Continuous Representation of Machining Processes Using 4-Dimensional Geometric Models –Cutter-Workpiece Engagement Analysis and Processing Surface Estimation in Spatio-Temporal Space—

The study proposes strategies for conducting cutter-workpiece engagement (CWE) analysis and representation based on 4-dimensional (4D) geometric models. To achieve the CWE condition, two 4D models representing the workpiece and the machinable volume of the tool are introduced for Boolean subtraction and CWE calculation. However, performing set operations and mesh transformations on high-accuracy 4D mesh models can be complex and time-consuming. Therefore, a simplified CWE analysis process between the time-invariant workpiece-occupied region (WOR) and the tool-occupied region (TOR) has been implemented to illustrate the validity of the set operation algorithm. The results demonstrate the effectiveness of the proposed 4D Set operation algorithm and its application in CWE analysis to a certain extent.