R-surfaces: A novel tool for partitioning of a sculptured surface

• Authors: Stephen P. Radzevich
• Venue: Mathematical and Computer Modelling: An International Journal
• Year: 2007

This paper presents a systematic scheme for developing feasible tool-paths for machining a sculptured surface on a multi-axis NC machine. In our previous paper (in CAD journal), a simplified problem of CT-dependent partitioning of a sculptured surface is solved with application of the focal surfaces. The derived solution to the problem is convenient for particular cases when the angle of the surfaces P and T local relative orientation is identical to zero (@m=0). In general case of sculptured surface machining on multi-axis NC machine, the identity @m=0 often doesn't observe. Here this problem is enhanced up to cases when the actual value of the angle @m could be of arbitrary value. The reported approach is based on application of the characteristic surfaces of novel kind. The characteristic surfaces of the newly discovered kind are referred to as the characteristic R-surfaces. The reported solution to the problem is based on implementation of the DG/K-method of surface generation. The methodology presented here is a general one. It combines the activities of exploration of topology of a given sculptured surface, of the generating surfaces of the cutting tool, of the cutting tool configuration and of the cutting tool motion that it performs in the machining operation relative to the work, thus making the production process flexible, automatic and controllable. The approach is the CAD/CAM orientated one. The effectiveness of the proposed approach is verified from numerical simulation. Perfect correlation of the reported results with those previously published by the author, as well as by other researchers, is observed.