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

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Content : MMotivation LLiterature review DDesign of Experiment IImplementation RRestrictions 2

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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 3

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Content : Motivation Literature review Design of Experiment Implementation Restrictions 4

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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 5

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Literature review The process of turning spinning-top: 6

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Literature review The process of turning spinning-top: 7

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Content : Motivation Literature review Design of Experiment Implementation Restrictions 8

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Design of Experiment Factor Decomposition Implementation of the experiments Data analysis The results of the design 9

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Factor Decomposition Response Variable: Response Variable: Slewing time Control variable: ① Ground surface （ cement / plastic / ceramic ） ② Height （ low / high ） ③ Weight （ light / heavy ） Fixed variables: Fixed variables: Force （ held constant ） Nuisance factor: ① Surface homogeneous ② Wind speed 10

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Factor Level Definition Control Variable CodeLevelsLevel Code Ground SurfaceA Cement Ground1 Plastic Ground(playground)2 Ceramic Ground3 HeightB Low(H=10cm)1 High(H=20cm)2 Gyro WeightC Light1 Heavy(with plasticine)2 11

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Preliminary Experiment Choose rotating handle gyro to do the preliminary experiment to control the fixed factor Ground Surface cement Height H=10cm Weight light 12

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Control the fixed factor 13

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Control the fixed factor 14

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Content : Motivation Literature review Design of Experiment Implementation Restrictions 15

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Implementation 1:cement 2:plastic 3:ceramic A: ground surface 1:H=10cm 2:H=20cm B: height 1:light 2:heavy C: weight 16

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Implementation Full Factorial Design 17

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Data analysis Significant effect A: type of ground surface C: the weight of the gyro No significant effect B: the height 18

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Data analysis （ cont. ） No interaction effect A and B B and C Significant effect A and C On the ceramic ground, the difference is bigger. 19

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Data analysis （ cont. ） Normality assumption Normal probability plot √ Histogram √ Equal variance assumption Residual VS fitted value ╳ 20

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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 P A B C A*B A*C B*C A*B*C 误差 合计 S = R-Sq = 93.92% R-Sq （调整） = 92.52% 项 系数 系数标准误 T P 常量 A B C A*B A*C B*C A*B*C

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Another experiment 1:cement 2:plastic 3:ceramic A: ground surface 1:H=30cm 2:H=1m B: height 1:light 2:heavy C: weight Clockwork gyro 22

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Data analysis 23

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Data analysis 24

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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 P A B C A*B A*C B*C A*B*C 误差 合计 S = R-Sq = 93.11% R-Sq （调整） = 91.53% 项 系数 系数标准误 T P 常量 A B C A*B A*C B*C A*B*C

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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 26

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Content : Motivation Literature review Design of Experiment Implementation Restrictions 27

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Restrictions on the experiment Force control: Force control: Though we have practice to keep force constant, there is still personal error. Difficult to control the weight: Difficult to control the weight: To control the weight, we choose to cover plasticine to plus weight. Data acquisition: Data acquisition: Each run we use stopwatch to record data, which may have measuring error. Wearing restriction: Wearing restriction: With the increasing of run times, the gyro wearing increases. 28

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Thank you for listening Q&A 30

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