Modeling the surface swept by a generalized cutter for NC verification

Presented in this article is a procedure for representing the cutterswept surface (CSS) of a generalized cutter in a single-valued form, z = f(x, y). The key idea is that the z-value of the CSS at a 2D point (x, y) is expressed as the sum of 1) the z-value at a point on the silhouette curve of the cutter bottom surface and 2) the incremental z-value along the cutter movement direction. Thus, the main part of the modeling method is to obtain the silhouette curve equations, which becomes a root finding problem for a quartic polynomial (when the cutter bottom surface contains a toroidal surface). The proposed method not only renders a single-valued representation for the CSS of a generalized cutter (which was not possible with the existing methods) including rounded endmill but also results in a computational scheme that is faster than the existing schemes for ball- and flat endmills.