Abstract
In the manufacturing industry, three-dimensional (3D) geometric models are used to represent and analyze cutter-workpiece engagement (CWE). But the dynamic state of the milling process is always represented by the position and shape data of a series of discrete snapshots. Comparing to 3D geometric methods, 4D geometric modeling enables to static and integrated representation of, variable shape, position and orientation of target objects. In other words, 4D models is continuous in time, cutting 4D model into 3D slices can achieve all states at this breakpoint.Authors proposed a strategy for realizing CWE analysis and representation based on 4-dimensional (4D) mesh models. It computes the subtraction between workpiece occupied region (WOR) and tool accumulated volume (TAV). WOR and TAV can represent a still workpiece in spatio-temporal space and the history of tool occupation during the machining process. The basic idea of 4D set operation is to distinguish parts of a model is in or out of another one, then union them to the set operation result. Therefore, the algorithm finds, segments, classifies and combines these parts to construct new meshes. After that, the set operation result enables to be achieved and used to estimate processing surface in CWE analysis.
