Real-Time Interpolator of CNC Parametric Curves with Chord-Error and Feed-rate Constraints

Acknowledging that the core in computer numerical control (CNC) machining is the interpolator of the controller, the work presents a real-time interpolator of a class of non-uniform rational basis splines, NURBS curve, which is inherently parametric. Teardrop 2-dimensional NURBS curve was selected based on varying features, shapes and dimensions. The curve characteristics cover variations of dimensional geometry, origin position, closed or open-ended curves, varying loop count, segment type, either convex or concave, turning profile smoothness and different reflection symmetry about the x and y axes. The real-time interpolator algorithm, when applied to all the selected curves exclusively and simultaneously, satisfies both of its designed constraints, which cover its feed-rate and its chord-error tolerance. The resulting feed-rate profiles throughout the entire path of the curves are continuous and smooth. The feed-rate constraints comprise dynamic equations for allowable CNC machine parameters like the maximum and minimum axial velocities and the maximum and minimum axial accelerations. The chord-error constraints comprise geometric and kinematic properties of different parametric curves, covering bends and sharp turns. The resulting algorithm was executed both in real-time, online mode by driving the CNC machine directly, and in an offline mode by using a stored RS274/NGC G-code file. The plot conclusively shows that the chord-error (u) at every u-point in the full range of 0.00 ≤ u ≤ 1.00 lies below the chord-error tolerance, which was set at 1x10-6 mm.