Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

Blisk blades manufacturing technologies analysis

Ponencia presentada a 8th Manufacturing Engineering Society International Conference, MESIC 2019, 19-21 June 2019, Madrid, SpainThe paper presents blisk blades manufactured by different manufacturing processes. In this sense, different milling trajectories are presented, and, super abrasive machining strategies and EDM technologies are also tested. Machining times, costs and surface finish are analysed in order to determine optimal machining process for blisk manufactured in low machinability materials.The authors wish to acknowledge the financial support received from HAZITEK program, from the Department of Economic Development and Infrastructures of the Basque Government and from FEDER founds, related to the projects with acronym HARDCRAFT and TURALOY. Besides, thanks are also addressed to the Vice chancellor of innovation, social compromise and cultural action from UPV/EHU (Bizialab program from Basque Government) and to Spanish Project MINECO RTC-2017-6039-5

On initialization of milling paths for 5-axis flank CNC machining of free-form surfaces with general milling tools

We propose a path-planning algorithm for 5-axis flank CNC machining with general tools of varying curvature. Our approach generalizes the initialization strategy introduced for conical tools [Bo et al., 2017] to arbitrary milling tools. Given a free-form (NURBS) surface and a rotational milling tool, we look for its motion in 3D to approximate the input reference surface within a given tolerance. We show that for a general shape of the milling tool, there exist locally and generically four 3D directions in which the point-surface distance follows the shape of the tool up to second order. These directions form a 3D multi-valued vector field and its integration gives rise to a set of integral curves. Among these integral curves, we seek straight line segments that correspond to good initial positions of the axes of the milling tool. We validate our method against synthetic examples with known exact solutions and, on industrial datasets, we detect approximate solutions that meet fine machining tolerances. We also demonstrate applicability of our method for efficient flank milling of convex regions that is not possible using traditional conical tools.RYC-2017-2264

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

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

Blisk blades manufacturing technologies analysis

The paper presents blisk blades manufactured by different manufacturing processes. In this sense, different milling trajectories are presented, and, super abrasive machining strategies and EDM technologies are also tested. Machining times, costs and surface finish are analysed in order to determine optimal machining process for blisk manufactured in low machinability materials.RYC-2017-2264

Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining

We propose a new algorithm to detect patches of free-form surfaces that can be well approximated by envelopes of a rotational cone under a rigid body motion. These conical envelopes are a preferable choice from the manufacturing point of view as they are, by-definition, manufacturable by computer numerically controlled (CNC) machining using the efficient flank (peripheral) method with standard conical tools. Our geometric approach exploits multi-valued vector fields that consist of vectors in which the point-surface distance changes linearly. Integrating such vector fields gives rise to a family of integral curves, and, among them, linear segments that further serve as conical axes are quickly extracted. The lines that additionally admit tangential motion of the associated cone along the reference geometry form a set of candidate lines that are sequentially clustered and ordered to initialize motions of a rigid truncated cone. We validate our method by applying it on synthetic examples with exact envelopes, recovering correctly the exact solutions, and by testing it on several benchmark industrial datasets, detecting manufacturable conical envelope patches within fine tolerances

Efficient 5-axis CNC trochoidal flank milling of 3D cavities using custom-shaped cutting tools

A novel method for trochoidal flank milling of 3D cavities bounded by free-form surfaces is proposed. Existing 3D trochoidal milling methods use on-market milling tools whose shape is typically cylindrical or conical, and is therefore not well-suited for meeting fine milling tolerances required for finishing of benchmark free-form surfaces like blades or blisks. In contrast, our variational framework incorporates the shape of the tool into the optimization cycle and looks not only for the trochoidal milling paths, but also for the shape of the tool itself. High precision quality is ensured by firstly designing flank milling paths for the side surfaces that delimit the motion space, in which the trochoidal milling paths are further computed. Additionally, the material removal rate is maximized with the cutter-workpiece engagement being constrained under a given tolerance. Our framework also supports multi-layer approach that is necessary to handle deep cavities. The ability and efficacy of the proposed method are demonstrated by several industrial benchmarks, showing that our approach meets fine machining tolerances using only a few trochoidal paths.RYC-2017-2264

Highly-accurate 5-axis flank CNC machining with conical tools

A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization based approach is then applied to globally minimize the error between the design surface and the conical envelope. Our computer simulation are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software

Definition of tailor made cutting tools for machining of complex surfaces based on final surface shape

In this work a design methodology to define the best geometry of cutting tool for complex surfaces is defined, being based on the final part surface geometry. The manufacture of components with tailor made shaped tools, based on algorithm calculation and adapted to the geometry of the final piece surface, reduces manufacturing time and maintains piece quality in comparison with traditional cutting tools. Cutting tools are usually cylindrical (end mills) or ball-end mills. With mathematical algorithms can be defined diamond & CBN electroplated form tools, multi-tooth endmills, abrasive grinding tools and so on. The approach here presented can enable the production of tools for manufacturing process such as Super Abrasive Machining (SAM) and Flank milling strategies. Comparison between standard tools and traditional machining processes versus custom-shaped tools was studied in terms of process time. Final applications are numerous, such as, integral blade rotors, spiral bevel gears, blisks and impellers, complex screws, and others

Characterizing envelopes of moving rotational cones and applications in CNC machining

Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address ruled surfaces and their offsets. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. To this purpose, the isotropic model of Laguerre geometry is used as there rotational cones correspond to curves (isotropic circles) and higher order contact is computed with respect to the image of the input surface in the isotropic model. Therefore, one studies curve-surface contact that is conceptually simpler than the surface-surface case. We show that, in a generic case, there exist at most six positions of a fixed rotational cone that have third order contact with the input surface. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.RYC-2017-2264