A 3D model for rubber tyres contact, based on Kalker's methods through the STRIPES model

Abstract

A project on the pavement-rutting evolution under the effect of a tram on tyre, led the author to make a link between road and railway approaches to the problem of rolling contact. A simplified model is proposed with a fine description of the contact patch between a tyre and the road, and a more realistic pressure and shear stresses distribution than that available from basic models previously available. Experimental measurements are used to identify some characteristics of the force description, while the geometric shape of the tyre-road section are used, like in the traditional rail–wheel contact models, to build the 3D model. The last part validates a plausible contact pressure shape from self-aligning torque measurements and from Kalker's contact stresses gradient applied to the real tyre used in the project. The final result is a brush model extended from the wheel-rail STRIPES one, applicable to dynamics or contact studies of real tyres, with a physical coupling between longitudinal, lateral and spin effects, and a relatively fine description of the contact stresses along each strip of each tyre of the vehicle on an uneven road.

Keywords:

• contact mechanics
• creep forces
• models
• Hertzian contact
• simulation

Acknowledgements

This work has been supported by the French research program PREDIT in the context of the DEVIN project, partly dedicated to the tyre contact stress estimation and their effects on the pavement durability.

Notes

Similar parabolic and linear distributions are used in tyre contact brush models like 27.

In this figure, we have added in grey the bristles which are deformed in the contact area, in both longitudinal and lateral direction.

The numerical values and the creepages must be translated in MKSA.

This last hypothesis is suggested in the complete theory of Kalker, showing a ‘S’-shaped gradient, while the simplified theory in FASTSIM supposes a linear gradient.