The Design of Free Surface Interpolator for CNC Machining

Abstract

This article provides a design for the real-time interpolator of the B-Spline free surface. The goal is to increase both the accuracy and the speed of manufacturing production by eliminating the bottleneck caused by the off-line interpolator of the CNC tool machines, by reducing manufacturing errors, and by resolving the issue of long numeric control code (NC code). The design of the surface interpolator includes location planning using the real-time cutter contact data, the interpolation of the cutter contact data, and the cutting compensation of the cutter location data. This paper provides a surface interpolation method for reading the surface NC code of a three-dimensional surface and for implementing the surface interpolation. To simplify the complexity of the calculation, one can first use knot interpolation to decompose the B-Spline surface into sections of Bezier surface, which are then used as the surface for real-time surface interpolation. Subsequently, the approximation of the second order Taylor expansion is used to obtain the location interpolation points. Fixed machining parameters are adopted to avoid the low efficiency and low quality of manufacturing caused by variation of the feeding speed. The derived cutting locations are further combined to obtain the cutting locations of the original B-Spline surface. The verification of the experiments is shown with comparing the manufacturing profile errors and any variation of the feeding speed derived from computer simulation and the corresponding data obtained from the off-line interpolators.