Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification. (September 2017) - Machchhar, Jinesh; Plakhotnik, Denys; Elber, Gershon
Abstract: This paper presents an algebraic based approach and a computational framework for the simulation of multi-axis CNC machining of general freeform tools. The boundary of the swept volume of the tool is precisely modeled by a system of algebraic constraints, using B-spline basis functions. Subdivision-based solvers are then employed to solve these equations, resulting in a topologically guaranteed construction of the swept volume. The presented algebraic-based method readily generalizes to accept tools of arbitrary free-form shape as input, and at the same time, delivers high degree of precision. Being a common representation in CNC simulations, the computed swept volume can be reduced to a dexels' representation. Several multi-axis test cases are exhibited using an implementation of our algorithm, demonstrating the robustness and efficacy of our approach. Highlights: A computational framework for multi-axis CNC machining simulation is proposed. Algebraic modeling of the swept volume of the cutter leads to high precision. Topological guarantees are given regarding correctness of the solution. Dexel-grid representation of the swept volume yields computational efficiency. Graphical abstract: