## 1 Introduction
### Drum Testing Machine  
Testing a tire on a real runway still remains an expensive and difficult task, especially at high velocity. Therefore, drum-tire machines represent a suitable alternative. Tires could be tested in contact with the inner or the outer surface of the drum. The internal contact drum tests are frequently used to investigate the influence of the tread pattern design, tread groove, water depth, cornering and braking force capability of the tire on a wet runway. External contact drums with diameter of 1.8 m or 2.0 m are usually used to measure the rolling resistance of vehicle tires (Figure 1). The rolling resistance measured on these test rigs is higher than the rolling resistance measured on a flat surface. This deviation is caused by the drum's curvature. [PERSON] et al. [10] developed a model, which converts the rolling resistance of a tire measured on a curved surface into the corresponding rolling resistance on a plane runway. Indoor laboratory drum tests are generally run on large diameter drums, at an ambient temperature of 23 \({}^{\circ}\)C. Most industry high speed tire tests call for 80% of the maximum loading. In these tests, in order to avoid tire wear, velocity increases by 10 km/h every 10 min increment until the specified speed is achieved. Inflation pressure varies according to the tire type and velocity rating. The reduced pressure is an adjustment to obtain an equivalent tire deflation on the drum's curved surface to the one expected on a flat runway surface.  
In tire/drum tests proposed in [11], it was noted that the tire tread temperature increases linearly as a function of velocity and loading. This is due to the absence of cooling air and the effects of the runway interface. That is why all experimental tests are carried out at different vertical loadings and velocities.  
[PERSON] [13] has performed full-scale physical tests to characterize the behavior of the stationary tire under vertical loading, the rolling tire behavior under free-rolling and in cornering conditions. The rolling experiments were carried out on flat and drum surfaces. It was demonstrated that the normal pressures at the tire/drum interface are higher than those experienced on the flat surface. The maximum value exceeds the inflation pressure by a factor between 1.75 and 2.25. This indicates that the contact patch on the drum surface is smaller than that the one obtained on plane surface. The longitudinal and lateral shear stresses are similar under free-rolling and camber angle conditions. Under skidding angle conditions, the contact stresses on the drum surface differ considerably from those observed on the flat surface. The maximum pressure is much higher and the contact patch length at the lateral tire center increases with the skidding angle. [PERSON] [13] noted that this phenomenon has not been previously identified and no explanation is currently at hand.  
[PERSON] et al. [14] have worked on a finite element analysis of a tire in steady rolling on a drum and the results were compared with experimental results. They developed a FEM model of rolling on the drum, which was used to quickly find out the optimal tire design parameters. Equipment and methods have been used for experimental determination of braking and cornering characteristics of the tire as well as for experimental determination of the friction coefficient of tire tread. For experimental testing of tire parameters, a drum of diameter of 1.20 m has been used and a maximum speed of 150 km/h was applied. For the cornering test the skidding angles were varied from \(-10^{\circ}\) to \(+10^{\circ}\). It was noted that the differences between experimental and numerical results were decreased after friction calibration and that the FEM model helps designers to quickly find out the optimal parameters for tire design.