Swept volume of a generic cutter

Calculation of the swept volume of a cutter is the heart of any numerical controlled (NC) simulation system. In NC machining, a wide variety of cutter shapes are used such as flat end mills, dome end mills, ball nose end mills, angle cutters, face mills and side-and-face cutters. There are also many types of cutter paths along which the cutter is guided by the NC controller: rapid motion, linear motion and circular motion are the most commonly used cutter paths among them. Furthermore, the kinematics of the NC machines also differ leading to 2.5-axis, 3-axis and a variety of 5-axis configurations. The swept volume algorithms have to take into account all these variations of cutter shapes, motion types and machine kinematics. In this paper, first the parametric definition of a generic cutter is presented that can emulate all types of cutter shapes. Subsequently, the motions are classified into six types considering the cutter path and kinematic variations for ease of swept volume calculations. Finally, the swept volume algorithms for each of these six motion types are presented. These algorithms are used in a volumetric NC simulation system for which applications are envisaged in (a) NC verification and (b) optimization of the feed rate.