.07 0.000
time 77.50 38.75 9.550 4.06 0.001
area 111.25 55.62 9.550 5.82 0.000
concentration 3.75 1.87 9.550 0.20 0.847
roughness -158.75 -79.37 9.550 -8.31 0.000
time*area 2.50 1.25 9.550 0.13 0.897
time*concentration -2.50 -1.25 9.550 -0.13 0.897
time*roughness -35.00 -17.50 9.550 -1.83 0.086
area*concentration -6.25 -3.12 9.550 -0.33 0.748
area*roughness -23.75 -11.88 9.550 -1.24 0.232
concentration*roughness 13.75 6.88 9.550 0.72 0.482
time*area*concentration 47.50 23.75 9.550 2.49 0.024
time*area*roughness 10.00 5.00 9.550 0.52 0.608
12
time*concentration*roughness 35.00 17.50 9.550 1.83 0.086
area*concentration*roughness 33.75 16.87 9.550 1.77 0.096
time*area*concentration*roughness -25.00 -12.50 9.550 -1.31 0.209
S = 54.0255 PRESS = 186800
R-Sq = 89.72% R-Sq(预测) = 58.90% R-Sq(调整) = 80.09%
force 的方差分析(已编码单位)
来源 自由度 Seq SS Adj SS Adj MS F
主效应 4 348787 348787 87197 29.87
time 1 48050 48050 48050 16.46
area 1 99013 99013 99013 33.92
concentration 1 113 112 112 0.04
roughness 1 201612 201612 201612 69.07
2因子交互作用 6 16238 16238 2706 0.93
time*area 1 50 50 50 0.02
time*concentration 1 50 50 50 0.02
time*roughness 1 9800 9800 9800 3.36
area*concentration 1 312 312 312 0.11
area*roughness 1 4512 4512 4512 1.55
concentration*roughness 1 1513 1513 1513 0.52
3因子交互作用 4 37762 37762 9441 3.23
time*area*concentration 1 18050 18050 18050 6.18
time*area*roughness 1 800 800 800 0.27
time*concentration*roughness 1 9800 9800 9800 3.36
area*concentration*roughness 1 9112 9112 9112 3.12
4因子交互作用 1 5000 5000 5000 1.71
time*area*concentration*roughness 1 5000 5000 5000 1.71
残差误差 16 46700 46700 2919
纯误差 16 46700 46700 2919
合计 31 454487
来源 P
主效应 0.000
time 0.001
area 0.000
concentration 0.847
roughness 0.000
2因子交互作用 0.502
time*area 0.897
time*concentration 0.897
time*roughness 0.086
area*concentration 0.748
area*roughness 0.232
concentration*roughness 0.482
13
3因子交互作用 0.040
time*area*concentration 0.024
time*area*roughness 0.608
time*concentration*roughness 0.086
area*concentration*roughness 0.096
4因子交互作用 0.209
time*area*concentration*roughness 0.209
残差误差
纯误差
合计
In the ANOVA table obtained above, the significant items whose p-value is less than
0.05 is marked by yellow color. And this result is consistent with the Pareto plot.
Then we omit all the insignificant items and formulate the regression model:
拟合因子: force 与 time, area, concentration, roughness
force 的估计效应和系数(已编码单位)
系数标
项 效应 系数 准误 T P
常量 268.13 10.26 26.12 0.000
time 77.50 38.75 10.26 3.78 0.001
area 111.25 55.62 10.26 5.42 0.000
concentration 3.75 1.87 10.26 0.18 0.856
roughness -158.75 -79.37 10.26 -7.73 0.000
time*area*concentration 47.50 23.75 10.26 2.31 0.029
S = 58.0616 PRESS = 132772
R-Sq = 80.71% R-Sq(预测) = 70.79% R-Sq(调整) = 77.01%
force 的方差分析(已编码单位)
来源 自由度 Seq SS Adj SS Adj MS F P
主效应 4 348787 348787 87197 25.87 0.000
time 1 48050 48050 48050 14.25 0.001
area 1 99013 99013 99013 29.37 0.000
concentration 1 113 112 112 0.03 0.856
roughness 1 201612 201612 201612 59.81 0.000
3因子交互作用 1 18050 18050 18050 5.35 0.029
time*area*concentration 1 18050 18050 18050 5.35 0.029
残差误差 26 87650 87650 3371
失拟 10 40950 40950 4095 1.40 0.263
纯误差 16 46700 46700 2919
合计 31 454487
The residual plot is as follows
14
100500-50-100
99
90
50
10
1
残差
百分
比
500400300200100
100
50
0
-50
-100
拟合值
残差
120600-60-120
10.0
7.5
5.0
2.5
0.0
残差
频率
3230282624222018161412108642
100
50
0
-50
-100
观测值顺序
残差
正态概率图 与拟合值
直方图 与顺序
force 残差图
Figure 12 Residual plots
From the plot we can see that the regression result is good enough.
According to the results of coefficients in the table above, we can formulate the
regression model with binary variables:
force=268.13+38.75×time+55.62×area+1.87×concentration-
79.37×roughness+23.75×time×area×concentration
6.7 Response optimization
We would like to find out how to set the levels of time, area, concentration and
roughness to maximize the response variable, the viscosity of glue. So we perform
response optimization and have the following results.
15
曲线高
低1.0000D
优化
d = 1.0000
最大值force
y = 467.5000
1.0000合意性复合
-1.0
1.0
-1.0
1.0
-1.0
1.0
-1.0
1.0area concentr roughnestime
[1.0] [1.0] [1.0] [-1.0]
Figure 13 Response optimization
From the response optimization plot, we can get when the factors time, area and
concentration are all at its high level and the factor roughness is at its low level, the
responding result force is largest, which is consistent with the model built above.
7. Conclusion
From the analysis above, we can conclude that:
1) The experiment time shows a positive correlation with the result, which is just as
what we thought before. With the time going, the viscous force of glue becomes
more solid.
2) The size of area also has a positive effect on force. As the area becomes larger,
the glue can hold heavier objects. Since the coefficient of area is quite large, it
affects the force significantly.
3) The concentration shows a weak positive correlation with the force, which I think
is caused by the small difference between the high and low level of concentration.
4) The roughness of the wall has a quite large negative effect on the final result. If
the roughness becomes larger, the effective contact area will decrease sharply and
then the force will go down at the same time.
5) The interaction among the three factors time, area and concentration also has a
significant impact on the result.
16
References
[1] Kinloch, A.J. (1987). Adhesion and Adhesives : Science and Technology (Reprinted. ed.).
London: Chapman and Hall. p. 1. ISBN 0-412-27440-X.
[2] History of Glue (2013). http://www.huiruiglue.com/jdwt/1908.htm
[3] Murray, G. T. (1997), Handbook of materials selection for engineering applications, CRC
Press, p. 242, ISBN 978-0-8247-9910-6.
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