Self-excited fluctuation of sliding velocity induced by LuGre friction in a minimal mechanical model

The paper explores various bifurcations that can occur due to the variation of the linear internal damping (bristle damping) term in the LuGre friction model. To capture the essence of the nonlinear effects associated with friction, we consider a minimal mechanical model: a block sliding on a horizontal surface, which is subjected to a constant external force and the LuGre friction force with a viscous damping term. Despite the simplicity of the mechanical model, six different bifurcation scenarios are identified, involving Hopf bifurcations. Due to the emerging limit cycles – that may undergo fold or homoclinic bifurcations, as well – the slipping velocity and the friction force fluctuate near the Stribeck characteristic at sufficiently large bristle damping values. This phenomenon can be considered as a self-excited counterpart of the well-known frictional lag phenomenon.