ESTIMATION OF THE ROLLING RESISTANCE OF TIRESBrian Paul Wiegand, Northrop Grumman (Retired)

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Conceptual Design of Unusual Automotive Configurations May Require Unusual Tire Sizing:• Alec Issigonis, BMC (Austin/Morris) Mini Design

– Concept 5.2×8, Production 5.2×10• Pierre Jules Boulanger, Citroen 2CV Design

– Concept/Early Production 125R400 (125R15.75)– Later Production (Post-1960) 125R380 (125R15)

Computer Simulation of Historic Automotive ConfigurationsMay Require Historic Tire Evaluation:

• 1969 Dodge Charger R/T– F70-14 Firestone Wide Oval Redline Polyester, Fiberglass Belted

• 1965 Ford Shelby Mustang – F60-15 Goodyear Polyglas Power Cushion HP Blue Dot

Estimation of the Rolling Resistance of Tires;Why? Various Possibilities:

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A Primary or “Static” (Low Speed) Aspect “Csr”: Hysteresis Loss Due to Flexing of Tire Body Frictional Loss Due to Squirming of Tread on Road A Secondary or “Dynamic” (High Speed) Aspect “Cdr”:

Aerodynamic Loss Due to Atmospheric Contact Tire Outer Surface Aerodynamic Loss Due to Inflation Gas Contact Tire Inner Surface

Both Aspects Are Always Present, in Tire Testing and Operation:

Estimation of the Rolling Resistance of Tires;How? Divide into Two Aspects:

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Estimation of the Rolling Resistance of Tires;1938 Stuttgart Institute of Technology Model (Reference Tire):

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FR = [Csr + 3.24 Cdr (V/100)2.5 ] N

FR = [Cr ] N

(Reference: Taborek, Jaroslav J.; Mechanics of Vehicles, Cleveland, OH; Penton Publishing Company, 1957)

6.00×16 BIAS, INNER TUBE

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Estimation of the Rolling Resistance of Tires;Use Ref Tire to Estimate Unknown Tire Static & Dynamic Coeffs:

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1) “fvol” is a Deformed Material Volume Ratio Factor.

2) “fLOT” is a “Level of Technology” Ratio Factor. 3) “fRi” is an Inflated (No Load) Radius Ratio Factor.

4) “farea” is an Exposed Surface Area Ratio Factor.

5) “frough” is an Exposed Surface Area Roughness Ratio Factor.

Note Use of Five “Unknown-to-Reference” Ratio Factors:

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Estimation of the Rolling Resistance of Tires;The Five Factors, “fvol”:

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1) “fvol” is a Deformed Material Volume Ratio Factor.

REFERENCE TIRE UNKNOWN TIRE

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Estimation of the Rolling Resistance of Tires;The Five Factors, “fLOT” :

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2) “fLOT” is a “Level of Technology” Ratio Factor, Which Has To Do With the Transition in Time From Natural Materials to Synthetic Materials, From Inner Tube to Tubeless, and From Bias to Radial Construction, Etc.

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Estimation of the Rolling Resistance of Tires;The Five Factors:

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3) “fRi” is an Inflated (No Load) Radius Ratio Factor.

This “Wheel Size” Factor Proved Necessary Upon Analysis of the Original Results, and Was Determined from a Regression Analysis of Those Initial Results:

10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.000.400.500.600.700.800.901.001.101.201.301.40

fRi FACTOR vs Ri

Inflated Radius (in)

Radi

us S

ize

Fact

or (d

imen

sion

less

)

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Estimation of the Rolling Resistance of Tires;The Five Factors:

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4) “farea” is an Exposed Surface Area Ratio Factor.

REFERENCE TIRE UNKNOWN TIRE

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Estimation of the Rolling Resistance of Tires;The Five Factors:

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5) “frough” is an Exposed Surface Area Roughness Ratio Factor.

(Reference: http:etyres.co.uk/glossary-type-terms/?term=land-sea-ratio, July 2015)

The “Openess” or Void Factor of the Tread Pattern is Taken as Being Indicative of Tire Surface Roughness (at Least of the Tread) Relative to the “General Touring” Tire (frough = Void FactorTire Type / Void FactorGeneral Touring):

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Estimation of the Rolling Resistance of Tires;Determination of “SH”, “Ri”, “tw”, “KZ”, “d0”, and “d”:

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Determination of Tire Parameter Values Begins With Tire Designation (Exempli Gratia: 152/92R16 Means SN = 152 mm, AR = 92, Dr = 16 in):

(Reference: Gent, Alan N.; and Joseph D. Walter (Co-Editors); The Pneumatic Tire, National Highway Traffic Safety Administration, Washington, DC; 2006, DOT HS 810 561)

Ri = (2 SH + Dr)/2

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Estimation of the Rolling Resistance of Tires;Determination of “td”:

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Determination of “td” Tread Depth Parameter:

(Reference: Tires and Passenger Vehicle Fuel Economy, Washington, DC; Transportation Research Board Special Report 286, 2006, IBSN 0-309-09421-6)

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Estimation of the Rolling Resistance of Tires;Summation of the Methodology:

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1) Use Designation of Unknown Tire to Determine Tire Parameter Values.

2) Use Parameter Values of Unknown Tire to Determine the Five Factors.

3) Use the Five Factors to Determine the “Static” and the “Dynamic” Coefficient Values for the Unknown Tire.

4) Use the “Static” and “Dynamic” Coefficient Values in the Stuttgart Rolling Resistance Coefficient Equation and Evaluate at “V” = 50 mph (80 kph) as per SAE J1269 SP.

5) The Resultant Value is an Estimated Rolling Resistance Coefficient “Cr” for the Unknown Tire that is Comparable to a Coefficient Obtained Empirically per Test Standard SAE J1269 SP.

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Estimation of the Rolling Resistance of Tires;Validation of the Methodology:

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“Validation” consisted of taking 90 tires for which an empirically obtained “Cr” value (with corresponding normal load and inflation pressure) was presented in the literature. This involved a span of wheel sizes 13 to 16 inches (330 to 406 mm) for bias, bias-belted, and radial tires over the years 1958 to 2008. Those tires were then treated as being of “unknown” “Cr” value and, utilizing the rolling resistance estimation methodology as presented, estimated “Cr” values were determined.The comparison of the estimated with empirical “Cr” values indicated that the methodology is accurate on average within a range of about ±8% (but with a maximum range of variation of +32%/-21% due to possible data point outliers); the R2 correlation coefficient between estimated and empirical is a reasonable .86 value.:

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Estimation of the Rolling Resistance of Tires;Validation of the Methodology:

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The Following Plot of Estimated Versus Empirical Values Makes Clear the Strong But Far From Perfect Relationship

If Each Estimated Value Exactly Equaled Each Corresponding Empirical Value Then the Agreement With the Trend Line Would Be Perfect (R2 = 1) and There Would Be No Intercept Value (Line Through “0,0”)

However, That Can Never Quite Be Achieved; Even If the Estimation Methodology Were Perfected the Empirical Values Would Still Be Subject to Random Experimental Variations.

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Estimation of the Rolling Resistance of Tires;Limitations of the Methodology (as Presented):

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• Passenger Car Tires Only, With:

• No Hi-Performance Tires (Speed Ratings “V”, “W”, “Y”, or “Z”).

• No Ultra Hi-Efficiency (“Eco”) Tires.

• No Mud and Snow (“M/S”) Tires.

• No Off-Road All-Terrain (“A/T”) Tires.

• Years 1938 to 2015 Only (Further Extrapolation Possible But Risky).

• Inflation Pressures 15 to 50 psi (103 to 345 kPa) Only.

• Wheel (“Rim”) Sizes 13 to 16 Inch Diameter Only.

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More Precise Calculation of Area and Volume Factors. A “Wheel Rotational Speed Factor” @ 50 mph (80 kph). Add More Individual Factors (Ultimately Obviating the LOT Factor Table):

“Cord Material Factor”. “Belt Material Factor”. “Rubber Material Factor”. “Inner Tube/Tubeless Factor”. “Bias/Bias-Belt/Radial Factor”.

Have “Wheel Size Factor” Based on Rolling Radius (Not Inflated Radius). Base Methodology on Database Expanded Beyond 90 Tires. Expand Database to Include:

Wheel (“Rim”) Sizes Less Than 13 and Greater Than 16 Inch Diameter. Hi-Performance Tires (Speed Ratings “V”, “W’, “Y”, or “Z”). Ultra Hi-Efficiency (“Eco”) Tires. Mud and Snow (“M/S”) Tires. Off-Road All-Terrain (“A/T”) Tires.

Vary Reference Tire Parameter Values to Correspondence With Unknown Tire’s Inflation Pressure.

Narrow Down and Modernize the Time Interval Focus of the Study.

Estimation of the Rolling Resistance of Tires;Possible Future Development of the Methodology:

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Estimation of the Rolling Resistance of Tires;Conclusion:

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A Methodology for Estimation of a Tire’s Rolling Resistance (“Cr”) Was Obtained and Seems Reasonably Accurate As Presented, But There Is a Great Deal of Scope for Future Improvement.

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Estimation of the Rolling Resistance of Tires;Q&A:

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The Following Back-Up Slides Were Created in Anticipation of a Short Q&A Session Following the 20 Minute Presentation.

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Pillai, & Fielding-Russell; “Tire Rolling Resistance From Whole-Tire Hysteresis Ratio”, Rubber Chemistry and Technology, Vol. 65, No. 2, pp. 444-452, May 1992.

(Methodology: Tire Parameters, Including a “Whole-Tire Hysteresis” Parameter, Are Used to Estimate Rolling Resistance Coefficient, but the “Whole-Tire Hysteresis” Value Must Still Be Determined Empirically on a Tire Test Machine.)

Yokota, Higuchi, & Kitagawa; “Estimation of the Temperature Distribution and Rolling Resistance Under Running Conditions Including Environmental Factors”, SAE 2012-01-0796, doi: 10.4271/2012-01-0796.

(Methodology: FEM is Used to Determine Temperature Distribution at Equilibrium Which In Turn Is Used to Determine Rolling Resistance Coefficient.)

Cho, Lee, Jeong, Jeong, & Kim; “Finite Element Estimation of Hysteretic Loss and Rolling Resistance of 3-D Patterned Tire”, International Journal of Mechanics and Materials in Design, Vol. 9, Iss. 4, pp. 355-366, Dec. 2013.

(Methodology: FEM is Used to Determine Hysteresis Loss Which In Turn Is Used to Determine Rolling Resistance Coefficient.)

Estimation of the Rolling Resistance of Tires;Back-Up Slides: Other Rolling Resistance Estimation Methodologies

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Estimation of the Rolling Resistance of Tires;Back-Up Slides: Robustness of This Estimation Methodology

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Use of Factors Makes the “Csr” and “Cdr” Determination “Robust” (If the Methodology is Off By Some Percentage in the Numerator it Will Be Off By An Equal Percentage in the Denominator):

frough = Void Factor / Void FactorGeneral Touring

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Estimation of the Rolling Resistance of Tires;Back-Up Slides: Example of Estimated Rolling Resistance Use

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Computer Program “MAXGLONG.BAS” for Automotive Longitudinal Acceleration Simulation Requires “Csr” and “Cdr” Estimation for Input:

(Reference: Wiegand, B.P.; “Mass Properties and Automotive Longitudinal Acceleration”, SAWE Paper #1634, 1984.)

“…the elapsed times for the higher speed ranges tend to exhibit an almost parabolic relationship to weight. This is most likely a manifestation of the rolling resistance phenomenon; in the MAXGLONG.BAS program the rolling resistance is determined in accordance with the Stuttgart Institute of Technology formula…”

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Estimation of the Rolling Resistance of Tires;Back-Up Slides: Recent Example of Estimated vs. Empirical

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From a Presentation to the California Air Resources Board at Sacramento, CA (Vu-Graph #17), Empirical Data Drawn From Smithers Scientific Services Testing:

(Reference: Waddell, Walter H.; “Inflation Pressure Retention Effects on Tire Rolling Resistance and Vehicle Fuel Economy”, Global Specialty Polymers Technology Department of Exxon Mobile Chemical, 13 May 2008.)