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There is a relatively vast class of tool path optimization methods that minimize cost functions depending on a whole tool path. In these methods, cost functions are usually limited to convex function because the used optimization approaches cannot either handle nonsmooth functions or perform with an acceptable computational time. This paper describes a developed optimization method that finds a sequence of tool orientations that can minimize various cost functions including displacement of machine rotary axes. Every posture, tool feasible orientation can be represented in discrete fashion as nodes of a directed graph in which the edge weights denote an objective. Shortest paths are sought iteratively by applying Dijkstra's algorithms and narrowing intervals of feasible tool orientations around the previous solution. The developed algorithm is a derivative-free optimization method working in a linear time. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes an algorithm that predicts the shape of material removed by a flat-end milling tool, and this may be used to compute machining strip width and scallop height at different positions of the tool path track. The algorithm computes swept sections, profiles which are swept by a moving tool bottom by passing through given planes. The technique is applicable for finish and semi-finish multi-axis milling strategies that use flat-end tools. For these strategies, the algorithm complexity can be reduced from computation of the 3D envelope of swept volumes to computation of plane-circle intersections. A new adaptive derivative-free method to sample tool motion provides robust means to generate intermediate tool positions. The step length is constrained by and dependent on different geometrical measures. At each point of a tool path, in the plane perpendicular to the cutting direction, the bottom profile of the swept section is an estimate of the profile of material left. By calculating the distance between part geometry and the computed profile of removed material, machining strip width and a scallop profile can be derived. These results can be used by tool path generation and validation routines to accurately determine the step-over between tool path tracks and surface quality. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches. [ABSTRACT FROM AUTHOR]