Editorial Type:
Article Category: Research Article
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Online Publication Date: 01 Dec 2009

Experimental Determination of the Effect of the Surface Curvature on Rolling Resistance Measurements4

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Page Range: 254 – 278
DOI: 10.2346/1.3148299
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Abstract

REFERENCE: Freudenmann, T., Unrau, H.-J., and El-Haji, M., "Experimental Determination of the Effect of the Surface Curvature on Rolling Resistance Measurements," Tire Science and Technology, TSTCA, Vol. 37, No. 4, October - December 2009, pp. 254-278.

Vehicle and tire manufacturers usually perform rolling resistance measurements on external drums with diameters of 1.71 or 2.0 m. The rolling resistance measured on these test benches is higher than the actual rolling resistance measured on a flat surface. This deviation is caused by the drums’ curvature. In 1979, S. K. Clark aimed to solve this problem by developing a formula, which converts the rolling resistance of a tire measured on a curved surface into the corresponding rolling resistance on a plane. This formula is still used today in ISO and SAE standards. To verify Clark’s universally accepted formula, a research project was initiated at the Universität Karlsruhe. A combined test bench that allows measurements on two external drums of different diameter and a continuous flat track with the same wheel suspension was built up and came into operation. The rolling resistances of six different tires on the three surfaces were measured under variation in operational parameters, such as tire load and inflation pressure. Comparison of converted values from measurements on external drums with flat track measurements showed the necessity for an upgrade of the existing formula. By conducting a multiple regression analysis, which took various tire properties and operational parameters into account, a modified formula was derived. Application of this new formula on the measurement data of the six tires as well as on further measurements showed excellent results.

Keywords: rolling resistance; track; surface; curvature; external drum; flat track; test bench
Copyright: The Tire Society
FIG. 1.
FIG. 1.

Combined test bench for measurements on two external drums and a continuous flat track.

FIG. 2.
FIG. 2.

Effect of the lubricant wedge in the hydrodynamic surface bearing on the measured force Fspindle.

FIG. 3.
FIG. 3.

Rolling resistance of a steel wheel measured on the external drum at a speed of 50 km/h in both driving directions.

FIG. 4.
FIG. 4.

Operational parameters of the rolling resistance measurements of tires 1–6.

FIG. 5.
FIG. 5.

Rolling resistance curves of the load variants of tires 3 and 5.

FIG. 6.
FIG. 6.

F R,flat¯ and FR,Clark¯ of all test series of tires 1–6.

FIG. 7.
FIG. 7.

Curvature influence values of tire 5 plotted against wheel load.

FIG. 8.
FIG. 8.

Curvature influence values of tire 5 plotted against inflation pressure.

FIG. 9.
FIG. 9.

Residuals of the 180 data sets of the complete regression model.

FIG. 10.
FIG. 10.

Coefficient β3 calculated for each tire separately plotted against the aspect ratio.

FIG. 11.
FIG. 11.

Measured and converted rolling resistance curves of the load variants of tire 5.

FIG. 12.
FIG. 12.

Measured and converted rolling resistance curves of the pressure variants of tire 5.

FIG. 13.
FIG. 13.

Standard deviation of rolling resistance values calculated from measurements on the small and large drums with the new formula and Clark’s formula (tires1–6).

FIG. 14.
FIG. 14.

Standard deviation of rolling resistance values calculated from measurements on the small drum with the new formula and Clark’s formula (tires 7–9).

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