T1 1 rolling resistance

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T1 1 rolling resistance

  1. 1. Erasmus LLP Intensive Programme ROLLING RESISTANCE Eddy Versonnen Eddy.versonnen@kdg.be KdG University College AntwerpPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 1
  2. 2. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 2
  3. 3. Erasmus LLP Intensive Programme I. INTRODUCTION FUNCTIONS OF PNEUMATIC TIRES: - SUPPORT THE WEIGHT OF THE VEHICLE - CUSHION THE VEHICLE OVER SURFACE IRREGULARITIES - PROVIDE SUFFICIENT TRACTION FOR DRIVING AND BREAKING - PROVIDE ADEQUATE STEERING CONTROL AND DIRECTIONAL STABILITYPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 3
  4. 4. Erasmus LLP Intensive Programme I. INTRODUCTION THE CRITICAL PERFORMANCES OF A VEHICLE: - DRIVING - BRAKING - STABILITY - RIDE COMFORT - TRAVELING ARE RELATED TO PNEUMATIC TIRESPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 4
  5. 5. Erasmus LLP Intensive Programme I. INTRODUCTION GROUND FORCES ON THE TIRES WHEN THE VEHICLE DRIVES FORWARD WITHOUT SIDE FORCE: FZ : NORMAL FORCE FX : TRACTIVE FORCE TA = FX.R : TRACTIVE MOMENT MF = FZ.a : ROLLING RESISTANCE MOMENT R : ROLLING RADIUS a : FORWARD MOVING DISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 5
  6. 6. Erasmus LLP Intensive Programme I. INTRODUCTION GROUND FORCES ON THE TIRES WITHOUT SIDE FORCE UNDER BRAKING: FZ : NORMAL FORCE FX : BRAKING FORCE TB = FX.R : BRAKING MOMENT MF = FZ.a : ROLLING RESISTANCE MOMENT R : ROLLING RADIUS a : FORWARD MOVING DISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 6
  7. 7. Erasmus LLP Intensive Programme I. INTRODUCTION THE VEHICLE CHANGES DIRECTION OR LATERAL FORCE ON THE VEHICLE: - THE LATERAL ELASTICITY OF THE TIRE INCREASES GRADUALLY - LATERAL DEFORMATION OF THE TIRE - GROUND CONTACT PATCHPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 7
  8. 8. Erasmus LLP Intensive Programme I. INTRODUCTION THE VEHICLE CHANGES DIRECTION OR LATERAL FORCE ON THE VEHICLE: - DISTANCE e : PNEUMATIC TRAIL BETWEEN THE RESULTANT OF THE GROUND LATERAL FORCES AND THE CENTER OF THE CONTACT PATCH - THE MOMENT Fy.e DETERMINS THE SELF ALIGNMENT OF THE TIREPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 8
  9. 9. Erasmus LLP Intensive Programme I. INTRODUCTION COMMONLY USED AXIS SYSTEM RECOMMENDED BY SAE INTERNATIONAL:Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 9
  10. 10. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 10
  11. 11. Erasmus LLP Intensive Programme II. VERTICAL DYNAMICS OF PNEUMATIC TIRES VERTICAL STIFFNESS AND DAMPING CHARACTERISTICS OF TIRES - PNEUMATIC TIRES: CAN CUSHION OVER SURFACE IRREGULARITIES - THE CUSHIONING CHARACTERISTICS HAVE A DIRECT RELATIONSHIP WITH THE VERTICAL STIFFNESS AND DAMPING OF TIRES F = KS.δ F: LOAD KS: STATIC STIFFNESS δ: DEFLECTIONPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 11
  12. 12. Erasmus LLP Intensive Programme II. VERTICAL DYNAMICS OF PNEUMATIC TIRES VERTICAL STIFFNESS AND DAMPING CHARACTERISTICS OF TIRES LOAD- DEFLECTION RELATIONSHIP OF A TIRE: - FZ1: FORCE REQUIRED TO MAKE THE TIRE PRODUCE A DEFLECTION δ - FZ2: FORCE TO MAKE THE TIRE RESTORE FROM THE SAME DEFLECTION THE CLOSE-UP AREA REPRESENTS THE DISSIPATIVE POWER OF A ROLLING TIREPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 12
  13. 13. Erasmus LLP Intensive Programme II. VERTICAL DYNAMICS OF PNEUMATIC TIRES VERTICAL STIFFNESS AND DAMPING CHARACTERISTICS OF TIRES - ESPECIALLY THE RUBBER OF THE CONTACT PATCH OF THE TIRE IS DEFORMED - 60 TO 70% OF THE POWER THE DISSIPATION IS LOCATED AT THE PATCH OF THE TIRE CONTACTPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 13
  14. 14. Erasmus LLP Intensive Programme II. VERTICAL DYNAMICS OF PNEUMATIC TIRES VERTICAL STIFFNESS AND DAMPING CHARACTERISTICS OF TIRES - LESS DEFORMATION OF THE TIRE CONTACT PATCH REDUCES THE DISSIPATIVE POWER OF A ROLLING TIRE - A REDUCTION OF THE DEFORMATION OF THE TIRE CONTACT PATCH ALSO LEADS TO A REDUCTION OF THE COEFFICIENT OF ROAD ADHESION ON A WET ROAD SURFACEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 14
  15. 15. Erasmus LLP Intensive Programme II. VERTICAL DYNAMICS OF PNEUMATIC TIRES VERTICAL STIFFNESS AND DAMPING CHARACTERISTICS OF TIRES Kd: DYNAMIC STIFFNESS, VARIES FROM KS WITH THE FREQUENCY OF THE DYNAMIC LOAD - Kd DECREASES WITH THE INCREASE OF THE EXCITATION FREQUENCY (10 to 15%) - INFLATION PRESSURE HAS A NOTICEABLE INFLUENCE ON THE TIRE STIFFNESS (THE COMPRESSED AIR SUPPORTS 85% OF THE TIRE LOAD)Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 15
  16. 16. Erasmus LLP Intensive Programme II. VERTICAL DYNAMICS OF PNEUMATIC TIRES INFLUENCE OF THE ROLLING RESISTANCE ON THE FUEL CONSUMPTION IN FUNCTION OF THE SPEED OF THE VEHICLE INFLUENCE OF THE ROLLING RESISTANCE ON THE FUEL CONSUMPTION OF THE VEHICLE INFLUENCE OF THE ROLLING RESISTANCE ON THE POWER DISSIPATION OF THE VEHICLEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 16
  17. 17. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 17
  18. 18. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE - DUE TO THE DEFORMATION OF THE TIRE AT THE TIRE/ROAD INTERFACE - TIRE DEFORMATION CONSUMES ENERGY - AN UNEQUAL FORCE IS NEEDED DURING COMPRESSION AND ELASTIC RECOVARY - THEREFORE: THE NORMAL PRESSURE DISTRIBUTION OVER THE TIRE/ROAD CONTACT PATCH IS NOT UNIFORMPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 18
  19. 19. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE - THE NORMAL FORCE IS HIGHER IN THE LEADING HALF OF THE CONTACT PATCH THAN IN THE TRAILING HALF - THE NORMAL FORCE PRODUCES A MOMENT ABOUT THE AXIS OF ROTATION OF THE TIRE - ROLLING RESISTANCE MOMENT: Mf = Fz.aPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 19
  20. 20. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE - THE DRIVING FORCE Fax , APPLIED TO THE WHEEL PRODUCES A MOMENT TO BALANCE THE ROLLING RESISTANCE MOMENT: Fax . r = Mf Fax . r = Fz.a Fax = Fz . a/rPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 20
  21. 21. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE f: ROLLING RESISTANCE CEFFICIENT (NONDIMENSIONAL CEFFICIENT) SET f = a/r THEN Fax = Fz.f OR f = Fax/Fz THE ROLLING RESISTANCE CHANGES LINEARLY WITH THE NORMAL FORCE ON THE WHEEL Ff = f.FzPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 21
  22. 22. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE IN THE ACTUAL CASE OF A ROLLING WHEEL, BOTH THE WHEEL AND THE SURFACE WILL UNDERGO DEFORMATIONS DUE TO THEIR PARTICULAR ELASTIC CHARACTERISTICS. AT THE CONTACT POINTS, THE WHEEL FLATTENS OUT WHILE A SMALL TRENCH IS FORMED IN THE SURFACE.Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 22
  23. 23. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE EXPERIMENTS SHOW: ROLLING RESISTANCE IS: - PROPORTIONAL TO THE TIRE DEFORMATION - INVERSELY PROPORTIONAL TO THE RADIUS OF THE LOADED TIRE ACCORDING TO THE US STANDARD: - IF v<50 km/h : f = 0,0165 - IF v>50 km/h : f = 0,0165 [1 + 00,1.(v – 50)]Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 23
  24. 24. Erasmus LLP Intensive Programme III. ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 24
  25. 25. Erasmus LLP Intensive Programme III. ROLLING RESISTANCE INFLUENCE THE INFLATION PRESSURE AND THE NORMAL LOAD FN ON THE WHEELS ON THE ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 25
  26. 26. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 26
  27. 27. Erasmus LLP Intensive Programme IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN IN ACTUAL VEHICLE STRUCTURE: - THERE IS A TOE-IN ANGLE ON THE FRONT WHEEL - A TOE-IN RESISTANCE ACTING ON THE FRONT WHEEL - δvo = TOE-IN ANGLE OF THE FRONT WHEEL ON ONE SIDE - Fδv = SIDE FORCE DUE TO THE TIRE LATERAL DEFORMATION CAUSED BY THE ANGLE δvoPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 27
  28. 28. Erasmus LLP Intensive Programme IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN Fδv = Cr.δv0 Cr = THE CORNERING STIFFNESS OF THE TIRE THE TOE-IN RESISTANCE, ACTING ON THE WHEELS: Fv = 2.Fδv.sinδv0 FOR SMALL ANGLES: sinδv0 = δv0 Fv = 2.Fδv.δv0 Fv = 2.Cr.δv0.δv0 Fv = 2.Cr.δ²v0Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 28
  29. 29. Erasmus LLP Intensive Programme IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN fδ IS DEFINED AS THE TOE-IN RESISTANCE COEFFICIENT fδ = Cr/Fz.δ²v0 OR Cr.δ²v0 = fδ.Fz THE TOE-IN RESISTANCE WILL BE EXPRESSED AS: Fv = 2.fδ.FzPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 29
  30. 30. Erasmus LLP Intensive Programme IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN ROLLING RESISTANCE IN FUNCTION OF THE TIRE TOE-INPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 30
  31. 31. Erasmus LLP Intensive Programme IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN ROLLING RESISTANCE FORCE IN FUNCTION OF THE CAMBER γ AND THE VEHICLE SPEEDPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 31
  32. 32. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 32
  33. 33. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL THE ADDITIONAL ROLLING RESISTANCE OF A TURNING WHEEL DEPENDS ON: - THE VELOCITY OF THE VEHICLE - THE TURNING RADIUS - THE VEHICLE PARAMETERS THE ROLLING RESISTANCE COEFFICIENT fR OF A TURNING WHEEL: fR = f + ΔfPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 33
  34. 34. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL δ0 : STEERING ANGLE αF : SLIP ANGLE OF THE FRONT TIRES αR : SLIP ANGLE OF THE REAR TIRES Fyf and Fyr : CORNERING FORCES TO BALANCE THE CENTRIFUGAL FORCE OF THE VEHICLE WHEN STEERING m : MASS OF THE VEHICLE v : VELOCITY OF THE VEHICLE R : TURNING RADIUSPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 34
  35. 35. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL CORNERING FORCE AT THE FRONT WHEEL TO BALANCE THE CENTRIFUGAL FORCE OF THE VEHICLE WHEN STEERING:Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 35
  36. 36. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL THE ADITIONAL RESISTANCE, APPLIED ON THE FRONT WHEELS:Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 36
  37. 37. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL CORNERING FORCE AT THE REAR WHEEL TO BALANCE THE CENTRIFUGAL FORCE OF THE VEHICLE WHEN STEERING:Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 37
  38. 38. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL THE ADITIONAL RESISTANCE, APPLIED ON THE REAR WHEELS:Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 38
  39. 39. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL THE ADITIONAL ROLLING RESISTANCE COEFFICIENT UNDER THE CONDITIONING OF VEHICLE STEERING: THE ADITIONAL ROLLING RESISTANCE COEFFICIENT - INCREASES WITH THE VEHICLE VELOCITY AND THE STEARING ANGLE - DECREASES WITH THE TURNING ANGLEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 39
  40. 40. Erasmus LLP Intensive Programme V. ROLLING RESISTANCE OF A TURNING WHEEL INCREASE OF THE ROLLING RESISTANCE AT TURNING WHEELS LATERAL ACCELERATIONPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 40
  41. 41. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 41
  42. 42. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT THE TRACTIVE FORCE (OR BRAKING FORCE), DEVELLOPED BY A PNEUMATIC TIRE ON THE TIRE-GROUND CONTACT PATCH IS LIMITED TO THE CRITICAL COEFFICIENT OF ROAD ADHESION THE MAXIMUM ADHESION FORCE OF A TIRE ON A HARD SURFACE: Fφ = FZ.φ FZ: NORMAL FORCE ON THE WHEEL DURING DRIVING OR BRAKING φ: ADHESION COEFFICIENT (VARIES WITH THE STATE OF THE TIRE ROLLING OR SLIPPING)Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 42
  43. 43. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT THE TIRE WILL BE SLIPPING WHEN : MT > Fφ.rd MT: DRIVING TORQUE ON THE WHEEL Fφ.rd : TORQUE, PRODUCED BY THE ADHESION FORCE AROUND THE WHEEL CENTER rd: EFFECTIVE ROLLING RADIUSPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 43
  44. 44. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT THE TIRE WILL BE SKIDDING WHEN : Mb > Fφ.rd Mb: BRAKING TORQUE ON THE WHEEL Fφ.rd : TORQUE, PRODUCED BY THE ADHESION FORCE AROUND THE WHEEL CENTER rd: EFFECTIVE ROLLING RADIUSPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 44
  45. 45. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT WHEN: ω.rd = vX THERE WILL BE NO RELATIVE MOTION AT THE TIRE-GROUND CONTACT POINT THE TIRE IS IN STATE OF PURE ROLLING ω: ANGULAR SPEED OF THE ROLLING TIRE ω.rd : LONGITUDINAL SPEED OF THE TIRE TO THE TIRE-GROUND CONTACT POINT vX: LINEAR SPEED OF THE TIRE RELATIVE TO THE GROUNDPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 45
  46. 46. Erasmus LLP Intensive Programme VI. LONGITUDONAL ADHESION COEFFICIENT WHEN: ω.rd > vX THERE IS A NEGATIVE LINEAR VELOCITY AT THE TIRE-GROUND CONTACT POINT THE TIRE IS ROLLING AND SLIPPING AND DEVELLOPES A LONGITUDONAL TRACTIVE FORCE ω: ANGULAR SPEED OF THE ROLLING TIRE ω.rd : LONGITUDINAL SPEED OF THE TIRE TO THE TIRE-GROUND CONTACT POINT vX: LINEAR SPEED OF THE TIRE RELATIVE TO THE GROUNDPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 46
  47. 47. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT WHEN: ω.rd < vX THERE IS A POSITIVE LINEAR VELOCITY AT THE TIRE-GROUND CONTACT POINT THE TIRE IS ROLLING AND SLIDING AND DEVELLOPES A LONGITUDONAL BRAKING FORCE ω: ANGULAR SPEED OF THE ROLLING TIRE ω.rd : LONGITUDINAL SPEED OF THE TIRE TO THE TIRE-GROUND CONTACT POINT vX: LINEAR SPEED OF THE TIRE RELATIVE TO THE GROUNDPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 47
  48. 48. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT TO ACCURATELY DESCRIBE TIRE SLIP IN A BRAKING MANEUVER LONGITUDINAL SKID, Sb IS DEFINED AS: ω.rd : LONGITUDINAL SPEED OF THE TIRE TO THE TIRE-GROUND CONTACT POINT vX: LINEAR SPEED OF THE TIRE RELATIVE TO THE GROUND Sb = 0% → THE TIRE IS PURELY ROLLING Sb = 100% → THE TIRE IS PURELY SKIDDING 0% < Sb < 100% → THE TIRE IS ROLLING AND SKIDDINGPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 48
  49. 49. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT THE TIRE SLIP IN A TRACTIVE (DRIVING) MANEUVER: ω.rd : LONGITUDINAL SPEED OF THE TIRE TO THE TIRE-GROUND CONTACT POINT vX: LINEAR SPEED OF THE TIRE RELATIVE TO THE GROUND Sa = 0% → THE TIRE IS PURELY ROLLING Sa = 100% → THE TIRE IS PURELY SPINNING 0% < Sa < 100% → THE TIRE IS ROLLING AND SLIPPINGPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 49
  50. 50. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT DRIVING AND BRAKING ARE OPOSITE IN LONGITUDINAL DIRECTION → ONE SINGLE INDEX: THE SLIP RATIO S CAN BE USED TO EXPRESS BOTH LONGITUDINAL SLIP AND LONGITUDINAL SKIP ZERO = THE DEVISION VALUEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 50
  51. 51. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT 0% < S < 100% → BRAKING MANEUVER S = 100% → THE WHEEL LOCKS COMPLETELY -100% < S < 0% → DRIVING MANEUVER S = -100% → THE WHEELS ARE SPINNING AT A HIGH ANGULAR SPEED, BUT THE VEHICLE DOES NOT MOVE FORWARDPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 51
  52. 52. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT RELATIONSHIP BETWEEN THE COEFFICIENT OF ROAD ADHESION AND LONGITUDINAL SLIP, BASED ON AVAILABLE EXPERIMENTAL DATA: → MAXIMUM TRACTIVE OR BRAKING EFFORT WHEN THE TIRE IS ROLLING AND SLIPPING WITH: 15% < | S | < 30%Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 52
  53. 53. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT 0% < |S| < 15% → THE VALUE OF φ INCREASES LINEAR WITH S 15% < |S| < 30% → THE VALUE OF φ REACHES REACHES THE MAXIMUM (THE PEAK COEFFICIENT OF ROAD ADHESION) 15% < |S| < 30% → THE VALUE OF φ GRADUALLY FALLS WITH THE INCREASE OF S |S| = 100% → THE SLIDING COEFFICIENT OF ADHESIONPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 53
  54. 54. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT φP = THE PEAK VALUE OF THE COEFFICIENT OF ROAD ADHESIONI IT IS: 1,2 TIMES THE VALUE OF THE SLIDING VALUE ON A DRY SURFACE 1,3 TIMES THE VALUE OF THE SLIDING VALUE ON A WET SURFACEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 54
  55. 55. Erasmus LLP Intensive Programme VI. LONGITUDINAL ADHESION COEFFICIENT THE COFFICIENT OF ROAD ADHESION DEPENDS ON: - THE ROAD TEXTURE AND SURFACE - THE TIRE STRUCTURE - THE TREAD PATTERN - THE INFLATION PRESSURE - THE NORMAL LOADING ON THE WHEELS - THE TRAVEL SPEED OF THE VEHICLEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 55
  56. 56. Erasmus LLP Intensive Programme VI. LONGITUDONAL ADHESION COEFFICIENT THE TIRE ADHESION COEFFICIENT FORCE IS HIGHER: - IF THE AREA OF THE TIRE-ROAD CONTACT IS LARGE - ON DRY SURFACES THAN ON WET SURFACES - ON A TIRE WITH A WIDE TREAD THAN ON A TIRE WITH A NARROW TREAD - ON A RADIAL TIRE THAN ON A BIAS TIRE - FOR A TIRE WITH A LOW INFLATION PRESSURE THAN FOR A TIRE WITH A HIGH INFLATION PRESSURE - AT LOW VEHICLE SPEED THAN AT HIGH VEHICLE SPEEDPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 56
  57. 57. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 57
  58. 58. Erasmus LLP Intensive Programme VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES AS MENTIONED BEFORE: THE ROLLING RESISTANCE IS INFLUENCED BY: THE FORWARD SPEED,THE SURFACE ADHESION AND THE RELATIVE MICRO-SLIDING OTHER FACTORS ARE: - THE WHEEL RADIUS: LARGER WHEELS HAVE LESS ROLLING RESISTANCE BECAUSE (1) THEY WON’T DROP AS MUCH INTO A SMALLER HOLE AS A SMALL WHHEEL, (2) THEY HAVE GREATER LAVERAGE FOR LIFTING A WHEEL OVER BUMPS, (3) THERE IS LESS DEFORMATION OF THE TIRE AT THE CONTACT PATCH WITH THE GROUND, (4) THEY HAVE LESS WIND RESISTANCE DUE TO LOWER SPINNING SPEEDSPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 58
  59. 59. Erasmus LLP Intensive Programme VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES BUT THE ENERGY TO GET LARGER WHEELS UP TO SPEED IS GREATER - TIRE COMPOSITION: MATERIAL - DIFFERENT FILLERS AND POLYMERS CAN IMPROVE TRACTION WHILE REDUCING HYSTERESIS. THE REPLACEMENT OF SOME CARBON BLACK WITH HIGHER - PRICED SILICA–SILANE LEADS TO A REDUCTION OF THE ROLLING RESISTANCE - EXTEND OF INFLATION - LOWER PRESSURE IN TIRES RESULTS IN MORE FLEXING OF THE SIDEWALLS AND HIGHER ROLLING RESISTANCE. THIS ENERGY CONVERSION IN THE SIDEWALLS INCREASES THE RESISTANCE AND CAN ALSO LEAD TO OVERHEATINGPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 59
  60. 60. Erasmus LLP Intensive Programme VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES - OVER INFLATING TIRES (SUCH AS BICYCLE TIRES): MAY NOT LOWER THE OVERALL ROLLING RESISTANCE AS THE TIRE MAY SKIP AND HOP OVER THE ROAD SURFACE AND TRACTION IS SACRIFICED, AND THE OVERALL ROLLING FRICTION MAY NOT BE REDUCED AS THE WHEEL ROTATIONAL SPEED CHANGES AND SLIPPAGE INCREASESPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 60
  61. 61. Erasmus LLP Intensive Programme ROLLING RESISTANCE I. INTRODUCTION II. VERTICAL DYNAMICS OF PNEUMATIC TIRES III. ROLLING RESISTANCE IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN V. ROLLING RESISTANCE OF A TURNING WHEEL VI. LONGITUDINAL ADHESION COEFFICIENT VII. FACTORS THAT AFFECT THE ROLLING RESISTANCE OF TIRES VIII. EFFECTS OF ROLLING RESISTANCEPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 61
  62. 62. Erasmus LLP Intensive Programme VIII. EFFECTS OF ROLLING RESISTANCE - ROLLING FRICTION GENERATES HEAT AND SOUND (VIBRATIONAL ENERGY) MECHANICAL ENERGY IS CONVERTED TO THESE FORMS OF ENERGY DUE TO THE. (EXAMPLE: MOVEMENT OF MOTOR VEHICLE TIRES ON THE ROADWAY) THE SOUND GENERATED BY TIRES AS THEY ROLL (ESPECIALLY NOTICEABLE AT HIGHWAY SPEEDS) IS MOSTLY DUE TO THE PERCUSSION OF THE TIRE TREADS, AND THE COMPRESSION (AND SUBSEQUENT DECOMPRESSION) OF THE AIR TEMPORARLY CAPTURED WITHIN THE TREADS.Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 62
  63. 63. Erasmus LLP Intensive Programme VIII. EFFECTS OF ROLLING RESISTANCE - ROLLING FRICTION GENERATES HEAT AND SOUND (VIBRATIONAL ENERGY) THE GENERATED HEAT RAISES THE TEMPERATURE OF THE FRICTIONAL SURFACE. THIS INCREASES THE COEFFICIENT OF FRICTION. THIS IS WHY AUTOMOBILE RACING TEAMS PREHEAT THEIR TIRESPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 63
  64. 64. Erasmus LLP Intensive Programme THANK YOU FOR YOUR ATTENTIONPowering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 64
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