Study On Steady-State Tire Model Considering Inflation Pressure

Since tire is the only assembly to contact with the terrain,and it is also the only resouce of external force except for aerodynamic force,its mechanical property is critical to the driving performance of the vehicle.The chassis control systems are mostly based on tire mechanics.Tire inflation pressure,as a devisable and adjustable but constrained tire operating parameter,not only influences tire mechanics,but also is of great significance in vehicle dynamics.However,due to the complexity of structure and material,the research on tire mechanical characteristics is difficult.The study considering inflation pressure is relatively less,so that the influence mechanism reveals inadequately,and there are great limitations in the expression accuracy and expression ability of the tire model.In vehicle development,tire inflation pressure is merely an adjustable parameter in vehicle test,which can not make full use of its value.The paper is intended to reveal the mechanism of the effect of tire inflation pressure on tire mechanics,incorporate inflation pressure into Uni Tire model,and study the effect of tire inflation pressure on the vehicle dynamics performance.Firstly,through tire static experiments and tire steady-state cornering experiment at small slip angle,the effects of inflation pressure and vertical load on the basic tire physical parameters are analysed,and the relationships are built among inflation pressure,vertical load and the half-length of contact patch,carcass lateral translation stiffness,carcass bending stiffness,carcass twisting stiffness.Submit those relationships into the theoretical tire model with flexible carcass,explicit functions of the relationships are gotten among inflation pressure,vertical load and tire longitudinal slip stiffness,cornering stiffness and aligning stiffness.Then the effects of inflation pressure and vertical load on those stiffness are analysed.As vertical load increases,half-length of contact patch increases,then longitudinal slip stiffness and aligning stiffness increase,and cornering stiffness starts to increase at first and falls after the peak.As inflation pressure increases,half-length of contact patch decreases,carcass bending stiffness and carcass twisting stiffness increase,then longitudinal slip stiffness decrease,and cornering stiffness and aligning stiffness starts to increase at first and falls after the peak.Secondly,based on the full set of tire steady-state experiment,the researchs are carried out on how inflation pressure and vertical load affect on longitudinal slip,lateral slip and combined slip conditions.For the pure conditions,the stiffness,friction coefficient,curvature of transition region and the pneumatic trail are analysed in detail.For the combined condition,the detailed analysis are carried on the direction factor,the changes of cornering stiffness and aligning moment.Based on the basic equations of Uni Tire model,the expressions for vertical load are repaired,and the expressions for inflation pressure are extended.Then the effectiveness of the extended Uni Tire model is validated by comparison with the experimental data.For the pure conditions,residual error of forces are about 3% and residual error of moment is less than 10%.For the combined condition,residual error of forces are less than 10% and residual error of moment is 35%.Then,the compares are conducted on Uni Tire model and Magic Formula model considering the effects of inflation pressure and vertical load.In order to express the three coonditons of longitudinal,lateral and combined slip conditions,and two operating parameters of vertical load and inflation pressure,the number of parameters is roughly equal.From the perspective of expression accuracy,there is no big difference of longitudinal force and lateral force at pure conditons between the two models,but Uni Tire model has a greater accuracy on aligning moment at lateral slip and the forces and moment at combined slip.From the perspective of expression ability,compared with the Magic Formula model,the Uni Tire model has a stronger ability to express the large variation of vertical load and inflation pressure,aligning moment at lateral slip,the forces at combined slip with anisotropic stiffness.Finally,based on the study of the effect of inflation pressure on tire steady state mechanical properties,the extended Uni Tire model is applied to the vehicle dynamics simulation analysis.Through steady-state cornering test,the analysis are made for the influence of inflation pressure on the vehicle steering characteristics.Inflation pressure affects cornering stiffness,then affect the degree of understeer.The change of inflation pressure can even turn the car to oversteer.Through pylon course slalom test,the analysis are made for the influence of inflation pressure on the steering portability.It shows that the force on steering wheel changes a lot as front tire inflation pressure changes.At last,the effect of inflation pressure on brake performance is analysed.Inflation pressure affects the peak of tire longitudinal force and the corresponding slip ratio.Considering the effect of inflation pressure on the optimal slip ratio can shorten braking distance and braking time in anti-lock braking system.