Project No.6

Menber：Ryu Oguma・Yu Kamitani・Taiyo Nakayama

Ease of bouncing objects
Hypothesis: The ease with which an object bounces back(coefficient of repulsion) may be related to its hardness.

2.How to obtain the repulsion
factor“e" (Pliability)

1.Type of balls used

•Aluminum（Al）•Copper （Cu）
•Titanium（Ti）•Brass•Chrome steel（Cr） •Tungsten （W）•Stainless steel（SUS）•Tungsten carbide （WC）
•Nickel （Ni）
•Lead （Pb）

e=′ℎℎhSquare root ofratio of fall height
to bounce heightNiWCW

Originalheighth′BounceheightPb

3. Research Flow
① Drop a 50cm-high metal ball and measure the bounce height.
② Repulsion factor is calculated from the ratio of dropped height.
③ Hardness of each metal ball is measured with a Vickers tester.
④ Repulsion factors are calculated for coefficient of resilience andhardness values.
⑤ Consideration of whether there is a correlation between coefficientof rebound and Vickers hardness

Figure 1
Experimental
environment

4. Determining the number of drops
Standard deviation (variation of data) per number of drops
0.05

アルミニウムAluminum （Al）

Standard deviation

0.04

徐々に値が収束チタン（Ti）
Titanium
クロム鋼
Chrome（Cr）
steel

0.03

ステンレス（SUS）
Stainless steel
ニッケル
Nickel （Ni）

0.02

銅（Cu）
CopperCopper

0.01

真鍮
Brass
タングステン
Tungsten （W）

0020406080
Number of drops

Figure 2: Change in standard deviation by number of drops

100

Tungsten carbide （WC）
タングステンカーバイド
鉛（Pb）
Lead→Analysis with 100 data points for which the standard
deviation was estimated to have converged.

Repulsion factors

5. Experimental
results
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2

Average coefficient of repulsion obtained from 100 drop tests.
0.819

0.866

0.875 0.877

0.813 0.797

0.694

0.656

0.719

0.275
Al6. Hardness test

TiCr

Stainless

NiCu

Figure3: Experimental results

BrassWWC
Pb→ Different materials havedifferent Pliability

Vickers hardness test* performed in Mori Laboratory, MechanicalEngineering and Robotics Course (n=5)*Hardness is measured by the size of the indentation made by pressing adiamond indenter
Table 1 Results of hardness test

Test ballAluminum
Titanium
Chrome steel
Stainless steel
NickelHardness HV88231735248242

Test ballHardness HV
Copper102
Brass146
Tungsten
330
Tungsten carbide
235
Figure 4 Indentation
Lead6of hardness test

7. Relationship between repulsion factorand Hardness→Hardness varies depending on
the material

Repulsion factors

Statistical Test for Correlation between repulsion
Al1
factor and Hardness
0.9
Ti
correlation
betweenrepulsion
factorand0.8
CrHardness
0.7
Stainless
SUS
0.6
Null hypothesis ：No correlation between
Ni0.5
repulsion factor and Hardness
0.4
Cu
Authorization ：Pearson's product rate
0.3
Brass真鍮correlation
coefficientofTheT-test(one0.2tailed) for uncorrelated
W0.1
Reject null hypothesis when correlation
0WC
1
101001000 Pb
coefficient < statisticVickers Hardness HV・ Correlation coefficient → 0.624
Figure 5 Relationship between coefficient of ・ The statistic T → 25.2
rebound and Vickers hardness (one logarithm)

𝑇=

8. Conclusion

𝑟 𝑛−221−𝑟=0.624 × 1000 − 221 − 0.624= 25.20.624 < 25.2

Repulsion factors is positively The null hypothesis is rejected and thecorrelation
betweenthetwoisnotzero.
correlated with hardness
9. Future
Outlook

Identify parameters besides hardness that correlate with the repulsion
factors, and propose an experimental formula for determining therepulsion factors.