A non-linear model for pre-rolling friction force in precision positioning

Ultra-precision positioning is contaminated by the non-linearities and hysteresis caused by Hertzian contact at pre-rolling due to the absence of accurate models that could be implemented by positioning controllers to compensate for it. In this paper an attempt is made to model such behaviour at low speed and dry conditions while taking into account the mechanical characteristics of the bodies in contact. The proposed model simulates the non-linear behaviour, called non-linear spring behaviour (NSB), from pre-rolling to the steady state rolling without a transitional function. The model is compared to experimental measurements performed with several materials.