Keywords: friction, contact, rubber, tire tread, thermo-mechanical simulations, finite elements.

Rubber friction is a topic of considerable industrial interest. In the tire industry, the development of new tire lines is performed by means of numerical simulations to an increasing extent. A realistic description of the friction process between tire and road surface is a pre-requisite for reliable results of these numerical simulations.

The most crucial aspect of a tire simulation is the realistic description of the processes in the contact interface between the tire tread and the road surface. These processes determine the performance of the tire not only locally in the contact area, but also globally in its overall behavior.

Rubber friction is very challenging because of the distinct characteristics of rubberlike materials. Especially their pronounced viscoelastic behavior and their generally low Young's modulus bring about different friction mechanisms than observed for most other solids [1]. Furthermore, the pronounced temperature dependence of many properties of rubber, e.g. of its stiffness, results in a non-negligible influence of the local rise of contact temperature on the frictional behavior. The roughness of a road surface, which is encountered at different length scales, further complicates the matter. The interactions between the single microscale asperities have to be smeared to result in macroscopic relations for the description of the contact behavior.

In [2], a contact model was developed which provides suitable formulations for the stresses and the heat fluxes at the contact surface. It accounts for mechanical interactions at the contact surface as well as for thermal ones. The detachment of material particles from the contact surface in consequence of friction - i.e. abrasion of material at the contact surface - is also taken into account.

The established contact model manages to combine the demands arising from industrial applicability on the one hand and the requirements of a high affinity to reality on the other hand. It employs a macroscopic approach in order to maintain simplicity and efficiency of its application. The use of rather sophisticated formulations, on the contrary, enables to achieve a close affinity to reality. Perfectly smooth contact surfaces are assumed in the models for the numerical simulations. The effect of surface roughness is included in the formulations for the contact stresses and heat fluxes by means of statistical parameters of the surface profile. The model makes use of only macroscopic characteristics of the contact partners [3].

The contribution at hand focuses on applications of the described contact model for various purposes of predominantly practical - i.e. tire engineering - interest. Main emphasis is placed on two topics: (i) the application of the contact model for the simulation of tire tread patterns and (ii) the simulation of frictional sliding of tread blocks with simple geometries under consideration of abrasion.

Tire tread patterns are composed of rubber blocks with different shapes and arrangements. Their frictional behavior is examined in simulations of blocks with rectangular and parallelogram-shaped bases and with internal sipes at different positions. The simulations throw light on the interactions between the blocks and allow for the optimization of the pattern design in terms of frictional characteristics.

As regards abrasion, a simulation strategy reproducing the conditions of tread blocks during ABS braking was developed. It considers a sequence of short sliding events which are encountered by a tread block with each revolution of the tire. The simulation procedure predominantly aims at an examination of the abrasional characteristics of different block geometries and rubber compounds in qualitative respects.

All numerical simulations are accompanied by experimental investigations in order to validate the employed models and simulation procedures. These examination are performed at the Linear Friction Tester (LFT) which is a testing device developed at the Laboratory of the Institute for Strength of Materials at Vienna University of Technology on behalf of Continental AG. A detailed description of the device can be found in [4].

Mechanical characteristics (e.g. friction forces) as well as thermal ones (e.g. surface temperatures) measured in the experiments agree well with corresponding data obtained in numerical simulations. Also the geometries that results from numerical simulations of the abrasion process match closely to abrasion patterns of test specimens at the LFT.

The presented work is part of a research project sponsored by the Continental AG. Their approval to this contribution is gratefully acknowledged.

1

B.N.J. Persson, "On the Theory of Rubber Friction", Surface Science, 61, 119-136, 1998. doi:10.1016/S0039-6028(98)00051-X

2

K. Hofstetter, "Thermo-mechanical Simulation of Rubber Tread Blocks during Frictional Sliding, Ph.D. Thesis, Vienna University of Technology, 2004.

3

K. Hofstetter, J. Eberhardsteiner, H.A. Mang, "A Thermo-Mechanical Formulation Describing the Frictional Behavior of Rubber", Vehicle Dynamics, in print. doi:10.1002/pamm.200310104

4

J. Eberhardsteiner, W. Fidi, W. Liederer, "Experimentelle Bestimmung der adhäsiven Reibeigenschaften von Gummiproben auf ebenen Oberflächen (in German)", Kautschuk Gummi Kunststoffe, 51, 773-781, 1998.

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