Egbert Bakker

THE MAGIC FORMULA TYRE MODEL

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.

Tyre Modelling for Use in Vehicle Dynamics Studies

A new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions has been developed in order to further improve the Dynamic Safety of vehicles. The method makes use of a formula with coefficients which describe some of the typifying quantities of a tyre, such as slip stiffnesses at zero slip and force and torque peak values. The formula is capable of describing the characteristics of side force, brake force and self aligning torque with great accuracy. This mathematical representation is limited to steady-state conditions during either pure cornering or pure braking and forms the basis for a model describing tyre behaviour during combined braking and cornering.

Links between subjective assessments and objective metrics for steering, and evaluation of driver ratings

During the development of new vehicles, finding correlation links between subjective assessments (SA) and objective metrics (OM) is an important part of the vehicle evaluation process. Studying different correlation links is important in that the knowledge gained can be used at the front end of development, during testing and when creating new systems. Both SA from expert drivers using a rating scale of 1–10 and OM from different tests measured by a steering robot were collected using standard testing protocols at an automotive manufacturer. The driver ratings were evaluated and the correlations were analysed using regression analysis and neural networks through a case study approach. Links were identified and were compared with related research.

Findings from subjective evaluations and driver ratings of vehicle dynamics: steering and handling

This paper investigates subjective assessments (SA) of vehicle handling and steering feel tests, both numerical and verbal, to understand drivers’ use of judgement scales, rating tendencies and spread. Two different test methods are compared: a short multi-vehicle first-impression test with predefined-driving vs the standard extensive single-vehicle free-driving tests, both offering very similar results but with the former saving substantial testing time. Rating repeatability is evaluated by means of a blind test. Key SA questions are identified by numerical subjective assessment autocorrelations and by generating word clouds from the most used terms in verbal assessments, with both methods leading to similar key parameters. The results exposed in this paper enable better understanding of SA, allowing improving the overall subjective testing and evaluation process, and improving the data collection and analysis process needed before identifying correlations between SA and objective metrics.

Improving Subjective Assessment of Vehicle Dynamics Evaluations by means of Computer-Tablets as Digital Aid

Vehicle dynamics development relies on subjective assessments (SA), which is a resource-intensive procedure requiring both expert drivers and vehicles. Furthermore, development projects becoming sh ...

Correlations of subjective assessments and objective metrics for vehicle handling and steering: a walk through history

Achieving customer satisfaction concerning steering feel and vehicle handling requires subjective assessments and tuning of vehicle components by expert test drivers and engineers. Extensive subjective testing is expensive, time consuming and requires physical vehicles, which is in conflict with reduction of development time and cost. Objective testing and model-based development are constantly increasing but translating subjective requirements into objective ones is non-trivial. This paper summarises, discusses and classifies the methods, strategies and findings in previously published research regarding correlations of subjective assessments and objective metrics for vehicle handling and steering. The aim is twofold: (i) to identify key parameters of steering, handling and their preferred values and (ii) to compile and discuss the fundamental issues to deal with in the continued search for correlations between objective metrics and subjective assessments. The paper gives a comprehensive overview and insight of different aspects to take into account when conducting research in this field.

Machine learning to classify and predict objective and subjective assessments of vehicle dynamics: the case of steering feel.

ABSTRACT Objective measurements and computer-aided engineering simulations cannot be exploited to their full potential because of the high importance of driver feel in vehicle development. Furthermore, despite many studies, it is not easy to identify the relationship between objective metrics (OM) and subjective assessments (SA), a task further complicated by the fact that SA change between drivers and geographical locations or with time. This paper presents a method which uses two artificial neural networks built on top of each other that helps to close this gap. The first network, based solely on OM, generates a map that groups together similar vehicles, thus allowing a classification of measured vehicles to be visualised. This map objectively demonstrates that there exist brand and vehicle class identities. It also foresees the subjective characteristics of a new vehicle, based on its requirements, simulations and measurements. These characteristics are described by the neighbourhood of the new vehicle in the map, which is made up of known vehicles that are accompanied by word-clouds that enhance this description. This forecast is also extended to perform a sensitivity analysis of the tolerances in the requirements, as well as to validate previously published preferred range of steering feel metrics. The results suggest a few new modifications. Finally, the qualitative information given by this measurement-based classification is complemented with a second superimposed network. This network describes a regression surface that enables quantitative predictions, for example the SA of the steering feel of a new vehicle from its OM.

Evaluation of vehicle-based tyre testing methods

The demand for reduced development time and cost for passenger cars increases the strive to replace physical testing with simulations. This leads to requirements on the accuracy of the simulation models used in the development process. The tyres, the only components transferring forces from the road to the vehicle, are a challenge from a modelling and parameterization perspective. Tests are typically performed on flat belt tyre testing machines. Flat belt machines offers repeatable and reliable measurements. However, differences between the real world road surface and the flat belt can be expected. Hence, when using a tyre model based on flat belt measurements in full vehicle simulations, differences between the simulations and real prototype testing can be expected as well. Vehicle-based tyre testing can complement flat belt measurements by allowing reparameterization of tyre models to a new road surface. This paper describes an experimental vehicle-based tyre testing approach that aims to parameterize force and moment tyre models compatible with the standard tyre interface. Full-vehicle tests are performed, and the results are compared to measurements from a mobile tyre testing rig on the same surface and to measurements on a flat belt machine. The results show that it is feasible to measure the inputs and outputs to the standard tyre interface on a flat road surface with the used experimental setup. The flat belt surface and the surface on the test track show similar characteristics. The maximum lateral force is sensitive to the chosen manoeuvres, likely due to temperature differences and to vibrations at large slip angles. For tyre models that do not model these effects, it is vital to test the tyres in a manoeuvre that creates comparable conditions for the tyres as the manoeuvre in which the tyre model will be used.

Analysis and optimisation of objective vehicle dynamics testing in winter conditions

ABSTRACT Objective testing of vehicle handling in winter conditions has not been implemented yet because of its low repeatability and its low signal-to-noise ratio. Enabling this testing, by identifying robust manoeuvres and metrics, was the aim of this study. This has been achieved by using both experimental data, gathered with steering-robot tests on ice, and simulation models of different complexities. Simple bicycle models with brush and MF-tyre models were built, both optimally parameterised against the experimental data. The brush model presented a better balance in complexity performance. This model was also implemented in a Kalman filter to reduce measurement noise; however, a simpler low-pass filter showed almost similar results at lower cost. A more advanced full vehicle model was built in VI-CarRealTime, based on kinematics and compliance data, damper measurements, and real tyre measurements in winter conditions. This model offered better results and was therefore chosen to optimise the initial manoeuvres through test design and simulations. A sensitivity analysis (ANOVA) of the experimental data allowed one to classify the robustness of the metrics. Finally, to validate the results, the proposed and the initial manoeuvres were tested back to back in a new winter campaign.