Calculation of variable feed rate and spindle speed for nurbs based CNC machining

In traditional CNC manufacture of free-form surfaces a mesh of lines and circular cutting paths that are close to the original surface is used to approximate the surface. This results in a need for generating cutting paths that are linear and circular. A new generation of CNC machine controllers that are capable of moving along a Non-Uniform Rational B-Spline (NURBS) curve and take in control points of the NURBS curve as their input have been developed. These machines are capable of moving at high velocities. However, these CNC controllers utilize a constant feed rate and spindle speed resulting in less than optimal cutting conditions. Also while moving along the NURBS curve, the cutter is subjected to various material conditions that would require modifying the feed rates. A constant feed rate for each NURBS command can be inefficient or result in incorrect cutting during NURBS motion. Algorithms for variable feed rate have to be developed as an option to ensure that the cutting is at more optimal conditions. This paper presents algorithms that have been developed for continuously and optimally varying feed rate and spindle speed during CNC machining of NURBS curves.