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m t. c z. k z. P. δ z. {X sae } 1. {Z sae } 1. Bergamo University Italy 12 th -14 th June 2012. Lecture 6 – Tyre Force and Moment Characteristics. Professor Mike Blundell Phd , MSc, BSc ( Hons ), FIMechE , CEng. γ. Angular Velocity ( ω ) Wheel Torque (T). Spin Axis. - PowerPoint PPT Presentation
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Bergamo University Italy12th-14th June 2012
Professor Mike BlundellPhd, MSc, BSc (Hons), FIMechE, CEng
Lecture 6 – Tyre Force and Moment Characteristics
mt
kzcz
δ
z
{Zsae}
1
{Xsae}
1
P
SAE Tyre Axis System
2
{Ysae}1{Zsae}1
{Xsae}1
P
γ
α
Spin Axis
{V}1
Angular Velocity (ω)Wheel Torque (T)
WC
Direction of Wheel Heading
Direction of Wheel Travel
Lateral Force (Fy)Normal Force (Fz)
Tractive Force (Fx)
ISO Tyre Axis System
3
Normal Force (Fz)
{Yiso}1
{Ziso}1
{Xiso}1
P
γ
α
Spin Axis
{V}1
Angular Velocity (ω)Wheel Torque (T)
WC
Direction of Wheel Heading
Direction of Wheel Travel
Lateral Force (Fy)
Tractive Force (Fx)
Definition of Tyre Radii
4
ω
P
VRu
AB
Rl
FrontRear
Re
C
Generation of Tyre Lateral Forces due to Conicity
5
FY
FY
YSAE
YSAE
XSAE
XSAE
Direction of Travel
Left
Right
Generation of Tyre Lateral Forces due to Plysteer
6
XSAE
YSAE
XSAE
FY
Left
Right
Direction of Travel
YSAE
FY
YSAE
FY
YSAE
FY
Frictional Force Component due to Adhesion
7
Direction of Sliding
Tyre Material
Road Surface
Adhesive Forces due to Molecular Bonding
Hysteresis in Rubber
8
F
δ
F
δ
Unloading
Loading
Loading and Unloading of Tyre Rubber in the Contact Patch
9
Direction of Sliding
Road Surface
Unloading
Loading
Pressure Distribution in a Stationary Tyre Contact Patch
10
Over Inflation
Normal Inflation
Under InflationPressure Distribution in the Tyre Contact Patch
Tyre Contact Patch
Tyre Forces and Moments Shown Acting in the SAE Tyre Axis System
11
{Ysae}1
{Zsae}
1
{Xsae}1
P
γ
α
Spin Axis
Rolling ResistanceMoment (My)
WC
Lateral Force(Fy)
Normal Force(Fz)
Tractive Force(Fx)
Self Aligning Moment
(My)
Overturning Moment
(Mx)
Measurement of Stiffness in a Non-Rolling Tyre
12
φ
Fx
Fy
δy
δx
Tz
Fx
δx
Longitudinal Stiffness
Fy
δy
Lateral Stiffness
Tz
φ
Torsional Stiffness
Vertical Tyre Force Model Based on a Linear Spring Damper
13
mt
kzcz
δz
{Zsae}1
{Xsae}1
P
Generation of Slip in a Free Rolling Tyre
14
ω
V= ω Re
Rl
Rear
Re
O
Vt = ω Ru
Ru
TreadMaterial
Compression
Front
Vt = ω Rl
Vt = ω Re
Vt = ω Ru
Direction of slip relative to the road surface
{Xsae}1
Longitudinal Shear Stress
Tangential velocity of tread relative to O
B PD C A
Vt = ω Re
Lateral Distortion of the Contact Patch for a Free Rolling Tyre
15
Lateral slip movement(Moore, 1975)
FrontRear
Un-deformed Tyre
Deformed Tyre
Squirm through the contact patch (Gillespie, 1992)
Generation of Rolling Resistance in a Free Rolling Tyre
16
ω
FRxO
δx
Fz
Fz
FRx
P
Rl
Rear {Xsae}1Front
My = Fz δx
Generation of Force in a Braked Tyre
17
ω
V = ω Re
Rear
O
Compression
Front
{Xsae}1
Tread Def.
TB
TensionFB
PressureDistribution
LongitudinalSlip
LongitudinalShear Stress
δxFz
Braking Force versus Slip Ratio
18
0.0 Slip Ratio 1.0
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Braking Force versus Slip Ratio
Slip Angle = 0Camber Angle = 0
Longitudinal Stiffness Cs = tan φφ
BrakingForceFx (N)
The Effect of Road Contamination on Braking
19
0.0 Slip Ratio 1.0
Aquaplaning
Good Tread on Wet Road
Dry Road
Braking Force versus Slip Ratio
Slip Angle = 0Camber Angle = 0
BrakingForceFx (N)
Poor Tread on Wet Road
Generation of Force in a Driven Tyre
20
V = ω Re
ω
Rear
O
Compression
Front
{Xsae}1
Tread Def.
TD
Tension
FD
LongitudinalShear Stress
PressureDistribution
δxFz
LongitudinalSlip
Forces and Moments due to Slip and Camber Angle
21
Slip Angle Camber Angle
Lateral Force Camber Thrust
Lateral Force
Camber ThrustPneumatic
TrailAligning Moment
due to slip angle
AligningMoment due to camber
angle
γ
α
Direction of Travel Direction of Travel
Generation of Lateral Force and Aligning Moment due to Slip Angle
22
Limit Lateral Stress μp
Direction of Wheel Heading
Pressure p
Front Rear
Direction of Wheel Travel
α
Slipping Starts
Slipping Starts
Lateral Stress
Lateral Stress
Fy
Pneumatic Trailxpt
Mz = Fy xpt
Side View
Top View
Tyre Contact Patch
Plotting Lateral Force versus Slip Angle
23
-Slip Angle α (degrees)
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Lateral Force versus Slip Angle
Camber Angle = 0
Lateral ForceFy (N)
Cornering Stiffness Cs = tan φ
φ
Plotting Aligning Moment versus Slip Angle
24
Slip Angle α (degrees)
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Aligning Moment versus Slip Angle
Camber Angle = 0
AligningMomentMz (Nm)
Aligning Moment Stiffness = tan φ
φ
Generation of Lateral Force due to Camber Angle
25
Spin Axis
Camber Thrust Fy
{Ysae}1
{Zsae}1
γ
Resultant Force FR
Tyre Load Fz
Plotting Lateral Force versus Camber Angle
26
Camber Angle γ (degrees)
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Lateral Force versus Camber Angle
Slip Angle = 0
Lateral ForceFy (N)
Camber Stiffness Cγ = tan φφ
Generation of Self Aligning Moment due to Camber Angle
27
A B C
A C B C
{Ysae}1
{Xsae}1
A Fy
Mz
Front
Rear
Spin Axis
A C Camber Thrust Fy{Ysae}1
{Zsae}1
γ
B
Plotting Aligning Moment Versus Camber Angle
28
Camber Angle γ (degrees)
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Aligning Moment versus Camber Angle
Slip Angle = 0
AligningMomentMz (Nm)
Aligning Moment Camber Stiffness = tan φ φ
The Effect of Combined Camber and Slip Angle on Lateral Force
29
-Slip Angle α (degrees)
Lateral Force versus Slip AngleLateral ForceFy (N)
Camber Angle = 0Camber Angle = 5Camber Angle = 10
Generation of Overturning Moment in the Tyre Contact Patch
30
y
Fz
PYSAE
Wheel Plane
OWheel Centre
ZSAE
Mx = Fz δy
Slip Angle
y
Fz
PYSAE
O
Camber Angle
ZSAE
Mx=Fzδy
Pure and Combined Braking and Cornering Forces
31
Direction ofTravel
YSAE
XSAE
Maximum Cornering ForceFy = μ Fz
Large Slip Angle α Pure Cornering
α
Fy = μ Fz
Fy
Direction of Travel
YSAE
XSAE
Maximum Braking Force Fx = μ Fz
ContactPatch
Pure Braking
S
Fx = μ Fz
Fy
Direction ofTravel
YSAE
XSAE
Maximum RoadPlane Force
FR = μ Fz
Fy
Fx
Combined Braking and Cornering
Large Slip Angle α
Direction of Travel
YSAE
XSAE Braking Force Fx
Fy
Combined Braking and Cornering
Moderate Slip Angle α
ContactPatch
ContactPatch
ContactPatch
Plotting Lateral Force Against Longitudinal Force (Friction Circle)
32
Friction Circle
Braking Force Fx Driving Force Fx
Lateral Force Fy
α =1
α =2
α =6
α =10
α =4
A B
C
D
Resultant Force FR
Development of Lateral Force Following Step Steering Input
33
Time (sec)
Lateral Force versus timeLateral ForceFy (N)
t1t0 t2
Fymax
0.632 Fymax
Steady State
High Speed Dynamics Machine for Tyre Testing Formerly at Dunlop Tyres Ltd.
34
Courtesy of Dunlop Tyres Ltd.
Flat Bed Tyre Test Machine at Coventry University
35
Lateral Force Fy with Slip Angle α
36
Courtesy of
Dunlop Tyres Ltd.
Aligning Moment Mz with Slip Angle α
37
Courtesy of
Dunlop Tyres Ltd.
Lateral Force Fy with Aligning Moment Mz (Gough Plot)
38
Courtesy of
Dunlop Tyres Ltd.
Cornering Stiffness with Load
39
Courtesy of
Dunlop Tyres Ltd.
Aligning Stiffness with Load
40
Courtesy of
Dunlop Tyres Ltd.
Lateral Force Fy with Camber Angle α
41
Courtesy of
Dunlop Tyres Ltd.
Aligning Moment Mz with Camber Angle α
42
Courtesy of
Dunlop Tyres Ltd.
Camber Stiffness with Load
43
Courtesy of
Dunlop Tyres Ltd.
Aligning Camber Stiffness with Load
44
Courtesy of
Dunlop Tyres Ltd.
Braking Force with Slip Ratio
45
