The Magic Formula Tyre Model

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.

The magic formula tyre model

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...

Magic Formula Tyre Model with Transient Properties

Lack of driver’s knowledge about the abrupt changes in pavement’s friction and poor performance of the vehicle’s stability, traction, and ABS controllers on the low friction surfaces are the most important factors affecting car crashes. Due to its direct relation to vehicle stability, accurate estimation of tire-road friction is of interest to all vehicle and tire companies. Many studies have been conducted in this field and researchers have used different tools and have proposed different algorithms. This literature survey introduces different approaches, which have been widely used to estimate the friction or other related parameters, and covers the recent literature that contains these methodologies. The emphasize of this review paper is on the algorithms and studies, which are more popular and have been repeated several times. The focus has been divided into two main groups: experiment-based and model-based approaches. Each of these main groups has several sub-categories, which are explained in the next few sections. Several summary tables are provided in which the overall feature of each approach is reviewed that gives the reader the general picture of different algorithms, which are widely used in friction estimation studies.

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A technical survey on tire-road friction estimation

Being a typical representative of detailed mechanical tyre models that are less than true finite-element (FE) models, the present author's flexible-ring tyre model FTire will be presented here. FTi...

FTire: a physically based application-oriented tyre model for use with detailed MBS and finite-element suspension models

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.

Determination of magic tyre model parameters

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.

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 most important consequences from the TYDEX Workshop.

TYDEX Workshop: Standardisation of Data Exchange in Tyre Testing and Tyre Modelling

As a result of the 1st International Colloquium on Tire Models for Vehicle Dynamics Analysis in 1991, the international TYDEX Workshop working group was established. This workshop concentrated on the standardization of the exchange of tire measurement data and the interface between tire and vehicle models in order to improve the communications between vehicle manufacturers, suppliers, and research organizations. The development and knowledge of tire behavior is of great importance to both the tire and vehicle industries and will be intensified. Therefore the TYDEX Workshop received great interest from all parties to come to some kind of standardization. In the two expert groups, one of which focused on Tire Measurements — Tire Modeling and the other on Tire Modeling — Vehicle Modeling, the TYDEX‐Format and the standard tire interface have been developed, which will be explained in this paper. Furthermore, a short overview of the European TIME project aiming at a standard tire testing procedure wi...

Standardization in Tire Modeling and Tire Testing — TYDEX Workgroup, TIME Project

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.

E. Bakker

Papers

Determination of magic tyre model parameters

Determination of magic tyre model parameters

TYDEX Workshop: Standardisation of Data Exchange in Tyre Testing and Tyre Modelling

Standardization in Tire Modeling and Tire Testing — TYDEX Workgroup, TIME Project

Determination of Magic Formula tyre model parameters