The aim of tool path planning is to maximize the efficiency against some given precision criteria. In practice, scallop height should be kept constant to avoid unnecessary cutting, while the tool path should be smooth enough to maintain a high feed rate. However, iso-scallop and smoothness often conflict with each other. Existing methods smooth iso-scallop paths one-by-one, which make the final tool path far from being globally optimal. This paper proposes a new framework for tool path optimization. It views a family of iso-level curves of a scalar function defined over the surface as tool path so that desired tool path can be generated by finding the function that minimizes certain energy functional and different objectives can be considered simultaneously. We use the framework to plan globally optimal tool path with respect to iso-scallop and smoothness. The energy functionals for planning iso-scallop, smoothness, and optimal tool path are respectively derived, and the path topology is studied too. Experimental results are given to show effectiveness of the proposed methods.
There also exist some efforts to generate smooth tool paths without considering the overlapping between neighbor machining strips (i.e., the iso-scallop condition). Generally, such methods are based on the Laplacian. For example, Bieterman and Sandstrom @cite_10 proposed a Laplacian based contour parallel tool path generation method by selecting the level sets of a harmonic function defined over a pocket as the tool path. But how to choose the level sets for it still remains an open problem, namely there is no formula for path interval calculation so far. Similarly, Chuang and Yang @cite_34 combined the Laplacian method and iso-parametric method to generate tool paths for pockets with complex topology, i.e., complex boundaries and islands. However, the smoothness of the tool path cannot be guaranteed through Laplacian energy as small Laplacian value does not necessarily mean small curvature of the level set curves. And solving a Laplace equation over a surface can only generate a unique and uncontrollable scalar function (scaling has no impact on the shape of tool paths). Another drawback of the Laplacian based approach is the severe overlapping between machining strips of neighbor paths, especially for paths near the boundary, which results in too much redundant machining.
@cite_34 @cite_10
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In this paper, a method for generating boundary-conformed pocketing toolpaths is developed. Based on the 2D Laplace parameterization of pocket contours and the redistribution of the original Laplace isoparametrics, continuous toolpaths are generated. These generated toolpaths have neither thin walls nor leftover tool marks. Detailed algorithms are formulated in steps. The method can be applied to general pockets either with or without islands. Some examples are provided to demonstrate the applicability of this method. In most cases, the method can successfully generate satisfactory toolpaths for arbitrary shaped pockets. However, according to the shape of the pockets and the distribution of the islands, when using this method, over machining may occur in some narrow or bottlenecked areas. Further investigation on how to alleviate this problem is needed. We believe that this method provides an alternative choice for pocket machining. In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results. This paper presents a simple and efficient automatic mesh segmentation algorithm that solely exploits the shape concavity information. The method locates concave creases and seams using a set of concavity-sensitive scalar fields. These fields are computed by solving a Laplacian system with a novel concavity-sensitive weighting scheme. Isolines sampled from the concavity-aware fields naturally gather at concave seams, serving as good cutting boundary candidates. In addition, the fields provide sufficient information allowing efficient evaluation of the candidate cuts. We perform a summarization of all field gradient magnitudes to define a score for each isoline and employ a score-based greedy algorithm to select the best cuts. Extensive experiments and quantitative analysis have shown that the quality of our segmentations are better than or comparable with existing state-of-the-art more complex approaches. A novel curvilinear tool-path generation method is described for planar milling of pockets. The method uses the solution of an elliptic partial differential equation boundary value problem defined on a pocket region. This mathematical function helps morph a smooth low-curvature spiral path in a pocket interior to one that conforms to the pocket boundary. This morphing leads to substantial reductions of tool wear in cutting hard met als and of machining time in cutting all met als, as experiments described here show. A variable feed-rate optimization procedure is also described. This procedure incorporates path, tool-engagement, and machine constraints and can be applied to maximize machine performance for any tool path.