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+34 946 567 842
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+34 946 567 842
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mbarton@bcamath.org
Information of interest
Michael Barton received his Ph.D. degree in computational and applied mathematics from the Charles University in Prague, Faculty of Mathematics and Physics, in 2007. He worked as a Postdoctoral Fellow and Research Scientist at JKU Linz, Technion, and KAUST. His research interests span geometric modelling and manufacturing, computer aided design, and isogeometric analysis.
He serves as an associate editor of Computer-aided Design (CAD), Graphical Models (GMOD), and Computer Graphics Forum (CGF) and is a member of a scientific programme committee at the Eurographics Symposium on Geometry Processing (SGP), Solid and Physical Modeling (SPM), and Geometric Modeling and Processing (GMP).
In 2019, he received the Young Investigator Award from the Solid Modeling Association and Horizon 2020 FET-OPEN grant on Analysis, Design, and Manufacturing using Microstructures (ADAM^2). He was selected in the Ikerbasque Group Leader call in 2019.
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On shape design and optimization of gerotor pumps
Pedrera-Busselo, A.; Mejia-Parra, D.; Moreno, A.; Posada, J.; Pareja-Corcho, J.C; Barton, M.
; Posada (2024-06)
A gerotor pump is a two-piece mechanism where two rotational components, interior and exterior, engage each other via a rotational motion to transfer a fluid in a direction parallel to their rotational axes. A natural ...
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Collision-free tool motion planning for 5-axis CNC machining with toroidal cutters
Reckova, A.; Zaragoza, J.; Bizzarri, M.; Barton, M. (2024-06)
Collision detection is a crucial part of CNC machining, however, many state-of-the-art algorithms test collisions as a post-process, after the path-planning stage, or use conservative approaches that result in low machining ...
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On tiling spherical triangles into quadratic subpatches
Vrsek, J.; Bizzarri, M.; Lavicka, M.; Barton, M.; Kosinka, J. (2024-06)
Various interpolation and approximation methods arising in several practical applications in geometric modeling deal, at a particular step, with the problem of computing suitable rational patches (of low degree) on the ...
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Design, motion-planning, and manufacturing of custom-shaped tools for 5-axis super abrasive machining of a turbomachinary blade like component
Martinez, M.; Gomez, G.; Bo, P.; Barton, M.; Gonzalez, H.; Calleja, A.; López de Lacalle, L.N. (2024-05-18)
Free-form surfaces generated by Non-Uniform Rational B-Splines (NURBS) are evolving to face turbomachinery components requirements, such as turbine blades to enhanced efficiency. Super Abrasive Machining (SAM) is presented ...
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On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
Ponce Vanegas, F.; Bizzarri, M.; Barton, M. (2023-10)
We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, ...
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Solving boundary value problems via the Nyström method using spline Gauss rules
Hashemian, A.; Sliusarenko, H.; Remogna, S.; Barrera, D.; Barton, M. (2023-08-01)
We propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the ...
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Towards $G^1$-continuous multi-strip path-planning for 5-axis flank CNC machining of free-form surfaces using conical cutting tools
Rajain, K.; Bizzarri, M.; Lavicka, M.; Kosinka, J.; Barton, M. (2023-06)
Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method ...
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Cloud benchmarking and performance analysis of an HPC application in Amazon EC2
Dancheva, T.; Alonso, U.; Barton, M. (2023)
Cloud computing platforms have been continuously evolving. Features such as the Elastic Fabric Adapter (EFA) in the Amazon Web Services (AWS) platform have brought yet another revolution in the High Performance Computing ...
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Numerical quadrature for Gregory quads
Zhou, J.; Barendrecht, P.; Barton, M.; Kosinka, J. (2023)
We investigate quadrature rules in the context of quadrilateral Gregory patches, in short Gregory quads. We provide numerical and where possible symbolic quadrature rules for the space spanned by the twenty polynomial/rational ...
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On inverse construction of isoptics and isochordal-viewed curves
Rochera, D.; Barton, M. (2023)
Given a regular closed curve α in the plane, a $\phi$-isoptic of $\alpha$ is a locus of points from which pairs of tangent lines to $\alpha$ span a fixed angle $\phi$. If, in addition, the chord that connects the two points ...
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Constant probe orientation for fast contact-based inspection of 3D free-form surfaces using (3+2)-axis inspection machines
Sliusarenko, O.; Gomez Escudero, G.; Gonzalez, H.; Calleja, A.; Barton, M.; Ortega, N.; López de Lacalle, L.N. (2023)
A new probe optimization method for contact based (3+2)-axis inspection machines is proposed. Given an inspection path of a stylus on a free-form surface, an optimal orientation of the stylus is computed such that (i) the ...
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Constant probe orientation for fast contact-based inspection of 3D free-form surfaces using (3+2)-axis inspection machines
Sliusarenko, O.; Gomez Escudero, G.; Gonzalez, H.; Calleja, A.; Barton, M.; Ortega, N.; Lopez de Lacalle, N. (2023)
A new probe optimization method for contact based (3+2)-axis inspection machines is proposed. Given an inspection path of a stylus on a free-form surface, an optimal orientation of the stylus is computed such that (i) the ...
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Screw rotor manufacturing via 5-axis flank CNC machining using conical tools
Bizzarri, M.; Bo, P.; Barton, M. (2022-12)
We propose a new method for 5-axis flank computer numerically controlled (CNC) machining of screw rotors using conical tools. The flanks of screw rotors consist of helical surfaces, which predetermines the motion of the ...
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Machining-induced characteristics of microstructure-supported LPBF-IN718 curved thin walls
Mishra, S.; Escudero, G.; Gonzalez, H.; Calleja, A.; Martinez, S.; Barton, M.; Lopez de Lacalle, N.; Mishra (2022-07)
The microstructure-supported design of engineering components is recently gaining attention due to their high strength-to-weight and high stiffness-to-weight properties. The present study investigates the hybrid manufacturing ...
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Efficient 5-axis CNC trochoidal flank milling of 3D cavities using custom-shaped cutting tools
Bo, P.; Fan, H.; Barton, M. (2022-05)
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 ...
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Curve-guided 5-axis CNC flank milling of free-form surfaces using custom-shaped tools
Rajain, K.; Sliusarenko, O.; Bizzarri, M.; Barton, M. (2022-03)
A new method for 5-axis flank milling of free-form surfaces is proposed. Existing flank milling path-planning methods typically use on-market milling tools whose shape is cylindrical or conical, and is therefore not ...
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On numerical solution of Fredholm and Hammerstein integral equations via Nystr\"{o}m method and Gaussian quadrature rules for splines
Barrera, D.; Barton, M.; Chiarella, A.; Remogna, S. (2022-01)
Nystr\"{o}m method is a standard numerical technique to solve Fredholm integral equations of the second kind where the integration of the kernel is approximated using a quadrature formula. Traditionally, the quadrature ...
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Solving Boundary Value Problems Via the Nyström Method Using Spline Gauss Rules
Hashemian, A.; Sliusarenko, H.; Remogna, S.; Barrera, D.; Barton, M. (2022)
We propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the ...
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5-axis double-flank CNC machining of spiral bevel gears via custom-shaped tools – Part II: physical validations and experiments
Gomez, G.; Bo, P.; Gonzalez, H.; Calleja, A.; Barton, M.; Lopez de Lacalle, N. (2021-10)
Recently, a new methodology for 5-axis flank computer numerically controlled (CNC) machining, called double-flank machining, has been introduced (see “5-axis double-flank CNC machining of spiral bevel gears via custom-shaped ...
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Geometry and tool motion planning for curvature adapted CNC machining
Barton, M.; Bizzarri, M.; Rist, F.; Sliusarenko, O.; Pottmann, H. (2021)
CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate ...
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The Construction of Conforming-to-shape Truss Lattice Structures via 3D Sphere Packing
van Sosin, B.; Rodin, D.; Sliusarenko, H.; Barton, M.; Elber, G. (2020-11)
Truss lattices are common in a wide variety of engineering applications, due to their high ratio of strength versus relative density. They are used both as the interior support for other structures, and as structures on ...
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Manufacturing of screw rotors via 5-axis double-flank CNC machining
Bizzarri, M.; Barton, M. (2020-11)
We investigate a recently introduced methodology for 5-axis flank computer numerically controlled (CNC) machining, called double-flank milling [1]. We show that screw rotors are well suited for this manufacturing approach ...
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Characterizing envelopes of moving rotational cones and applications in CNC machining
Skopenkov, M.; Bo, P.; Barton, M.; Pottmann, H. (2020-10)
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 ...
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SPM 2020 Editorial
Li, X.; Barton, M.; Nelaturi, S. (2020-07)
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Reparameterization of ruled surfaces: toward generating smooth jerk-minimized toolpaths for multi-axis flank CNC milling
Hashemian, A.; Bo, P.; Barton, M. (2020-05)
This paper presents a novel jerk minimization algorithm in the context of multi-axis flank CNC machining. The toolpath of the milling axis in a flank milling process, a ruled surface, is reparameterized by a B-spline ...
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Definition of tailor made cutting tools for machining of complex surfaces based on final surface shape
Gomez, G.; De Lucio, P.; Gonzalez, H.; de Lacalle, N.; Calleja, A.; Barton, M. (2020)
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, ...
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Machining of developable ruled surfaces using mathematical algorithms
Calleja, A.; Gonzalez, H.; Polvorosa, R.; Amigo, F.; Gomez, G.; Fernandez, P.; Barton, M.; Bo, P.; de Lacalle, N. (2020)
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Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines
Barton, M.; Puzyrev, V.; Deng, Q.; Calo, V.M. (2019-12-14)
Calabr{\`o} et al. [10] changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of ...
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5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools -- Part I: modeling and simulation
Bo, P.; Gonzalez, H.; Calleja, A.; Lopez de Lacalle, N.; Barton, M. (2019-11-20)
A new category of 5-axis flank computer numerically controlled (CNC) machining, called \emph{double-flank}, is presented. Instead of using a predefined set of milling tools, we use the shape of the milling tool as a free ...
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Blisk blades manufacturing technologies analysis
Calleja, A.; Gonzalez, H.; Polvorosa, R.; Gomez, G.; Ayesta, I.; Barton, M.; de Lacalle, N. (2019-06)
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. ...
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Accessibility for Line-Cutting in Freeform Surfaces
van Sosin, B.; Barton, M.; Elber, G. (2019-04-26)
Manufacturing techniques such as hot-wire cutting, wire-EDM, wire-saw cutting, and flank CNC machining all belong to a class of processes called line-cutting where the cutting tool moves tangentially along the reference ...
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On initialization of milling paths for 5-axis flank CNC machining of free-form surfaces with general milling tools
Bo, P.; Barton, M. (2019-03-27)
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 ...
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FREE-FORM TOOLS DESIGN AND FABRICATION FOR FLANK SUPER ABRASIVE MACHINING (FSAM) NON DEVELOPABLE SURFACES
Gómez-Escudero, G.; Gonzalez, H.; Barton, M.; Bo, P.; Fernández-Lucio, P.; Lopez de Lacalle, N.; Calleja, A. (2019)
Manufacturing improvements are becoming a real need in industry. In order to satisfy these industrial requirements, they should be targeted in two different directions: new manufacturing processes and surface optimization ...
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Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles
Kosinka, J.; Barton, M. (2018-10-31)
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud [14]. The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
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Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis
Barton, M.; Calo, V.M.; Deng, Q.; Puzyrev, V. (2018-10-13)
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ...
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Efficient quadrature rules for subdivision surfaces in isogeometric analysis
Barendrecht, P.; Kosinka, J.; Barton, M. (2018-10)
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
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On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles
Barton, M.; Kosinka, J. (2018-08-01)
The quadrature rule of Hammer and Stroud [16] for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ...
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Highly-accurate 5-axis flank CNC machining with conical tools
Calleja, A.; Bo, P.; González, H.; Barton, M.; Lopez de Lacalle, N. (2018-04)
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 ...
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Super Abrasive Machining of Integral Rotary Components Using Grinding Flank Tools
González, H.; Calleja, A.; Pereira, O.; Ortega, N.; Lopez de Lacalle, N.; Barton, M. (2018-01-01)
Manufacturing techniques that are applied to turbomachinery components represent a challenge in the aeronautic sector. These components require high resistant super-alloys in order to satisfy the extreme working conditions ...
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Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining
Bo, P.; Barton, M.; Pottmann, H. (2017-10)
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 ...
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Dispersion-minimizing quadrature rules for $C^1$ quadratic isogeometric analysis
Deng, Q.; Barton, M.; Puzyrev, V.; Calo, V.M. (2017-09-20)
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ...
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Optimally refined isogeometric analysis
Garcia, D.; Barton, M.; Pardo, D. (2017-06)
Performance of direct solvers strongly depends upon the employed discretization method. In particular, it is possible to improve the performance of solving Isogeometric Analysis (IGA) discretizations by introducing multiple ...
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Gaussian quadrature rules for $C^1$ quintic splines with uniform knot vectors
Barton, M.; Ait-Haddou, R.; Calo, V.M. (2017-03-22)
We provide explicit quadrature rules for spaces of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. ...
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Towards optimal advection using stretch-maximizing stream surfaces
Barton, M.; Kosinka, J. (2017-03-01)
We investigate a class of stream surfaces that expand in time as much as possible. Given a vector field, we look for seed curves that locally propagate in time in a stretch-maximizing manner, i.e., curves that infinitesimally ...
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Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
Barton, M.; Calo, V.M. (2016-07-01)
We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature ...
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Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution
Bo, P.; Barton, M.; Plakhotnik, D.; Pottmann, H. (2016-06-30)
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 ...
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Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
Barton, M.; Calo, V.M. (2016-01-01)
We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Barton and Calo, 2016) that ...
CL file
Datasets (Zenodo) for the paper "Geometry and tool motion planning for curvature adapted CNC machining"
Authors: Michael Barton, Michal Bizzarri, Oleksii Sliusarenko, Florian Rist, Helmut Pottmann
License: Zenodo
CL file
Datasets (Zenodo) for the paper "Manufacturing of screw rotors via 5-axis double-flank CNC machining"
Authors: Michael Barton, Michal Bizzarri
License: Zenodo