A Systematic Mathematical Modeling Approach for the Design and Machining of Concave-Arc Ball-End Milling Cutters with Constant Helical Pitch

As the use of NC techniques to machine the freeform and complex surfaces of dies and molds has increased, the demand for revolving helical cutters with specialized geometries has risen. This paper develops a systematic modeling approach for the design and NC machining of concave-arc ball-end milling cutters with a constant helical pitch. The section profile of groove and grinding wheel in the NC machining of the concave-arc ball-end milling cutters with constant pitch are concluded. The cutting edge is defined with a constant pitch and the grinding wheel is specified in terms of the maximum radius of the cutter. By employing the envelope and inverse envelope theories, the sections of grinding wheel and the radial feed, axis feed, and relative displacement of the grinding wheel during NC machining of the cutter are systematically designed. Based on the maximum sectional radius of the cutter, the principles of inverse envelope theory are then employed to establish the sectional profile of the grinding wheel required to produce the designed cutter using a two-axes NC machine. Models are then presented to continue the radial and axial feeding velocities of the grinding wheel during machining, together with its relative displacement. The proposed models are verified via computer simulation and are found to yield satisfactory results. The models presented in this study are intended to supply a general reference for the automatic design and manufacture of helical cutters with a constant pitch.