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Journal ArticleDOI

The magic formula tyre model

01 Jan 1992-Vehicle System Dynamics (Taylor & Francis Group)-Vol. 21, pp 1-18
TL;DR: The Magic Formula model as mentioned in this paper provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously.
Abstract: An account is given of the latest version 3 of the Magic Formula tyre model. The model provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously. The model aims at an accurate description of measured steady-state tyre behaviour. The coefficients of the basic formula represent typifying quantities of the tyre characteristic. By selecting proper values, the characteristics for either side force, aligning torque or fore and aft force can be obtained. The new version of the model contains physically based formulations to avoid the introduction of correction factors. Double-sided, possibly non-symmetric pure slip curves are employed as the basis for combined slip calculations. Suggestions are given to estimate the driving part of the longitudinal slip curve and to represent the characteristic at rolling backwards.
Citations
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Journal ArticleDOI
TL;DR: In this article, the steady-state empirical "Magic Formula" tire model was used to model the acceleration and braking properties of the Delft Tyre 97, and a full set of equations of the steady state part of the model of the new version was presented.
Abstract: 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...

458 citations

Journal ArticleDOI
TL;DR: In this paper, the dual extended Kalman filter (DEKF) technique is used for combined estimation of vehicle states and parameters, which can be used to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained.
Abstract: The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus ‘splitting’ the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

338 citations

Journal ArticleDOI
TL;DR: In this paper, the estimation process is based on two blocks in series: the first block contains a sliding-mode observer whose principal role is to calculate tire-road forces, while in the second block an extended Kalman filter estimates sideslip angle and cornering stiffness.

279 citations

Journal ArticleDOI
TL;DR: Comparison with several other vehicle control system approaches shows how the system operational envelope for CRVDC is significantly expanded in terms of vehicle global trajectory and planar motion responses.
Abstract: A coordinated reconfigurable vehicle dynamics control (CRVDC) system is achieved by high-level control of generalized forces/moment, distributed to the slip and slip angle of each tire by an innovative control allocation (CA) scheme. Utilizing control of individual tire slip and slip angles helps resolve the inherent tire force nonlinear constraints that otherwise may make the system more complex and computationally expensive. This in turn enables a real-time adaptable, computationally efficient accelerated fixed-point (AFP) method to improve the CA convergence rate when actuation saturates. Evaluation of the overall system is accomplished by simulation testing with a full-vehicle CarSim model under various adverse driving conditions, including scenarios where vehicle actuator failures occur. Comparison with several other vehicle control system approaches shows how the system operational envelope for CRVDC is significantly expanded in terms of vehicle global trajectory and planar motion responses.

262 citations

Journal ArticleDOI
TL;DR: A review of recent developments and trends in tire/road friction modeling is presented, with attempts to provide a broad perspective of the initiatives and multidisciplinary techniques for related research.
Abstract: A proper tire friction model is essential to model overall vehicle dynamics for simulation, analysis, or control purposes since a ground vehicle's motion is primarily determined by the friction forces transferred from roads via tires. Motivated by the developments of high-performance antilock brake systems (ABSs), traction control, and steering systems, significant research efforts had been put into tire/road friction modeling during the past 40 years. In this paper, a review of recent developments and trends in this area is presented, with attempts to provide a broad perspective of the initiatives and multidisciplinary techniques for related research. Different longitudinal, lateral, and integrated tire/road friction models are examined. The associated friction-situation monitoring and control synthesis are discussed with a special emphasis on ABS design

220 citations

References
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Journal ArticleDOI
TL;DR: In this article, a review of the generation of shear forces by pneumatic tyres under steady state conditions is presented, in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer.
Abstract: SUMMARY 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 beha...

367 citations

01 Jan 1993
TL;DR: In this paper, a set of MAGIC TYRE FORMULA PARAMETERS out of the DELFT TYRE MEASUREMENT TRAILER is compared to the "MONTE CARLO" version of the model.
Abstract: TYRE BEHAVIOUR PLAYS AN IMPORTANT ROLE IN VEHICLE DYNAMICS STUDIES. THE "MAGIC FORMULA" TYRE MODEL IS A SEMI-EMPIRICAL TYRE MODEL WHICH CAN DESCRIBE TYRE BEHAVIOUR QUITE ACCURATELY. A SET OF MAGIC TYRE FORMULA PARAMETERS OUT OF TYRE MEASUREMENT DATA PRODUCED BY THE DELFT TYRE MEASUREMENT TRAILER IS DEALT WITH IN THIS PAPER. PROBLEMS THAT MAY OCCUR DURING THE "FITTING PROCESS" ARE INDICATED AS WELL. THE COMPARISON BETWEEN THE LATEST VERSION AND THE "MONTE CARLO VERSION" OF THE TYRE MODEL SHOWS THAT THE LATEST VERSION RESULTS IN BETTER FITTING RESULTS ESPECIALLY FOR CAMBER INFLUENCES AND, EVEN MORE IMPORTANTLY, IN AN IMPROVEMENT ON THE FITTING PROCESS. (A) FOR THE COVERING ABSTRACT OF THE COLLOQUIUM SEE IRRD 859025.

65 citations

01 Jan 1991
TL;DR: In this article, the Magic Formula Tyre Model is compared with the Monte Carlo version of the model and the comparison between the two versions shows that the latest version results in better fitting results especially for camber influences and (even more important) in an improvement on the fitting process.
Abstract: Tyre behaviour plays an important role in vehicle dynamics studies. The Magic Formula Tyre Model is a semi-empirical tyre model which can describe tyre behaviour quite accurately. A set of Magic Formula parameters constitutes the basis of the model. The determination of these parameters out of tyre measurement data produced by the Delft tyre measurement trailer is dealt with in this paper. Problems that may occur during the 'fitting process' are indicated as well. The comparison between the latest version and the 'Monte Carlo version' of the tyre model shows that the latest version results in better fitting results especially for camber influences and (even more important) in an improvement on the fitting process.

11 citations