The contact forces are dependent on many parameters, such as contact stiffnesses, surface profiles, material parameters, temperature distribution, relative motion and normal pressure distribution. These parameters can change within the contact area and from here, it is impossible to derive a general force law. The only possibility to overcome this problem is to discretize the contact areas, since in general the relative motion and the contact parameters are not constantly distributed within the contact surface. This leads to a point contact model, which has to include all main physical effects as described above, which are important, when simulating dynamical contact problems with friction.
The friction model includes the main parameters such as the roughness of the contact surfaces, the nonlinear friction law, the contact stiffnesses in normal and tangential direction. The decreasing characteristic of the friction coefficient with respect to the relative velocity has to be modeled in a sufficient way. With respect to the dissipation of energy, the hysteretic behavior is studied with respect to the normal and tangential direction. Separation of the contact is included.
This point contact model is be applied to real dynamical contact problems. In the first example, a simple impact oscillator with an elastic contact is used to check the overall modeling with respect to the elastic normal contact. Then, a self excited friction oscillator is investigated with respect to the tangential contact. Here, the modeling of surface waviness leads to high periodic solutions, which is also observed within the experiments. In both examples, the comparison of measurements and calculated phase plots is good.
Furthermore, the influence of wear on to the surface profile, contact area and normal pressure distribution is investigated. From here, it follows, that friction leads to time dependent systems.