# Comparison of Achieved Rolling Resistance Values of Two Selected Tires on a Solid Surface
## 2 Materials and Methods
The tire inflation pressures and their vertical loads have been chosen to meet the technical requirements set by the tire manufacturer and to avoid unnecessary overloading, reducing their service life. In the method of measuring the rolling resistances of tires conceived in this way, the total measured tensile force consists not only of the rolling resistance components, but also of other resistance forces, which must be considered in the calculation (Figure 3). The following applies to the total measured resistive force according to Figure 3.  
\[F_{c}=F_{v}+F_{vv}+F_{mt}\left[N\right] \tag{5}\]  
\(F_{v}\)--rolling resistance of the trailing tire, \(\left[N\right]\)  
\(F_{vv}\)--resistance in the guide frame, \(\left[N\right]\)  
\(F_{mt}\)--frictional resistance force in bearings, \(\left[N\right]\). Figure 3: Force action when pulling a pneumatic wheel (measurement on a concrete surface). \(F_{c}\)—Total drag force, \(F_{n}\)—Normal tire force, \(F_{v}\)—Rolling resistance, \(F_{mt}\)—Friction resistance force in bearings, \(F_{vv}\)—Resistance force in guide frame guide. From Equation (5), the value of rolling resistance can be expressed in the form as follows:  
\[F_{v}=F_{c}-F_{vv}-F_{mt}\ [N] \tag{6}\]  
The friction resistance in the guide of the guide frame \(F_{vv}\) based on the free pulling of the guide frame without the connected main frame with the wheel was determined. This measurement was performed before the actual measurement of tire rolling resistances using the measuring set described above. Its value was around 79.82 N.  
The relation for the resistive friction torque in the wheel shaft bearings is as follows:  
\[M_{mt}=\mu\times P\times\frac{d}{2}\ [N\times m] \tag{7}\]  
\(\mu\)**--coefficient of friction in bearings, \([-]\)  
\(P\)**--equivalent dynamic bearing load, \([N]\)  
\(d\)**--the diameter of the shaft at the bearing location, \([m]\)  
The disadvantage of this relation is that it applies exactly to a bearing load of size \(P=0.1\times C\), where \(C\) is the basic dynamic bearing capacity [14]. In many cases, this strength was overcome. Regarding the choice of the coefficient of friction in the bearings, the value \(\mu\) = 0.001 was used for the given type of bearings and the given method of lubrication with that's all right.The force of frictional resistance in the bearings is then calculated according to the following formula:  
\[F_{mt}\ =\frac{M_{mt}}{R}\ [N] \tag{8}\]  
\(R\)**--tire wheel rolling radius, \([m]\)  
The radial reactions of the wheel shaft bearings were not measured. The measurement was based on the force diagram and the dimensions of the shaft mounting in the bearings. This means that from the known value of the vertical load of the wheel, the reactions of the bearings were calculated, which determined the equivalent dynamic load of the bearings. According to the performed calculations, the force of friction resistance in the bearings \(F_{mt}\) is very small and ranges at the level of max. \(1.5\,N\). In order to reduce this resistance, the wheel bearing housings are not equipped with a contact seal. Thus, only friction in the bearings was applied. The rolling radius of the monitored tires at each tire inflation pressure level and the given vertical load were measured using a mechanical altimeter. The appropriate value of the rolling resistance coefficient was calculated according to the following formula:  
\[f_{v}=\frac{F_{v}}{F_{n}}\ [-] \tag{9}\]  
\(F_{n}\)**--normal (vertical) tire load, \([N]\). The rolling resistance measurement was repeated three times for each load level and tire inflation pressure, which determined the resulting value as the arithmetic mean of these measured values. When measuring the rolling resistances of the monitored tires, the dependence of the tire slip on the load and inflation pressure was not determined.