Rolling Resistance

Erasmus LLP Intensive Programme

ROLLING RESISTANCE Eddy Versonnen [email protected] KdG Univer University sity College College Antw Antwerp erp

Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011

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ROLLING RESIST RESISTANCE ANCE 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 RESISTANCE


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I. INTRODUCTION FUNCTIONS OF PNEUMA PNEUM ATIC TIRES: TIR ES: - SUPPORT SUPPORT THE WEIGHT WEIGHT OF THE VEHICLE VEHICLE - CUSHION CUSHION THE VEHICLE VEHICLE OVER OVER SURFAC SURFACE E IRREGULAR IRREGULARITIE ITIES S - PROVIDE PROVIDE SUFFICI SUFFICIENT ENT TRACTIO TRACTION N FOR DRIVING DRIVING AND AND BREAKING BREAKING - PROVIDE ADEQUA ADEQUATE TE STEERING CONTROL AND DIRECTIONA DIRECTIONAL L STABILITY


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I. INTRODUCTION THE CRITICAL PERFORMANCES OF A VEHICLE: - DRIVING - BRAKING - STABILITY - RIDE COMFORT - TRAVELING ARE RELATED TO PNEUMATIC TIRES


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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 DISTANCE


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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 DISTANCE


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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 PATCH


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I. INTRODUCTION THE VEHICLE CHANGES DIRECTION OR LATERAL FORCE ON THE VEHICLE: - DISTANCE DISTANCE e : PNEUMATIC PNEUMATIC TRAIL BETWEEN THE RESULTANT OF THE GROUND LATERAL LATERAL FORCES FORC ES AND THE CENTER OF THE CONTACT PATCH - THE MOME MOMENT NT Fy.e DETERMINS THE SELF ALIGNMENT OF THE TIRE


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I. INTRODUCTION COMMONLY COMMONLY USED AXIS SYSTEM RECOMMENDED BY SAE INTERNATIONAL:


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ROLLING RESIST RESISTANCE ANCE 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 RESISTANCE


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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: DEFLECTION


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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 TIRE


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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 CONTACT


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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 SURFACE


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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)


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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 VEHICLE


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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 RESISTANCE


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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 UNIFORM Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011

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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.a


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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/r


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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.Fz


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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.


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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)]


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III. ROLLING RESISTANCE


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III. ROLLING RESISTANCE INFLUENCE THE INFLATION PRESSURE AND THE NORMAL LOAD FN ON THE WHEELS ON THE ROLLING RESISTANCE


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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 δvo


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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 .δ²v0 Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011

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IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN f δ IS DEFINED AS THE TOE-IN RESISTANCE COEFFICIENT f δ = C /F r z.δ²v0 OR

Cr .δ²v0 = f δ.Fz

THE TOE-IN RESISTANCE WILL BE EXPRESSED AS:

Fv = 2.f δ.Fz Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011

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IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN

ROLLING RESISTANCE IN FUNCTION OF THE TIRE TOE-IN


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IV. ROLLING RESISTANCE OF A TIRE WITH TOE-IN

ROLLING RESISTANCE FORCE IN FUNCTION OF THE CAMBER γ AND THE VEHICLE SPEED


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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 f R OF A TURNING WHEEL:

f R = f + Δf


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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 RADIUS


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V. ROLLING RESISTANCE OF A TURNING WHEEL CORNERING FORCE AT THE FRONT WHEEL TO BALANCE THE CENTRIFUGAL FORCE OF THE VEHICLE WHEN STEERING:


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V. ROLLING RESISTANCE OF A TURNING WHEEL

THE ADITIONAL RESISTANCE, APPLIED ON THE FRONT WHEELS:


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CORNERING FORCE AT THE REAR WHEEL TO BALANCE THE CENTRIFUGAL FORCE OF THE VEHICLE WHEN STEERING:


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THE ADITIONAL RESISTANCE, APPLIED ON THE REAR WHEELS:


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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 ANGLE


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V. ROLLING RESISTANCE OF A TURNING WHEEL INCREASE OF THE ROLLING RESISTANCE AT TURNING WHEELS

LATERAL ACCELERATION


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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)


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VI. LONGITUDINAL ADHESION COEFFICIENT

THE TIRE WILL BE SLIPPING WHEN :

MT > Fφ.r d MT: DRIVING TORQUE ON THE WHEEL Fφ.r d : TORQUE, PRODUCED BY THE ADHESION FORCE AROUND THE WHEEL CENTER r d: EFFECTIVE ROLLING RADIUS


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VI. LONGITUDINAL ADHESION COEFFICIENT

THE TIRE WILL BE SKIDDING WHEN :

Mb > Fφ.r d Mb: BRAKING TORQUE ON THE WHEEL Fφ.r d : TORQUE, PRODUCED BY THE ADHESION FORCE AROUND THE WHEEL CENTER r d: EFFECTIVE ROLLING RADIUS


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VI. LONGITUDINAL ADHESION COEFFICIENT WHEN:

ω.r d = 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.r d :

LONGITUDINAL SPEED OF THE TIRE TO THE TIRE-GROUND CONTACT POINT

vX: LINEAR SPEED OF THE TIRE RELATIVE TO THE GROUND


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VI. LONGITUDONAL ADHESION COEFFICIENT WHEN:

ω.r d > 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:


ω.r d :




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VI. LONGITUDINAL ADHESION COEFFICIENT WHEN:

ω.r d < 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:


ω.r d :




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VI. LONGITUDINAL ADHESION COEFFICIENT TO ACCURATELY DESCRIBE TIRE SLIP IN A BRAKING MANEUVER LONGITUDINAL SKID, Sb IS DEFINED AS: ω.r d :



Sb = 0%

→ THE TIRE IS PURELY ROLLING

Sb = 100% → THE TIRE IS PURELY SKIDDING 0% < Sb < 100% → THE TIRE IS ROLLING AND SKIDDING


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VI. LONGITUDINAL ADHESION COEFFICIENT THE TIRE SLIP IN A TRACTIVE (DRIVING) MANEUVER: ω.r d :



Sa = 0%

→ THE TIRE IS PURELY ROLLING

Sa = 100% → THE TIRE IS PURELY SPINNING 0% < Sa < 100% → THE TIRE IS ROLLING AND SLIPPING


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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 VALUE


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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 FORWARD


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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 IS ROLLING AND SLIPPING WITH:

TIRE

15% < | S | < 30%


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VI. LONGITUDINAL ADHESION COEFFICIENT 0% < |S| < 15% → THE VALUE OF φ INCREASES LINEAR WITH S 15% < |S| < 30% → THE VALUE OF φ REACHES MAXIMUM (THE PEAK COEFFICIENT OF ROAD ADHESION)

REACHES

THE

15% < |S| < 30% → THE VALUE OF φ GRADUALLY FALLS WITH THE INCREASE OF S |S| = 100% → THE SLIDING COEFFICIENT OF ADHESION Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011

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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 SURFACE


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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 VEHICLE


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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 SPEED


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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 SPEEDS


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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 OVERHEATING


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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 INCREASES


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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.


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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 TIRES


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Rolling Resistance

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