A two-stage friction model and its application in tracking error pre-compensation of CNC machine tools

Friction modelling and compensation is an important artifice to improve the tracking accuracy of CNC machine tools used for welding, 3D printing and milling, etc. This paper proposes a two-stage friction model to describe the characteristics of friction. First, a novel method is proposed to distinguish the boundary between the pre-sliding and sliding regimes of non-linear friction by estimating the breakaway velocity of static friction based on its elastic characteristics. Then, a two-stage feedforward friction compensation model which only has relationship with the velocity is developed. The proposed friction model not only can describe the Stribeck phenomena of friction, but also represent the characteristics of the static friction. A tracking error pre-compensation model is developed thereafter based on the good performances of feedforward friction compensation, in order to further reduce the tracking error of CNC machine tools. Extensive experiments and analyses verify that the proposed friction model and tracking error pre-compensation method can significantly improve the tracking accuracy of CNC machine tools. Specifically, comparison with existing tracking-error based friction model shows that the proposed model can reduce maximum and average tracking errors more than 70% and 20%, respectively. Furthermore, contouring errors of multi-axis motion are also reduced to some extent.