The Magic Formula Tyre Model

Pacejka, Hans B.; Bakker, Egbert

doi:10.1080/00423119208969994

Cited by 956 publications

(204 citation statements)

References 2 publications

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“…One of the most well known models is the semiemprirical tyre model proposed by (Bakker et al, 1987;Pacejka and Bakker, 1991), also known by the name of Magic Formula. This model uses measured data, obtained under particular conditions of constant linear and angular velocity, and fits a predetermined shaped curve by minimizing the sum-squared between the measured data and the model outputs.…”

Section: Introductionmentioning

confidence: 99%

Neural-empirical tyre model based on recursive lazy learning under combined longitudinal and lateral slip conditions

Boada¹,

García-Pozuelo²,

Díaz³

2011

Int.J Automot. Technol.

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The behaviour of the tyre plays an important role in the vehicle handling. An accurate tyre model that estimates these forces and moments it is highly essential for the studies of vehicle behaviour. For the last ten years neural networks have attracted a great deal of attention in vehicle dynamics and control. Neural networks have been effectively applied to model complex systems due to their good learning capability. In this paper a recursive lazy learning method based on neural networks is considered to model the tyre characteristics under combined braking and cornering. The proposed method is validated by comparison with experimental obtained responses. Results show the estimated model correlates very well with the data obtained experimentally. Moreover, the neural model proposed allows to include the asymetric tyre behaviour in the tyre model without difficulty.

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Section: Introductionmentioning

confidence: 99%

Neural-empirical tyre model based on recursive lazy learning under combined longitudinal and lateral slip conditions

Boada¹,

García-Pozuelo²,

Díaz³

2011

Int.J Automot. Technol.

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“…For this reason, up to now, conventional traction control methods have been, with a great deal of effort, seeking to calculate or measure the chassis velocity as a way of making use of the slip ratio in the nonlinear tire model, e.g. Magic Formula [7], to get the maximum friction force from the tire-road surface.…”

Section: Introductionmentioning

confidence: 99%

Traction Control for EV Based on Maximum Transmissible Torque Estimation

Yin

Hori

2010

Int. J. ITS Res.

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Research on motion control of EVs has progressed considerably, but traction control has not been so sophisticated and practical because the velocity of vehicles and the friction force are immeasurable. This work takes advantage of the features of driving motors to estimate the maximum transmissible torque output in real time based on a purely kinematic relationship, and then proposes an innovative controller to follow the estimated value directly and constrain the torque reference for slip prevention. By comparison with prior control methods, the resulting control design approach is shown to be more effective and robust both in simulation and on an experimental EV.

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“…with individual parameters for longitudinal and lateral dynamics D ¼ μ max F z , B ¼ C F =CD , and C F ¼ c 1 sin 2arctan F z =c 2 ðÞ ðÞ , while χ represents the slip λ or sideslip α [5]. Using this representation, the function maximum varies linearly over the (side)slip with changing maximum friction coefficient (cf.…”

Section: Tire Modelmentioning

confidence: 99%

“…A further detailed description of the forces acting on the vehicle's tire is developed in Ref. [5] and utilized in Ref. [6].…”

Section: Introductionmentioning

confidence: 99%

Unscented Kalman Filter for State and Parameter Estimation in Vehicle Dynamics

Wielitzka¹,

Busch²,

Dagen³

et al. 2018

Kalman Filters - Theory for Advanced Applications

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Automotive research and development passed through a vast evolution during past decades. Many passive and active driver assistance systems were developed, increasing the passengers' safety and comfort. This ongoing process is a main focus in current research and offers great potential for further systems, especially focusing on the task of autonomous and cooperative driving in the future. For that reason, information about the current stability in terms of dynamic behavior and vehicle environment are necessary for the systems to perform properly. Thus, model-based online state and parameter estimation have become important throughout the last years using a detailed vehicle model and standard sensors, gathering this information. In this chapter, state and parameter estimation in vehicle dynamics utilizing the unscented Kalman filter is presented. The estimation runs in real time based on a detailed vehicle model and standard measurements taken within the car. The results are validated using a Volkswagen Golf GTE Plug-In Hybrid for various dynamic test maneuvers and a Genesys Automotive Dynamic Motion Analyzer (ADMA) measurement unit for highprecision measurements of the vehicle's states. Online parameter estimation is shown for friction coefficient estimation performing maneuvers on different road surfaces.

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The Magic Formula Tyre Model

Cited by 956 publications

References 2 publications

Neural-empirical tyre model based on recursive lazy learning under combined longitudinal and lateral slip conditions

Neural-empirical tyre model based on recursive lazy learning under combined longitudinal and lateral slip conditions

Traction Control for EV Based on Maximum Transmissible Torque Estimation

Unscented Kalman Filter for State and Parameter Estimation in Vehicle Dynamics

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