Verification of NC machining processes using swept volumes

A numerically controlled (NC) machining verification method is developed based on a formulation for delineating the volume generated by the motion of a cutting tool on the workpiece (stock). The motion of a cutting tool is modeled as a surface undergoing a sweep operation along another geometric entity where machine tool trajectory includes translational and rotational movements. A rank-deficiency condition is imposed on the Jacobian of the sweep to determine the singular surfaces. Singular entities are then intersected to determine sub-entities that may exist on the boundary of the volume. A perturbation method is used to identify the boundary envelope of the material volume to be removed. Numerical examples illustrating the formulation are presented. Benefits of this method are its ability to depict and visualize the manifold and to compute a value for the volume.