T1 1 rolling resistance

Erasmus LLP Intensive Programme

ROLLING

RESISTANCEEddy Versonnen

[email protected]

KdG University College Antwerp

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

mailto:[email protected]


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


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T1 1 rolling resistance