R*-Tree Localization for Polyhedral Model Based Cutter/Workpiece Engagements Calculations in Milling

Process modeling requires the calculation of cutter/workpiece engagement (CWE) geometry, which is especially challenging when the geometry of the workpiece is changing un-predictably. Polyhedral models have a simple geometric complexity, independent of the complexity of the workpiece shape. This paper presents a polyhedral model based CWE calculation method, which is both stable and robust as numerical calculations are avoided because of the simplicity of the model geometry. To reduce the amount of data and calculations, the proposed method works on removal volumes instead of in-process workpieces, and further adopts an R*-tree based localization technique to reduce the number of facets that are considered in a given CWE calculation. The method uses a set of connected straight-line segments to represent the real intersection curves between the removal volume and the cutter. It first calculates the intersection points between the facet edges and the cutter, removing invalid ones based on a kinematics model of the cutter then creates intersection segments between these intersection points by a proposed Mark Circle method. Finally, an undirected graph is adopted to connect all the intersection segments to form the resultant intersection lines. Implementation and examples prove that polyhedral model based CWE calculation is a correct, effective and efficient method.