Study On The Steady State Tire Model Under Combined Conditions

Tire mechanical characteristics are the basis of vehicle dynamics. The tirecharacteristics under combined cornering and braking/driving with camber have significanteffects on the vehicle driving stability and safety. However, it is still a challenge to develop amodel for describing tire characteristics under combined slip conditions with stronganisotropy and large camber at present. In other hand, the study of the prediction model isquite important and has been becoming a hot topic, because it will avoid elaborate testing ofcombined conditions, which are always difficult, expensive and time consuming. Hence, thestudy on the steady state tire model under combined conditions is investigated detailed, andthe main contributions of this dissertation are listed as follows.Firstly, a simplified brush tire model combined cornering and braking/driving isestablished, and considering the influence of camber, a simplified theoretical model forcornering properties is modeled. It is our concern the change of the resultant force and thepneumatic trail and the effect of the camber for the lateral force and the pneumatic trail innon-dimensional space. This paper reveals that the normalized resultant force and pneumatictrail are the single variable function of normalized slip ratio under combined slip conditions,which have a unified expression with pure slip. However, this relationship will change whenthere is a camber. The traditional method which takes the camber as an equivalent slip angle(lateral slip ratio) is not accurate enough to express the influence of camber on tire forcesand moments, and the change of transition processes of the normalized lateral force and thepneumatic trail should be concerned. The significance of the simplified theoretical model isto grasp macroscopic mechanical characteristics and to possess simple expression. Moreimportantly, it can be expressed as a non-dimensional form, and this can be taken as thedirect theoretical frame for UniTire semi-empirical tire model.Secondly, the changing mechanism of the resultant force direction is analyzedconsidering the effect of carcass compliance. Then, with the complex carcass deformation,arbitrary pressure distribution and dynamic friction properties, a detailed theoretical modelcombined camber, cornering and braking/driving is established, in which the effect of tirewidth is also considered. The model has a widespread applicability. The simulation with thetire model under different conditions is made and reveals that the model can give a reasonable explanation for various detailed mechanical phenomena existed in tests. And themodel can well describe tire characteristics under combined camber, cornering andbraking/driving conditions with anisotropic tire stiffness and large camber. The influence ofcarcass compliance for crucial tire characteristics is analyzed and reveals the mechanism ofmany important mechanical phenomena: the lateral bending elasticity and twisting elasticityof carcass can decrease cornering stiffness. In general case, the relative cornering stiffnesswill decrease gradually with the increase of load, which will has a significant effect on thesteering characteristic of vehicle; the lateral translational elasticity will make the longitudinalforce produce the aligning moment, which lead to the generation of twisting angle; thetwisting elasticity can also arouse the “S” shape of the lateral force under combined camber,cornering and braking/driving conditions and so on. All these analysis can make the UniTiremodel more detailed, after the theoretical frame has been provided by the simplifiedtheoretical model, and it is a significant theoretical foundation for high precise UniTire semi-empirical model.Furthermore, based on the simplified brush model and utilizing the detailed theoreticalmodel to express the detailed characteristics, and with the qualitative analysis of somespecial phenomena existed in tests, the UniTire semi-empirical model can be established,which can express the tire characteristics under anisotropic tire stiffness and large camberconditions.1) For modeling tire characteristics under combined cornering andbraking/driving conditions, three aspects should be considered: the magnitude of resultantforce can be calculated by basic UniTire formula; the direction factor is proposed to describethe change of resultant force direction, which satisfy the boundary conditions; the changingmechanism about cornering stiffness is analyzed under the action of longitudinal force, and asemi-empirical expression is proposed.2) The influence of camber to cornering properties isanalyzed based on the theoretical analysis and test data. The curvature factor and frictioncoefficient of lateral force, the curvature factor of pneumatic trail and the residual aligningmoment influenced by camber are analyzed, and the corresponding semi-empirical modelsare established.3) Based on the previous model and the analysis of detailed theoreticalmodel, the semi-empirical model of tire characteristics for longitudinal slip and combinedslip with camber is established. The equivalent lateral slip ratio induced by longitudinal forceis proposed to express the “S” shape of the lateral force. The lateral pneumatic trail isintroduced to express the variation of aligning moment. The UniTire semi-empirical modelis validated by the comparison with a great deal of experimental data, which indicates that the accuracy is pretty good.At last, the concept of resultant slip circle is introduced and tire characteristics with thesame resultant slip ratio are analyzed. Based on this concept, considering the changingmechanism about resultant force direction under combined slip conditions with anisotropictire stiffness, the state stiffness method is proposed to predict the tire characteristics undercombined conditions, after that, the camber is considered and the UniTire prediction modelfor combined camber, cornering and braking/driving is established. The model has extensiveapplicability and need not any combined test data, which is validated by vast measurementsand shows that the model has satisfactory accuracy.Major Innovations of the Dissertation:(1) The changing mechanism about resultant force direction under combined slip conditionswith anisotropic tire stiffness is analyzed, and the direction factor is proposed which candescribe the variation process of resultant force direction accurately;(2) The detailed steady state theoretical model combined camber, cornering andbraking/driving is established. It is important for understanding and analyzing tirecharacteristics physically;(3) Extensive and detailed theoretical analysis and corresponding semi-empirical model isestablished for tire characteristics with the effect of camber. It can describe the tirecharacteristics under large camber conditions accurately;(4) A novel prediction method (state stiffness method) is proposed for combined corneringand braking/driving forces. It can predict tire characteristics accurately under anisotropictire stiffness conditions.