The Direct Solving Strategy Of Steady Tire Temperature Field And Rolling Resistance For Tire Design

The steady temperature field (as well as rolling resistance) due to the viscous dissipation in a rolling tire plays a key role in controlling the overall tire performance. However, the analysis of temperature field in a rolling tire is a very complex thermo-mechanical problem. Therefore obtaining the accurate temperature field in a rolling tire is a basic but challenging problem which attracts the long-term attention in the academic and engineering field of tire.Many researchers have studied on this problem for several decades and recently a relatively complete solving strategy (named non-direct strategy) based on the two-way iterative approach was established by our research group.However, this solving strategy depends on the calculation of tire temperature field and the test of surface temperature distribution, thereby it cannot be used for tire design directly. Aimed to establish a reliable and effective solving strategy (named direct strategy) of steady tire temperature field as well as rolling resistance which can be used for tire design directly, a series of studies are carried out in this dissertation.With the aid of infrared thermal imager, a method to measure the outer surface temperature field in a rolling tire from three directions is presented. On this basis,a correction procedure for eliminating the measurement deviation is given. Firstly, the measurement deviation related to the radiative incident angle (a) of the surface point is corrected based on the cosine-fourth law. Then the measurement deviation related to the angle between the direction of incidence and the normal at the point (β) is corrected according to the identity of the temperature at an arbitrary surface point. And an empirical relationship between the surface emissivity and β is derived. Finally, the Dual-angle (α and β) correction function and the corresponding temperature correction formula are derived. The measured temperatures in different directions for the same tire surface tend to be the same after correction, thus the accurate outer surface temperature field is obtained. A wireless testing system (KTWTS) for the inner surface and the contained air temperature field is developed and necessary calibration is conducted. Then the tire inner surface and contained air temperature field at different speed is obtained by this system. Based on MTS rolling resistance testing machine, the tire steady rolling resistance is obtained according to the ISO28580standard. The above-mentioned test results of surface and contained air temperature field, as well as the tire rolling resistance, provide the solid foundation for the verification of the solving strategy proposed in this dissertation.The experimental study on the prestrain dependence of the viscoelastic properties for tire rubbers, by means of Dynamic Mechanical Thermal Analyzer (DMTA), reveals the correlation of the Payne effect and prestrain relative fully for the first time. A modified Kraus model to characterize the dynamic strain, temperature and prestrain dependence of dynamic modulus for tire rubbers is presented based on the work of Wu Fuqi. The modified Kraus model is able to characterize the dynamic strain dependence, temperature dependence and prestrain dependence of dynamic modulus for tire rubbers accurately.The RNG k-ε turbulence model is selected, and the corresponding numerical model is established by means of Fluent software. The velocity and temperature field of the contained air and the ambient air for a steady rolling tire at different speed are then obtained; furthermore the convective heat transfer coefficients on the inner and outer tire surface are calculated. The calculated temperature distribution of the tire contained air agree the test results well, provided the wall temperature boundary condition is set to be the test results of the inner tire surface temperature distribution. This indicates the adopted physical and numerical models are reliable and effective, and also demonstrates the obtained convective heat transfer coefficients on the inner and outer tire surface are correct. The presented solving strategy of the convective heat transfer coefficients based on Fluent software, can be applied to the tire design directly.Taking into consideration the above new modified Kraus model and new thermal boundary conditions together, the direct solving strategy of steady temperature field as well as rolling resistance in a rolling tire for tire design is thus established based on the non-direct solving strategy. The comparisons between the calculated results of the surface temperature field and rolling resistance by two strategy and the corresponding test results, indicate the direct strategy is more reliable, effective and accurate. The comparisons also indicate different dynamic modulus models have a significant influence on the tire rolling resistance, while different thermal boundary conditions have a significant influence on the tire temperature field. Finally, the steady tire temperature field and rolling resistance under different working conditions are calculated based on the direct solving strategy. The results indicate the steady tire temperatures increase, while the steady tire rolling resistance decreases with the increase of the tire speed. The results also indicate the steady tire temperatures increase, and the steady tire rolling resistance increase with the increase of the tire load.