Friction Compensation Method Based on a Dual-Segment Simplified Static–Dynamic Friction Model

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.