A Mechanical Model for the Dynamical Contact of Elastic Rough Bodies with Viscoelastic Properties

The contact between viscoelastic materials e.g. elastomers and a rough surface leads to a special friction characteristic, which differs greatly in its properties comparing to other materials like metals. In practice, this friction combination occurs for example in the tire-road contact, or in the use of rubber gaskets. Due to the frictional forces a system is significantly influenced in its vibrational properties. The friction force is composed of two main components adhesion and hysteresis. The adhesion results from molecular bounds between the contact partners, while the deformation of the viscoelastic material by the roughness of the counter body leads to power loss. This internal friction results in an additional frictional force, which is described by the hysteresis. To simulate the frictional behaviour of elastomers on rough surfaces and thus to determine the energy dissipation in contact, it is necessary to develop a mechanical model which considers the roughness of the contact partners, as well as dynamic effects and the dependence on normal pressure and sliding speed. The viscoelastic material behaviour must also be considered. The contact between two rough surfaces is modelled as a rough rigid layer contacting a rough elas- tic layer. The elastic layer is modelled by point masses connected by Maxwell-elements. This allows the viscoelastic properties of the elastomer to be considered. The behaviour of whole system can be described by equations of motion with integrated constraints. The degrees of freedom of the model depends on the varying contact conditions. A point mass not in contact has two degrees of freedom. A point mass in contact moving along the roughness path can be described by only one degree of freedom. For each Maxwell-Element also an inner coordinate and thus a further degree of freedom is needed. Because of varying contact conditions dur- ing the simulation, the simulation interrupts in case the contact conditions change. Then the equations of motions are adapted with respect to the contact constraints. As a result of the simulation one obtain the energy dissipation and thus the friction char- acteristic during the friction process. It is possible to use these results in three dimensional point-contact elements in order to model contact surfaces on lager length scales.