# Intra- and Inter-Repeatability of Profile Deviations of an AlSi10Mg Tooling Component Manufactured by Laser Powder Bed Fusion

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Protocol

^{®}v.16 (Innovmetric Metrological Software, Quebec, QC, Canada). The data were then loaded into a Matlab

^{®}2017b (software of MathWorks, Natick, MA, USA), using a code to extract the deviation at each point. Minitab

^{®}v.17 (a statistical software of Minitab Inc., State College, PA, USA) was used for the graphics and statistical studies (Figure 2d).

#### 2.1. Intra-Build Variations Study

^{®}v.16 for each part, and represented by their nonparametric medians. In the first part of this intra-build variation study (Analysis 1a), visualizing the repartition of the profile deviations in the manufacturing chamber was the main interest. The second object of interest was the deviations of the external diameter of the parts at a height of z = 1.2 mm (Analysis 1b). This plan z = 1.2 mm has been chosen because it is the mid-value between the chamfer and the holes in the cylindrical feature of the part. For each of the 147 parts, the absolute difference between the measured diameter (using best fit criteria) and the nominal diameter (∅19.05 mm) was extracted using the IMInspect module of PolyWorks

^{®}v.16 and plotted using Minitab

^{®}v.17. The Analysis 1c consisted of a correlation study of the two previous variables, the overall 3D profile deviation and the external diameter at a height of z = 1.2 mm. This analysis was carried out using a regression equation, which is an algebraic representation of the regression line used to describe the relationship between the response and predictor variables. In our case, the measured diameter was used as a predictor variable, while the overall 3D profile deviation represented by its median was considered as a response variable. Minitab v.17 linear regression analysis was used to obtain the equations for the three builds. Finally, a basic statistical study was also conducted with the overall 3D profile deviations and the external diameter at a height of z = 1.2 mm (Analysis 1d).

#### 2.2. Inter-Build Variations Study

^{®}v.16. The KS test and visual comparison were performed using the data acquired before cutting the parts off the plate for Build #2 and Build #3 (Build #1 data before cutting the parts were not available). The KS test is a nonparametric goodness-of-fit test that compares cumulative distribution functions (CDF). It is explained below in Equations (1)–(3). In this case, the KS test was used to compare the CDF of the 3D profile deviation of Build #2 and Build #3 acquired before the part removal.

#### 2.3. Capability Study

^{®}2017b. For each part, the overall deviations were fitted to a normal distribution at a 95% confidence level. The MCS was then performed on the 147 normal distribution parameters, and the overall capability was extracted (Analysis 3b).

## 3. Results

#### 3.1. Intra-Build Variations

#### 3.2. Inter-Build Variations

#### 3.3. Capability

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Experimental protocol: (

**a**) manufacturing sequence, (

**b**) stress relief heat treatment, (

**c**) geometrical deviation measurements, and (

**d**) data analysis.

**Figure 4.**Contour plot of the profile deviation distribution using a median deviation of each part for all three builds.

**Figure 5.**Bubble plot of the diameter deviation of each part of the three builds; the size of the bubble illustrates the absolute difference between the measured diameter and the nominal size of the part.

**Figure 6.**Correlation between the diameter deviation (predictor) and the profile deviation (response).

**Figure 9.**Capability and diameter deviation analyses: (

**a**) Diameter quantification, (

**b**) 49 parts’ (one build) diameter distribution, (

**c**) 3D profile deviation capability, and (

**d**) 49 parts’ (one build) 3D profile deviation capabilities distribution.

Build | ${\mathit{\mu}}_{\mathbf{\varnothing}}$ | $\mathit{S}\mathit{t}\mathit{D}\mathit{e}{\mathit{v}}_{\mathbf{\varnothing}}$ | $\mathit{M}\mathit{i}{\mathit{n}}_{\mathbf{\varnothing}}$ | $\mathit{M}\mathit{e}\mathit{d}\mathit{i}\mathit{a}{\mathit{n}}_{\mathbf{\varnothing}}$ | $\mathit{M}\mathit{a}{\mathit{x}}_{\mathbf{\varnothing}}$ |
---|---|---|---|---|---|

#1 | 19.053 | 0.054 | 18.970 | 19.041 | 19.243 |

#2 | 19.017 | 0.025 | 18.964 | 19.015 | 19.108 |

#3 | 19.012 | 0.038 | 18.936 | 19.011 | 19.095 |

**Table 2.**Descriptive statistics of the measured Profile $\left({L}_{99\%}-{L}_{1\%}\right)$ for 49 parts (dimensions in mm).

Build | |||||
---|---|---|---|---|---|

#1 | 0.148 | 0.058 | 0.108 | 0.131 | 0.501 |

#2 | 0.152 | 0.023 | 0.124 | 0.149 | 0.276 |

#3 | 0.147 | 0.014 | 0.116 | 0.148 | 0.181 |

**Table 3.**3D profile deviation (mm) and equivalent IT grade (International Tolerance Grade defined in ISO 286).

Build | 95% | 97.73% | ||
---|---|---|---|---|

#1 | 0.005 | 0.034 | 0.136 | 0.240 |

#2 | 0.000 | 0.032 | 0.127 | 0.225 |

#3 | −0.002 | 0.030 | 0.121 | 0.191 |

Overall | 0.001 | 0.032 | 0.128 (IT 11) | 0.228 (IT 12) |

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## Share and Cite

**MDPI and ACS Style**

Zongo, F.; Tahan, A.; Aidibe, A.; Brailovski, V.
Intra- and Inter-Repeatability of Profile Deviations of an AlSi10Mg Tooling Component Manufactured by Laser Powder Bed Fusion. *J. Manuf. Mater. Process.* **2018**, *2*, 56.
https://doi.org/10.3390/jmmp2030056

**AMA Style**

Zongo F, Tahan A, Aidibe A, Brailovski V.
Intra- and Inter-Repeatability of Profile Deviations of an AlSi10Mg Tooling Component Manufactured by Laser Powder Bed Fusion. *Journal of Manufacturing and Materials Processing*. 2018; 2(3):56.
https://doi.org/10.3390/jmmp2030056

**Chicago/Turabian Style**

Zongo, Floriane, Antoine Tahan, Ali Aidibe, and Vladimir Brailovski.
2018. "Intra- and Inter-Repeatability of Profile Deviations of an AlSi10Mg Tooling Component Manufactured by Laser Powder Bed Fusion" *Journal of Manufacturing and Materials Processing* 2, no. 3: 56.
https://doi.org/10.3390/jmmp2030056