PH curve-based feedrate optimization ensuring analytical compliance with drive axis constraints in five-axis machining

The existing feedrate scheduling methods for five-axis machining either employ spline-based smoothing to satisfy single-axis kinematic constraints through iterative adjustments or blend motions between adjacent G01 segments without optimizing feedrate. This study presents an innovative feedrate optimizing method that ensures analytical compliance with single-axis kinematic constraints while maximizing feedrate and adapting to varying depths of cut. The proposed method utilizes Pythagorean-hodograph (PH) curve parameterization by arc length to establish the analytical relationship between tool feedrate and drive axis velocities, guaranteeing adherence to kinematic constraints. By analytically determining depth-of-cut variations via smoothed PH curve expressions, an approach is proposed to replace conventional constant feedrate profiles with multiple linked $C^3$-continuous acceleration or deceleration profiles. This ensures the realization of optimal feedrates and superior motion control performance while adhering to drive constraints by adjusting parameters (e.g., attainable maximum acceleration and jerk) according to the analytical relationship between feeding and single-axis motions. Experimental validation through flank milling and end milling demonstrates that the proposed method satisfies single-axis kinematic constraints, enhances machining efficiency without compromising accuracy, and outperforms existing methods based on constant feedrate.