Friction Modeling and PD Compensation at Very Low Velocities

It is a well-known empirical result that stick-slip can often be eliminated from a system by stiffening it. More recently, it has been shown that for a negatively-sloped friction-velocity curve, a frictional lag must be present for machine/controller stiffness to produce this stabilizing effect. In this paper, experiments involving dry and lubricated line contacts of hardened tool steel are described which demonstrate the existence of frictional lag in boundary lubrication. It is also shown that a single-state-variable friction model provides a good representation of the actual friction dynamics. The model and associated parameter values provide a means for computing lower bounds on the machine stiffness and PD gains necessary for steady motion at velocities on the order of microns per second.