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Rubber Friction is a topic of huge importance in numerous technological applications. However in most theoretical or numerical (such as FEM) studies, rubber friction is described using very simple phenomenological models, e.g., the Coulomb friction law with a friction coefficient which may depend on the local sliding velocity. Rubber friction depends in general on the history of the sliding motion due to frictional heating of the rubber and the rubber-substrate contact regions. Thus, unless the frictional behaviour, e.g., in tire dynamics, is accurately described no tire model, independent of how detailed the description of the tire body may be, will provide an accurate picture of tire dynamics!
 
Based on the Contact Mechanics approach, we at Multiscale Consulting have developed a physical model to calculate rubber friction. It takes into account the energy dissipated due to time-dependent deformations of the rubber and the energy dissipated in the contact regions due to shearing of the real area of contact. The only input parameters needed for the calculations are basically the surface roughness power spectrum (as obtained as output from the power spectrum software), the complex viscoelastic modulus (output from the Eshift and Nonlinear Processing software) as well as some other material properties. Depending on the quantity which should be calculated the input might vary a little. More important, please note that our theory is a parameter free theory. There are no free parameters which could be used to fit the results. This is up to now the only physically based approach on rubber friction which takes into account different energy dissipation mechanisms in a correct way. It has been shown, both numerically and experimentally, that the theory correctly predicts friction between a rubber block in sliding contact with a hard, rough substrate.
 
The friction model also takes into account temperature effects arising from the heating of the rubber during sliding. This results in a powerful description of rubber friction which also takes into account the sliding history. For more information and detailed background know-how we suggest these two publications: Rubber Friction, Tire Model as well as visit our rubber friction site in the "Our Research" section.

The figure below illustrates the latest version of our rubber friction software for Windows:

 

Windows version of the rubber friction software

 

The figure of the interface illustrates that the software does not require any fitting parameter input. The information which needs to be specified is directly output from the other software which we have developed. Below we show some results to demonstrate the output of the program. First we show the calculated total rubber friction coefficient (green dotted line) as a function of log10 of the velocity. The solid green curve represents the total friction coefficient including temperature effects.

 

Here two different dissipation mechanisms are taken into account, the viscoelastic deformations of the rubber due to the roughness profile (blue curves) and the contact area contribution resulting from shearing the real area of contact (red curve). For all curves the dotted line is without flash temperature while the solid line includes flash temperature effects.

 

The coefficient of friction as a function of the sliding velocity (green curves, with log10 as basis). Shown are the contribution from viscoelastic deformations (blue curves) and from shearing the contact area (red curves). The dotted lines neglect temperature effects while the solid lines are with flash temperature in the contact.

 

Below are two additional plots showing the dependency of the flash temperature on the magnification or resolution (with log10 as basis) on the left and the real area of contact as a function of the velocity (with log10 as basis) on the right. One can see that the rubber bulk temperature on large length scales is basically unchanged compared to the background temperature which was 20°C in this calculation. The smaller the volume element which we consider in the contact, or the larger the resolution, one can find higher temperatures at the interface.

The other figure shows how the real area of contact decreases with increasing velocity. The reason for this is that the rubber material becomes effectively stiffer as with increasing velocity the frequencies induced by the surface roughness asperities gets larger. Note also that when including flash temperature effects the contact area is quiet a bit larger at high velocities. This is due to a shift of the viscoelastic modulus to higher frequencies with increasing temperature. The rubber becomes effectively softer again.

 

Temperature in the contact as a function of the magnification (with log10 as basis)
Area of contact as a function of sliding velocity (with log10 as basis)

 

In the rubber friction program there is also a simple 2D tire model included as described in the second reference above. Here one can learn how, e.g., the footprint shape influences the dynamics of the tire or simulate an ABS braking situation. The tire model also shows that it is easily possible to implement the rubber friction code in an already existing tire model!

 

For further information on the rubber friction software please consider the following information:

The manual of the rubber friction software for the Windows version. Coming Soon
The Data.Out file is a summary of the different options chosen for a particular calculation. The options are briefly explained and the most important results summarized. The Data.Out file is always created after the calculation is finished. Download Data.Out
An example rubber friction output file. Download Example Rubber Friction Results

 

In case you are interested in using the rubber friction program or you have further questions concerning the software please feel free to contact us.