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Numerical simulation and experimental validation of deposited corners of any angle in direct ink writing

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Abstract

Direct ink writing (DIW) belongs to material extrusion–based additive manufacturing (MEAM), and the molding quality of deposited corners has an impact on the geometrical quality of three-dimensional (3D) parts fabricated by DIW. To fully understand the DIW process and improve the geometrical quality of parts, numerical simulations have been widely used to model the DIW process. However, the previous research works for numerical simulation of deposited corners could only achieve the corner simulation under the condition of small angle and failed to realize corner simulation of any angle. Herein, an improved numerical simulation of deposited corners of any angle is proposed based on the use of volume of fluid (VOF) method and then the simulation is validated experimentally. In the numerical simulation, deposited corner is realized by constructing two calculation areas where two nozzle velocities with the corner angle are applied on the substrates of two calculation areas. The effectiveness of the proposed numerical model is validated through corner deposition experiments using a commercially available microcrystalline wax (MW)-based ink in a DIW 3D printer as the simulated corner angles fit experimental angles well and the maximum value of maximum distance deviation between simulated and experimental outlines (MDDSEO) is 1.06 ± 0.06 mm. It was observed that the MDDSEO of corners is larger than MDDSEO of straight filaments and decreases as corner angle increases. The current work demonstrates an effective approach for the prediction of the deposited corners of any angle in DIW based on numerical simulations.

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Abbreviations

\(\alpha\) :

Phase fraction

\(V_{i}\) :

Volume of ink in a mesh

\(V_{m}\) :

Total volume of a mesh

\(\rho_{s}\) :

Density of single continuum

\(\mu_{s}\) :

Viscosity of single continuum

\(\rho\) :

Density of ink

\(\rho_{a}\) :

Density of air

\(\mu\) :

Viscosity of ink

\(\mu_{a}\) :

Viscosity of air

\(\dot{\gamma }\) :

Shear rate

\(\mu_{0}\) :

Limiting dynamic viscosity

\(\tau_{0}\) :

Yield stress

\(K\) :

Consistency index

\(n\) :

Flow index

\(U\) :

Velocity field

\(p\) :

Pressure

\(g\) :

Gravitational acceleration vector

\(F_{{{\varvec{\upsigma}}}}\) :

Surface tension

\(\sigma\) :

Surface tension coefficient

\(\kappa\) :

Surface curvature

\(n\) :

Normal vector to ink surface

\(\hat{n}\) :

Unit vector normal to ink surface

\(\hat{n}_{w}\) :

Unit vector normal to wall

\(\hat{t}_{w}\) :

Unit vector tangent to wall

\(\theta_{c}\) :

Static contact angle

\(U_{{\mathbf{r}}}\) :

Velocity vector compressing two-phase free surface

\(c\) :

Controllable compression factor

\(v_{e}\) :

Average velocity in nozzle

\(D_{p}\) :

Piston diameter

\(D_{n}\) :

Outer diameter of nozzle

\(d_{n}\) :

Inner diameter of nozzle

\(v_{p}\) :

Piston velocity

\(L_{n}\) :

Nozzle length

\(h\) :

Distance between nozzle bottom and substrate

\(v_{{{\mathbf{n1}}}}\) :

Nozzle velocity applied on substrate 1

\(v_{{{\mathbf{n2}}}}\) :

Nozzle velocity applied on substrate 2

\(\theta\) :

Corner angle

\(v_{nx}\) :

Nozzle velocity component along x axis

\(v_{ny}\) :

Nozzle velocity component along y axis

p*:

Statistical significance

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Funding

This work has been supported by the China Scholarship Council (no. 201906020135).

Author information

Authors and Affiliations

  1. Additive Manufacturing Institute, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Yongqiang Tu & Zhangwei Chen

  2. ERPI, Université de Lorraine, 54000, Nancy, France

    Alaa Hassan

  3. LCFC, Arts et Métiers ParisTech, 57000, Metz, France

    Ali Siadat

  4. School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing, 100191, People’s Republic of China

    Gongliu Yang

Authors
  1. Yongqiang Tu
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  2. Alaa Hassan
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  3. Ali Siadat
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  4. Gongliu Yang
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  5. Zhangwei Chen
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Contributions

YT: methodology, simulation, test, writing—original draft. AH: conceptualization, writing—review and editing. AS: supervision. GY: supervision. CZ: conceptualization, writing—review and editing.

Corresponding author

Correspondence to Alaa Hassan.

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Tu, Y., Hassan, A., Siadat, A. et al. Numerical simulation and experimental validation of deposited corners of any angle in direct ink writing. Int J Adv Manuf Technol 123, 559–570 (2022). https://doi.org/10.1007/s00170-022-10195-2

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