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Bruce Maclaurin - One of the best experts on this subject based on the ideXlab platform.
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using a modified version of the Magic Formula to describe the traction slip relationships of tyres in soft cohesive soils
Journal of Terramechanics, 2014Co-Authors: Bruce MaclaurinAbstract:Abstract The tractive force/slip relationships of pneumatic tyres are required as inputs to vehicle performance prediction models such as the NATO Reference Mobility Model. They can also be used to calculate the tractive efficiency and work output of vehicles such as farm tractors, especially important when the vehicles are performing high drawbar pull operations; the effects of altering tyre size, tyre pressure and ballast can be predicted. The so-called Magic Formula is widely used for describing the force/slip relationships of pneumatic tyres on hard road surfaces. The coefficients in the Magic Formula are derived from experimental measurements. Relationships are then developed to describe the coefficients as functions of normal load on the tyre. The paper describes how the Magic Formula can be adapted to describe the tractive force/slip relationships of tyres in soft cohesive soils. The coefficients are made functions of Mobility Number instead of normal load. Mobility Number is an empirical system for estimating the tractive performance of tyres in soft soils at a single value of slip. The method could be extended to cover lateral tyre forces or other soil types if suitable experimental data is available.
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Using a modified version of the Magic Formula to describe the traction/slip relationships of tyres in soft cohesive soils
Journal of Terramechanics, 2014Co-Authors: Bruce MaclaurinAbstract:Abstract The tractive force/slip relationships of pneumatic tyres are required as inputs to vehicle performance prediction models such as the NATO Reference Mobility Model. They can also be used to calculate the tractive efficiency and work output of vehicles such as farm tractors, especially important when the vehicles are performing high drawbar pull operations; the effects of altering tyre size, tyre pressure and ballast can be predicted. The so-called Magic Formula is widely used for describing the force/slip relationships of pneumatic tyres on hard road surfaces. The coefficients in the Magic Formula are derived from experimental measurements. Relationships are then developed to describe the coefficients as functions of normal load on the tyre. The paper describes how the Magic Formula can be adapted to describe the tractive force/slip relationships of tyres in soft cohesive soils. The coefficients are made functions of Mobility Number instead of normal load. Mobility Number is an empirical system for estimating the tractive performance of tyres in soft soils at a single value of slip. The method could be extended to cover lateral tyre forces or other soil types if suitable experimental data is available.
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A skid steering model using the Magic Formula
Journal of Terramechanics, 2011Co-Authors: Bruce MaclaurinAbstract:Abstract The paper describes a computer model for predicting the steering performance and power flows of a notional skid steered tracked vehicle. The force/slip characteristics of the rubber track pads are calculated by means of the so-called Magic Formula. Relevant parameters for the Magic Formula are derived from the limited amount of data available from traction tests with a tracked vehicle on a hard surface. The computer model considers the vehicle in steady state motion on curves of various radii and allows for lateral and longitudinal weight transfer, roll and pitch motions and the effects of track tension forces. Vehicle dimensions, Magic Formula parameters and the equations of motion are set up in a Microsoft Excel spreadsheet and solutions obtained using the Solver routine. Model outputs are described in terms of driver control input and various power flows against lateral acceleration. Maximum lateral acceleration is generally limited by the available engine power. In some conditions the outer track sprocket could be transmitting almost twice the maximum net engine power. For vehicles with a single electric motor/inverter driving each sprocket, these units would need to be able to transmit these high intermittent powers.
Hans B Pacejka - One of the best experts on this subject based on the ideXlab platform.
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Semi-Empirical Tire Models
Tire and Vehicle Dynamics, 2012Co-Authors: Hans B PacejkaAbstract:The present chapter treats models that have been specifically designed to represent the tire as a vehicle component in a vehicle simulation environment. The modeling approach is termed ‘semi-empirical’ because the models are based on measured data but may contain structures that find their origin in physical models like those treated in the preceding chapter. The mathematical descriptions are restricted to steady-state situations. The first model that is known as The Similarity Method is based on the observation that the pure slip curves remain approximately similar in shape when the tire runs at conditions (e.g., road friction and wheel load) that differ from the reference condition. The second model referred to as The Magic Formula Tire Model is being treated extensively in this chapter. Car, truck, and motorcycle tire characteristics at many different pure slip and combined slip conditions have been computed with the Magic Formula Model and are presented in comparison with over-the-road tire measurement results. A series of turn slip (also in combined slip conditions) are computed with the Magic Formula Model . Tire ply-steer and conicity are considered and the generation of the overturning moment is modeled.
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an improved Magic Formula swift tyre model that can handle inflation pressure changes
Vehicle System Dynamics, 2010Co-Authors: Ijm Igo Besselink, Ajc Antoine Schmeitz, Hans B PacejkaAbstract:This paper describes extensions to the widely used TNO MF-Tyre 5.2 Magic Formula tyre model. The Magic Formula itself has been adapted to cope with large camber angles and inflation pressure changes. In addition, the description of the rolling resistance has been improved. Modelling of the tyre dynamics has been changed to allow a seamless and consistent switch from simple first-order relaxation behaviour to rigid ring dynamics. Finally, the effect of inflation pressure on the loaded radius and the tyre enveloping properties is discussed and some results are given to illustrate the capabilities of the model.
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An Improved Magic Formula/SWIFT Tyre Model that Can Handle Inflation Pressure Changes
Vehicle System Dynamics, 2010Co-Authors: Ijm Igo Besselink, Ajc Antoine Schmeitz, Hans B PacejkaAbstract:This paper describes extensions to the widely used TNO MF-Tyre 5.2 Magic Formula tyre model. The Magic Formula itself has been adapted to cope with large camber angles and inflation pressure changes. In addition, the description of the rolling resistance has been improved. Modelling of the tyre dynamics has been changed to allow a seamless and consistent switch from simple first-order relaxation behaviour to rigid ring dynamics. Finally, the effect of inflation pressure on the loaded radius and the tyre enveloping properties is discussed and some results are given to illustrate the capabilities of the model.
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The MF-Swift tyre model : extending the Magic Formula with rigid ring dynamics and an enveloping model
Jsae Review, 2005Co-Authors: Ijm Igo Besselink, Ajc Antoine Schmeitz, Hans B Pacejka, S.t.h. JansenAbstract:The Magic Formula tyre model is typically used in vehicle handling simulations. This paper summarises developments which extend the validity range of the Magic Formula to higher frequencies, short wavelength excitation and rolling over arbitrary three dimensional obstacles. This new tyre model has been validated extensively using experimental results which show that the extended demands can be met. Examples are given, illustrating that the new tyre model can be used successfully in areas normally not associated with a Magic Formula tyre model.
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Magic Formula Tyre Model with Transient Properties
Vehicle System Dynamics, 1997Co-Authors: Hans B Pacejka, Ijm Igo BesselinkAbstract: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...
Ijm Igo Besselink - One of the best experts on this subject based on the ideXlab platform.
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an improved Magic Formula swift tyre model that can handle inflation pressure changes
Vehicle System Dynamics, 2010Co-Authors: Ijm Igo Besselink, Ajc Antoine Schmeitz, Hans B PacejkaAbstract:This paper describes extensions to the widely used TNO MF-Tyre 5.2 Magic Formula tyre model. The Magic Formula itself has been adapted to cope with large camber angles and inflation pressure changes. In addition, the description of the rolling resistance has been improved. Modelling of the tyre dynamics has been changed to allow a seamless and consistent switch from simple first-order relaxation behaviour to rigid ring dynamics. Finally, the effect of inflation pressure on the loaded radius and the tyre enveloping properties is discussed and some results are given to illustrate the capabilities of the model.
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An Improved Magic Formula/SWIFT Tyre Model that Can Handle Inflation Pressure Changes
Vehicle System Dynamics, 2010Co-Authors: Ijm Igo Besselink, Ajc Antoine Schmeitz, Hans B PacejkaAbstract:This paper describes extensions to the widely used TNO MF-Tyre 5.2 Magic Formula tyre model. The Magic Formula itself has been adapted to cope with large camber angles and inflation pressure changes. In addition, the description of the rolling resistance has been improved. Modelling of the tyre dynamics has been changed to allow a seamless and consistent switch from simple first-order relaxation behaviour to rigid ring dynamics. Finally, the effect of inflation pressure on the loaded radius and the tyre enveloping properties is discussed and some results are given to illustrate the capabilities of the model.
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The MF-Swift tyre model : extending the Magic Formula with rigid ring dynamics and an enveloping model
Jsae Review, 2005Co-Authors: Ijm Igo Besselink, Ajc Antoine Schmeitz, Hans B Pacejka, S.t.h. JansenAbstract:The Magic Formula tyre model is typically used in vehicle handling simulations. This paper summarises developments which extend the validity range of the Magic Formula to higher frequencies, short wavelength excitation and rolling over arbitrary three dimensional obstacles. This new tyre model has been validated extensively using experimental results which show that the extended demands can be met. Examples are given, illustrating that the new tyre model can be used successfully in areas normally not associated with a Magic Formula tyre model.
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Extending the Magic Formula and SWIFT tyre models for inflation pressure changes
2005Co-Authors: Ajc Antoine Schmeitz, Ijm Igo Besselink, De J Joost Hoogh, H NijmeijerAbstract:The Magic Formula and SWIFT tyre models are well-known semi-empirical tyre models for vehicle dynamic simulations. Up to now, the only way to account for inflation pressure changes is to identify all model parameters for each inflation pressure that has to be considered. Since this is a time consuming and consequently expensive activity, research at TNO and Eindhoven University of Technology was started to extend the Magic Formula and SWIFT tyre model so that tyre inflation pressure changes can be accounted for. This paper discusses the influence of inflation pressure changes on the quasi-static force and moment characteristics and on the enveloping properties of tyres.
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Magic Formula Tyre Model with Transient Properties
Vehicle System Dynamics, 1997Co-Authors: Hans B Pacejka, Ijm Igo BesselinkAbstract: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...
E. Bakker - One of the best experts on this subject based on the ideXlab platform.
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Tyre measurements and modelling for parking manoeuvres
2017Co-Authors: Shenhai Ran, Matthijs Klomp, E. BakkerAbstract:In order to develop and verify the steering system, especially during parking manoeuvres with numerical methods, a tyre model that generates accurate lateral force and self-aligning moment is definitely essential. This paper first reviews the tyre parking measurements from the recently developed tyre test rig at Camber Ridge. After that, a new method is introduced to describe the tyre force and moment for parking as an extension of the combined slip Magic Formula. The turn slip effect is implicitly incorporated by shifting the acting point with an effective width and length of the contact patch. The validations between the measurements and simulations suggest that proposed method is promising for improving the correlation of measured tyre force and moment generation for parking manoeuvres over the standard Magic Formula tyre model.
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THE Magic Formula TYRE MODEL
1993Co-Authors: Hans B Pacejka, E. BakkerAbstract: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 UNDER LONGITUDINAL, LATERAL AND CAMBER SLIP CONDITIONS. ALL THREE CONDITIONS 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 ABOUT HOW TO ESTIMATE THE DRIVING PART OF THE LONGITUDINAL SLIP CURVE ARE PROVIDED, AS ARE METHODS FOR REPRESENTING THE CHARACTERISTIC WHEN THE TYRE IS ROLLING BACKWARDS. (A) FOR THE COVERING ABSTRACT OF THE COLLOQUIUM SEE IRRD 859025.
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THE Magic Formula TYRE MODEL
Vehicle System Dynamics, 1992Co-Authors: Hans B Pacejka, E. BakkerAbstract: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.
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DETERMINATION OF Magic TYRE MODEL PARAMETERS
Vehicle System Dynamics, 1992Co-Authors: J.j.m. Van Oosten, E. BakkerAbstract: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.
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Determination of Magic Formula tyre model parameters
1991Co-Authors: J.j.m. Van Oosten, E. BakkerAbstract: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.
Francesco Timpone - One of the best experts on this subject based on the ideXlab platform.
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TRIP-ID: A tool for a smart and interactive identification of Magic Formula tyre model parameters from experimental data acquired on track or test rig
Mechanical Systems and Signal Processing, 2018Co-Authors: Flavio Farroni, Raffaele Lamberti, Nicolò Mancinelli, Francesco TimponeAbstract:Abstract Tyres play a key role in ground vehicles' dynamics because they are responsible for traction, braking and cornering. A proper tyre-road interaction model is essential for a useful and reliable vehicle dynamics model. In the last two decades Pacejka's Magic Formula (MF) has become a standard in simulation field. This paper presents a Tool, called TRIP-ID (Tyre Road Interaction Parameters IDentification), developed to characterize and to identify with a high grade of accuracy and reliability MF micro-parameters from experimental data deriving from telemetry or from test rig. The tool guides interactively the user through the identification process on the basis of strong diagnostic considerations about the experimental data made evident by the tool itself. A motorsport application of the tool is shown as a case study.
