Smooth path planning using biclothoid fillets for high speed CNC machines

In high speed Computer Numerical Control (CNC) machines, cut velocities greater than 60 m per minute and accelerations higher than 2 g are used. In such high feedrates and accelerations, even a small discontinuity in curvature or in tangency can result in jerk spikes and consequently in machine vibrations, poor cut quality and decreased lifespan of the equipment. To prevent these consequences, using path smoothing techniques is necessary. Many path smoothing methods have been proposed in the literature to eliminate toolpath discontinuities. However the usage of almost all of these techniques is limited to purely linear toolpaths. In this paper a new path smoothing method using biclothoid fillets is introduced. The proposed method can be used to convert any given path consisted of lines and arcs to a curvature continuous path. The generated path is arc length parameterised which makes it easy to interpolate. The distance between the G2-continuous path and the original toolpath is limited to an adjustable tolerance. The proposed method has been tested on a CNC laser cutting machine and the results are reported. The main contribution of this paper is a fillet fitting method which is not limited to line to line transitions. The proposed smoothing fillets can be fitted between two arcs or a line and arc as well. A comparison with Bezier fillets, shows that using the proposed method results in a smoother curvature profile, higher feedrates and shorter cycle times.