1 experimental and computational studies of contact mechanics for tire longitudinal response jacob...
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Experimental and Computational Studies of ContactExperimental and Computational Studies of Contact
Mechanics for Tire Longitudinal ResponseMechanics 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
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• OEM’s are requiring improved Stopping Distance performanceOEM’s are requiring improved Stopping Distance performance
• ABS systems are now standard safety features, and the ABS systems are now standard safety features, and the potential for improvement is enhancedpotential for improvement is enhanced
• European & Asian countries have active NCAP programs to European & Asian countries have active NCAP programs to Test & Improve Dry Stopping Distance for SafetyTest & Improve Dry Stopping Distance for Safety
• Consumers Union & IIHS generate and publish U.S. vehicle Consumers Union & IIHS generate and publish U.S. vehicle ratings and include Stopping Distance as a measure of Safetyratings and include Stopping Distance as a measure of Safety
• SAE Committee has developed a standardized stopping SAE Committee has developed a standardized stopping distance test proceduredistance test procedure
Motivation for Interest in Motivation for Interest in Dry Braking PerformanceDry Braking Performance
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Vground
BeltTread
Ω
Vbelt
Shear zx (Vg /Vb)
Belt Tread
VBelt
VGroundGROUND
z
x
Free Rolling
Bra
ke
Dri
ve
1D Concept “Brush” Model
Free Rolling
Brake
Drive
Bra
ke
Dri
ve
• Tread Shears until it Reaches Friction LimitTread Shears until it Reaches Friction Limit• Slip Zones Evolve from the Rear of FootprintSlip Zones Evolve from the Rear of Footprint
Friction limit =
Slip Zone Evolution
Friction limit =
Drive-Brake Force Generation & Slip Zone EvolutionDrive-Brake Force Generation & Slip Zone Evolution
Sh
ear
Str
ess
• Vg/Vb is the Basic Mechanism Vg/Vb is the Basic Mechanism of Tread Shear Developmentof Tread Shear Development
Brake
Drive
Sh
ear
Str
ess
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Free RollingFree Rolling Moderate Braking (SR=6%)Moderate Braking (SR=6%)
Contact Behavior – Free-Rolling & Braking ConditionsContact Behavior – Free-Rolling & Braking Conditions
5
Slip Zone Evolution & Mu-Slip Curve - Brush ModelSlip Zone Evolution & Mu-Slip Curve - Brush Model
Shape of the mu-Slip Curve is Affected by Slip Zone Evolution(Rate of Fx generation diminishes as Slip Zone Increases)
-70
-50
-30
-10
10
30
0 1 2 3 4 5 6 7 8 9 10
Distance
Str
ess [psi]
Driving
Braking
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0% 5% 10% 15% 20% 25%
Increasing Slip Rate
Fx/F
z
0.00.0910.180.270.36
Shape Controlled by Slip Zone Evolution
0/0
Increasing 0/σ0
Slip Rate at Peak is Altered as well
INCREASING BRAKE TORQUEFREE ROLLING
Str
es
s
Free Rolling Torque Ramp
Concept ModelConcept Model
FREE ROLLING
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
SLIPSTICK SLIPSTICKSLIPSTICK
0
0Driving
Braking
6
µ vs Slip Rate
µ (
Fx
/Fz)
Drive Torque
Brake Torque
Brake Torque re-plotted in Drive Quadrant
Slip Rate (%)0 2.5 5.0 7.5 10.0 12.5 15.0-2.5-5.0-7.5-10.0-12.5-15.0
0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
1.2
1.0
0.8
0.6
0.4
0.2
Experimental Measurement FEA Prediction
Rolling Tire Simulator SST Braking & Cornering
Slip Zone Growth – Effects on µ-Slip ShapeSlip Zone Growth – Effects on µ-Slip Shape
µ vs Slip Rate
µ (
Fx
/Fz)
Drive Torque
Brake Torque
Brake Torque re-plotted in Drive Quadrant
Slip Rate (%)0 2.5 5.0 7.5 10.0 12.5 15.0-2.5-5.0-7.5-10.0-12.5-15.0
0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
1.2
1.0
0.8
0.6
0.4
0.2
7
zx/zz
-20
-10
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8 9 10
-20
-10
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8 9 10
Drive & Brake mu-Slip Curves Differ due to Slip Zone EvolutionDrive & Brake mu-Slip Curves Differ due to Slip Zone Evolution
Travel
LEADING EDGE
TRAILING EDGE
SLIP
zx/zz
Brake Torque - FEA
Drive Torque - FEA
µ vs Slip Rate
µ (
Fx
/Fz)
Drive Torque
Brake Torque
Brake Torque re-plotted in Drive Quadrant
Slip Rate (%)0 2.5 5.0 7.5 10.0 12.5 15.0-2.5-5.0-7.5-10.0-12.5-15.0
0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
1.2
1.0
0.8
0.6
0.4
0.2
Experimental Measurement FEA Prediction
INCREASING TORQUE
Brake Torque – Concept Model
Drive Torque – Concept Model
Example of Contrasting Slip Zone Growth RatesExample of Contrasting Slip Zone Growth Rates
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
SLIPSTICK
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
SLIPSTICK
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
SLIPSTICKFREE ROLLING
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 1 2 3 4 5 6 7 8 9 10
SLIPSTICKSLIPSTICKSLIP
STICK
ZONE SLIP ZONE
SLIP ZONE
µ vs Slip Rate
µ (
Fx
/Fz)
Drive Torque
Brake Torque
Brake Torque re-plotted in Drive Quadrant
Slip Rate (%)0 2.5 5.0 7.5 10.0 12.5 15.0-2.5-5.0-7.5-10.0-12.5-15.0
0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
1.2
1.0
0.8
0.6
0.4
0.2
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SR = 0%SR = 0% SR = 2%SR = 2%
SR = 8%SR = 8%SR = 6%SR = 6%SR = 4%SR = 4%
zz
LOW
Slip Zone Evolution for All-Season Tire Under Braking Slip Zone Evolution for All-Season Tire Under Braking
Rolling Direction
HIGH
Slip Zone Slip Zone
GrowthGrowth
FRONT REAR
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Increased Braking
“All Season”
Contrasting Contrasting Lift-OffLift-Off
“Summer”
“Winter”
Free Rolling Medium Braking Heavy Braking
Fundamental Studies of Lift-OffFundamental Studies of Lift-Off
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Lug Lift-Off Reduces Contact Area and Increases Dry Stopping Distance. WHY??
Coef. of Friction is Pressure Sensitive
Reduced Area Increased z Reduced COF Increased DSD
Lug
Braking Shear
0.8
1.0
1.2
1.4
1.6
1.8
100150
200250
300
2040
60
80
100
Co
effi
cien
t o
f F
rict
ion
Velocity (in/s)
Pressure (Psi)
0.8 1.0 1.2 1.4 1.6 1.8
FRICTION DATA USED IN BRAKING SIMULATIONS (Based on TCE Data)
Lug Lift
Friction – Impact of Pressure DependenceFriction – Impact of Pressure Dependence
Velocity (mm/sec)
250375
500625
750
Pressure (kPa)700
560420
280140
Z
LIFT-OFF WHEN Z=0
Free-Rolling Braking
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400
COF
Pressure [psi]
Friction Models for Sliding Lug Simulations
Variable COF
Constant COF
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
Mu
[Fx/
Fz]
Time [sec]
2-Sipe - Constant vs Variable COF - Fz=50 lbf
2-Sipe Variable COF
2-Sipe Constant COF
18% Decrease
Constant COF
Variable COF
Impact of Friction Law on Braking PerformanceImpact of Friction Law on Braking Performance
Apply Apply LoadLoadApply Apply LoadLoad
Sliding Sliding DirectionDirectionSliding Sliding
DirectionDirectionUn-Deformed LugUn-Deformed LugUn-Deformed LugUn-Deformed Lug
Distance
Mu
(F
x/F
z)
Mu vs Distance – Comparison between Friction Laws
Pressure
CO
F
12
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
Mu
[Fx/
Fz]
Time [sec]
Solid Block vs 2-Sipe Lug - Variable COF - Fz=50lbf
Solid Block
2-Sipe Lug
0.75
0.63
19% Decrease
Lift-Off Zone
Lug Sliding (Mesh)
Contact Pressure
(kPa)
Impact of Sipes on Braking PerformanceImpact of Sipes on Braking Performance
Contact Pressure while Sliding
Solid LugSolid Lug 2-Sipe Lug2-Sipe Lug
Solid LugSolid Lug 2-Sipe Lug2-Sipe Lug
Lift-Off Zones
- 1900- 330- 300- 270- 240- 210- 180- 150- 120- 90- 60- 30- 0
Solid Lug
2-Sipe Lug
Distance
Mu
(F
x/F
z)
Mu vs Distance – Siping Impact
2-Sipe Lug
Solid Lug
2-Sipe Lug
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0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
Mu
Time [sec]
Multi-Fz Comparison - 2-Sipe Lug Model - Reduced COF (mu max=1.0)
Fz=50 lb
Fz=65 lb
Fz=80 lb
Mu drops with increased FzMu drops with increased Fz
6% Drop6% Drop
Fz = 300 NFz = 225 N
Moderate Pressure @ Leading Edge Increased Pressure @ Leading EdgeVery High Pressure @ Leading Edge
Fz = 375 N
Impact of Contact Stress on Braking PerformanceImpact of Contact Stress on Braking Performance
Contact Pressure
(kPa)
- 360- 330- 300- 270- 240- 210- 180- 150- 120- 90- 60- 30- 0
Mu
(F
x/F
z)
Distance
Mu vs Distance – Impact of Contact Stress
Fz = 225 N
Fz = 300 N
Fz = 375 N
14
• 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.
Stopping Distance Stopping Distance PerformancePerformance
Implications for ABS Braking PerformanceImplications for ABS Braking Performance
Vehicle A
140
141142
143144
145146
147148
149150
151
1 2 3 4 5 6 7 8Tire Spec.
DS
D [f
t]
Vehicle B
160161
162163
164165
166167
168169
170171
1 2 3 4 5 6 7 8
Tire Spec.
DS
D [f
t]
SHORTEST
LONGER
LONGEST
SHORTER
EIGHT TIRE SPECS TESTED ON TWO VEHICLES FOR ABS DSD
42.7
43.0
43.343.6
43.9
44.244.5
44.8
45.145.4
45.7
46.0
48.8
49.1
49.449.7
50.0
50.350.6
50.9
51.251.5
51.8
52.1
DS
D (
m)
DS
D (
m)
15
Implications for ABS Braking PerformanceImplications for ABS Braking PerformanceM
u (
Fx
/Fz)
Slip Rate
Mu-Slip Curves for Various Tires
Tire ATire BTire C
Stopping Distance for Various Tires
Sto
pp
ing
Dis
tan
ce
Tire A
Tire BTire C
Slip Ratio
Fx
Tire Mu-Slip Curves & ABS Cycling
SR Cycling with Phase Lag
Fz1
Fz2
Fz3
Fz4
Fz5
0%
5%
10%
15%
20%
25%
30%
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Time [sec]
EE876P --- Firestone FR710 - 225/60R18 - 18x7.5 --- 40psi
TEST_000_LF SR TEST_000_RF SR
Slip
Rat
e [%
]
TEST 000
Tire Slip Rate vs TimeLF SR RF SR
Time (sec)
Slip
Rat
e
Mu
(F
x/F
z)
Slip Rate
16
Implications for ABS Braking PerformanceImplications for ABS Braking Performance
Slip Rate
Mu-Slip Curves for Various Tires
Tire ATire BTire C
ABS Operating Range(SR-Based ABS Controller)
2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%
Mu
(F
x/F
z)
0% 26%
•Peak Is Constant•Slope & Curvature Varied•CONSIDER A “SLIP RATE-BASED” ABS CONTROLLER
17
Implications for ABS Braking PerformanceImplications for ABS Braking Performance
Mu
(F
x/F
z)
Slip Rate
Mu-Slip Curves for Various Tires
Tire ATire BTire C
2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%
ABS Operating Efficiency is Influenced by the Shape
of the mu-Slip Curve
0% 26%
ABS Operating Range(SR-Based ABS Controller)
•Peak Is Constant•Slope & Curvature Varied•CONSIDER A “SLIP RATE-BASED” ABS CONTROLLER
18
Implications for ABS Braking PerformanceImplications for ABS Braking Performance
Mu
(F
x/F
z)
Slip Rate
Base Mu-Slip Curves for Different TiresB
raki
ng
Fo
rce,
Fx
Slip Rate
Mu-Slip Behavior for Different Tires during an ABS Simulation
Penalty for Excessive Pressure Release
Bra
kin
g F
orc
e, F
x
Time
Mu-Slip Curves for Different Tires
Transient Steady ABS Operation
Tire B
Tire A
PERFORMANCE LOSS
BETTER PERFORMANCE
Tire B
Tire A
Tire B
Tire A
ABS Operating Efficiency is Influenced by the Shape
of the mu-Slip Curve
•Peak Is Constant•Slope & Curvature Varied•CONSIDER A “PEAK-SEEKING” ABS CONTROLLER