Nonlinear friction in the mechanical transmission system of machine tools induces transient stagnation of the feed axis as its velocity crosses zero, thereby giving rise to contouring errors in multi-axis machining and significantly degrading machining accuracy. To address this issue, a feedforward compensation strategy is proposed based on a simplified static friction model (SSFM) with dual-segment and dual-parameter characteristics. The nonlinear friction is represented by a combination of a linear segment and an exponential segment, while the model incorporates two essential parameters that characterize the maximum friction force and the negative damping effect. Experimental results from two-axis circular trajectory tests show that the proposed SSFM reduces contour errors by approximately 73.4% and 79.2% at 600 mm/min and 2100 mm/min, respectively. To improve compensation under high-speed conditions, an acceleration-dependent dynamic correction is further introduced to establish the SDFM. The results show that the maximum contour error is further reduced to 1.44 μm and 1.49 μm at 3600 mm/min and 5000 mm/min, respectively. Compared with many existing reduced-order or hybrid friction models that rely on more parameters or more complex identification procedures, the proposed method provides a more compact and compensation-oriented modeling strategy for the velocity-reversal region of CNC feed systems.
Chen et al. (Wed,) studied this question.