Comparison of Parametrically Programmed Machining with CAM System Machining for NURBS Curves Based on Various Parameters

Abstract

Non-Uniform Rational B-Spline (NURBS) curves are the de facto standard for representing complex free-form shapes in modern Computer-Aided Design (CAD) environments. Their application in manufacture—turbine blades, automotive bodies, mould cavities, and aerospace surfaces—demands CNC programs capable of faithfully reproducing curved geometry. Conventional CNC controllers, however, natively support only linear (G01) and circular (G02/G03) interpolation, compelling Computer-Aided Manufacturing (CAM) software to approximate NURBS profiles by discretising them into large numbers of tiny linear or circular segments. The resulting NC programs are voluminous, consume substantial controller memory, and are difficult to modify in real time. This paper proposes and experimentally evaluates an alternative approach: parametric (macro) part programming, in which the NURBS curve definition—comprising control points, knot vector, order, and weight vector—is encoded directly into a compact macro programme executed on a Mitsubishi M80 CNC controller. A 2-D NURBS profile was first modelled in MATLAB and transferred to CAD; the geometry was subsequently imported into Siemens NX CAM for tool-path generation, and a corresponding macro programme was developed from first principles. Both programmes were executed on a Cosmos CVM-800 Vertical Machining Centre using an aluminium workpiece under identical cutting conditions. Dimensional accuracy of each machined profile was evaluated using a Hexagon Coordinate Measuring Machine (CMM). The parametric programme reduced the instruction-line count from 144 to 135, shortened machining cycle time from 2 min 45 s to 2 min 30 s, decreased average error from 0.135 mm to 0.097 mm, and achieved a Root Mean Square Error (RMSE) of 0.111 mm against 0.154 mm for the CAM approach. These results confirm that parametric programming offers superior dimensional accuracy, programme compactness, and real-time adaptability for NURBS-based CNC machining.