No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Tire Modeling
Abstract
Tire is the only component of a vehicle that makes contact with the road; thus, much important vehicle performance relies on the complex interaction between the tire and road. Tire models are used to describe tire behaviors in terms of mechanical, thermal and wear properties. These models are considered critical in various areas, such as vehicle dynamics and advanced vehicle control, ride comfort, and energy efficiency.
ResearchGate has not been able to resolve any citations for this publication.
In order to verify the fatigue-durability performance of chassis components, the simulation and analysis process is established in this paper based on CDTire model. High-accuracy tire model is constructed by CDTire modeling software according to the tire test data. The multi-body dynamics simulation is completed by combining the CDTire model with the vehicle model. The load of chassis components is extracted and imported into fatigue software. The swing arm is taken as an example for calculation. This analysis process can guide the analysis of chassis components and shorten the development cycle.
High accuracy tire modeling is essential to study the automotive fatigue-durability, handling-stability, and NVH performance in the virtual proving ground. Compared with other tire models, CDTire/3D can be directly used in multi-body dynamics simulation, and its linearized version can be adopted in road noise analysis. In consideration of its high generality for cost saving, CDTire/3D has an extensive engineering application prospective in the automotive industry. It is the critical technique to accomplish high-efficiency and high-precision CDTire/3D modeling by investigating the mechanical mechanism of tire and the influence of parameters on all test conditions, based on which a parameter identification strategy is conducted in this paper. The effectiveness of the strategy is verified by a tire modeling case.
While in the automotive field the relationship between road adherence and tire temperature is mainly investigated with the aim to enhance the vehicle performance in motorsport, the motorcycle sector is highly sensitive to such theme also from less extreme applications. The small extension of the footprint, along with the need to guarantee driver stability and safety in the widest possible range of riding conditions, requires that tires work as most as possible at a temperature able to let the viscoelastic compounds-constituting the tread and the composite materials of the whole carcass structure-provide the highest interaction force with road. Moreover, both for tire manufacturing companies and for single track vehicles designers and racing teams, a deep knowledge of the thermodynamic phenomena involved at the ground level is a key factor for the development of optimal solutions and setup. This paper proposes a physical model based on the application of the Fourier thermodynamic equations to a three-dimensional domain, accounting for all the sources of heating like friction power at the road interface and the cyclic generation of heat because of rolling and to asphalt indentation, and for the cooling effects because of the air forced convection, to road conduction and to turbulences in the inflation chamber. The complex heat exchanges in the system are fully described and modeled, with particular reference to the management of contact patch position, correlated to camber angle and requiring the adoption of an innovative multi-ribbed and multi-layered tire structure. The completely physical approach induces the need of a proper parameterization of the model, whose main stages are described, both from the experimental and identification points of view, with particular reference to non-destructive procedures for thermal parameters definition. One of the most peculiar and challenging features of the model is linked with its topological and analytical structure, allowing to run in real-time, usefully for the application in co-simulation vehicle dynamics platforms, for performance prediction and setup optimization applications.
The prediction of structure-borne noise using numerical methods has a crucial influence during the development process of modern passenger cars. In order to minimise the dynamic forces from the chassis transferred to the body structure, multibody simulation (MBS) can be used. The link between the road surface and the chassis is established by the tyre and its own structural dynamic characteristics. Therefore, it is substantial and the main goal of the present paper to investigate the Noise, Vibration and Harshness (NVH) performance of two commercial physical tyre models available and commonly used in the market. The intention is to point out what kind of results (up-to-date) a user of these structural dynamic tyre models, namely FTire and CDtire/3D, will get with a focus on NVH. The authors strictly follow the established process of how to obtain the fitted tyre property files, as any other user of FTire and CDTire currently does. This process includes a measurement campaign of the real tyre and a subsequent fitting of the tyre property file. The fitting in this case is provided by the tyre model developers themselves, namely cosin and Fraunhofer ITWM. The tyre models are then integrated into the MBS software MSC.Adams where their performance will be assessed based on measured wheel-hub forces in the time and frequency domain up to 300 Hz.
For the dynamic simulation of on-road vehicles, the model-element “tire/road” is of special importance, according to its influence on the achievable results. Sufficient description of the interaction between tire and road is one of the most challenging tasks of vehicle modeling. Two groups of tire models can be classified: handling models and structural or high-frequency models. Usually, various assumptions are made in modeling vehicles as multibody systems. Therefore, in the interest of balanced modeling, the precision of the complete vehicle model should stand in reasonable relation to the performance of the applied tire model. Handling tire models are characterized by a useful compromise between user friendliness, model complexity, and efficiency in computation time on the one hand, and precision in representation on the other hand.
A novel predictable tire model has been proposed for combined braking and cornering forces, which is based on only a few pure baking and pure cornering tests. It avoids elaborate testing of all kinds of combinations of braking and side forces, which are always expensive and time consuming. It is especially important for truck or other large size tires due to the capability constraints of tire testing facilities for combined shear forces tests. In this paper, the predictive model is based on the concept of slip circle and state stiffness method. The slip circle concept has been used in the COMBINATOR model to obtain the magnitude of the resultant force under combined slip conditions; however the direction assumption used in the COMBINATOR is not suitable for anisotropic tire slip stiffness. The state stiffness method, by which the variation of resultant force direction caused by anisotropy of tire slip stiffness can be described well and then the longitudinal and lateral forces under combined situations can be obtained separately. In addition, the friction ellipse is introduced in state stiffness method to express the anisotropic friction coefficients. The UniTire pure slip model is introduced firstly in this paper, and then the slip circle concept and state stiffness method are discussed. Finally, the UniTire prediction tire model for combined braking and cornering forces is proposed and the effectiveness of the model is validated by the comparison with the experimental data.
1 Modelization Being a typical representative of detailed mechanical tire models 'below' true FEM models, the author's model family FTire (Flexible Ring Tire Model) will be discussed in greater detail here. FTire development started in 1998, using certain ideas and numerical concepts of the author's 'coarse-mesh' FE model DNS-Tire ([1], [2], [4]) and the spatial non-linear 'rigid-ring' model BRIT ([3], [5], [6]). This first version of FTire has been essentially improved since then. It is one of the advanced tire models of MSC.ADAMS™, and is as well implemented into several 'in-house' simulation programs at different companies, and as a sub-system block in MATLAB/SIMULINK™. Recently, FTire has been completed by a new rigid-ring model (called RTire), and a redesign of DNS-Tire (called FETire). RTire, FTire, and FETire together set up the FTire Model Family. FTire and FETire are discussed below.
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.
RMOD-K Formula is an open source collection of two simple tire models and related stuff like optimisation tools and simulation interfaces. It was intended to build a package reaching from parameter optimisation based on measurements of steady state force and moment to simulation models of steady state tire behaviour in vehicle dynamics. This may be used for instance in some field of education or any other field, where steady state tire behaviour is of interest. The basic idea was to provide an algebraic formula with physical meaningfully parameters and a discrete version of tangential contact formulation to get some insights in tangential contact mechanics. The analytic formula allows for instance to investigate the stability of small vehicle models by analytical linearisation
even in combined slip situation. This may lead to stability maps with respect to certain
tire parameters expressing friction or stiffness properties. The extended discrete version takes into account more detailed information about normal stress distribution, contact area shape and friction properties and is able to deal with camber.
This documentation explains the basic theory behind the models and how to create custom version within the framework of optimisation and simulation interfaces. The structure of the documentation is divided into two parts, in which the first deals with the model equations and assumptions made while the second part explains the software tools and gives some application examples. The author is grateful for all further developments and information about the application of the package.
Everybody is invited to use the software, to contribute to the development and to give related comments.
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.
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.
In recent years, the ever-increasing interest in intelligent tyre technology has led to the formulation of different empirical models correlating deformation measurements provided by the sensors with tyre dynamics. In this paper, a real-time physical model, suitable for describing the dynamics of intelligent tyres based on measurements of strains and/or displacements of the tyre carcass, is presented. The proposed flexible ring model can reproduce the tyre dynamics for both concentrated and distributed forces by introducing a discrete approach that also allows to analyse the longitudinal dynamics of the tyre in real-time. The analytical description of the problem allows to obtain solutions in closed form and to quickly identify model parameters from experimental data. The comparison between the simulated results and the ones provided by indoor tests of two intelligent tyre concepts highlighted that the proposed tyre model can estimate with an acceptable precision both the carcass deformations and the forces acting on the tyre.
tIn recent years, a large amount of research has been focused on intelligent tire technology. Several systemshave been developed based on different sensors installed on tires. Nowadays one of the major researchproblems for intelligent tire development is how to correlate measurements provided by sensors to thetire dynamics. The methods mostly presented in literature are based on empirical correlations betweenmeasurements and tire working conditions obtained with extensive experimental activities which areexpensive and time consuming.In this paper, a real-time physical model suitable to describe the longitudinal dynamics of strain-basedintelligent tires is described. The mathematical tire model consists of a flexible ring on a viscoelasticfoundation. The solution of the model dynamics has been obtained in closed form and the model param-eters have been identified from experimental data. The comparison between the simulated strains andthe ones provided by an intelligent tire prototype highlighted that the proposed tire model can estimatewith an acceptable precision the tire deformations for several operative working conditions.
The most effective mathematical model to characterize tire behavior is the Magic formula. Current study presents a brief review of existing tire models namely Dugoff and modified Dugoff models and its comparison with Magic formula tire model. The mathematical equations represents these models were understood and the tire behavior is predicted for various normal load conditions and a comparative study is made. The longitudinal and lateral forces were plotted against slip ratio and slip angle respectively to compare with the results obtained from the Magic Formula under the same normal load conditions. This work also highlights the disadvantages of the older version of the Dugoff Model [1] when compared with the Magic Formula [2]. Furthermore, there was a new modification introduced in the Dugoff formula to make it comparable with the Magic formula at lower slip angles/slip ratios thereby reducing the error that was vividly evident in the older version of the Dugoff Model.
The definitive book on tire mechanics by the acknowledged world expert. © 2012 Hans Pacejka Published by Elsevier Ltd All rights reserved.
Optimization is a key tool used by automakers to efficiently design and manufacture vehicles. During vehicle design, much effort is devoted to efficiently simulate and optimize as many vehicle parameters as possible to save development costs during physical testing. One area of vehicle development that heavily relies on physical testing and subjective driver feedback is the tire design process. Optimizing tire parameters relies either on this subjective feedback from trained drivers, or use of existing tire data or scaling of a reference tire model simulate the desired design change and provide feedback. These data are often difficult to obtain and properly scale to represent the appropriate design changes. Michelin’s TameTire model is a force and moment tire model. It includes thermal tire effects and is physically derived, thereby allowing quick access to scaling factors to change a tire’s behavior based on pertinent tire design changes such as tread depth and tread stiffness. In this paper, a multi-objective optimization is performed to observe the trade-off between tire wear and handling performance by using the scaling factors available in the TameTire model.
In order to accurately predict vehicle dynamic responses when traversing high obstacles or large bumps, appropriate tyre models need to be developed and characterised. Tyre models used in vehicle ride and durability are usually characterised by experimental tests on the tyre. However, limitations in rig design and operating conditions restrict the range of test conditions under which the tyre can be tested, hence characterisation of the tyre behaviour during extreme manoeuvres may not be possible using physical tests. In this study, a combination of experimental tests and finite-element (FE) modelling is used in deriving Flexible Ring Tire (FTire) Models appropriate for different levels of tyre/road interaction severity. It is shown that FE modelling can be used to accurately characterise the behaviour of a tyre where limitations in experimental facilities prevent tyre characterisation using the required level of input severity in physical tests. Multi-body simulation is used to demonstrate that the FTire model derived using extended range of obstacles produces more accurate transient dynamic response when traversing low and high road obstacles.
Tire modeling is an ever-growing area of interest for vehicles as more efficient development processes are desired in terms of time and resources. Vehicle simulations offer an opportunity for development teams to predict tire and vehicle performance before the construction of a physical prototype. Michelin has identified the need for more robust and accurate tire models that can be used for such simulations to give an accurate description of the transient mechanical and thermal behavior of a tire. Rubber’s viscous and elastic properties are heavily dependent on their thermal state; when this effect is not modeled, it results in mathematical tire models that insufficiently predict tire performance. TameTire aims to fill this void for a broad range of maneuvers, track characteristics, and operating conditions based on the ability to predict tire forces and moments with physically based parameters. Some physical characteristics contained within a TameTire model include contact patch dimensions, tread, sidewall and belt stiffnesses, and rubber compound properties. Empirical tire models for handling have limited representation of tire physical properties due to the dependence on the measurement protocol and lack of identification of the thermal state of the tire. TameTire’s advance modeling techniques include capturing a tire’s thermal effects, thereby allowing for a more accurate and thorough analysis of tires behavior while being physically based (e.g., parameters for stiffness, rubber properties) and allowing the model to be grounded in the actual physics of a tire operating.
The tire mechanics characteristics are essential for analysis, simulation and control of vehicle dynamics. This paper develops the UniTire model for tire forces and moments under combined slip conditions with anisotropic tire slip stiffness. The anisotropy of tire slip stiffness, which means the difference of tire longitudinal slip stiffness and cornering stiffness, will cause that the direction of tire resultant shear stress in adhesion region is different from that in sliding region. Eventually the tire forces and moments under combined slip conditions will be influenced obviously. The author has proposed a "direction factor" before to modify the direction of resultant force in the tire-road contact patch, which can describe tire forces at cornering/braking combination accurately. However, the aligning moments which are very complicated under combined slip conditions are not considered in previous analysis. The simplified physical tire model is introduced firstly in this paper to analyze the tire mechanics characteristics under combined cornering/braking situations, containing the tire forces and aligning moments. Then considering the influence of anisotropic tire slip stiffness and the expression of "direction factor", a semi-physical tire model for tire forces and moments is given. Finally, the effectiveness of the model for tire forces and moments under combined slip conditions with anisotropic tire slip stiffness is validated by the comparison with the experimental data.
The objective of this paper is to enhance the accuracy of tire model combined tire cornering and braking forces with anisotropic tread and carcass stiffness. The difference of tire longitudinal slip stiffness and cornering stiffness will arouse that the direction of tire resultant shear stress in adhesion region is not the same as that in sliding region. Then the direction of total friction force in the whole tire-road contact patch will change under different combined cornering/braking situations. Generally speaking, there is a basic premise: "the direction of resultant shear stress in sliding region will be the same as that in adhesion region" in the existing tire models, in which the anisotropy of tread and carcass stiffness is neglected. Therefore, these models don't work well when the tire tread and carcass stiffness has a strong anisotropy. The direction of tire shear stress in the adhesion and the sliding region of the contact patch is discussed in this paper and a modification factor is proposed basing on the UniTire semi-physical model to modify the direction of resultant shear stress, which can describe the variation tendency of the total friction force direction in the tire-road contact patch with different combination of cornering and braking conditions. Finally, the UniTire semi-physical tire model contained modification factor is validated by the experimental data, which indicates the accuracy of combined tire forces has been enhanced significantly.
Easy-to-use tire models for vehicle dynamics have been persistently studied for such applications as control design and model-based on-line estimation. This paper proposes a modified combined-slip tire model based on Dugoff tire. The proposed model takes emphasis on less time consumption for calculation and uses a minimum set of parameters to express tire forces. Modification of Dugoff tire model is made on two aspects: one is taking different tire/road friction coefficients for different magnitudes of slip and the other is employing the concept of friction ellipse. The proposed model is evaluated by comparison with the LuGre tire model. Although there are some discrepancies between the two models, the proposed combined-slip model is generally acceptable due to its simplicity and easiness to use. Extracting parameters from the coefficients of a Magic Formula tire model based on measured tire data, the proposed model is further evaluated by conducting a double lane change maneuver, and simulation results show that the trajectory using the proposed tire model is closer to that using the Magic Formula tire model than Dugoff tire model.
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.
Summary When modelling vehicles for the vehicle dynamic simulation, special attention must be paid to the modelling of tyre-forces and -torques, according to their dominant influence on the results. This task is not only about sufficiently exact representation of the effective forces but also about user-friendly and practical relevant applicability, especially when the experimental tyre-input-data is incomplete or missing. This text firstly describes the basics of the vehicle dynamic tyre model, conceived to be a physically based, semi-empirical model for application in connection with multi-body-systems (MBS). On the basis of tyres for a passenger car and a heavy truck the simulated steady state tyre characteristics are shown together and compared with the underlying experimental values. In the following text the possibility to link the tyre model TMeasy to any MBS-program is described, as far as it supports the ‘Standard Tyre Interface’ (STI). As an example, the simulated and experimental data of a heavy truck doing a standardized driving manoeuvre are compared.
In this paper, an overview of the TNO MF-SWIFT model is given. After an historical overview of the model development and the intended range of application, the model is described briefly. Next, the implementation in multibody and other simulation software is discussed, including also the available road models. After that, the parameterization of the tire model is described and the available identification tool is discussed. Finally, comments are given on the TMPT from the TNO point of view.
The first version of the tire simulation software Flexible ring Tire model (FTire) had been released in December 1998. Being subject to permanent improvement and several far-reaching model extensions since then, today it is one of the most widely used and generally accepted tire models for ride comfort, handling, and road load prediction.Strength of FTire is the strictly physical background, which perfectly fits both to Multi-Body Systems (MBS) and Finite Element Method (FEM) environments. Even though certain simplifications are unavoidable, this clean mechanical, thermo-dynamical, and tribological structure of the model guarantees a consistent and plausible model behavior even in situations that are not covered by respective measurements.The modelization takes into account most of the relevant excitation sources and non-linear transfer mechanisms, up to very high frequencies and extremely short wavelengths. The model's high level of detail is accompanied by a very comfortable program interface and a numerically robust and efficient solver. This allows the simulation of even extreme manoeuvres with moderate computation time. FTire can be used together with most of the important MBS packages and specialized vehicle dynamics programs.This contribution gives an overview on history, application, modelization, road models, parameterization, interfacing, availability, and future perspectives of FTire.
This paper describes the semi-physical tire model TMeasy for vehicle dynamics and handling analyses, as it was applied in the ‘low frequency tire models’ section of the research programme tire model performance test (TMPT). Despite more or less weak testing input data, the effort for the application of TMeasy remains limited due to its consequent ‘easy to use’ orientation. One particular feature of TMeasy is the wide physical meaning of its smart parameter set, which allows to sustain the identification process even under uncertain conditions. After a general introduction, the modelling concept of TMeasy is compactly described in this paper. Taking the standard tire interface (STI) to multibody simulation system (MBS) software into account, the way to apply TMeasy is briefly shown. This includes three selected examples of application. The final comments of the authors on TMPT describe the experiences and earnings received during the participation in that programme.
This paper discusses the tire model performance test (TMPT) participation of the LMS International comfort and durability tire model (LMS CDTire). CDTire is a family of three models based on a macroscopic physical description of tires, which is a compromise between scope of applicability and calculation time. A short overview of the CDTire model suite, including parameter identification (PI) software and road surface models, is complemented with application examples of full vehicle simulations utilizing different sub-models and different road surface models. The PI procedure for the TMPT tire, a non-commercial 205/55 R 16 passenger car tire, is reviewed and the results of the TMPT validation and capability tests are discussed.
The tyre force and moment generating properties connected with the vehicle's horizontal motions are considered. Knowledge of tyre properties is necessary to properly design vehicle components and advanced control systems. For this purpose, mathematical models of the tyre are being used in vehicle simulation models. The steady-state empirical ‘Magic Formula tyre model’ is discussed. The aligning torque description is based on the concepts of pneumatic trail and residual torque. This facilitates its combined slip description. Following Michelin, weighting functions have been introduced to model the combined slip force generation. A full set of equations of the steady-state part of the model of the new version ‘Delft Tyre 97’ is presented. The non-steady state behaviour of the tyre is of importance in rapid transient maneuvres, when cornering on uneven roads and for the analysis of oscillatory braking and steering properties. A relatively simple model for longitudinal and lateral transient responses restricted to relatively low time and path frequencies is introduced.
As a result of the '1st International Colloquium on Tyre Models for Vehicle Dynamics Analysis' in 1991, the international 'TYDEX Workshop' working group was established. This workshop concentrated on the standardisation of the exchange of tyre measurement data and the interface between tyre and vehicle models in order to improve the communication between vehicle manufacturers, suppliers and research organisations. The development and knowledge of tyre behaviour is of great importance to both tyre and vehicle industry and will be intensified. Therefore the TYDEX Workshop showed great interest from all parties to come to some kind of standardisation. In the two expert groups - one focused on Tyre Measurements - Tyre Modelling and the other on Tyre Modelling - Vehicle Modelling - the TYDEX-Format and the Standard Tyre Interface have been developed, which will be explained in this paper. Furthermore a short overview of the European TIME project aiming at a standard tyre testing procedure will be given, which is reliable and consistent with realistic driving conditions. Elaborating standard testing procedures is one of the important consequences from the TYDEX Workshop.
Notes: Originally dated 13 June 1972 National Bureau of Standards, Washington, D.C. National Highway Traffic Safety Administration, Washington, D.C. http://deepblue.lib.umich.edu/bitstream/2027.42/253/2/27053.0001.001.pdf
National Bureau of Standards, Washington, D.C. National Highway Safety Bureau, Washington, D.C. http://deepblue.lib.umich.edu/bitstream/2027.42/1387/2/10161.0001.001.pdf
Motor Vehicle Manufacturers Association, Inc., Detroit, Mich. http://deepblue.lib.umich.edu/bitstream/2027.42/330/2/28983.0001.001.pdf
The in-plane dynamics of tires deals with the forces and motion in the plane of rotation of the wheel. Three aspects of tire in-plane dynamics can be identified: the rolling contact between the tire and the road surface; the transmission of forces and motion from the contact patch to the wheel axle; and the vibration of the tire treadband. The main objective of the investigation reported in this thesis is to develop a tire model which is suitable to study all three aspects of the in-plane dynamics of tires in both low and high frequency ranges. The tire model is finally validated by experimental modal analysis of a test tire. Laboratory tests are conducted to establish the modal shapes and natural frequencies of the test tire. The tests are carried out for two different configurations of the tire: one with the wheel rim fixed in space and one with the tire-wheel system suspended freely in the air. Good agreement is found between the experimental and theoretical results.
The magic formula tyre model
- HB Pacejka
- E Bakker
From mechanical system to tire performance impact: DAS (Dual Axis Steering) explained thanks to advanced modeling
- G Tranquillo
- A Sorrentino
- V Van
Seitenkraften am rollenden luftreifen
- E Fiala
Multiphysics model for tire performance optimization
- F Farroni
- A Sakhnevych
- A Sammartino
- F Timpone