## 4 Simulation and Thermo-Investigation of Rolling Tires on the Flat Road Affected by Some Factors
### Thermal Analysis
#### 4.3.2 Change in Pressure  
The variations in the strain energy density, averaged temperature, and total temperature with an increasing inflated pressure are demonstrated in Figure 10a-c. All three variables are observed to increase linearly when the pressure is increased from 27 psi to 35 psi. The variations in all three variables are lower than the increased rate of changing loading. The maximum temperature ranges between 32.9 \({}^{\circ}\)C and 34.5 \({}^{\circ}\)C. It is generally observed that the temperature is inversely proportional to the inflated pressure for high-loaded vehicles. However, for the lightweight loads below 3 kN this paper studied, the phenomenon is quite the opposite, despite low levels of fluctuation. Nevertheless, this is still in accordance with the findings of some research found in the literature on tire subjected to lightweight loads and low pressures [22]. Figure 8: Distribution of temperature within rubber with different loadings (unit: \({}^{\circ}\)C): (a) 1 kN; (b) 3 kN; (c) 5 kN. Figure 9: Distribution of heat flux within rubber with different loadings (unit: W/m\({}^{3}\)): (a) 1 kN; (b) 3 kN; (c) 5 kN. Figure 11a-c shows the distributions of temperature on the 2D plane section of half the tire with inflation pressures of 30 psi, 32 psi, and 34 psi. It was discovered that the regions of high temperature were at the same position as those analyzed above. The high-temperature zones slightly expanded as the inflation pressure increased. Figure 11a-c shows the distributions of the heat flux generated by the strain energy density on a 2D plane segment of half the tire with inflation pressures of 30, 32, and 34 psi. It was found that the distribution of heat flux remains the same with varying pressures. However, the region that experiences the highest heat flux at different pressures becomes  
Figure 11: Distribution of temperature within rubber with different pressures and the loading of 3 kN (unit: \({}^{\circ}\)C): (**a**) 30 psi; (**b**) 32 psi; (**c**) 34 psi. Figure 10: Variation in the three variables with a varying inflated pressure and a loading of 3 kN for (**a**) strain energy density; (**b**) averaged temperature; and (**c**) highest temperature. more prominent at the contact region between the road and the tire. This is due to the more inflated tire, with the contact region between the tire and the road thus shrinking. This leads to a higher stress being applied to this contact region and it becoming more deformed. On the other hand, since the relationship between pressure and temperature is proportional, this is quite controversial. It is common knowledge that the temperature decreases as the tire inflation pressure increases due to the lower deformation level. However, reference [22; 30] also notes a rising temperature trend as the inflated pressure increases for the tire at a low loading and low pressure. Thus, simulations for the tire with an increasing pressure with a higher loading (i.e., 6 kN) were conducted to observe whether the presented model shows the expected behavior for higher loads. The variations in the strain energy density, averaged temperature, and total temperature with increasing inflated pressure and 6 kN of loading are demonstrated in Figure 13a-c. As expected, the three variables decrease with the increase in the inflated pressure due to the lower deformation of the tire and the lower contact areas between the tire and the road. The maximum temperature decreased from 36.4 \({}^{\circ}\)C at an inflated pressure of 27 psi, and to 33.8 \({}^{\circ}\)C at an inflated pressure of 34 psi. Moreover, the trend seen for the variables drop in its rate of decline as the variables converge to their asymptotic values. Furthermore, it is evident that the rubber in this study behaves similarly to that of earlier studies after evaluating the distributions of temperature and heat flux for the three analyzed pressures of 28 psi, 32 psi, and 34 psi in Figures 14 and 15. However, an exception exists for the high loading and high pressure at 6 kN and 34 psi.