Jacob Svendenius

A semi-empirical dynamic tire model for combined-slip forces

This article presents a semi-empirical combined-slip tire model including transient behavior. It is assumed that the transient behavior is a result from the dynamic deformation of the tire carcass and that the interaction between the lateral and longitudinal slip, and forces can be explained by the deformation of the rubber treads. The deformation of the tire carcass makes the tread slip deviate from the wheel-rim motion in a way that may be described by differential equations. A method based on brush-model tire mechanics is used to construct the combined-slip forces as nonlinear scalings of corresponding pure-slip forces.

A novel semi-empirical tyre model for combined slips

A new tyre-force model for simultaneous braking and cornering is presented, which is based on combining existing empirical models for pure braking and cornering with brush-model tyre mechanics. The aim is to offer an easy-to-use, accurate model for vehicle-handling simulations. On a working tyre the contact patch between the tyre and the road is, in general, divided into an adhesion region where the rubber is gripping the road and a sliding region where the rubber slides on the road surface. The total force generated by the tyre is then composed of components from these two regions. The brush model describes this in a mechanical framework. The proposed model is based on a new method to extract adhesion and sliding forces from empirical pure-slip tyre models. These forces are then scaled to account for the combined-slip condition. The combined-slip self-aligning torque is also described. A particular feature of the model is the inclusion of velocity dependence, even if this is not explicitly present in the empirical pure-slip model. The approach is quite different from most previous combined-slip models, in that it is based on a rather detailed mechanical model in combination with empirical pure-slip models. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model and in this work the Magic Formula is used in examples. Results show good correspondence with experimental data.

Experimental Validation of the Brush Tire Model

The paper contains an experimental validation of the physically based brush-tire model toward the tire behavior in a number of different realistic conditions. Results of measurements performed with summer, winter, and studded tires on different road foundations such as wet and dry asphalt, basalt, snow, and ice are presented. The purpose behind the validation is to study the possibilities of using the brush model to estimate the friction coefficient from measurements or estimates of the longitudinal tire forces and tire slip. The sensitivity of the included tire parameters toward various factors that may change during normal run of the vehicle is also investigated.

A Brush-Model Based Semi-Empirical Tire-Model for Combined Slips

This paper presents a new method to derive the tire forces for simultaneous braking and cornering, by combining empirical models for pure braking and cornering using brush-model tire mechanics. The method is aimed at simulation of vehicle handling, and is of intermediate complexity such that it may be implemented and calibratedby the end user. The brush model states that the contact patch between the tire and the road is divided into an adhesion region where the rubber is gripping the road and a sliding region where the rubber slides on the road surface. The total force generated by the tire is then composed of components from these two regions. In the proposed method the adhesion and the sliding forces are extracted from anempirical pure-slip tire model and then scaled to account for the combined-slip condition. The combined-slip self-aligning torque is described likewise. The separation of the adhesive and sliding forces makes it possible to let the sliding force depend on the relative velocity between the tire and the road. This introduces a velocity dependence in the model, even though this is not explicitly present inthe pure-slip model. The approach is quite different from most previous combined-slip models, in that it is based on a rather detailed mechanical model in combination with empirical pure-slip models. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model and in this work the Magic Formula is used in examples. Results show good correspondence with experimental data. (Less)

A semi-empirical tyre model for combined slips including the effects of cambering

This article presents the addition of camber to a previously published semi-empirical tyre model by the same authors. The model combines empirical models for pure braking, cornering and cambering with a model for simultaneous braking, cornering and cambering. It is based on brush-model tyre mechanics and aims to offer an easy-to-use accurate model for vehicle-handling simulations. The proposed model is a method to extract and rescale the adhesion and sliding forces from empirical pure-slip tyre models to account for the combined-slip condition. The combined-slip self-aligning torque is described likewise. Cambering affects the natural path of the tyre carcass on the road surface and deforms the threads to produce an additional force in the lateral direction. Thereby, the proportions of the sliding and adhesive forces changes. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model.

Evaluation of Tyre to Road Friction Estimators, Test Methods and Metrics

The tyre to road contact friction is one of the most important properties when it comes to manoeuvrability of ground vehicles and information, to driver and vehicle, is of vital importance in critical situations. Different characteristics of different friction estimation methods make it hard to determine and compare performance of estimators. This article is an attempt to define and evaluate the performance of tyre to road friction estimators. The objective of the performance evaluation is to define and grade the performance of estimators based on all sorts of approaches and combinations of these. The result may be used in the context of benchmarking as well as a tool in the development process of the estimator. The test methods and metrics presented are illustrated with a comparative study of three different estimation approaches.