1. 1 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 30 th Tire Society Conference Akron, Ohio September 14, 2011

2. 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 potential for improvement is enhancedABS 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 SafetyEuropean & 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 SafetyConsumers 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 procedureSAE Committee has developed a standardized stopping distance test procedure Motivation for Interest in Dry Braking Performance

3. 3 V ground Belt Tread Ω V belt Shear  zx  (Vg /Vb) BeltTread V Belt V Ground GROUND z x Free Rolling Brake Drive 1D Concept “Brush” Model Free Rolling Brake Drive Brake Drive Tread Shears until it Reaches Friction Limit Tread Shears until it Reaches Friction Limit Slip Zones Evolve from the Rear of Footprint Slip Zones Evolve from the Rear of Footprint Friction limit =  Slip Zone Evolution Friction limit =  Drive-Brake Force Generation & Slip Zone Evolution Shear Stress Vg/Vb is the Basic Mechanism of Tread Shear Development Vg/Vb is the Basic Mechanism of Tread Shear Development Brake Drive Shear Stress

4. 4 Free Rolling Moderate Braking (SR=6%) Contact Behavior – Free-Rolling & Braking Conditions

5. 5 Slip 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) Driving Braking 00  0 Shape Controlled by Slip Zone Evolution 0/00/0 Increasing 0/σ00/σ0 Slip Rate at Peak is Altered as well INCREASING BRAKE TORQUE FREE ROLLING Stress Free RollingTorque Ramp Concept Model FREE ROLLING SLIPSTICK SLIPSTICKSLIPSTICK 00 00 Driving Braking

6. 6 µ vs Slip Rate µ (Fx/Fz) Drive Torque Brake Torque Brake Torque re-plotted in Drive Quadrant Slip Rate (%) 02.55.07.510.012.515.0-2.5-5.0-7.5-10.0-12.5-15.0 0 -0.2 -0.4 -0.6 -0.8 -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 Shape µ vs Slip Rate µ (Fx/Fz) Drive Torque Brake Torque Brake Torque re-plotted in Drive Quadrant Slip Rate (%) 02.55.07.510.012.515.0-2.5-5.0-7.5-10.0-12.5-15.0 0 -0.2 -0.4 -0.6 -0.8 -1.2 1.2 1.0 0.8 0.6 0.4 0.2

7. 7  zx /  zz  Drive & Brake mu-Slip Curves Differ due to Slip Zone Evolution Travel LEADING EDGE TRAILING EDGE SLIP  zx /  zz Brake Torque - FEA Drive Torque - FEA Experimental MeasurementFEA Prediction INCREASING TORQUE Brake Torque – Concept Model Drive Torque – Concept Model Example of Contrasting Slip Zone Growth Rates SLIPSTICKSLIPSTICK SLIP STICK ZONE SLIP ZONE

8. 8 SR = 0% SR = 2% SR = 8% SR = 6% SR = 4%  zz LOW Slip Zone Evolution for All-Season Tire Under Braking Rolling Direction HIGH Slip Zone Growth FRONTREAR

9. 9 Increased Braking “All Season” Contrasting Lift-Off “Summer” “Winter” Free Rolling Medium Braking Heavy Braking Fundamental Studies of Lift-Off

10. 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 Contact Pressure Coef. of Friction Lug Braking Shear Lug Lift Friction – Impact of Pressure Dependence Velocity (mm/sec) 250 375 500 625 750 Pressure (kPa) 700 560 420 280 140 ZZ LIFT-OFF WHEN  Z =0 Free-RollingBraking

11. 11 18% Decrease Constant COF Variable COF Impact of Friction Law on Braking Performance Apply Load Sliding Direction Un-Deformed Lug Distance Mu (Fx/Fz) Mu vs Distance – Comparison between Friction Laws Pressure COF

12. 12 19% Decrease Lift-Off Zone Lug Sliding (Mesh) Contact Pressure (kPa) Impact of Sipes on Braking Performance Contact Pressure while Sliding Solid Lug 2-Sipe Lug Solid Lug 2-Sipe Lug Lift-Off Zones - 1900 - 330 - 300 - 270 - 240 - 210 - 180 - 150 - 120 - 90 - 60 - 30 - 0 Solid Lug 2-Sipe Lug DistanceMu (Fx/Fz) Mu vs Distance – Siping Impact 2-Sipe Lug Solid Lug 2-Sipe Lug

13. 13 Mu drops with increased Fz 6% Drop F z = 300 NF z = 225 N Moderate Pressure @ Leading Edge Increased Pressure @ Leading Edge Very High Pressure @ Leading Edge F z = 375 N Impact of Contact Stress on Braking Performance Contact Pressure (kPa) - 360 - 330 - 300 - 270 - 240 - 210 - 180 - 150 - 120 - 90 - 60 - 30 - 0 Mu (Fx/Fz) Distance Mu vs Distance – Impact of Contact Stress F z = 225 N F z = 300 N F z = 375 N

14. 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 Performance Implications for ABS Braking Performance 42.7 43.0 43.3 43.6 43.9 44.2 44.5 44.8 45.1 45.4 45.7 46.0 48.8 49.1 49.4 49.7 50.0 50.3 50.6 50.9 51.2 51.5 51.8 52.1 DSD (m)

15. 15 Implications for ABS Braking Performance Mu (Fx/Fz)Slip Rate Mu-Slip Curves for Various Tires Tire A Tire B Tire C Stopping Distance for Various Tires Stopping Distance Tire A Tire B Tire C Tire Mu-Slip Curves & ABS Cycling SR Cycling with Phase Lag Fz 1 Fz 2 Fz 3 Fz 4 Fz 5 Tire Slip Rate vs Time LF SRRF SR Time (sec) Slip Rate Mu (Fx/Fz)Slip Rate

16. 16 Implications for ABS Braking Performance Slip Rate Mu-Slip Curves for Various Tires Tire A Tire B Tire C ABS Operating Range (SR-Based ABS Controller) 2%4%6%8%10%12%14%16%18%20%22%24% Mu (Fx/Fz) 0%26% Peak Is Constant Slope & Curvature Varied CONSIDER A “SLIP RATE-BASED” ABS CONTROLLER

17. 17 Implications for ABS Braking Performance Mu (Fx/Fz) Slip Rate Mu-Slip Curves for Various Tires Tire A Tire B Tire 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. 18 Implications for ABS Braking Performance Mu (Fx/Fz) Slip Rate Base Mu-Slip Curves for Different Tires Braking Force, Fx Slip Rate Mu-Slip Behavior for Different Tires during an ABS Simulation Penalty for Excessive Pressure Release Braking Force, Fx 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