A system of algorithms is presented for material removal simulation, automatic dimensional verification and integrated error correction of numerically controlled (NC) milling tool paths. Several different approaches to these problems have been proposed including direct solid modeling, discrete vector intersection, and spatial partitioning. However, each of these methods suffer inherent restrictions that limit their practical application. This dissertation presents a discrete dexel NC verification algorithm based on a spatial partitioning technique (dexel representation) which incorporates the advantages of the discrete vector intersection approach. Hence, real-time animated five-axis milling simulation is supported by efficient regularized Boolean set operations, and dimensional milling errors are verified simultaneously with the simulation process. Based on intermediate dimensional verification results, a reduction of intersection volume algorithm is developed to eliminate detected gouges on the part surface. In addition, a technique for detection and elimination of unexpected collisions between the tool assembly and the workpiece is developed. These combined algorithms automatically correct tool paths to avoid gouges and collisions resulting in tool paths that are ready for immediate industrial application. A major disadvantage of dexel-based spatial partitioning, as originally proposed, is view dependency, i.e., dexels are constructed along a specific viewing vector so reconstruction of dexels is required for each new viewing direction. To overcome this problem, a contour display method is developed to transform dexel-based objects into a set of parallel planar contours thus enabling dynamic viewing transformations. In summary, this dissertation describes a unique hybrid approach to NC milling verification which provides for efficient, accurate and automatic assessment and correction of five-axis milling tool paths.
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