Cnc Interpolators: Algorithms and Analysis

CAD systems today interpolate general curves by dividing each curve into many straight-line segments which are downloaded to the CNC. Determining the number of lines to be transferred from the CAD to the CNC poses a conflict between the desired precision of the part and the feedrate fidelity. The current method results in severe variations in the feedrate, leading, in turn, to variations in the surface smoothness and a substantial increase in machining time. These problems are caused by the acceleration/deceleration at the ends of each segment. Moreover, the problems are inherent in the CNC interpolator, as is thoroughly discussed in this paper. These problems can be solved by the development of curve interpolation algorithms for CNC. In this paper, a real-time interpolation algorithm for curves presented in their parametric forms is proposed and compared with the existing CAD interpolators. Analysis shows that with this new interpolator, a constant feed is maintained along the cut and the machining time is as expected. In addition, the amount of geometric information transferred from the CAD system to the CNC is reduced by orders of magnitude. Moreover, the contour errors caused by the new interpolator are much smaller than those caused by conventional CAD interpolators.