A Measurement Based Tyre Characteristics Approximation

Key words modelling of mechanical systems, vehicle dynamics, model of automobile, car and control modelling MSC (2000) 04A25A general problem formulation and the resulting scheme of modelling dynamical system behaviour is introduced before a specification with respect to automobiles is done. An essential component for the vehicle behaviour is the tyre. Models of different complexity with respect to its mathematical-mechanical formulation are presented. Simple models of the automobile itself allow a separation of longitudinal, lateral, and vertical dynamics and a partially analytical derivation of corresponding equations of motion. These models are usually also the approximations used for the design of a state observer and controller to influence the vehicle behaviour. For a more detailed representation of the vehicle 3D-models are assembled by their individual components, e.g. suspensions, drive train, and steering system. In this way a good agreement between measurements and simulation results can be realized up to the nonlinear range of vehicle behaviour. Nowadays MBS-models, established with professional software packages, are applied. They integrate all essential components, taking into account different linkages, e.g. bushings and joints. For component strength design, a rough road surface description can be implemented additionally. To improve by simulation the active safety or handling of the vehicle, these models represent the controlled complex vehicle in the global control loop whereas linearized models as mentioned above are applied for the controller design. As an example the design of an extended ESP-controller and its consequences for severe braking conditions during cornering are discussed showing the necessary steps in modelling and their mathematical formulation.

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“…The simplest form is a mathematical-mechanical approximation of measured tyre characteristics [4], like…”

Section: Modelling Of the Tyrementioning

confidence: 99%

Modelling in vehicle dynamics of automobiles

Lugner

Plöchl

2004

Z Angew Math Mech

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“…The approved model [2], [3], [4] in Fig. 2 can describe the vehicle motion on a horizontal flat road.…”

Section: Vehicle Modelmentioning

confidence: 99%

“…The detailed mathematical description is given in [4]. This kind of modelling is essential to calculate the longitudinal slip s~ of each wheel and thus to be able to consider the behaviour on p-split surfaces.…”

Section: Vehicle Modelmentioning

confidence: 99%

Additional 4WS and Driver Interaction

Lugner¹,

Plöchl

1995

Vehicle System Dynamics

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This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle. The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedfonvard scheme can provide desired steering characteristics. T o get information for critical situations a cornering manoeuvre with sudden p-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.

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“…Although there are many alternative schemes [2][3][4][5], the state-of-the-art is arguably the ''Magic Formulae'' [1]. They can be characterized as accurately describing comprehensive measurement data by a set of equations of some complexity, containing a very large number of parameter values.…”

Section: Introductionmentioning

confidence: 99%

Testing and Improving a Tyre Shear Force Computation Algorithm

Sharp¹

2004

Vehicle System Dynamics

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Existing computational procedures are applied to the parametric description of tyre shear force and moment data under pure slip conditions and to the subsequent generation of combined slip results. The methods rely on the Magic Formula, normalization of forces and slips and nonlinear slip transformations. These contribute to equivalence between longitudinal and lateral slips when, as is usual, tyre forces are substantially anisotropic.Recently published experimental results are used to test the methods. It is shown that good descriptions of pure slip behaviour result and that the combined slip results are smooth and reasonable. Systematic differences are shown to occur between computed and measured results however and the physics behind the differences are explained. Modifications to the computational algorithm are made, based on the physics, and the combined slip results retain their smoothness and improve their accuracy significantly.It is concluded that the method is effective in allowing information to be gleaned from pure slip testing and to be applied to the calculation of completely general steady state forces and moments. The information can be contained in a relatively small number of parameters. It is apparent that little accuracy is lost, as compared with a full spectrum of tests and much more extensive parameter identification. Considerable potential for economy of testing is implied and some computational economy is also likely to result from use of the methods. The updated algorithm is given in an appendix to the paper.

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A Measurement Based Tyre Characteristics Approximation

Cited by 7 publications

References 3 publications

Modelling in vehicle dynamics of automobiles

Modelling in vehicle dynamics of automobiles

Additional 4WS and Driver Interaction

Testing and Improving a Tyre Shear Force Computation Algorithm

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