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Computer supported toolpath planning for LMD additive manufacturing based on cylindrical slicing

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Abstract

In laser metal deposition of overhanging geometries, non-planar layers are used to partially avoid the highly inconvenient support structures. Multi-axis machines provide extra degrees of freedom that allow the deposition of non-planar layers. However, path planning for non-planar slicing is complex because, in most geometries, it encourages non-homogeneous metal deposition among the dispenser paths. For workpieces presenting a direction normal to which all cross sections have non-null common kernel (called here “revolute workpieces”), it is possible to use a cylindrical (i.e., iso-radial) slicing which still enables homogeneous path generation and metal deposition. This manuscript presents the implementation and experimental validation of a path-planner for laser deposition metal dispensers which build revolute workpieces by stacking iso-radial layers. Isometry is preserved between each 3D cylindrical layer and the 2D parametric space \((\kappa ,\gamma )\) where the dispenser path is planned, so deposed metal density can be homogenized. The path-planner takes advantage of the natural isometry between the \((\kappa ,\gamma )\) flat surface and the 3D cylinder (due to the cylinder developability). This isometry allows for (i) the application of conventional 2D dispenser path planning for 3D iso-radial layers and (ii) the control of inter-bead distance and dispenser velocity. The implemented path-planner also allows the control of the deposed thickness for each iso-radial layer. To validate experimentally our strategy, we manufacture spur and helical gear teeth on a cylindrical substrate. The results of these experiments show that our strategy generates toolpaths suitable for the manufacturing of industrial workpieces via laser metal deposition.

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Data Availability

The data in this study is not available due to industrial secrecy related to this project.

Abbreviations

AM:

Additive manufacturing.

B-Rep:

Boundary representation of a solid object in \(\mathbb {R}^3\).

LMD:

Laser metal deposition.

(x, y, z):

Convention triplet for Cartesian coordinates.

\((\theta ,\rho ,u)\) :

Convention triplet for cylindrical coordinates. \(\theta \) is the azimuth angle. \(\rho \) is the axial distance from the z-axis. u is the height.

\((\kappa ,\gamma ,v)\) :

Convention triplet for the coordinates on the parametric space (isometry cylinder-plane). In this space, the planes \(v = c\) are isometric to a cylinder in Cartesian coordinates with radius c and axis the z-axis.

\(\pmb {g}: \mathbb {R}^3 \rightarrow \mathbb {R}^3\) :

Function to transform from Cartesian (x, y, z) to cylindrical coordinates \((\theta , \rho ,\) u).

\(\pmb {w}: \mathbb {R}^3 \rightarrow \mathbb {R}^3\) :

Function to transform from cylindrical \((\theta , \rho , u)\) to parametric coordinates \((\kappa , \gamma , v)\).

\(\pmb {h}: \mathbb {R}^3 \rightarrow \mathbb {R}^3\) :

Function to transform from parametric \((\kappa , \gamma , v)\) to Cartesian coordinates (x, y, z).

\(\textrm{dist}(\pmb {W}_1, \pmb {W}_2)\) :

Euclidean distance between \(\pmb {W}_1\) and \(\pmb {W}_2\).

\(\textrm{dist}_\textrm{geod}(\pmb {P}_1, \pmb {P}_2)\) :

Geodesic distance (arc-length measured on the cylinder surface) between \(\pmb {P}_1\) and \(\pmb {P}_2\).

\(\mathcal {M} \subset \mathbb {R}^3\) :

2-Manifold embedded in \(\mathbb {R}^3\). Geometry to be manufactured.

\(\mathcal {F} \subset \mathcal {M}\) :

Face of \(\mathcal {M}\) that is also a subset of a cylinder.

\(\textrm{Ker}(Q) \subset \mathbb {R}^2\) :

Kernel of a planar polygon Q. Convex subset of Q from which every point on the boundary of Q is visible.

\(M = (V,T)\) :

Triangular mesh. V and T are the set of vertices and triangles, respectively. Piecewise linear discretization of the 2-manifold \(\mathcal {M}\).

\(t > 0\) :

Layer thickness (mm).

\(d > 0\) :

Step-over distance, i.e., distance between two consecutive deposition lines (beads) (mm).

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Funding

This work has been partially funded by the Basque Government under ELKARTEK program (grants KK-2018/00115 (ADDISEND) and KK-2018/00071 (LANGILEOK)) and by the INZU Group (Talens Systems and Ikergune A.I.E.).

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Authors and Affiliations

  1. Vicomtech Foundation, Basque Research and Technology Alliance (BRTA), Mikeletegi 57, Donostia-San Sebastian, 20009, Spain

    Diego Montoya-Zapata, Aitor Moreno & Jorge Posada

  2. Laboratory of CAD CAM CAE, Universidad EAFIT, Cra 49 no 7-sur-50, Medellín, 050022, Colombia

    Diego Montoya-Zapata & Oscar Ruiz-Salguero

  3. Ikergune A.I.E., INZU Group, San Antolin 3, Elgoibar, 20870, Spain

    Diego Montoya-Zapata & Igor Ortiz

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  1. Diego Montoya-Zapata
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  2. Aitor Moreno
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  3. Igor Ortiz
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  4. Jorge Posada
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Correspondence to Diego Montoya-Zapata.

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Montoya-Zapata, D., Moreno, A., Ortiz, I. et al. Computer supported toolpath planning for LMD additive manufacturing based on cylindrical slicing. Int J Adv Manuf Technol 128, 4667–4683 (2023). https://doi.org/10.1007/s00170-023-12177-4

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