# Analysis of the Flatness Form Error in Binder Jetting Process as Affected by the Inclination Angle

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{(green)}= Δz × cos(θ

_{g})

_{g}is the angle between the fabrication direction and the plane vector in the green state.

^{−1}mbar. Sintered samples were measured using the procedure previously developed for green parts, with proper corrections due to shrinkage.

_{(sintered)}= Δz (1 + ε

_{z}) cos(θ

_{s})

_{z}is the dimensional change along the Z direction (fabrication direction), derived by the normalized difference in dimensions parallel to the Z axis, and expressed by Equation (3)

_{z}= (l

_{s}− l

_{g})/l

_{g}

_{s}represents the dimension at sintered state, and l

_{g}is the dimension at green state. θ

_{s}is the novel angle resulting from anisotropic dimensional changes in sintering, which is expressed by Equation (4), as detailed in [21].

_{s}= tan

^{−1}[tan(θ

_{g})(1 + ε

_{x})/(1 + ε

_{z})]

## 3. Results

_{g}) is derived from CAD geometry and the dimensional changes in X and Z directions (ε

_{x}and ε

_{z}) are assumed to be equal to −15.5% and −17.8%, respectively, corresponding to the average dimensional change in the linear dimensions, as reported in Reference [21].

## 4. Discussion and Conclusions

- The staircase error, which is generally considered the main source of irregularities in layer-by-layer manufacturing processes, is not the predominant cause of the flatness form error in the green products. The experimental results evidence a prevailing effect of layer shifting. According to the literature, the origin of layer shifting can be attributed to powder spreading or insufficient drying. In the present study, layer shifting mainly occurred due to powder spreading, but a direct relationship was also revealed between the temperature drops in the powder bed and layer drift in the opposite direction, likely due to insufficient drying.
- The distortion is the major cause of flatness form error in the sintered state. The results show a thermal deformation related to the higher radiation that occurred on one side of the samples. When distortion was not observed, a dimensional change in sintering amplifies the inhomogeneity in surface morphology observed at the green state.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Buj-Corral, I.; Tejo-Otero, A.; Fenollosa-Artés, F. Development of am technologies for metals in the sector of medical implants. Metals
**2020**, 10, 686. [Google Scholar] [CrossRef] - Yusuf, S.M.; Cutler, S.; Gao, N. Review: The impact of metal additive manufacturing on the aerospace industry. Metals
**2019**, 9, 1286. [Google Scholar] [CrossRef] [Green Version] - Del Prete, A.; Primo, T. Innovative methodology for the identification of the most suitable additive technology based on product characteristics. Metals
**2021**, 11, 409. [Google Scholar] [CrossRef] - Li, M.; Du, W.; Elwany, A.; Pei, Z.; Ma, C. Metal Binder Jetting Additive Manufacturing: A Literature Review. J. Manuf. Sci. Eng.
**2020**, 142, 1–17. [Google Scholar] [CrossRef] - Ziaee, M.; Crane, N.B. Binder jetting: A review of process, materials, and methods. Addit. Manuf.
**2019**, 28, 781–801. [Google Scholar] [CrossRef] - Taufik, M.; Jain, P.K. Role of build orientation in layered manufacturing: A review. Int. J. Manuf. Technol. Manag.
**2013**, 27, 47–73. [Google Scholar] [CrossRef] - Salem, H.; Abouchadi, H.; El Bikri, K. Design for additive manufacturing. J. Theor. Appl. Inf. Technol.
**2020**, 10, 3043–3054. [Google Scholar] [CrossRef] - Rosso, S.; Savio, G.; Uriati, F.; Meneghello, R.; Concheri, G. Optimization approaches in design for additive manufacturing. Proc. Int. Conf. Eng. Des. ICED
**2019**, 2019, 809–818. [Google Scholar] [CrossRef] [Green Version] - Arni, R.; Gupta, S.K. Manufacturability analysis of flatness tolerances in solid freeform fabrication. J. Mech. Des. Trans. ASME
**2001**, 123, 148–156. [Google Scholar] [CrossRef] - Paul, R.; Anand, S. Optimization of layered manufacturing process for reducing form errors with minimal support structures. J. Manuf. Syst.
**2015**, 36, 231–243. [Google Scholar] [CrossRef] - Crane, N.B. Impact of part thickness and drying conditions on saturation limits in binder jet additive manufacturing. Addit. Manuf.
**2020**, 33, 101127. [Google Scholar] [CrossRef] - Rishmawi, I.; Salarian, M.; Vlasea, M. Binder jetting additive manufacturing of water-atomized iron. In Proceedings of the 2018 Annual International Solid Freeform Fabrication Symposium—An Additive Manufacturing Conference, Austin, TX, USA, 13–15 August 2020; pp. 160–170. [Google Scholar]
- Huang, S.J.; Ye, C.S.; Zhao, H.P.; Fan, Z.T. Parameters optimization of binder jetting process using modified silicate as a binder. Mater. Manuf. Process.
**2020**, 35, 214–220. [Google Scholar] [CrossRef] - Miyanaji, H.; Momenzadeh, N.; Yang, L. Effect of printing speed on quality of printed parts in Binder Jetting Process. Addit. Manuf.
**2018**, 20, 1–10. [Google Scholar] [CrossRef] - Parab, N.D.; Barnes, J.E.; Zhao, C.; Cunningham, R.W.; Fezzaa, K.; Rollett, A.D.; Sun, T. Real time observation of binder jetting printing process using high-speed X-ray imaging. Sci. Rep.
**2019**, 9, 1–10. [Google Scholar] [CrossRef] - Cao, S.; Qiu, Y.; Wei, X.F.; Zhang, H.H. Experimental and theoretical investigation on ultra-thin powder layering in three dimensional printing (3DP) by a novel double-smoothing mechanism. J. Mater. Process. Technol.
**2015**, 220, 231–242. [Google Scholar] [CrossRef] - Maximenko, A.L.; Olumor, I.D.; Maidaniuk, A.P.; Olevsky, E.A. Modeling of effect of powder spreading on green body dimensional accuracy in additive manufacturing by binder jetting. Powder Technol.
**2021**, 385, 60–68. [Google Scholar] [CrossRef] - Miyanaji, H.; Orth, M.; Akbar, J.M.; Yang, L. Process development for green part printing using binder jetting additive manufacturing. Front. Mech. Eng.
**2018**, 13, 504–512. [Google Scholar] [CrossRef] - Chen, H.; Zhao, Y.F. Process parameters optimization for improving surface quality and manufacturing accuracy of binder jetting additive manufacturing process. Rapid Prototyp. J.
**2016**, 22, 527–538. [Google Scholar] [CrossRef] - Wang, Y.; Zhao, Y.F. Investigation of Sintering Shrinkage in Binder Jetting Additive Manufacturing Process. Procedia Manuf.
**2017**, 10, 779–790. [Google Scholar] [CrossRef] - Zago, M.; Lecis, N.F.M.; Vedani, M.; Cristofolini, I. Dimensional and geometrical precision of parts produced by Binder Jetting process as affected by the anisotropic shrinkage on sintering. Addit. Manuf.
**2021**, 43, 102007. [Google Scholar] [CrossRef] - Baselli, S.; Torresani, E.; Zago, M.; Amirabdollahian, S.; Cristofolini, I.; Molinari, A. Sintering shrinkage of uniaxial cold compacted iron: Influence of the microstructure on the anisothermal and isothermal shrinkage of uniaxial cold-compacted iron. Powder Metall.
**2018**, 61, 276–284. [Google Scholar] [CrossRef] - Molinari, A.; Amirabdollahian, S.; Zago, M.; Larsson, M.; Cristofolini, I. Effect of geometry and green density on the anisotropic sintering shrinkage of axisymmetric iron parts. Powder Metall.
**2018**, 61, 267–275. [Google Scholar] [CrossRef] - Cristofolini, I.; Molinari, A.; Zago, M.; Amirabdollahian, S.; Coube, O.; Dougan, M.J.; Larsson, M.; Schneider, M.; Valler, P.; Voglhuber, J.; et al. Design for Powder Metallurgy: Predicting Anisotropic Dimensional Change on Sintering of Real Parts. Int. J. Precis. Eng. Manuf.
**2019**, 20, 619–630. [Google Scholar] [CrossRef] - Zago, M.; Cristofolini, I.; Molinari, A. New interpretation for the origin of the anisotropic sintering shrinkage of AISI 316L rings based on the anisotropic stress field occurred on uniaxial cold compaction. Powder Metall.
**2019**, 62, 115–123. [Google Scholar] [CrossRef] - Zago, M.; Larsson, M.; Cristofolini, I. An Improved Design Method for Net-Shape Manufacturing in Powder Metallurgy; Lecture Notes in Mechanical Engineering Springer Nature: Cham, Switzerland, 2020; Volume 1, ISBN 9783030311537. [Google Scholar]
- Lecis, N.; Mariani, M.; Beltrami, R.; Emanuelli, L.; Casati, R.; Vedani, M.; Molinari, A. Effects of process parameters, debinding and sintering on the microstructure of 316L stainless steel produced by binder jetting. Mater. Sci. Eng. A
**2021**, 828, 142108. [Google Scholar] [CrossRef] - Vitolo, F.; Martorelli, M.; Gerbino, S.; Patalano, S.; Lanzotti, A. Controlling form errors in 3D printed models associated to size and position on the working plane. Int. J. Interact. Des. Manuf.
**2018**, 12, 969–977. [Google Scholar] [CrossRef] - ISO, I.S.O. 10360-2; 2009—Geometrical Product Specifications (GPS)—Acceptance and Reverification Tests for Coordinate Measuring Machines (CMM)—Part 2: CMMs Used for Measuring Linear Dimensions. ISO: Geneva, Switzerland, 2009.
- Kumar, A.; Bai, Y.; Eklund, A.; Williams, C.B. Effects of Hot Isostatic Pressing on Copper Parts Fabricated via Binder Jetting. Procedia Manuf.
**2017**, 10, 935–944. [Google Scholar] [CrossRef] - Mostafaei, A.; Rodriguez De Vecchis, P.; Nettleship, I.; Chmielus, M. Effect of powder size distribution on densification and microstructural evolution of binder-jet 3D-printed alloy 625. Mater. Des.
**2019**, 162, 375–383. [Google Scholar] [CrossRef] - Miyanaji, H.; Rahman, K.M.; Da, M.; Williams, C.B. Effect of fine powder particles on quality of binder jetting parts. Addit. Manuf.
**2020**, 36, 101587. [Google Scholar] [CrossRef] - Li, M.; Wei, X.; Pei, Z.; Ma, C. Binder Jetting Additive Manufacturing: Observations of Compaction-induced Powder Bed Surface Defects. Manuf. Lett.
**2021**, 28, 50–53. [Google Scholar] [CrossRef] - Tang, Y.; Huang, Z.; Yang, J.; Xie, Y. Enhancing the capillary force of binder-jetting printing Ti6Al4V and mechanical properties under high temperature sintering by mixing fine powder. Metals
**2020**, 10, 1345. [Google Scholar] [CrossRef] - Lores, A.; Azumendi, N.; Agote, I.; Andres, U. A step towards a robust binder jetting technology: Process parameter optimization for 17-4 PH steel to increase powder bed homogeneity. In Proceedings of the Euro PM2020 Virtual Congress, Online, 5–7 October 2020. [Google Scholar]
- Barthel, B.; Janas, F.; Wieland, S. Powder condition and spreading parameter impact on green and sintered density in metal binder jetting. Powder Metall.
**2021**, 64, 1–9. [Google Scholar] [CrossRef]

**Figure 1.**Scheme of the different steps of printing process (powder spreading, binder deposition and drying) and secondary operations: curing, de-powdering, de-binding and sintering.

**Figure 5.**Graphical interpretation of the staircase error caused by a layer-by-layer manufacturing process.

**Figure 6.**(

**a**) Flatness form error of plane D measured in the green state along with the flatness predicted by Equation (1); (

**b**) flatness form error of plane D measured in the sintered state along with the flatness predicted by Equation (2). The error bars represent one standard deviation in the measurements.

**Figure 7.**Sample 0°: (

**a**) points measured at the green state and reconstruction of the plane; (

**b**) points measured at the sintered state and reconstruction of the plane.

**Figure 10.**Points measured on datum plane B on each geometry: the dashed lines represent the layer corresponding to the temperature drops that occurred during the printing procedure.

**Figure 13.**Analysis of the shape distortion of datum plane B and plane D of the sintered sample 90°.

**Figure 14.**Sample 30° (

**a**) points measured at the green state and reconstruction of the plane; (

**b**) points measured at the sintered state and reconstruction of the plane.

**Figure 15.**Sample 45° (

**a**) points measured at the green state and reconstruction of the plane; (

**b**) points measured at the sintered state and reconstruction of the plane.

**Figure 16.**Sample 60° (

**a**) points measured at the green state and reconstruction of the plane; (

**b**) points measured at the sintered state and reconstruction of the plane.

Layer Thickness | Saturation Level | Recoat Speed | Roller Speed | Ultrasonic Intensity | Bed Temp | Dry Time |
---|---|---|---|---|---|---|

50 μm | 55% | 90 mm/s | 500 rpm | 100% | 55 °C | 12 s |

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**MDPI and ACS Style**

Zago, M.; Lecis, N.; Mariani, M.; Cristofolini, I.
Analysis of the Flatness Form Error in Binder Jetting Process as Affected by the Inclination Angle. *Metals* **2022**, *12*, 430.
https://doi.org/10.3390/met12030430

**AMA Style**

Zago M, Lecis N, Mariani M, Cristofolini I.
Analysis of the Flatness Form Error in Binder Jetting Process as Affected by the Inclination Angle. *Metals*. 2022; 12(3):430.
https://doi.org/10.3390/met12030430

**Chicago/Turabian Style**

Zago, Marco, Nora Lecis, Marco Mariani, and Ilaria Cristofolini.
2022. "Analysis of the Flatness Form Error in Binder Jetting Process as Affected by the Inclination Angle" *Metals* 12, no. 3: 430.
https://doi.org/10.3390/met12030430