Cutter-Workpiece Engagement Calculations by Parallel Slicing for Five-Axis Flank Milling of Jet Engine Impellers

Cutter-workpiece engagement maps, or cutting flute entry/exit locations as a function of height, are a requirement for prediction of cutting-forces on the tool and workpiece in machining operations such as milling. This paper presents a new method of calculating tool-part intersection maps for five-axis flank milling of jet engine impellers with tapered ball-end mills. It is called the parallel slicing method (PSM) and is a semi-discrete solid modeling technique written in C++ using the ACIS B-rep solid modeling environment. Although it is tailored towards five-axis flank milling, it can also be applied to both planar and multi-axis milling processes. The tool swept envelope is generated and intersected with the workpiece to obtain the removal volume. The removal volume is then sliced into a number of parallel planes along a given axis and the intersection curves with the tool and each plane are determined analytically. The swept area between the intersection curves of successive tool moves is calculated by solving for the area enclosed by the tangent lines. This area is removed from the workpiece material, which deletes the material cut between tool moves. Finally, the intersection curves are compared with the planar slices of the updated part, which results in a series of arcs. The end points of these arcs are joined with linear segments to form the engagement polygon which is used to calculate the engagement maps. Using this method, cutter-workpiece engagement maps are generated for a five-axis flank milling toolpath on a prototype integrally bladed rotor (IBR) with a tapered ball-end mill. These maps are compared with those obtained from a benchmark cutter-workpiece engagement calculation method – the Manufacturing Automation Laboratory’s Virtual Machining Interface (MAL-VMI). The MAL-VMI uses an application programming interface (API) in a commercial NC verification software package to obtain cutter-part intersections through a fast, z-buffer technique. Overall, the parallel slicing method appears to obtain more accurate engagement zones than those given by the MAL-VMI, although the calculation time is longer.