1 / 35

Steel balls

3. Steel balls. Reporter: Ali Farajollahi. 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

braeden
Download Presentation

Steel balls

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3 Steel balls Reporter: Ali Farajollahi

  2. 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.

  3. 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

  4. Initial Observations

  5. Initial Observation Burning Waves Radial rupture Deformation

  6. Initial Observation Tissue Aluminum Styrofoam

  7. 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

  8. Material Strength Background • Stress & Strain • Poisson’s Ratio F Δl l x y F

  9. Static Loaded Balls • To be able to simulate the collision… • Finding the deformation of two steel balls under a specific load F F

  10. Static Loaded Balls

  11. 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 contact δ: Maximum length of deformation α : Radius of contact R : Half of the radius of the balls E* : Young’s modulus P0 : Pressure in the middle of contact F : Force

  12. Dynamic collision simulation • Simulating the system considering to be quasi-static • F will be calculated as explained • Euler method was used

  13. Different Strains • By assuming that the thickness of sheet is negligible, we are able to find different strains in the sheet. F F

  14. Different Strains Before Collision After collision θ r Before collision r r+Δr Δr Maximum Collision z Top x Side

  15. Tensile Stress r r+Δr P0 : Initial perimeter P1 : Perimeter after collision r : Initial radius r+Δr : Increased radius εx : Deformation through x-Axis

  16. Two Kinds of Behaviors • Materials may rip because of tensile or pressing stress • σz: Pressing • σy: Tensile Δr

  17. Two Kinds of Behaviors Pressing stress m/s Critical Pressure m/s m/s m/s

  18. Two Kinds of Behaviors Tensile stress m/s m/s σy m/s Critical Pressure

  19. Experimental Setup Holding the balls

  20. Experimental Setup Using two electronic magnets to hold and release the balls on time

  21. 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

  22. Experiments • Paper, thickness of 0.2mm • Released from different heights 15cm 20cm 30cm 40cm 5cm 10cm

  23. Experiments

  24. Experiments • Paper thickness 0.1 mm 10cm 15cm 20cm 30cm 40cm

  25. Experiments Release Height (cm)

  26. Experiments • Balsa Wood 2.5mm Thick 10cm 15cm 20cm 25cm 30cm 35cm 40cm

  27. Experiments

  28. Comparison with Theory • There are 2 main Causes, • Pressure Stress • Tensile Stress • Calibrating the Critical Stress in Both Causes

  29. Theory Comparison • Paper 0.2 mm thick • The Maximum contact area is smaller than the experiments radius Pressing Stress Velocity (m/s)

  30. Theory Comparison • Paper • Tensile stress radius Tensile Stress Velocity (m/s)

  31. Theory Comparison • Balsa Wood • Pressing Stress Radius Pressing Stress Velocity (m/s)

  32. Theory Comparison • Balsa Wood • Tensile stress radius Tensile Stress Velocity (m/s)

  33. 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

  34. 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.

  35. Thank you for your attention

More Related