3D Axis Machining Path Design Using Minkowski Subtraction
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Solution Overview
Problem
Current 3D axis machining design methods lack efficiency in determining the optimal path for machining tools, particularly for non-convex parts and tools, and are sensitive to meshing accuracy, limiting their applicability in industrial scenarios.
Innovation Solution
A computer-implemented method that uses Minkowski subtraction to determine the boundary of the machining tool's cutting head and the machined part, computing a polyhedral cycle to establish a path for the machining tool, which is robust and convexity-free, allowing for non-convex cases and independent of meshing accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional 3D axis machining design methods are used, then the machining path can be determined for convex parts, but the method fails or becomes unreliable for non-convex parts and tools
Solution Approach 1:
The patent changes the mathematical approach from traditional boundary representation to Minkowski subtraction, fundamentally altering how the machining boundary is computed. This parameter change in the computational method enables reliable handling of non-convex geometries by using set-theoretic operations that naturally accommodate complex shapes without requiring convexity assumptions.
Solution Approach 2:
The patent replaces traditional geometric modeling mechanisms with Minkowski subtraction operations. Instead of using conventional boundary representation methods that assume convexity, the invention uses mathematical morphological operations (dilation and erosion) to compute the machining boundary, substituting the mechanical geometric reasoning with a more robust mathematical framework.
2Productivity
If traditional machining path determination methods are used, then the process may work for simple geometries, but the computational efficiency and accuracy deteriorate for complex non-convex geometries
Solution Approach 1:
The patent segments the complex machining boundary computation into distinct Minkowski subtraction operations. By breaking down the boundary determination into sequential mathematical morphological operations (dilation of tool head, erosion of part geometry), the method achieves both computational efficiency and accuracy for complex non-convex geometries, avoiding the exponential complexity of traditional approaches.
Solution Approach 2:
The patent introduces Minkowski subtraction as an intermediary computational mechanism between the tool head geometry and the part geometry. This intermediary operation (computing the boundary of M - P) serves as a mathematical mediator that efficiently translates geometric inputs into an accurate machining boundary, regardless of convexity, thereby improving both speed and precision.
3Measurement precision
If meshing accuracy is increased to improve boundary determination, then the precision may improve for simple cases, but the computational complexity and sensitivity increase for non-convex cases
Solution Approach 1:
The patent uses Minkowski subtraction to create a mathematical copy relationship between the tool head and part geometries. The boundary computation B = ∂(M - P) creates a precise copy of the machining boundary directly from the input geometries without requiring high-fidelity meshing. This copying mechanism through set-theoretic operations reduces sensitivity to meshing accuracy while maintaining boundary precision.
Data Source
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AI summary
The disclosure notably relates to a computer-implemented method for 3D axis machining design. The method comprises providing a first mesh. The first mesh represents a head of a machining tool. The method comprises providing a second mesh. The second mesh represents a machined part. The first mesh is closed. The method further comprises determining a boundary of a Minkowski subtraction of the surface represented by the second mesh by the volume delimited by the first mesh. The determining of the boundary includes computing the boundary as a polyhedral cycle by computing, for each element of the boundary, a multiplicity of the element in the polyhedral cycle. The method further comprises determining a path of the machining tool for 3D axis machining of the machined part based on the determined boundary. This constitutes an improves solution for 3D axis machining design.