Time-optimal control of the race car: influence of a thermodynamic tyre model

Kelly, Daniel; Sharp, R. D.

doi:10.1080/00423114.2011.622406

Cited by 35 publications

(51 citation statements)

References 25 publications

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“…The use of rather simplistic assumptions to characterise the contact patch dimensions, frictional mechanism and bristle properties, such as adopting a constant value over a range of different operating conditions, creates an unrealistic tyre model with poor performance. Work by Sorniotti and Velardocchia (2008) and Kelly and Sharp (2012) attempts to model more realistic brush tyre models. Sorniotti and Velardocchia investigated the behaviour of tyre tread elements by using a brush model with parabolic contact pressure distribution, which incorporates anisotropic stiffness properties, and have outlined the potential improvements for a brush model based on bristle and contact patch characteristics.…”

Section: Basic Tyre Modelling Methodsmentioning

confidence: 99%

“…Finally, they considered simple mechanisms for the tyre thermal behaviour to derive a set of ordinary differential equations to predict the temperature changes in the tyre. Although they have proposed a great amount of theoretical work with the model, the model has not been compared against experimental data (Kelly and Sharp, 2012). Sorniotti also proposed a semi-empirical method to predict the tyre temperatures and incorporated the effects in a brush model (Sorniotti, 2009).…”

Section: Basic Tyre Modelling Methodsmentioning

confidence: 99%

“…As the tyre rolls, the bristles pass through the tyre contact patch area, and are allowed to deflect, due to the driving motion which generates adhesive forces at the road surface. The bristles are deflected in the contact patch until the local friction force can no longer withstand any further shear deformation and transitions into a sliding state over the road surface (Kelly and Sharp, 2012). The combination of the shear forces arising from the adhesive and sliding regions determines the overall tyre forces.…”

Section: Basic Tyre Modelling Methodsmentioning

confidence: 99%

“…As mentioned earlier, another influence on the tyre rubber and the road surface friction is directly related to temperature. Earlier work by Kelly and Sharp (2012) proposed an empirical formulation to describe a master curve for the characterisation of the kinetic coefficient of friction between the rubber and the road surface, which was implemented in determining the frictional characteristics of the proposed tyre model in this work. The equation is a modified Savkoor-type empirical rubber friction model (Mavros, 2009), which is a function of both the sliding speed of the bristles' tips over the road surface and the surface temperature of the tyre tread.…”

Section: Brush Model Mathematical Formulationmentioning

confidence: 99%

“…The temperature effects are ignored for the steady-state non-thermal model. In addition, the reduction in friction coefficient as a result of increasing contact pressure is accounted for using a linear relationship (Kelly and Sharp, 2012). The reduction factor, C cp , is given by:…”

Section: Brush Model Mathematical Formulationmentioning

confidence: 99%

See 4 more Smart Citations

A brush-based thermo-physical tyre model and its effectiveness in handling simulation of a Formula SAE vehicle

Ozerem

Morrey

2018

Proceedings of the Institution of Mechanical Engineers, Part D:

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The ability to model tyre dynamics precisely is often one of the most critical elements for realistic vehicle dynamics control and handling investigations. The industry-standard empirical models are able to predict the important tyre forces accurately over a short range of vehicle operating conditions, which is often restricted to the operating conditions experienced during the tyre testing process. In this paper an alternative and practical method to model Formula SAE tyres has been proposed and studied in a series of possible running scenarios. A simple, analytically-solved brush type tyre model is considered for the physical part with the introduction of a novel approach for defining the contact length formulation that incorporates the influence of inflation pressure, camber angle and velocity while a set of ordinary differential equations are employed to predict the thermal behaviour of the tyre model, which are mostly based on an already-existing method that has not been experimentally validated before. The resulting tyre models provide realistic and informative behaviour of the tyre, which has the ability to consider the majority of the typical operating conditions experienced on a FSAE vehicle. The performance of the proposed tyre models are compared against experimental tyre test data, which show good agreement and indicates that the tyre models have the ability to give realistic predictions of the tyre forces and thermal behaviour in the case of thermal tyre model. Furthermore, the temperature-dependent tyre model has been incorporated into a two-track model of Oxford Brookes Racing's Formula SAE vehicle to study the effectiveness of the tyre model during transient handling simulation. The resulting simulations suggest that the proposed tyre model has the ability to represent realistic operating conditions of tyres, and also that tyre temperatures influence the vehicle dynamic behaviour significantly during on-limit scenarios.

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Section: Basic Tyre Modelling Methodsmentioning

confidence: 99%

Section: Basic Tyre Modelling Methodsmentioning

confidence: 99%

Section: Basic Tyre Modelling Methodsmentioning

confidence: 99%

Section: Brush Model Mathematical Formulationmentioning

confidence: 99%

Section: Brush Model Mathematical Formulationmentioning

confidence: 99%

See 3 more Smart Citations

A brush-based thermo-physical tyre model and its effectiveness in handling simulation of a Formula SAE vehicle

Ozerem

Morrey

2018

Proceedings of the Institution of Mechanical Engineers, Part D:

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A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles

Veneri

Massaro

2020

Lecture Notes in Mechanical Engineering

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A numerical methodology for thermo-fluid dynamic modelling of tyre inner chamber: towards real time applications

et al. 2021

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The characterization and reproduction of tyre behaviour for vehicle modelling is a topic of particular interest both for real-time driver in the loop simulations and for offline performance optimization algorithms. Since the accuracy of the tyre forces and moments can be achieved by the accurate physical modelling of all the phenomena concerning the tyre-road interaction, the link between the tyre thermal state and the tyre frictional performance turns into a crucial factor. An integrated numerical methodology, allowing to couple the full 3D CFD (Computational Fluid Dynamics) flux within the internal chamber of the tyre with an equivalent discrete 3D structure model, is proposed with the aim to completely represent the tyre thermodynamic convective behaviour in the steady-state operating conditions. 3D CFD model enables the evaluation of the internal distribution of the gas temperature and of the thermal powers exchanged at each sub-wall in detail. This allows to increase the reliability of the tyre thermodynamic modelling with a particular reference to the proper managing of the aero-thermal flow of the brake disc impact on the rim temperature and therefore on the internal gas dynamics in terms of temperature and pressure, being able to optimize the tyre overall dynamic performance in both warm-up and stabilized thermal conditions. The steady RANS (Reynolds Averaged Navier–Stokes) simulations have been performed employing the 3D CFD model in a wide range of angular velocities with the aim to calculate the convective thermal flux distributions upon rim and inner liner surfaces. The simulation results have been then exploited to derive the convective heat transfer coefficients per each sub domain to be employed within the real-time tyre physical thermal model, with the peculiar advantage of an enhanced model reliability for thermal characteristics. To validate the proposed methodology, the tyre thermal model outputs, in terms of temperatures of internal and external layers, have been validated towards the acquired ones within the specific routine performed on tyre force and moment test bench, confirming an excellent agreement with the experimental data in the entire range of operating conditions explored.

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Time-optimal control of the race car: influence of a thermodynamic tyre model

Cited by 35 publications

References 25 publications

A brush-based thermo-physical tyre model and its effectiveness in handling simulation of a Formula SAE vehicle

A brush-based thermo-physical tyre model and its effectiveness in handling simulation of a Formula SAE vehicle

A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles

A numerical methodology for thermo-fluid dynamic modelling of tyre inner chamber: towards real time applications

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