Experimental and Computational Studies of Contact
Mechanics for Tire Longitudinal Response
Jacob Kidney, Neel Mani, Vladimir Roth, John Turner, & Tom Branca
Bridgestone Americas Tire Operations
Product Development Group
Akron, OH
30th Tire Society Conference
Akron, Ohio
September 14, 2011
1
Motivation for Interest in
Dry Braking Performance
• OEM’s are requiring improved Stopping Distance performance
• ABS systems are now standard safety features, and the
potential for improvement is enhanced
• European & Asian countries have active NCAP programs to
Test & Improve Dry Stopping Distance for Safety
• Consumers Union & IIHS generate and publish U.S. vehicle
ratings and include Stopping Distance as a measure of Safety
• SAE Committee has developed a standardized stopping
distance test procedure
2
Drive-Brake Force Generation & Slip Zone Evolution
Tread
1D Concept “Brush” Model
Belt
Tread
Belt
Ω
z
VBelt
Vbelt
x
VGround
GROUND
Shear
zx  (Vg /Vb)
Vground
Brake
• Vg/Vb is the Basic Mechanism
of Tread Shear Development
Drive
Brake
Free Rolling
Drive
Shear Stress
Drive
Drive
Brake
Shear Stress
Friction limit = 
Free
Rolling
Slip Zone
Evolution
Brake
Friction limit = 
• Tread Shears until it Reaches Friction Limit
• Slip Zones Evolve from the Rear of Footprint
3
Contact Behavior – Free-Rolling & Braking Conditions
Free Rolling
Moderate Braking (SR=6%)
4
Slip Zone Evolution & Mu-Slip Curve - Brush Model
0
0
1
2
3
4
5
6
20
20
FREE ROLLING
0
10
-10

Driving
20
7
STICK
10
SLIP
9
10
-10
SLIP
0
1
2
3
4
5
6
7
8
9
10
-10
1
2
3
4
5
6
7
8
9
10
-10
-20
-20
-30
-30
-30
-30
-40
-40
-40
-40
-50
-50
-50
-60
-60
-60
-70
-70
-70
Braking

-50

-60
-70
0
FREE ROLLING
SLIP
0
0
-20
-20
STICK
10
0
0
8
20
STICK
10
0
1
2
3
4
5
6
7
8
9
10
INCREASING BRAKE TORQUE
1
0
Driving
Torque Ramp
10
0.8
Increasing
0.7
Braking
0/σ0
0.6
Stress
Stress [psi]
Free Rolling
0.9
30
-10 0
1
2
3
4
5
6
7
8
9
10
0/0
Fx/Fz
Concept Model
0.5
0.0
0.091
0.18
0.27
0.36
0.4
-30
0.3
-50
0
-70
Shape Controlled by
Slip Zone Evolution
0.2
0.1
0
Distance
0%
5%
10%
15%
20%
25%
Increasing Slip Rate
Slip Rate at Peak is Altered as well
Shape of the mu-Slip Curve is Affected by Slip Zone Evolution
(Rate of Fx generation diminishes as Slip Zone Increases)
5
Slip Zone Growth – Effects on µ-Slip Shape
Experimental Measurement
FEA Prediction
µ vs Slip Rate
µ vs Slip Rate
1.2
1.0
1.2
1.0
Drive Torque
0.8
0.8
0.6
0.6
Brake Torque re-plotted
in Drive Quadrant
0.2
0
-0.2
0.4
µ (Fx/Fz)
µ (Fx/Fz)
0.4
0
-0.2
-0.4
-0.6
-0.6
Brake Torque
-0.8
Brake Torque
-1.0
-1.2
-15.0 -12.5 -10.0 -7.5
Brake Torque re-plotted
in Drive Quadrant
0.2
-0.4
-0.8
Drive Torque
-1.0
-5.0
-2.5
0
2.5
5.0
7.5
Slip Rate (%)
Rolling Tire Simulator
10.0
12.5
15.0
-1.2
-15.0 -12.5 -10.0 -7.5
-5.0
-2.5
0
2.5
5.0
7.5
10.0
12.5
15.0
Slip Rate (%)
SST Braking &
Cornering
6
Example of Contrasting Slip Zone Growth Rates
Experimental Measurement
FEA Prediction
µ vs Slip Rate
µ vs Slip Rate
1.2
1.0
1.0
Drive Torque
0.8
0.8
0.6
0.6
µ (Fx/Fz)
0.4
0
-0.2
0
-0.2
-0.4
-0.6
-0.6
TRAILING
EDGE
Brake Torque
-0.8
Brake Torque
-1.0
LEADING
EDGE
Brake Torque re-plotted
in Drive Quadrant
0.2
-0.4
-0.8
Drive Torque
0.4
Brake Torque re-plotted
in Drive Quadrant
0.2
µ (Fx/Fz)
Travel
1.2
-1.0
-1.2
-15.0 -12.5 -10.0 -7.5
-5.0
-2.5
0
2.5
5.0
7.5
-1.2
-15.0 -12.5 -10.0 -7.5
10.0 12.5 15.0
-5.0
Slip Rate (%)
-2.5
0
2.5
5.0
7.5
10.0 12.5 15.0
Slip Rate (%)
zx/zz
20
20
FREE ROLLING
10
SLIP
ZONE
-10
0
1
2
3
4
5
6
7
8
9
10
-10
20
STICK
10
SLIP
0
1
2
3
4
5
6
7
8
9
10
-10
STICK
10
0
SLIP
0
0
1
2
3
4
5
6
7
8
9
10
-10
-20
-20
-20
-20
-30
-30
-30
-30
-40
-40
-40
-40
-50
-50
-50
-50
-60
-60
-60
-60
-70
-70
-70
-70
0
1
2
3
4
5
6
7
SLIP
ZONE
8
9
10
Brake Torque – Concept Model
INCREASING TORQUE
70
70
60
60
50
50
50
50
40
40
40
40
30
30
30
30
20
20
20
20
10
-20
70
STICK
1
2
3
4
5
6
7
8
9
10
-10
-20
70
SLIP
1
2
3
4
5
6
7
8
9
10
-10
SLIP
SLIP
ZONE
10
0
0
STICK
60
10
0
0
STICK
60
10
0
-10
Drive Torque - FEA
SLIP
0
Brake Torque - FEA
zx/zz
20
STICK
10
0
0
0
1
2
3
4
5
6
7
8
9
10
-20
-10
0
1
2
3
4
5
6
7
8
9
10
-20
Drive Torque – Concept Model
 Drive & Brake mu-Slip Curves Differ due to Slip Zone Evolution
7
Slip Zone Evolution for All-Season Tire Under Braking
FRONT
REAR
Rolling
Direction
Slip Zone
Growth
zz
LOW
HIGH
SR = 0%
SR = 4%
SR = 2%
SR = 6%
SR = 8%
8
Fundamental Studies of Lift-Off
Increased Braking
Free Rolling
Medium Braking
Heavy Braking
“Summer”
Contrasting
Lift-Off
“All Season”
“Winter”
9
Friction – Impact of Pressure Dependence
Free-Rolling
Braking
Lug Lift
Z
Lug
LIFT-OFF WHEN
Z=0
Braking Shear
Lug Lift-Off Reduces Contact Area and Increases Dry Stopping Distance. WHY??
0.8
1.0
1.2
1.4
1.6
1.8
1.6
1.4
Coefficie
nt of Fri
ction
1.8
Coef. of Friction is
Pressure Sensitive
1.2
1.0
0.8
20
140
Pre
40
280
ssu
375
150
60
420
re
(
500
200
625
250
Ps
80
560
i)
100
700
750
300
Reduced Area
lo
Ve
y
cit
250
100
Contact Pressure
/s)
(in
Increased z
Coef. of Friction
FRICTION DATA USED IN
BRAKING SIMULATIONS (Based on TCE Data)
Reduced COF
Increased DSD
10
Impact of Friction Law on Braking Performance
Sliding
Direction
Apply
Load
Un-Deformed Lug
2-Sipe–- Constant
vs Variable
COF - Fz=50Friction
lbf
Mu vs Distance
Comparison
between
Laws
1.0
Friction Models for Sliding Lug Simulations
Constant COF
0.9
1.2
Variable COF
1.1
0.8
Constant COF
1.0
0.7
18%
Decrease
0.9
Mu (Fx/Fz)
0.6
Mu [Fx/Fz]
0.8
COF
COF
0.7
0.6
0.5
Variable COF
0.4
0.5
0.4
0.3
0.3
0.2
0.2
0.1
2-Sipe Variable COF
0.1
0.0
0
25
50
75
100
125
150
175 200 225
Pressure
Pressure [psi]
250
275
300
325
350
375
2-Sipe Constant COF
400
0.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Distance
0.16
0.18
0.20
0.22
0.24
Time [sec]
11
Impact of Sipes on Braking Performance
vs 2-Sipe Lug -–Variable
COF - Fz=50lbf
MuSolid
vsBlock
Distance
Siping
Impact
1.0
Solid Lug
0.9
19%
Decrease
0.8
0.75
Mu (Fx/Fz)
0.7
Mu [Fx/Fz]
0.6
0.63
0.5
2-Sipe Lug
0.4
0.3
Solid Lug
Contact
Pressure
(kPa)
0.2
2-Sipe Lug
2-Sipe Lug
2-Sipe Lug
0.0
0.00
- 1900
- 330
- 300
- 270
- 240
- 210
- 180
- 150
- 120
- 90
- 60
- 30
-0
Solid Block
0.1
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Distance
0.16
0.18
0.20
0.22
0.24
Time [sec]
Lug Sliding (Mesh)
Contact Pressure while Sliding
Lift-Off
Zone
Solid Lug
Lift-Off
Zones
2-Sipe Lug
Solid Lug
2-Sipe Lug
12
Impact of Contact Stress on Braking Performance
Multi-Fz
- 2-Sipe
Model - Reduced
COF (mu max=1.0)
Mu
vs Comparison
Distance
– Lug
Impact
of Contact
Stress
0.80
0.75
0.70
0.65
0.60
0.55
6% Drop
6% Drop
Mu (Fx/Fz)
0.50
Mu
0.45
Mu drops with increased Fz
0.40
0.35
0.30
0.25
0.20
0.15
Fz=50
lb N
Fz = 225
0.10
Fz = 300
Fz=65
lb N
0.05
Fz = 375
Fz=80
lb N
0.00
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Distance
0.16
0.18
0.20
0.22
0.24
Time [sec]
Fz = 225 N
Moderate Pressure @ Leading Edge
Fz = 300 N
Increased Pressure @ Leading Edge
Fz = 375 N
Contact
Pressure
(kPa)
Very High Pressure @ Leading Edge
- 360
- 330
- 300
- 270
- 240
- 210
- 180
- 150
- 120
- 90
- 60
- 30
-0
13
Implications for ABS Braking Performance
Stopping Distance
Performance
(m)
DSD
DSD [ft]
EIGHT TIRE SPECS TESTED ON
TWO VEHICLES FOR ABS DSD
46.0
151
45.7
150
45.4
149
45.1
148
44.8
147
44.5
146
44.2
145
43.9
144
43.6
143
43.3
142
43.0
141
42.7
140
Vehicle A LONGER
SHORTER
1
2
3
4
5
6
7
8
6
7
8
• If several different tire sets are tested on
multiple vehicles, Stopping Distance rank
order will likely change.
• A tire-vehicle interaction is involved that
influences performance.
DSD [ft]
(m)
DSD
Tire Spec.
52.1
171
170
51.8
169
51.5
168
51.2
167
50.9
166
50.6
50.3
165
164
50.0
49.7
163
162
49.4
49.1
161
160
48.8
Vehicle B
1
2
3
LONGEST
4
5
Tire Spec.
SHORTEST
14
Implications for ABS Braking Performance
Mu-Slip Curves for Various Tires
Stopping Distance for Various Tires
Mu (Fx/Fz)
Stopping Distance
Tire A
Tire A
Tire B
Tire C
Tire B
Tire C
Slip Rate
Tire Slip Rate vs Time
EE876P --- Firestone FR710 - 225/60R18 - 18x7.5 --- 40psi
LF SR
RF SR
TEST_000_LF SR
TEST_000_RF SR
Fx
30%
SR Cycling with
Phase Lag Fz5
Fz4
Mu (Fx/Fz)
25%
[%]
Rate
Slip
Rate
Slip
20%
15%
Fz3
Fz2
Fz1
10%
5%
Tire Mu-Slip Curves & ABS Cycling
0%
0.0
TEST 000
0.5
1.0
1.5
Time
(sec)
Time [sec]
2.0
2.5
3.0
Slip
Ratio
Slip
Rate
15
Implications for ABS Braking Performance
Mu-Slip Curves for Various Tires
Mu (Fx/Fz)
•Peak Is Constant
•Slope & Curvature Varied
•CONSIDER A “SLIP RATE-BASED”
ABS CONTROLLER
ABS Operating Range
(SR-Based ABS Controller)
Tire A
Tire B
Tire C
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
Slip Rate
16
Implications for ABS Braking Performance
Mu-Slip Curves for Various Tires
Mu (Fx/Fz)
•Peak Is Constant
•Slope & Curvature Varied
•CONSIDER A “SLIP RATE-BASED”
ABS CONTROLLER
ABS Operating Efficiency
is Influenced by the Shape
of the mu-Slip Curve
ABS Operating Range
(SR-Based ABS Controller)
Tire A
Tire B
Tire C
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
Slip Rate
17
Implications for ABS Braking Performance
Base Mu-Slip Curves for Different Tires
Tire A
Mu (Fx/Fz)
Tire B
•Peak Is Constant
•Slope & Curvature Varied
•CONSIDER A “PEAK-SEEKING”
ABS CONTROLLER
ABS Operating Efficiency
is Influenced by the Shape
of the mu-Slip Curve
Slip Rate
Mu-Slip Curves for Different Tires
Mu-Slip Behavior for Different Tires
during an ABS Simulation
Transient
Steady ABS Operation
Tire A
Penalty for Excessive
Pressure Release
Braking Force, Fx
Braking Force, Fx
Tire B
PERFORMANCE
LOSS
BETTER
PERFORMANCE
Slip Rate
Time
Tire A
Tire B
18