## 3 Results and Discussion  
The simulation can be divided into three stages. The first was the application of pressure to the tyre in a range from 0.18 MPa to 0.22 MPa. This stage finished after exactly one second. During this stage, contact between the tyre and the fixed basis occurred. This phenomenon was demonstrated clearly (see Figure 5) by increasing the normal force between the tyre and basis to the value \(\sim\)1000 N. The second stage started after one second and continued until the ninth second. During this stage, the contact force was applied to the component responsible for the asphalt concrete basis, a vertical displacement towards the inflated tyre. The normal force \(F_{n}\) started to increase from \(\sim\)1000 N to \(\sim\)6000 N, when the second stage finished. The tangential force component behaved slightly differently in the second stage (time range 1-9 s). It was flat from the beginning of the vertical movement of the fixed basis until the fifth second, increased by approximately a factor of three between the fifth and seventh seconds, and flattened again until the end of vertical movement at the ninth second. Finally, the starting tangential velocity component of basis movement began true tangential interaction between the tyre and the loaded basis. The quantitative character was slightly different for different external loads and internal tyre pressures (Figure 4, normal forces \(F_{n18}\), \(F_{n20}\), \(F_{n22}\) and tangential forces \(F_{118}\), \(F_{120}\), \(F_{122}\), where the indices 18, 20 and 22 denote internal pressure inside a tyre). Figure 6 presents velocities of the tread geometric centres in the x (a), z (b) and y (c) directions. Figure 7 shows the tread displacements which were used to calculate the tread velocities. Figure 6a shows that velocities \(v_{x}\) of treads are distributed in opposite directions relative to the labelled eleventh tread (Figure 2a) in the centre of the tyre pattern. The velocity \(v_{x}\) of the eleventh tread was slightly shifted to the x direction. Figure 6b demonstrates that the velocity \(v_{z}\) was symmetrical about the pattern centre of the eleventh tread. Finally, Figure 6c shows the asymmetrical behaviour of the tread centre velocities in the y direction, which is normal to the road-tyre interface surface. Next, friction coefficients were obtained for different tyre external load regimes, with different ratios of tangential and normal forces on the tread block. Six cases in total were investigated: three cases for \(\sim\)4 kN external load and 0.2, 0.18 and 0.22 MPa internal tyre pressures (see Figure 8--the exact values of the normal external load were 3.869, 3.528 and 4.2 kN) and three cases for \(\sim\)6 kN external load and 0.2, 0.18 and 0.22 MPa internal tyre pressures (see Figure 9--the exact values of the normal external load were 6.888, 6.517 and 7.283 kN). Each friction case in Figures 8 and 9 is followed by the normal and tangential force distribution over all of the road surface that made contact with the tread blocks. The 2D friction distribution shown in Figure 8 can be characterised by the mean and standard deviation values of 0.542448 \(\pm\) 0.046138 for internal pressure 0.2 MPa, 0.556167 \(\pm\) 0.038144 for internal pressure 0.18 MPa and 0.533904 \(\pm\) 0.047833 for internal pressure 0.22 MPa, respectively. In the same manner, the 2D friction distribution in Figure 8 can be characterised by mean and standard deviation values of 0.472007 \(\pm\) 0.085539 for internal pressure 0.2 MPa, 0.477212 \(\pm\) 0.083172 for internal pressure 0.18 MPa and 0.449233 \(\pm\) 0.089224 for internal pressure 0.22 MPa. A comparison of the results shows a 'flatter' distribution of friction coefficients of tread blocks  
Figure 5: The model’s resulting forces on tyre vs time for displacement of 15 mm, tyre internal pressure 0.18, 0.2 and 0.22 MPa and tyre–road friction coefficient 0.6.  
for external tyre load values equal to \(\sim\)4 kN, or approximately double the standard deviation of the overloaded tyre.