Steel Balls (1)

8/10/2019 Steel Balls (1)

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IYPT 2010 Austria, I. R. Iran


STEEL BALLS

Reporter: Ali Farajollahi

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The Question

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

Investigate this effect for variousmaterials.

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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

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Initial Observations

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Initial Observation

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Deformation

Waves

Radial rupture

Burning


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Initial Observation

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Aluminum

Tissue

Styrofoam


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Burning (Chemical) orRupture (Physical)?

Temperature rises because of sheetdeflection

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

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Material Strength Background

Stress & Strain

Poissons Ratio

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l l

A

F

F

F

l

l

x y y

x



Static Loaded Balls To be able to simulate the

collision Finding the deformation of two

steel balls under a specific load

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FF



Static Loaded Balls

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Static Loaded Balls According to references, Contact

mechanics and Hertz theory, theforce and shape of two steel ballscan be calculated as follows:

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r : Distance between a plot and center of contact : Maximum length of deformation : Radius of contact R : Half of the radius of the ballsE* : Youngs modulus

P 0 : 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

Updatingtime

Calculatingforces

Findingacceleration

Updating positions

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at

x

m

F 2

2



Different Strains By assuming that the thickness of

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

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FF



Different Strains

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r

Top

r

r+ r

After collision

Before collision

r

Before Collision

Side

x

zMaximum Collision



Tensile Stress

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r

r+ r

P 0 : Initial perimeterP 1 : Perimeter after collisionr : Initial radiusr+ r : Increased radiusx : Deformation through x-Axis



Two Kinds of Behaviors Materials may rip because of

tensile or pressing stress

z: Pressing

y: Tensile

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r

dr

r

dr

r

dx z z r y

r

z

x



Two Kinds of Behaviors

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Critical Pressure

Pressing stress

m/sm/s

m/s

m/s



Two Kinds of Behaviors

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y

m/s

m/s

m/s

Tensile stress

Critical Pressure


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Experimental Setup

Holding the balls

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Experimental Setup

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

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Experiments Changing the release height,

calculating the velocity

Scanning the holes, developing a

program with MATLAB to calculatethe area and radius of holes

Compare with theory

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Experiments Paper, thickness of 0.2mm

Released from different heights

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5cm 10cm 15cm 20cm 40cm30cm


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Experiments

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20 25 30 35 40 45

H o

l e R a

d i u s

( c m

)

Release Height (cm)


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Experiments

Paper thickness 0.1 mm

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10cm 15cm 20cm 30cm 40cm


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Experiments

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Release Height (cm)


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Experiments

Balsa Wood 2.5mm Thick

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10cm 15cm 20cm 30cm

40cm

25cm

35cm


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Experiments

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Comparison with Theory

There are 2 main Causes, Pressure Stress Tensile Stress

Calibrating the Critical Stress inBoth Causes

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

experiments radius

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Velocity (m/s)


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Theory Comparison Paper

Tensile stress radius

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Velocity (m/s)


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Theory Comparison Balsa Wood

Pressing Stress Radius

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Velocity (m/s)


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Theory Comparison Balsa Wood

Tensile stress radius

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Velocity (m/s)


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Conclusion Most of the phenomena happens

because of stresses in the sheet

Burning is negligible in describingthe phenomena, although it exists.

Materials are different in thestresses they stand Paper is weak in tensile stress Balsa wood is weak in pressing stress

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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.

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Steel Balls (1)

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