IYPT 2010 Austria, I. R. Iran Reporter: Ali Farajollahi 1.

IYPT 2010 Austria, I. R. IranIYPT 2010 Austria, I. R. Iran

Problem No.

1

STEEL BALLS

Reporter: Ali Farajollahi

3

IYPT 2010 Austria, I. R. Iran2

The Question

• Colliding two large steel balls with a thin sheet of material (e.g. paper) in between may "burn" a hole in the sheet.

• Investigate this effect for various materials.


Contents• Initial Observations• Theoretical background

– Burning or Physical Rupture?– Material Background

• Theory: The balls– Static loaded balls– Balls collision simulation

• Theory: The sheet– Different strains

• Experiments– Setup– Comparison with Theory– Different Materials & Behaviors

• Conclusion


Initial Observations


Initial Observation

Deformation

Waves

Radial rupture

Burning


Initial Observation

Aluminum

Tissue

Styrofoam


Burning (Chemical) or Rupture (Physical)?

– Temperature rises because of sheet deflection

– Not enough energy to start flaming– Not enough Oxygen in the contact

point

• Burning occurs incompletely, but the burnt amount is too low

• Main Happening: Physical Rupture


Material Strength Background

• Stress & Strain

• Poisson’s Ratiol

lA

F

F

F

l

Δl

x yy

x


Static Loaded Balls• To be able to simulate the

collision…• Finding the deformation of two

steel balls under a specific load

FF


Static Loaded Balls


Static Loaded Balls• According to references, Contact

mechanics and Hertz theory, the force and shape of two steel balls can be calculated as follows:

r : Distance between a plot and center of contactδ : Maximum length of deformationα : Radius of contactR : Half of the radius of the ballsE* : Young’s modulusP0 : Pressure in the middle of contactF : Force


Dynamic collision simulation• Simulating the system considering

to be quasi-static– F will be calculated as explained

– Euler method was used

Updating time

Calculating

forces

Finding accelera

tion

Updating

positions

at

x

m

F

2

2


Different Strains• By assuming that the thickness of

sheet is negligible, we are able to find different strains in the sheet.

FF


Different Strains

r

Top

r

r+Δr

After collision

Before collisionθ

Δr

Before Collision

Side

x

zMaximum Collision


Tensile Stress

r

r+Δr

P0 : Initial perimeterP1 : Perimeter after collisionr : Initial radius r+Δr : Increased radiusεx : Deformation through x-Axis


Two Kinds of Behaviors• Materials may rip because of

tensile or pressing stress

– σz: Pressing

– σy: Tensile

r

dr

r

dr

r

dx zzr

y

Δr

z

x


Two Kinds of Behaviors

Critical Pressure

Pressing stress

m/s

m/s

m/s

m/s


Two Kinds of Behaviorsσ

y

m/s

m/s

m/s

Tensile stress

Critical Pressure


Experimental Setup

Holding the balls


Experimental Setup

Using two electronic magnets to hold and release the balls on time


Experiments• Changing the release height,

calculating the velocity

• Scanning the holes, developing a program with MATLAB to calculate the area and radius of holes

• Compare with theory


Experiments• Paper, thickness of 0.2mm

• Released from different heights

5cm 10cm 15cm 20cm 40cm30cm


Experiments

0 5 10 15 20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Release Height (cm)

Hole

Rad

ius (

cm)


Experiments

• Paper thickness 0.1 mm

10cm 15cm 20cm 30cm 40cm


Experiments

Release Height (cm)


Experiments

• Balsa Wood 2.5mm Thick

10cm 15cm 20cm 30cm

40cm

25cm

35cm


Experiments


Comparison with Theory

• There are 2 main Causes,– Pressure Stress– Tensile Stress

• Calibrating the Critical Stress in Both Causes


Theory Comparison• Paper 0.2 mm thick• The Maximum contact area is smaller than the

experiments radius

Pressing Stress

Velocity (m/s)


Theory Comparison• Paper• Tensile stress radius

Tensile Stress

Velocity (m/s)


Theory Comparison• Balsa Wood• Pressing Stress Radius

Pressing Stress

Velocity (m/s)


Theory Comparison• Balsa Wood• Tensile stress radius

Tensile Stress

Velocity (m/s)


Conclusion• Most of the phenomena happens

because of stresses in the sheet

• Burning is negligible in describing the phenomena, although it exists.

• Materials are different in the stresses they stand– Paper is weak in tensile stress– Balsa wood is weak in pressing stress


References• Mechanics of Materials, Egor P. Popov, 2nd

Edition, 1976.• Contact mechanics, K.L. Johnson, Cambridge

University press, 1985.• Halliday Fundamentals of physics, Halliday-

Resnic-Walker, 1945.• A First Course in Numerical Analysis, Anthony

Ralston-Philip Rabinowitz, 2nd Edition, 2001.

IYPT 2010 Austria, I. R. IranIYPT 2010 Austria, National team of I. R. Iran

Thank you for your attention

IYPT 2010 Austria, I. R. Iran Reporter: Ali Farajollahi 1.

Documents

Transcript of IYPT 2010 Austria, I. R. Iran Reporter: Ali Farajollahi 1.