3D Machining Toolpath Design for Non-Convex Meshes
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Solution Overview
Problem
Existing 3D axis machining designs lack an efficient method for determining the path of a machining tool that can handle non-convex shapes and is robust to meshing accuracy, leading to inefficiencies in manufacturing processes.
Innovation Solution
A computer-implemented method that computes a polyhedral cycle as the boundary of a Minkowski subtraction between a machining tool's cutting head mesh and the machined part mesh, determining a path for the machining tool without convexity hypotheses, using Minkowski subtraction and multiplicity computations to account for non-convex shapes and mesh inaccuracies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional 3D axis machining design methods are used, then the machining process can handle simple convex shapes, but it fails to accurately process non-convex shapes and is sensitive to meshing accuracy errors
Solution Approach 1:
The patent transforms the machining path determination problem from direct geometric intersection computation to a topological boundary computation problem. By changing the mathematical parameters from coordinate-based geometry to combinatorial topology (polyhedral cycles and multiplicities), the method achieves invariance to meshing accuracy and enables handling of non-convex shapes without convexity hypotheses.
Solution Approach 2:
The patent replaces the traditional mechanical/geometric approach of computing tool-part intersections with a topological algebraic approach using Minkowski subtraction and polyhedral cycle boundaries. This substitution eliminates sensitivity to mesh quality and enables robust processing of complex non-convex geometries through purely topological operations.
2Productivity
If traditional machining path determination methods are used, then the computation is simpler for convex parts, but it becomes inefficient and inaccurate for non-convex parts with complex geometries
Solution Approach 1:
The patent changes the computational parameters from continuous geometric intersections to discrete topological boundaries. The polyhedral cycle representation with integer multiplicities provides exact arithmetic that is independent of mesh resolution, thereby improving both computational efficiency for complex shapes and manufacturing precision for non-convex parts.
Solution Approach 2:
The patent segments the continuous machining path problem into discrete topological elements (edges and vertices of polyhedral cycles). By computing boundaries as sums of weighted polyhedral cycles with integer multiplicities, the method breaks down complex non-convex geometry processing into manageable topological operations that are computationally efficient and precisely determinable.
3Ease of manufacture
If convexity hypotheses are imposed on the machining tool or part, then the computation becomes more straightforward, but it limits the applicability to non-convex shapes which are common in real-world manufacturing
Solution Approach 1:
The patent inverts the conventional approach by not trying to make non-convex shapes fit into convexity-based algorithms, but rather developing a topological framework where convexity is not required. By using Minkowski subtraction and polyhedral cycle boundaries, the method naturally handles both convex and non-convex geometries without requiring convexity hypotheses, thereby maintaining computational tractability while achieving universal applicability.
Data Source
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.