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A theoretical observation on empirical expression of tire shear forces
Abstract
Theoretically a unified tire model with non-isotropy of friction is presented as a foundation for studying the key features of a reasonable expression of tire shear force and alignment torque under combined slip conditions. The effects of longitudinal force and pressure distributionon tire cornering stiffness are analyzed. A unified semi-empirical tire model with high accuracy and convenience in vehicle dynamics simulation is proposed. Some experimental validations are shown.
... Referring to the dimensionless modeling method of UniTire tire model [56], the no malized curves of longitudinal force with respect to slip ratio and lateral force with respe to slip angle can be expressed as: 1 exp ...
... Referring to the dimensionless modeling method of UniTire tire model [56], the normalized curves of longitudinal force with respect to slip ratio and lateral force with respect to slip angle can be expressed as: ...
The empirical or semi-empirical model is widely used for vehicle simulation because of its high accuracy but relies on massive experimental data of tire force and moment. Therefore, tire mechanical prediction is of great significance to improve tire modeling efficiency and to reduce costs. Typical prediction methods or models based on normalization presented by Pacejka and Radt assume that different loads could be close to one normalized curve, but it is not always accurate enough to predict tire force under pure slip conditions and there is no mention of friction prediction methods. In the paper, a theoretical model considering the deformation of belt/carcass is established, which lays the foundation for a normalization model. A method for separation of friction from test data and the proportional assumption of longitudinal and lateral peak friction coefficient between target tire and reference tire are proposed, and the experimental results show that this assumption is acceptable. Finally, according to the separation of friction method and assumption, a new prediction method for tire force under pure slip conditions is presented and validated by comparison with the experimental data. It shows that the proposed method has good prediction capability with satisfactory accuracy.
... third-order derivatives of initial (φ → 0) and final (φ → ∞) boundary conditions for simplified physical tire model, and as a result, an accurate UniTire with fewer parameters was achieved [2]. In 1998, to satisfy the needs in complex and extreme operating conditions, such as starting and braking with low speeds, steering with sharp angles, and drastic combined slip scenarios, a non-steady-state UniTire model for a low-frequency range (<1 c/m) was proposed, which has a semi-physical form obtained from physical non-steady-state model through the concepts of slip propagation E-functions and quasi-steady state [3]. ...
... with the above boundary condition of simplified physical tire model, the semi-physical expression of the resultant force and pneumatic trail are written as [2, 4, 6], the longitudinal or lateral friction coefficient can be expressed separately. In general, the slip velocity of the contact patch has a very significant effect on the tire friction coefficient; here the following friction model (modified from Savkoor's formula to have a flat range at origin [7]) is employed to describe the relationship between the friction coefficients and slip velocity: ...
UniTire is a unified non-linear and non-steady tire model for vehicle dynamic simulation and control under complex wheel motion inputs, involving large lateral slip, longitudinal slip, turn-slip, and camber. The model is now installed in an ADSL driving simulator at Jilin University for studying vehicle dynamics and their control systems. In this paper, first, a brief history of UniTire development is introduced; then the application scope of UniTire and available interfaces to MBS software are presented; thirdly, a more detailed description of UniTire is given; fourthly, a tool aiming at parameterization of UniTire is also demonstrated; and finally, some comments on TMPT are made.
... The proposed model was capable of predicting tire contact patch pressure distribution and camber thrust with an acceptable amount of accuracy. Nonsymmetric and more general vertical force distributions in the contact patch were studied by [21], which expressed pressure distributions under different rolling resistance, inflation pressure and vertical loads conditions in a unified form. The combination of experimental investigation with either estimation or learning techniques for tire contact patch analysis was started by El-Gindy et al. [22] in late 90s. ...
Understanding the dynamic behavior of tires and their interactions with road plays an important role in designing integrated vehicle control strategies. Accordingly, having access to reliable information about the tire-road interactions through tire embedded sensors is very demanding for developing enhanced vehicle control systems. Thus, the main objectives of the present research work are i. to analyze data from an experimental accelerometer-based intelligent tire acquired over a wide range of maneuvers, with different vertical loads, velocities, and high slip angles; and ii. to develop a lateral force predictor based on a machine learning tool, more specifically the Gaussian Process Regression (GPR) technique. It is delineated that the proposed intelligent tire system can provide reliable information about the tire-road interactions even in the case of high slip angles. Besides, the lateral forces model based on GPR can predict forces with acceptable accuracy and provide level of uncertainties that can be very useful for designing vehicle control strategies.
... 目前比较典型的轮胎模型有"魔术公式(Magic formula, MF) " 模 型 [3][4][5][6] 和 UniTire 统 一 轮 胎 模 型 [1,[7][8][9] [14] 1 ( / ) ...
UniTire is a non-linear and non-steady tire model for vehicle dynamic simulation and control, which can describe tire properties accurately under complex conditions. Based on analytical tire model and by adopting the non-dimensional expression, the UniTire model has some unified characteristics: Unified definition of slip ratios; unified expression of non-dimensional contact pressure distribution; unified non-dimensional modeling of combined tire forces; unified expression of anisotropic tire friction; unified satisfactory of non-dimensional boundary conditions; unified expression of tire model under different travelling speeds; unified expression of tire steady and non-steady properties; unified expression of camber, turn slip and side slip. UniTire model not only can describe tire properties with high precision under variety of conditions, but also has the capacity of effective extrapolation and prediction. It is able to predict tire properties satisfactorily for combined slip condition, different roads and speeds. According to the modeling ideas of UniTire, the theoretical basis, steady and non-steady model of UniTire model will be introduced, and the capacity of expression and prediction will be validated by some test data.
... In the past, a huge number of tyre models have been studied for vehicle simulation and control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Tyre models may be divided into two basic groups: physical models and empirical models. ...
The UniTire model is a nonlinear and non-steady-state tyre model for vehicle dynamics simulation and control under complex wheel motion inputs involving large lateral slip, longitudinal slip, turn slip and camber. The model is now installed in the driving simulator in the Automobile Dynamic Simulation Laboratory at Jilin University for studying vehicle dynamics and their control systems. Firstly, the nonlinear semiphysical steady-state tyre model, which complies with analytical boundary conditions up to the third order of the simplified physical model, is presented. Special attention has been paid to the expression for the dynamic friction coefficient between the tyre and the road surface and to the modification of the direction of the resultant force under combined-slip conditions. Based on the analytical non-steady-state tyre model, the effective slip ratios and quasi-steady-state concept are introduced to represent the non-steady-state nonlinear dynamic tyre properties in transient and large-slip-ratio cases. Non-steady-state tyre models of first-order approximation and of high-order approximation are developed on the basis of contact stress propagation processes. The UniTire model has been verified by different pure and combined test data and its simulation covered various complex wheel motion inputs, such as large lateral slip, longitudinal slip, turn slip and camber.
Understanding the dynamic behavior of tires and their interactions with roads plays an important role in designing integrated vehicle control strategies. Accordingly, having access to reliable information about tire-road interactions through tire-embedded sensors is desirable for developing enhanced vehicle control systems. Thus, the main objectives of this research are: 1) to analyze data from an experimental accelerometer-based intelligent tire acquired over a wide range of maneuvers, with different vertical loads, velocities, and high slip angles and 2) to develop a lateral force predictor based on a machine learning tool, more specifically, the Gaussian process regression (GPR) technique. It is determined that the proposed intelligent tire system can provide reliable information about the tire-road interactions even in the case of high slip angles. In addition, lateral force models based on GPR can predict forces very well, outperforming other machine learning models and providing levels of uncertainty that can be useful for designing vehicle control strategies.
UniTire steady state model is a unified non-linear tire model for vehicle dynamic simulation and control under complex wheel motion inputs involving large lateral slip, longitudinal slip, turn-slip and camber. Firstly, brief history of UniTire development was introduced, and then more detailed features of UniTire steady state model were given, thirdly, a tool aiming at parameterization of UniTire was also demonstrated, finally, application scope of UniTire and available interfaces to MBS software were presented.
The purpose of this paper is to investigate the effects of dynamic road friction on a tyre’s mechanical properties. Despite the fact that most existing analytical tyre models tend to ignore the speed-dependent effects on the tyre’s forces, many experiments have demonstrated that the force and moment of a tyre actually vary with the travelling speed especially when the force and moment are nearly saturated. For this reason, the speed-dependent effects of tyre–road friction need to be reviewed intensively in an attempt to enhance the accuracy and reliability of the existing tyre models. In this paper, a tyre rubber friction tester and a series of testing methods are first developed. An analytical tyre model based on dynamic friction is then established by incorporating the speed effects into the model. Finally, comparison between test data and simulation results of the analytical model and the semiphysical model are conducted and analysed prior to the conclusions.
This study is to describe the transient force and moment characteristics of tyres involving large lateral slip, longitudinal slip, turn-slip and camber, and to develop a dynamic tyre model applicable to vehicle dynamic simulation and control for extreme operating conditions. Based on the steady state USES tire model [4,6], the effective slip ratios and quasi-steady concept are introduced to represent the non-linear dynamic tire properties in large slip cases. A high-order non-steady tyre model is presented. Special attention has been paid on the relationship between turn-slip and camber. Various kinds of experiments are performed to verify the tire model.
Modelling of the generation of shear forces by pneumatic tyres under steady state conditions is reviewed. The review is placed in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer. It will be of interest also to the student of rolling contact problems.The subject is divided into sections, covering physically founded models which require computation for their solution, physically based models which are sufficiently simplified to allow analytical solutions and formula based, empirical models. The classes are more nearly continuous than this strict division would imply, since approximations in obtaining analytical solutions may be made, empirical correction factors may be applied to analytical results and formula based methods may take into account tyre mechanical principles. Such matters are discussed in the relevant sections. Attention is given to the important matter of choosing model parameters to best represent the behaviour of a particular tyre.Conclusions relate to the structural and frictional mechanisms present in the shear force generation process, the contributions of carcass and tread elastic properties and of geometrical and frictional factors to the determination of the distributions of force through the contact region, the relationship between accuracy and computational load and the selection of methods for modelling tyre forces in a road vehicle dynamics context. Reference to the most pertinent literature in the field is made and possibilities for the further development of the state of the art are mentioned.
A new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions has been developed in order to further improve the Dynamic Safety of vehicles. The method makes use of a formula with coefficients which describe some of the typifying quantities of a tyre, such as slip stiffnesses at zero slip and force and torque peak values. The formula is capable of describing the characteristics of side force, brake force and self aligning torque with great accuracy. This mathematical representation is limited to steady-state conditions during either pure cornering or pure braking and forms the basis for a model describing tyre behaviour during combined braking and cornering.
Handling dynamics of automobiles
- K Guo