1

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

2

• 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

3

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

4

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

8

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

9

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

10

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

11

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

13

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