A numerical dynamic behaviour model for 3D contact problems with friction

•Influence of slip–stick transition on surface properties of contact materials.•Numeric modelling of 3D contact problems with friction.•Simulation of stick–slip behaviour of materials with different friction coefficients.

This paper proposes a novel algorithm for the condition detection in which the slip state transitions in a stick–slip motion, or the solution breaks down and also to study the state transition of nodes belonging to the contact area: stick, slip or open contact state. We designed a Matlab Simulink program to simulate the occurrence conditions for the slip–stick transition analysing three types of contact surface materials, with respectively 0.5, 0.75 and 0.9 friction coefficients, using finite element contact. The proposed method is able to detect the stick–slip motion and implicit the numerical instability of the model. By applying this method to control walking robots on uncertain, unknown and unstructured surfaces, the occurrence conditions for the slip–stick transition depending on the friction coefficient of contact material were determined. The presented simulations demonstrates through a numeric modelling of the dynamic behaviour of 3D contact problems with friction we can detect the slip/stick phenomenon for a walking robot motion on a uneven terrain, so it can improve the real time control in order to predict and avoid robot overthrow.