Design of ExperimentGroup member: Li Zheran Xu Zan She Manrong Lei Chen

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Content :

Motivation Literature review Design of Experiment Implementation Restrictions

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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

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Content :

Motivation Literature review Design of Experiment Implementation Restrictions

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Literature review

The history of spinning-top:

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。Wooden gyro

Clockwork gyro

Rotating handle gyro

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Literature review

The process of turning spinning-top:

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Literature review

The process of turning spinning-top:

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Content :

Motivation Literature review Design of Experiment Implementation Restrictions

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Design of Experiment

A full fractional design

• Factor Decomposition• Implementation of the experiments• Data analysis• The results of the design

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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

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Factor Level Definition

Control Variable Code Levels Level Code

Ground Surface A

Cement Ground 1Plastic

Ground(playground) 2

Ceramic Ground 3

Height B Low(H=10cm) 1High(H=20cm) 2

Gyro Weight C Light 1Heavy(with plasticine) 2

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Preliminary Experiment

Choose rotating handle gyro to do the preliminary experiment to control the fixed factor

Ground Surfac

e

•cementHei

ght •H=10cm

Weight

• light

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Control the fixed factor

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Control the fixed factor

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Content :

Motivation Literature review Design of Experiment Implementation Restrictions

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Implementation1:cement

2:plastic

3:ceramic

A: groun

d surfac

e

1:H=10cm

2:H=20cm

B: heigh

t

1:light

2:heavy

C: weigh

t

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Implementation

Full Factorial Design

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Data analysis

321

30

20

1021

21

30

20

10

A

均值

B

C

Sl ewi ng Ti me 主效应图数据均值

• Significant effect• A: type of

ground surface

• C: the weight of the gyro

• No significant effect• B: the height

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Data analysis （ cont. ）

45

30

15

21

21

45

30

15

321

45

30

15

A

B

C

123

A

12

B

12

C

Sl ewi ng Ti me 交互作用图数据均值

• No interaction effect

• A and B• B and C

• Significant effect

• A and C

• On the ceramic ground, the difference is bigger.

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Data analysis （ cont. ）

1050-5-10

99. 999

90

50

10

10. 1

残差

百分比

5040302010

5

0

-5

-10

拟合值

残差

840-4-8

24

18

12

6

0

残差

频率

605550454035302520151051

5

0

-5

-10

观测值顺序

残差

正态概率图 与拟合值

直方图 与顺序

Sl ewi ng Ti me 残差图• Normality

assumption• Normal

probability plot √

• Histogram √• Equal variance

assumption• Residual VS

fitted value ╳

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Slewing Time 的方差分析，在检验中使用调整的 SS来源 自由度 Seq SS Adj SS Adj MS F PA 2 7719.96 7719.96 3859.98 300.64 0.000B 1 2.05 2.05 2.05 0.16 0.691C 1 1189.04 1189.04 1189.04 92.61 0.000A*B 2 2.75 2.75 1.38 0.11 0.899A*C 2 575.56 575.56 287.78 22.41 0.000B*C 1 6.21 6.21 6.21 0.48 0.490A*B*C 2 18.10 18.10 9.05 0.70 0.499误差 48 616.28 616.28 12.84合计 59 10129.95

S = 3.58317 R-Sq = 93.92% R-Sq （调整） = 92.52%

项 系数 系数标准误 T P常量 19.6983 0.4626 42.58 0.000A1 -4.8033 0.6542 -7.34 0.0002 -10.8533 0.6542 -16.59 0.000B1 -0.1850 0.4626 -0.40 0.691C1 4.4517 0.4626 9.62 0.000A*B1 1 0.0400 0.6542 0.06 0.9512 1 0.2400 0.6542 0.37 0.715A*C1 1 -0.6967 0.6542 -1.06 0.2922 1 -3.3967 0.6542 -5.19 0.000B*C1 1 0.3217 0.4626 0.70 0.490A*B*C1 1 1 -0.6067 0.6542 -0.93 0.3582 1 1 -0.1167 0.6542 -0.18 0.859

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Another experiment1:cement

2:plastic

3:ceramic

A: ground

surface

1:H=30cm

2:H=1m

B: height

1:light

2:heavy

C: weig

ht

Clockwork gyro

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Data analysis

321

30

20

1021

21

30

20

10

A

均值

B

C

Sl ewi ng Ti me 主效应图数据均值

45

30

15

21

21

45

30

15

321

45

30

15

A

B

C

123

A

12

B

12

C

Sl ewi ng Ti me 交互作用图数据均值

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Data analysis

420-2-4

99. 999

90

50

10

10. 1

标准化残差

百分比

40302010

3. 0

1. 5

0. 0

-1. 5

-3. 0

拟合值

标准化残差

2. 41. 20. 0-1. 2-2. 4

20

15

10

5

0

标准化残差

频率

605550454035302520151051

3. 0

1. 5

0. 0

-1. 5

-3. 0

观测值顺序

标准化残差

正态概率图 与拟合值

直方图 与顺序

Sl ewi ng Ti me 残差图(加权)

1050-5-10

99. 999

90

50

10

10. 1

残差

百分比

40302010

10

5

0

-5

-10

拟合值

残差

1050-5-10

30

20

10

0

残差

频率

605550454035302520151051

10

5

0

-5

-10

观测值顺序

残差

正态概率图 与拟合值

直方图 与顺序

Sl ewi ng Ti me 残差图

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Slewing Time 的方差分析，在检验中使用调整的 SS来源 自由度 Seq SS Adj SS Adj MS F PA 2 273.476 308.292 154.146 291.91 0.000B 1 0.089 0.081 0.081 0.15 0.696C 1 38.019 64.031 64.031 121.26 0.000A*B 2 0.537 0.113 0.056 0.11 0.899A*C 2 29.137 29.028 14.514 27.49 0.000B*C 1 0.136 0.482 0.482 0.91 0.344A*B*C 2 0.973 0.973 0.487 0.92 0.405误差 48 25.347 25.347 0.528合计 59 367.714

S = 0.726677 R-Sq = 93.11% R-Sq （调整） = 91.53%

项 系数 系数标准误 T P常量 19.2759 0.4119 46.80 0.000A1 -4.7976 0.5450 -8.80 0.0002 -10.5211 0.4967 -21.18 0.000B1 -0.1617 0.4119 -0.39 0.696C1 4.5355 0.4119 11.01 0.000A*B1 1 0.0217 0.5450 0.04 0.9682 1 0.2241 0.4967 0.45 0.654A*C1 1 -0.7190 0.5450 -1.32 0.1932 1 -3.5094 0.4967 -7.07 0.000B*C1 1 0.3936 0.4119 0.96 0.344A*B*C1 1 1 -0.6616 0.5450 -1.21 0.2312 1 1 -0.2219 0.4967 -0.45 0.657

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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

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Content :

Motivation Literature review Design of Experiment Implementation Restrictions

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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.

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Thank you for listeningQ&A