Geometric Modeling of Cutter/Workpiece Engagements in Three-Axis Milling Using Polyhedral Representations

Modeling the milling process requires cutter/workpiece engagement (CWE) geometry in order to predict cutting forces. The calculation of these engagements is challenging due to the complicated and changing intersection geometry that occurs between the cutter and the in-process workpiece. This geometry defines the instantaneous intersection boundary between the cutting tool and the in-process workpiece at each location along a tool path. This paper presents components of a robust and efficient geometric modeling methodology for finding CWEs generated during three-axis machining of surfaces using a range of different types of cutting tool geometries. A mapping technique has been developed that transforms a polyhedral model of the removal volume from the Euclidean space to a parametric space defined by the location along the tool path, the engagement angle, and the depth of cut. As a result, intersection operations are reduced to first order plane-plane intersections. This approach reduces the complexity of the cutter/workpiece intersections and also eliminates robustness problems found in standard polyhedral modeling and improves accuracy over the $Z$-buffer technique. The CWEs extracted from this method are used as input to a force prediction model that determines the cutting forces experienced during the milling operation. The reported method has been implemented and tested using a combination of commercial applications. This paper highlights ongoing collaborative research into developing a virtual machining system.