Research On Modeling And Application Of Tire Dynamics Considering Turn Slip Input

It is of great practical significance and application prospect to establish or improve the tire model considering turn slip for the development of low-speed small turning radius application scenarios,for example the vehicle dynamics simulation evaluation of driving simulator and steering efforts as well as the virtual calibration force feedback accuracy of advanced chassis electronic control systems such as electronic power,advanced driving assistance and steer-by-wire,and meeting the dynamic characteristics analysis of aircraft landing gear under shimmy or turning conditions.Due to the difficulty of obtaining test data,it is a general and feasible method to study and model the tire dynamics considering the turn slip input based on the theoretical model.Researchers have done a lot on the tire dynamics theoretical model,but there are still some problems,such as inaccurate expression of contact patch under camber or lateral force,insufficient demonstration of belt deformation,unsteady solution method can not adapt to the turn slip input and poor convergence of numerical solution.MF/PAC2002 developed by Professor Pacejka is the most systematic and comprehensive semi-empirical model considering turn slip input.However,due to its incomplete and inaccurate description of the the steady-state mechanical characteristics,the accuracy of lateral force,longitudinal force and aligning moment is low when the turn slip is slightly high.Due to the lack of sufficient theory in the establishing process of unsteady state model,additional parameters of the model to be identified with unclear physical meaning are introduced,and its expression ability is unknown.Although existing study has tried parameter identification based on MF,the test and identification methods do not match.When the tire model developed by the user is used in Adams simulation,the interface development needs to be carried out,but the work considering turn slip input has not been published.Aiming at the above problems,this paper conducts systematic research on the mechanical theory and analysis,semi-empirical modeling and application considering turn slip.The main results and conclusions are as follows:(1)A high-precision contact patch modeling method considering camber and lateral force is proposed.A refined discrete theoretical model of turn slip,side slip,longitudinal slip and camber inputs is established,and the problems that the unsteady solution method in the existing literature which is not suitable for the nonlinear deformation of turn slip input and the unconvergence of force and moment calculation are solved.The consistency between the theoretical model and the test is realized,and the importance of lateral force coupling to the high-precision modeling of aligning moment and the problems existing in the camber equivalent turn slip processing method are demonstrated.It is revealed that the lateral deformation of the belt relative to the lateral force or the aligning moment does not change with the tire width or camber angle.The normalized curves of the lateral deformation under the different lateral forces or aligning moment are the same and the principle of lateral deformation superposition is proved to be correct,and a highprecision belt model is established.A modified geometric contact patch model is proposed,which realizes the high precision contact patch shape considering the camber input,and proves the high precision of the equivalent camber method for dynamic contact patch when the angle caused by the side force is less than 3°,the experiment verifies that the method can meet the accuracy requirements of the theoretical model for lateral force coupling dynamic imprinting modeling.A discrete solution method for tire deformation based on Euler method is proposed,which realized the unified solution of steady and unsteady state.A discrete solution method for tire deformation based on Euler method is proposed,which realizes the unified solution of steady state and unsteady state.The problem that the unsteady solution of the existing theoretical model cannot adapt to the deformation characteristics of the nonlinear parabola is proved and solved.0° and 6° static contact patch,pure camber,0° and ±5°camber combined with side slip quasi-steady state,nonlinear side slip step and parking conditions verify that the theoretical model is in good agreement with the experimental results.It is demonstrated that the lateral force coupling feedback is important for the accuracy improvement of the aligning moment.The treatment that equates camber to turn slip cannot express the phenomenon that the aligning moment decreases when the pure camber is large,and the lateral force and aligning moment relative to the turn slip curve are obviously different from the truth.(2)The mechanism of steady-state mechanical characteristics of the turn-side slip or turn-longitudinal slip input are systematically expounded,the modeling object and basic formula that can accurately and comprehensively describe the steady-state mechanical characteristics are defined,the expression function of the basic formula parameters are studied,and a high-precision steady-state semi-empirical model is established.Taking the curve of lateral force relative to side slip angle as modeling object,the basic formula is constructed using the magic formula sin expression.The influence of turn slip on the horizontal shift,curvature and stiffness parameters of the basic formula is studied and a semi-empirical model of the lateral force is established under turn-side slip inputs.Taking the curve of the aligning moment relative to the turn slip as the modeling object,the aligning moment generated by the pure side slip is regarded as the vertical shift of the curve which the asymmetric attenuation occurs with the turn slip.The influence of side slip on the basic formula stiffness and curvature parameters is studied and a semi-empirical model of the aligning moment is established under turn-side slip inputs.Taking the curve of longitudinal force relative to the turn slip as the modeling object,the modified magic formula cos form is used as the basic formula to express the attenuation of the turn slip to the pure longitudinal force.The influence of theoretical slip ratio on the proportion and exponential parameters of the basic formula is studied and a semi-empirical model of the longitudinal force is established under turn-longitudinal slip inputs.Taking the curve of the aligning moment relative to the theoretical slip ratio as the modeling object,and using the improved magic formula cos basic formula superimposed by the aligning moment generated by the belt translation deformation,the influence of the theoretical slip ratio on the proportional and exponential parameters of the basic formula is studied,and a semi-empirical model of the aligning moment is established under turn-longitudinal slip inputs.The verification based on the discrete theoretical model shows that the model error satisfies: the model established in this dissertation <PAC2002 after improved load expression<PAC2002.The experimental verification results show that the lateral force and aligning moment errors of the established steady-state model are reduced by 7.09% and 4.32%,respectively,compared with those of PAC2002 with improved load expression.(3)The response mechanism of the non-steady-state nonlinear characteristics of the turn slip relative to the distance and spatial frequency is revealed,and simplified spatial frequency response systems are constructed.Based on the consistency of the analytical model and the theoretical boundary conditions of the simplified system,the system parameters are obtained,and a high-precision turn slip non-steady-state semi-empirical model is established.Compared with the non-steady-state PAC2002 model,it achieves a better expression with fewer parameters.Different adhesion states have an important influence on the lateral deformation distribution of tread elements: when the transition point does not exceed the position of the contact patch center,the lateral deformation of the tread is approximately symmetrical relative to the center of the contact patch,which determines the "vortex" shape.In this case,the lateral force response with the path gradient is slow at the initial stage,and the aligning moment has a peak value with the path response.The belt translation stiffness has an important influence on the spatial frequency response of the lateral force and the aligning moment,while the torsional stiffness only affects the overshoot response of the aligning moment relative to the turn slip in the large adhesion state.According to the characteristics that the system response are consistent when the turn slip is not very large,and the unsteady response is not obvious when the turn slip is large.The simplified system is constructed based on the linear unsteady frequency response characteristics.According to the consistency of boundary conditions between the simplified system and the analytical model,the parameters of the simplified system model are derived,and the consistency of the simplified system model and the single-point contact model on the side force expression is verified,and the model is extended to the nonlinear expression.From the point of view of application of semiempirical model,it is verified that the unsteady aligning moment response can ignore the torsional stiffness of the belt.The verification based on the discrete theory model shows that the model parameters are obtained based on the theoretical boundary conditions,which achieves better representation with fewer model parameters than PAC2002.The experimental verification results show that the lateral force error of the unsteady model decreases by 1.68% and the aligning moment error decreases by 3.56% compared with the PAC2002 model.(4)A control method is proposed to maintain a free rolling state for a certain period of time in the beginning and end stages of each load test,so that the slip inputs are zero,and the force and moment are in the steady state value caused by the tire conicity and plysteer effect,which realizes the matching between the test method and the unsteady model parameter identification.Based on the Parameter Estimator module of Matlab Simulink,the parameter identification and verification of the semi-empirical model with side-turn slip inputs are completed: The average error of lateral force and aligning moment of the model is reduced by 8.78% and 7.88% respectively compared with that of the PAC2002 model with improved load expression.The comparison of Adams STI interface and Matlab simulation results proves that the developed interface is correct.The results of vehicle simulation show that the steering wheel torque and angle curve are greatly affected by the consideration of turn slip or not.