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.