A Study on Minimum Rolling Resistance
Tire rolling resistance has been a topic of study since the invention of the pneumatic tire. There is currently a heightened interest in this topic because of the need to minimize fuel consumption of vehicles and the introduction of regulations regarding both the maximum allowable rolling resistance and consumer labeling for rolling resistance. The question arises as to how low tire rolling resistance can go. Tire energy loss can be written as the product of the material deformations, the volume of material deformed, and the loss property of the material. The last two terms of the energy loss equation will be considered fixed. This article concentrates on the deformation term. The current paradigm of the steel-belted radial tire is assumed. The minimum deformations required for the function of the tire are established, and the assumption is made that all other deformations are parasitic and can in theory be eliminated. Analytical expressions for the dominant necessary deformations are developed, and the functional relationship for minimum rolling resistance is determined. The functioning point required to reach the minimum rolling resistance is established. The functional relationships are compared with experimental data taken by the whole tire hysteresis method.ABSTRACT:
Tire energy loss can be simply described as the product of the deformation magnitudes, the volume of deformed material, and the loss property of the material. This study is concerned with the first term, the deformation magnitudes. The last two terms will be considered as constants.
One of the dominant necessary deformations is tread compression. The tread compression is an imposed stress that is considered equal to the inflation pressure. Note that a tread pattern will increase the compression stress because of the void area in the pattern. That increase is ignored in this analysis.
One of the dominant necessary deformations is tread longitudinal shear strain. The tread shear strain is an imposed strain that increases linearly with distance from the center of the contact patch and inversely with the belt radius. This simple relationship somewhat overstates the magnitude of the actual shear strain seen in tires.
The rolling resistance coefficient is plotted versus inflation pressure. The other parameter values are appropriate for a 205/55R16 tire. The compression and shear terms of Eq. (13) are plotted individually. At low inflation pressure, the tread compression becomes a small part of the rolling resistance. The tread shear term becomes small at high inflation pressure, because of the short contact patch at constant load. The total coefficient is seen to have a minimum that occurs when the compression and shear terms are equal.
The rolling resistance coefficient, Eq. (13), is plotted versus inflation pressure for various values of tread rubber modulus. The minimum rolling resistance is found not to change, but the inflation pressure at which the minimum is reached shifts with tread modulus. The other parameter values are appropriate for a 205/55R16 tire.
The rolling resistance coefficient, Eq. (13), is plotted versus inflation pressure for various values of tire load. The minimum rolling resistance is found not to change, but the inflation pressure at which the minimum is reached shifts with load. The other parameter values are appropriate for a 205/55R16 tire.
The experimental data in this figure represent the quasi-static energy loss from loading and unloading a 235/45R17 tire. Each data point is an average of 6 to 12 load and unload cycles. This type of data has been shown to correlate with rolling resistance measured on a road-wheel using the standard methods. This method eliminates temperature and frequency effects from the results in keeping with the theoretical model. The data are fit with quadratic equations to allow extraction of energy loss data at constant load for the five different inflation pressures.
Comparison of measured tire energy loss as a function of pressure for various tire loads compared with the simple model theory given by Eq. (13). Note that the experimental data include all losses necessary and parasitic. The actual rolling resistance coefficient values are not comparable. The functional response of the experimental data in terms of minimum occurrence and functional shape at particular pressures is quite similar to the theoretical model.
The minimum rolling resistance at constant tread thickness depends only on the belt radius once the parameter group C is specified.
The minimum rolling resistance at constant tread volume depends on the belt radius and tread width once the parameter group C′ is specified.
The functioning point required to reach the minimum rolling resistance can be determined from this graph given a load of 4000 N and a tread rubber modulus of 4 MPa. Belt width and tread width determine the tire size. The curved lines indicate the inflation pressure required to reach the minimum rolling resistance given these parameters. The straight lines are constant aspect ratios. The gray area below the horizontal line indicates a reduction in load capacity relative to the reference 205/55R16 reference. The area above the gray area indicates a greater load capacity than the reference.
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