Design of Experiment
Group member:
Li Zheran
She Manrong
Xu Zan
Lei Chen
Content :

Motivation

Literature review

Design of Experiment

Implementation

Restrictions
2
Motivation

Find out the main effect on
spinning top

Design a model between
the effect and the response

Help understand the work
principle of spinning top
3
Content :

Motivation

Literature review

Design of Experiment

Implementation

Restrictions
4
Literature review

The history of spinningtop:
①
明代刘侗、于奕正《帝经
物略·二春场》载: “陀螺
者，木制，如小空钟，中
实而无柄。绕以鞭之绳，
卓于地，争制其鞭……”。
②
1852年, 博科(Foucault)首
先将高速旋转的刚体称为
陀螺。
Clockwork
gyro
Wooden gyro
Rotating handle
gyro
5
Literature review

The process of turning spinning-top:
6
Literature review

The process of turning spinning-top:
7
Content :

Motivation

Literature review

Design of Experiment

Implementation

Restrictions
8
Design of Experiment
A 31 × 22 full fractional design
• Factor Decomposition
• Implementation of the experiments
• Data analysis
• The results of the design
9
Factor Decomposition

Response Variable: Slewing time

Control variable:
①
Ground surface （cement / plastic / ceramic）
②
Height （ low / high ）
③
Weight （light / heavy）

Fixed variables: Force （ held constant）

Nuisance factor:
①
Surface homogeneous
②
Wind speed
10
Factor Level Definition
Control Variable
Ground Surface
Height
Gyro Weight
Code
A
B
C
Levels
Level Code
Cement Ground
1
Plastic Ground(playground)
2
Ceramic Ground
3
Low(H=10cm)
1
High(H=20cm)
2
Light
1
Heavy(with plasticine)
2
11
Preliminary Experiment
Choose rotating
handle gyro to do
Ground
Surface
•cement
the preliminary
experiment to
Height
•H=10cm
control the fixed
factor
Weight
• light
12
Control the fixed factor
13
Control the fixed factor
14
Content :

Motivation

Literature review

Design of Experiment

Implementation

Restrictions
15
Implementation
A:
ground
surface
B:
height
C:
weight
1:cement
1:H=10cm
1:light
2:plastic
2:H=20cm
2:heavy
3:ceramic
16
Implementation
Full Factorial Design
17
Data analysis
•
Significant effect
• A: type of
ground surface
• C: the weight of
the gyro
Slewing Time 主效应图
数据均值
A
B
30
20
•
No significant
effect
• B: the height
均值
10
1
2
C
3
1
2
30
20
10
1
2
18
Data analysis（cont.）
• No interaction
effect
• A and B
• B and C
• Significant effect
• A and C
Slewing Time 交互作用图
数据均值
1
2
45
A
1
2
3
30
A
15
45
30
B
1
2
B
• On the ceramic
ground, the
difference is bigger.
15
45
C
1
2
30
C
15
1
2
3
1
2
19
Data analysis（cont.）
Slewing Time 残差图
正态概率图
•
Normality assumption
• Normal probability
plot √
• Histogram √
•
Equal variance
assumption
• Residual VS fitted
value ╳
与拟合值
9 9.9
99
5
残差
百分比
90
50
10
0
-5
1
-10
0.1
-10
-5
0
5
10
10
20
30
残差
拟合值
直方图
与顺序
40
50
24
5
残差
频率
18
12
0
-5
6
-10
0
-8
-4
0
残差
4
8
1
5
10
15
20
25
30
35
40
45
50
55
60
观测值顺序
20
Slewing Time 的方差分析，在检验中使用调整的 SS
来源
A
B
C
A*B
A*C
B*C
A*B*C
误差
合计
自由度
2
1
1
2
2
1
2
48
59
S = 3.58317
Seq SS
7719.96
2.05
1189.04
2.75
575.56
6.21
18.10
616.28
10129.95
Adj SS
7719.96
2.05
1189.04
2.75
575.56
6.21
18.10
616.28
R-Sq = 93.92%
Adj MS
F
P
3859.98 300.64 0.000
2.05
0.16 0.691
1189.04
92.61 0.000
1.38
0.11 0.899
287.78
22.41 0.000
6.21
0.48 0.490
9.05
0.70 0.499
12.84
R-Sq（调整） = 92.52%
项
常量
A
1
2
B
1
C
1
A*B
1 1
2 1
A*C
1 1
2 1
B*C
1 1
A*B*C
1 1 1
2 1 1
系数
19.6983
系数标准误
0.4626
T
42.58
P
0.000
-4.8033
-10.8533
0.6542
0.6542
-7.34
-16.59
0.000
0.000
-0.1850
0.4626
-0.40
0.691
4.4517
0.4626
9.62
0.000
0.0400
0.2400
0.6542
0.6542
0.06
0.37
0.951
0.715
-0.6967
-3.3967
0.6542
0.6542
-1.06
-5.19
0.292
0.000
0.3217
0.4626
0.70
0.490
-0.6067
-0.1167
0.6542
0.6542
-0.93
-0.18
0.358
0.859
21
Another experiment
Clockwork
gyro
A:
ground
surface
B:
height
C:
weight
1:cement
1:H=30cm
1:light
2:plastic
2:H=1m
2:heavy
3:ceramic
22
Data analysis
Slewing Time 主效应图
Slewing Time 交互作用图
数据均值
数据均值
B
A
2
1
45
A
1
2
3
30
30
A
20
15
均值
45
10
3
2
C
1
1
2
30
B
1
2
B
15
30
45
20
C
1
2
30
C
15
10
1
2
1
2
3
1
2
23
Data analysis
Slewing Time 残差图
Slewing Time 残差图(加权)
90
百分比
残差
50
0
-5
10
1
3.0
99
5
90
50
10
-10
0.1
0
5
40
30
20
10
10
拟合值
标准化残差
拟合值
直方图
与顺序
直方图
与顺序
频率
残差
20
10
10
20
5
15
0
-5
-5
0
残差
5
10
3.0
10
5
-10
0
5
10 15
20
25
30
35
观测值顺序
40
45
50
55
60
1.5
0.0
-1.5
-3.0
0
1
40
30
20
10
残差
30
-10
-1.5
4
2
0
-2
-4
频率
-5
0.0
-3.0
0.1
-10
1.5
1
标准化残差
百分比
99.9
10
99
标准化残差
99.9
与拟合值
正态概率图
与拟合值
正态概率图
-2.4
-1.2
0.0
标准化残差
1.2
2.4
1
5
10 15
20 25
30 35
观测值顺序
24
40 45
50 55
60
Slewing Time 的方差分析，在检验中使用调整的 SS
来源
A
B
C
A*B
A*C
B*C
A*B*C
误差
合计
自由度
2
1
1
2
2
1
2
48
59
S = 0.726677
Seq SS
273.476
0.089
38.019
0.537
29.137
0.136
0.973
25.347
367.714
Adj SS
308.292
0.081
64.031
0.113
29.028
0.482
0.973
25.347
R-Sq = 93.11%
Adj MS
154.146
0.081
64.031
0.056
14.514
0.482
0.487
0.528
F
P
291.91 0.000
0.15 0.696
121.26 0.000
0.11 0.899
27.49 0.000
0.91 0.344
0.92 0.405
R-Sq（调整） = 91.53%
项
常量
A
1
2
B
1
C
1
A*B
1 1
2 1
A*C
1 1
2 1
B*C
1 1
A*B*C
1 1 1
2 1 1
系数
19.2759
系数标准误
0.4119
T
46.80
P
0.000
-4.7976
-10.5211
0.5450
0.4967
-8.80
-21.18
0.000
0.000
-0.1617
0.4119
-0.39
0.696
4.5355
0.4119
11.01
0.000
0.0217
0.2241
0.5450
0.4967
0.04
0.45
0.968
0.654
-0.7190
-3.5094
0.5450
0.4967
-1.32
-7.07
0.193
0.000
0.3936
0.4119
0.96
0.344
-0.6616
-0.2219
0.5450
0.4967
-1.21
-0.45
0.231
0.657
25
The results of the design

Main effect:
Ground surface & weight with 95% confidence

Ground surface effect:
Ceramic material increases the slewing time

Weight effect:
Lighter gyro increases the slewing time
26
Content :

Motivation

Literature review

Design of Experiment

Implementation

Restrictions
27
Restrictions on the experiment

Force control:
Though we have practice to keep force constant, there is still personal
error.

Difficult to control the weight:
To control the weight, we choose to cover plasticine to plus weight.

Data acquisition:
Each run we use stopwatch to record data, which may have measuring
error.

Wearing restriction:
With the increasing of run times, the gyro wearing increases.
28
Thank you for listening
Q&A
30