T1 1 rolling resistance

Erasmus LLP Intensive Programme

ROLLING
RESISTANCE
Eddy Versonnen
Eddy.versonnen@kdg.be
KdG University College Antwerp

Powering the Future With Zero Emission and Human Powered Vehicles – Terrassa 2011 1


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



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
STABILITY



I. INTRODUCTION

THE CRITICAL PERFORMANCES OF A VEHICLE:

- DRIVING

- BRAKING

- STABILITY

- RIDE COMFORT

- TRAVELING

ARE RELATED TO PNEUMATIC TIRES



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



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



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



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 TIRE



I. INTRODUCTION

COMMONLY USED AXIS SYSTEM RECOMMENDED BY SAE
INTERNATIONAL:



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




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



PNEUMATIC 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



PNEUMATIC 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



PNEUMATIC 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



PNEUMATIC 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)



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



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




- 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




- 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




- 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




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



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.




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)]




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



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




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



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



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.Fz



TIRE WITH TOE-IN

ROLLING RESISTANCE IN
FUNCTION OF THE TIRE TOE-IN



TIRE WITH TOE-IN

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



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




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 + Δf



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



TURNING WHEEL
CORNERING FORCE AT THE
FRONT WHEEL TO BALANCE
VEHICLE WHEN STEERING:



TURNING WHEEL

THE ADITIONAL RESISTANCE,
APPLIED ON THE FRONT WHEELS:



TURNING WHEEL

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



TURNING WHEEL

THE ADITIONAL RESISTANCE,
APPLIED ON THE REAR WHEELS:



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



TURNING WHEEL
INCREASE OF THE ROLLING RESISTANCE AT TURNING WHEELS

LATERAL ACCELERATION



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




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)



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 RADIUS



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 RADIUS



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 GROUND



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

POINT

TO THE GROUND



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

POINT

TO THE GROUND



COEFFICIENT
TO ACCURATELY DESCRIBE TIRE SLIP IN A BRAKING MANEUVER
LONGITUDINAL SKID, Sb IS DEFINED AS:

POINT

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 SKIDDING



COEFFICIENT
THE TIRE SLIP IN A TRACTIVE (DRIVING) MANEUVER:

POINT

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 SLIPPING



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



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



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%



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
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



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



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



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




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



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



- 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



ROLLING RESISTANCE
I. INTRODUCTION






TIRES




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.



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



THANK YOU FOR YOUR ATTENTION


T1 1 rolling resistance

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Andere mochten auch

Andere mochten auch (20)

T1 1 rolling resistance