Research On Tire Model Based On The Analysis Of The Contact Patch

Tire mechanics model is the basis of vehicle dynamics analysis and research. Currently, Tire model widely used experience or semi-empirical expression to accurately describe the mechanical characteristics of tire, such as Magic Formula empirical model and Uni Tire semi-empirical model. And Uni Tire semi-empirical model has a comprehensive theoretical framework to minimize model parameters and improve model prediction ability. However in order to expand the applications, the model parameters and required test data are continue to increase, which makes the model parameters difficult to obtain. On the other hand, the finite element model as complete physical model can express tire mechanical characteristics for a variety of conditions, and directly reflect the impact of the tire structure and material parameters on the mechanical properties of the tire. But the modeling complexity and low computational efficiency introduce difficulties to apply in the field of vehicle dynamics. Therefore it is of great importance to combine with the advantages of varioust model and develop a new tire model with a simple structure, high precision, wide application, and physically meaningful parameters that is easy to be obtained.In this thesis, the tire tread deformation characteristics during motion are descripted with details by discretizing the tread elements at the contact zone. The general expressions of the tire force with respect to the tread deflection are derived, such that the tire force can be calculated from arbitrary tread deflection. This approach overcomes the disadvantage of the semi-empirical tire model that the extra parameters are required in order to expand the application. First the tread deformation characteristics are studied under the combined longitudinal and lateral slip condition, and the simplified discretized model for such a condition is established. Next the carcass deformation characteristics, contact patch shape and vertical force distribution are explored by means of finite element virtual experiment. The results are used to develop the semi-empirical relations, and finally are introduced to the simplified discretized tire model. The proposed refined discretized tire model also includes the effects of tire width and turn slip, tire carcass deformation and dynamic friction property between the tire and ground. The aim of all the efforts is to express and analyze the tire force and moment characteristics under any condition. The main contents and conclusions of this thesis are summarized as follows:1. Develop the simplified discretized tire model for combined longitudinal and lateral slip. Without considering the tire width, carcass compliance, contact patch shape and different vertical force distribution, the tread the contact patch is divided into several elements along the circumference. The relation between tread element deflection and rolling motion of the tire is analyzed under the pure side slip, pure longitudinal slip and combined slip respectively. Then the simplified discretized tire model is established considering the adhesion and sliding of the tread elements. Such a model has a concise expression and can be used to analyze the tire force characteristics qualitatively.2. Analysis of carcass compliance, contact patch shape and vertical force distribution. The deformation of tire carcass, contact patch shape and vertical force distribution, which are usually difficult to measure, are studied based on the finite element virtual experiment. A finite element tire model is developed based on the tire dimension and material property. The finite elements model is then validated with the measurements which include longitudinal, lateral and vertical stiffness, and force characteristics under side and longitudinal slip. It is proofed that the finite element model has a relatively high precision and is suitable for the following research. The finite element model is used to study the tire carcass deformation undertaking pure longitudinal force, lateral force and self-aligning moment, and also in the case that those forces and moments are coupled. The results indicate that tire carcass has lateral translation and bending deformation when lateral force is acting. When longitudinal force and self-aligning moment exert on the carcass, the tire carcass has longitudinal translation and twisting deformation respectively. The finite element model is also used to study the contact patch shape and normal force distribution under the combined slip condition. It shows that the contact patch resemble a rectangle during free rolling. When lateral force is generated, either left or right side contact patch will increase, and reduce on the other side. The increasing contact patch area leads to normal force redistribution, which makes more vertical force on the larger area. When longitudinal force is applied, rear of the contact patch slightly increases in area while the front part area reduces correspondingly. However the change of contact patch is not as visible as the case of side slip. The vertical force also shifts backwards. The trend of contact patch change and vertical force distribution is opposite in the case of barking.3. Modeling of Refined discretized tire model. First the contact patch is divided into several elements along the length and width, such that the effect of tire width is taken into account. The empirical expression of contact length at different location in width with respect to lateral force is established based on the measurements and observations. The general vertical force distribution is extended considering the influence of tire force characteristics. The carcass compliance is introduced by considering the lateral translational stiffness, bending stiffness, twisting stiffness and longitudinal translational stiffness. Finally based the force equilibrium between the tire carcass and tread, the general expression for the tire forces and moments are derived in the tire tread coordinate system. The simulation method is also given when the tire is rolling with slip in order to finish the refined discretized tire model. The validation between the simulations and measurements under different conditions, such as pure longitudinal slip, pure side slip, combined longitudinal and side slip, stand still parking and step side slip, suggests that the refined discretized tire model possess a high accuracy and is cable of describing tire steady-state and transient force characteristics.4. Mechanism analysis of tire mechanical properties. The refined discretized tire model is used to study the tire tread deformation at the contact patch. Longitudinal slip, side slip and turn slip are considered in order to cover different conditions of tire motion, and the mechanism between tire motion and force characteristics can be explained then. When turn slip occurs, the tread lateral deformations are in the same direction in the leading and trailing parts of the contact patch when turn slip is small. On the other hand, their deformation are opposite with turn slip is large. Therefore the lateral force will increase at the beginning and reduce as turn slip gets large. The self-aligning moment increases gradually. Another event is studied by rolling the tire from low friction road to high friction one or vice versa at different side slip. The results show that the self-aligning moment transits smoothly when the friction coefficient changes at small side slip. However when side slip is large, a peak will occur due to the change of road surface. From the simulations of the refined discretized tire model under such conditions, the mechanism can be explained as the fact that the deformation of the newly entered element of the contact patch is mainly influenced by the side slip. At small side slip and change of friction coefficient, the different deformation between the front and rear parts of contact patch is also small. While the difference of tread element deformation become more notable when side slip is large. As a result, a peak of self-aligning moment can be observed at large side slip when the road surface changes.5. The prediction of tire force characteristics. The relation between the model parameters and tire physical structure is analyzed in order to study the method of parameter identification. According to the tread translational deformation characteristics, the tire shear force is expressed by the refined discretized tire model, and the model parameters are obtained by pure slip and stiffness measurements. The comparison between simulation and measurements in combined slip suggests that the refined discretized tire model has the capability to predict the tire force characteristics.Major Innovations of the Dissertation:(1) A new modelling methodology of tire handling and stability is proposed, focusing on the stress characteristics in the tire contact patch, with highlights of wide application range, high precision, and easy modelling.(2) Based on the force equilibrium between tire carcass and tread, the tire force characteristics are expressed using treading elements and road contact position. An iteration algorithm is proposed to calculate tire force fast and robustly.(3) The semi empirical formulas for the contact patch shape and vertical force distribution are introduced. The refined discretized tire model is developed based on the analysis of contact patch deformation. The tire model is then used to study the mechanism of tire force generation at side slip, longitudinal slip, combined slip, turn slip and road friction variation.