Abstract: Velocity planning for curved path interpolation in high CNC machining should be bounded by both dynamic properties of the machine tool and the geometrical properties of the curved path. Through building the electromechanical hybrid model of the machine feed system, the dynamical constraints of the high-speed CNC interpolating feed rate along a curved path are given. Based on them, an analytical formula of velocity limit curve is derived by using the “velocity-acceleration” phase plane method. And the formula is intrinsically coherent with the one of chord error velocity limit curve. So the constraints of feed rate planning will be simplified by estimating the max chord error value of dynamical constraints of machine. The experimental results show that the analytic velocity limit curves are efficacious and helpful to curved path interpolation feed rate planning in theory.

Key words: CNC machine, Hybrid model, Interpolation, Parametric curve, Velocity limit curve, Velocity planning