Lecture Slides: Lecture Mechanics

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The lecture slides of lecture Mechanics of the Modelling Course of Industrial Design of the TU Delft

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Lecture Slides: Lecture Mechanics

  1. 1. P-L-3 Mechanics The Modelling Team Department of Design Engineering Faculty of Industrial Design Engineering Delft University of Technology Challenge the future 1
  2. 2. Contents • Systems • Key components of Mechanical Systems • Spring • Damper • Mass-Spring-Damper Systems • Applications in product design Challenge the future 2
  3. 3. Aim 1 2 3 To develop a basic understanding of the properties of mass-spring-damper system and its applications in product designs To demonstrate that such a system might be modeled so as to provide useful data for designs To communicate with experts in their professional languages Knowledge Insight Communication Challenge the future 3
  4. 4. Systems Challenge the future 4
  5. 5. Repetition: What is a system? System System consists of a set of interacting or interdependent system components (or subsystems) -Structure & interconnectivity -Boundary -Input & Output -Surroundings Challenge the future 5
  6. 6. Example of a system … Saddle Tyre Tyre Courtesy of http://www.cycle9.com/carrboro-chapel-hill-store/batavus-bicycles-lets-go-dutch/ Courtesy of http://www.batavus.nl Challenge the future 6
  7. 7. System response Velocity in the  vertical direction Displacement in the  vertical direction Inputs Outputs Boundary Courtesy of http://www.batavus.nl Courtesy of http://reviews.mtbr.com/blog/tag/Cycle-Solutions/ Challenge the future 7
  8. 8. System response Velocity in the  vertical direction Displacement in the  vertical direction Inputs Outputs Boundary Courtesy of http://www.batavus.nl Courtesy of http://www.utilitycycling.org/2009/08/cycling-services/ Challenge the future 8
  9. 9. System response Velocity in the  vertical direction Inputs Outputs Boundary Displacement in the  vertical direction Courtesy of http://www.batavus.nl Courtesy of http://www.utilitycycling.org/2009/08/cycling-services/ Challenge the future 9
  10. 10. What are components of the bike’s model? Saddle Tyre Tyre Courtesy of http://www.batavus.nl Challenge the future 10
  11. 11. Components - Spring Challenge the future 11
  12. 12. Component - Spring Spring 2 meters 400 N A spring is an elastic object used to store mechanical energy Ref. http://en.wikipedia.org/wiki/Spring_(device) Challenge the future 12
  13. 13. Model a spring Courtesy of http://en.wikipedia.org/wiki/Spring_(device) Challenge the future 13
  14. 14. Rehearsal: Bungee jumping Courtesy of http://www.youtube.com/watch?v=sriUfHuHSXY Challenge the future 14
  15. 15. Components Spring  Human. ► Earth Bungee jumping system  Air. Challenge the future 15
  16. 16. Cause-effect Cause Mass of the person Gravity Spring Air friction Pull the person back Slow down the motion Effect Stretch the spring Inertia force 0 =0 0 0 0 1 0 1 Challenge the future 16
  17. 17. Modelling using Maple® Challenge the future 17
  18. 18. The solution Challenge the future 18
  19. 19. The solution Displacement Velocity Acceleration Challenge the future 19
  20. 20. The solution Displacement Velocity Acceleration The amplitude is  getting smaller,  Why?  Challenge the future 20
  21. 21. Is it different? - Trampoline Courtesy of http://www.youtube.com/watch?v=pSazagYBCM8 Challenge the future 21
  22. 22. Components Spring  Human. ► Earth Trampoline system  Air. Challenge the future 22
  23. 23. Cause-effect Cause Mass of the person Gravity Spring Air friction Push the person back Slow down the motion Effect Stretch the spring Inertia force 0 0 0 =0 0 0 0 1 0 1 Challenge the future 23
  24. 24. Modelling using Maple® Challenge the future 24
  25. 25. The solution Challenge the future 25
  26. 26. The solution Displacement Velocity Acceleration Challenge the future 26
  27. 27. The solution The amplitude is also  getting smaller. The  same reason?  Displacement Speed Acceleration Challenge the future 27
  28. 28. Bungee jumping vs Trampoline 0 0 Bungee jumping =0 0 0 =0 Trampoline Challenge the future 28
  29. 29. Components - Damper Challenge the future 29
  30. 30. Component - Damper Damper A damping elements resists relative velocity across them Shock absorber with internal reservoir. The components are: A - rod, B - the piston with seals, C - the cylinder, D - oil reservoir, E - floating piston, F - air chamber. Challenge the future 30 Courtesy of http://en.wikipedia.org/wiki/Shock_absorber
  31. 31. Model a damper Challenge the future 31
  32. 32. Case study: The slow closing toilet seat Courtesy of http://www.youtube.com/watch?v=tBK1rewI8vQ Challenge the future 32
  33. 33. System components The  toilet  seat Challenge the future 33
  34. 34. Cause-effect Cause Mass and geometry of the lid Damper Gravity Effect Inertia moment Slow down the motion The lid goes down /2=0 Challenge the future 34
  35. 35. Modelling using Maple® Challenge the future 35
  36. 36. Solving the model Challenge the future 36
  37. 37. The solution Angular displacement /2 Angular velocity Angular acceleration Challenge the future 37
  38. 38. The mass-spring-damper system Challenge the future 38
  39. 39. The mass-spring-damper system Courtesy of http://www.taiwan-bicycle.com.tw/Pd_Detail.asp?FKindNO=F000004&SKindNO=S000671&ItemNo=I00002896 Challenge the future 39
  40. 40. The mass-spring-damper system Regarding material Spring Damper Elasticity Young's Modulus Poisson's Ratio Anisotropy  Damping Coefficient Courtesy of http://www.taiwan-bicycle.com.tw/Pd_Detail.asp?FKindNO=F000004&SKindNO=S000671&ItemNo=I00002896 Challenge the future 40
  41. 41. The mass-spring-damper system Courtesy http://www.airliners.net/photo/Airbus-Industrie/Airbus-A380-861/1169635/L/ Challenge the future 41
  42. 42. Case study: The skateboard The movement in the vertical direction The World largest  skateboard Designer:  Rob Dyrde Courtesy of http://skateboardingmagazine.com/blog/2009/02/01/the-worlds-largest-skateboard/ Challenge the future 42
  43. 43. System components Spring Neglect Air Damper The skate board Neglect, why? Earth Person Challenge the future 43
  44. 44. System Cause Mass of the board Damper Spring Effect Inertia force Slow down the motion Drag the mass back =0 Challenge the future 44
  45. 45. Modelling using Maple® Challenge the future 45
  46. 46. Solution The step Displacement Velocity Acceleration Challenge the future 46
  47. 47. Discussion C=50 Displacement Velocity Acceleration K=1000 K=100 K=10 Challenge the future 47
  48. 48. Discussion K=100 Displacement Velocity Acceleration C=200 C=50 C=0.1 Challenge the future 48
  49. 49. Consider human also as a spring and a damper, can we model the shock to the head? d 2 x1 (t ) dx (t ) dx (t )  m1  k1 ( x1 (t )  x2 (t ))  c1 ( 1  2 )  0 dt 2 dt dt d 2 x2 (t ) dx (t ) dx (t ) dx (t ) dy (t )  m2  k1 ( x1 (t )  x2 (t ))  c1 ( 1  2 )  k2 ( x2 (t )  y (t ))  c2 ( 2  )0 dt 2 dt dt dt dt Challenge the future 49
  50. 50. The natural frequency 0  d 2 x(t ) dx(t ) m c  kx(t )  0 2 dt dt   k m c 2 mk d 2 x(t ) dx(t ) 2  20  0 x(t )  0 2 dt dt Challenge the future 50
  51. 51. The damping ratio Challenge the future 51
  52. 52. Resonance Challenge the future 52
  53. 53. Case study: Tacoma Narrow bridge Courtesy of http://www.youtube.com/watch?v=P0Fi1VcbpAI Challenge the future 53
  54. 54. d 2 x(t ) dx (t ) 2  20  0 x (t )  f step dt dt Settling time band Mp Steady-state error Interpret the response of a step function  xss xmax  x ss A   ln A    ln A  2 n  Challenge the future  tp 1  2 54 2
  55. 55. Interpret the response - 2 Example: If we know the response of a mass-spring-damper system regarding a step function F(t), can we extract parameter c and k from the response? x(t) Response xss  1 k t p  3.28 F(t) m xmax  1.3723 c Maximum overshoot ratio Damping ratio   ln A Damping ratio    ln A  2 Natural frequency From definitions 0  n  k m Maximum overshoot ratio A  2.686 xss xmax  x ss A 2  Natural frequency tp 1    2 c 2 mk   0.3 n  1 Suppose m=1kg k  1 kg/m, c  0.6 Ns/m Challenge the future 55
  56. 56. Industrial applications Challenge the future 56
  57. 57. The pogo-stick Question? Where is the damper? Courtesy of http://connect.in.com/pogo/photos-1-1-1-9ed7a7cecf4cb85de07b7f05697bfe43.html Challenge the future 57
  58. 58. The suspension systems (ref/auto.howstuffworks.com/) Courtesy of http://auto.howstuffworks.com/car-suspension4.htmAI Challenge the future 58
  59. 59. The door closer (ref. /www.usbuildersupply.com) Courtesy of http://www.usbuildersupply.com/index.php/hardware-basics/door-closer-overview/ Challenge the future 59
  60. 60. Thank You! Challenge the future 60

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