# A Virtual Design of Experiments Method to Evaluate the Effect of Design and Welding Parameters on Weld Quality in Aerospace Applications

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### Scope and Structure of the Paper

## 2. Materials and Methods

#### 2.1. Identifying Responses and Control Factors

#### 2.2. Case Specific—Conducting Physical Experiments to develop Welding Simulation

#### 2.3. Case Specific—Developing Welding Simulation

- Efficiency: how much energy gets into the material in comparison with the exiting weld gun energy.
- Percentage of energy in combined heat source: from the total energy, percentage of energy coming from the Gaussian heat source respective to the cone heat source.
- Depth of cone.
- Placement of the cone.
- Radius of the Gaussian heat source.
- Radius of the cone heat source.

- The radii of the Gaussian and Cone heat sources would change when tilting the beam angle. This phenomenon would also happen when tilting, for example, a light beam and looking at the projection on a straight surface. For an angle of 0°, it is a circle, while for larger angles, it is an ellipse.
- The percentage of fusion area with respect to keyhole area changes with the parameter beam angle. The hypothesis is that when tilting the beam angle, less key hole is created and more conduction occurs. This hypothesis relates to the parameter “percentage of energy in combined heat source”. The more tilted the beam angle is, the more percentage goes to the cone heat source, which models the keyhole.
- The decrement of efficiency is based on the growth of the fusion area as the beam angle increases.

#### 2.4. Virtual Design of Experiments—Designing the Experiment Matrix

^{®}[51] was selected in this study. This platform allows specifying specific linear constraints between the factors, or input parameters. In this way, optimal designs are custom built for specific experimental settings by an algorithmic approach.

^{2}= 0.7, that is, adequate accuracy. The plane shown in Figure 4a represents the linear constraint between speed, power, and thickness, which illustrates the experimental region. It can be observed that when thickness increases, power increases and speed decreases.

#### 2.5. Virtual Design of Experiments—Performing Welding Simulations

^{®}[52]. In Figure 5, an example of a 9 mm plate model and its corresponding mesh is shown. The element size around the weld path is approximately 1 × 1 × 1 mm. For every CAD model, the elements are adjusted for the different thicknesses so that each layer of the mesh has the same dimension. The elements further away from the weld path are larger elements, as no big gradients are expected. The mesh size was validated using a smaller mesh, in which each element was approximately 0.5 times the size of the original mesh. No significant change was observed.

## 3. Results

#### 3.1. Physical Experiments Results

_{C}) and keyhole area (A

_{K}); see Figure 6b.

^{2}indicate good adequacy of the models. Looking at the regression lines, it can be observed that the larger the beam incident angle, the larger the conduction area and the smaller the keyhole area. However, there is a distinction between the effect of the angle on both areas. The conduction area increases linearly from angle 0°, whereas the keyhole area starts to decrease quadratically from angle 5–10°.

#### 3.2. Heat Source Model to Cover the Effect of the Laser Beam Angle

#### 3.3. Virtual Experiments Results and Meta-Model

^{®}[51], the response function (meta-model) for the weld bead dimension C was obtained after reducing the models and can be expressed as in Equation (2):

^{2}assess the adequacy of the model, indicating that this model is adequate.

^{2}= 0.80 (RSq in graph legend) and p-value = 0.0002 indicate adequate accuracy of the model.

#### 3.3.1. Infeasible Region for Complete Penetration

#### 3.3.2. Robustness and Optimization of Input Parameters towards Penetration

^{®}. Figure 12 shows these profiles with black straight lines, which represent cross sections of the response surface for two different thickness values, 6 mm (Figure 12a) and 10 mm (Figure 12b). The grey areas around these cross sections represent statistical errors.

^{®}that pass through three control points defined by the optimization criterion. Looking at these indicators, it can be observed, for example, that for the 6 mm thickness graph in Figure 12a and optimal values of power and beam angle, the response C is more robust towards beam angle than towards power. This conclusion could support the designers’ and welding engineers’ decision regarding which parameters can be stricter and which can be more flexible.

#### 3.3.3. Response Surface for Distortion

## 4. Discussion

#### 4.1. Discussion of the Results

#### 4.2. Discussion of the Method

^{®}). Other studies, such as, for example, the one presented by Prakash et al. [28], have employed evolutionary optimization algorithms. Unlike deterministic algorithms, evolutionary algorithms allow for optimizing the process from a black box perspective without being sensitive to the objective function and constrains. However, evolutionary algorithms cannot guarantee that the optimum found is the global optimum [53]. In addition, they require more function evaluation, which can increase the calculation cost.

## 5. Conclusions

- Discovery of the unfeasible region containing the combination of design and welding process parameters for which it would not be possible to achieve complete penetration.
- Creation of a surface response that allows the making of optimization and robustness analysis for the responses’ penetration and distortion.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

- Rönnbäck, A.Ö.; Isaksson, O. Product development challenges for space sub-system manufacturers. In Proceedings of the 15th International Design Conference-Design, Dubrovnik, Croatia, 21–24 May 2018; pp. 21–24. [Google Scholar]
- Levandowski, C.; Forslund, A.; Söderberg, R.; Johannesson, H. Platform strategies from a PLM perspective–theory and practice for the aerospace industry. In Proceedings of the 53rd Structures, Structural Dynamics, and Materials Conference (SDM), Honolulu, HI, USA, 23–26 April 2012; p. 1810. [Google Scholar] [CrossRef]
- Fortescue, P.; Swinerd, G.; Stark, J. Spacecraft Systems Engineering; John Wiley & Sons: Hoboken, NJ, USA, 2011; ISBN 9780470750124. [Google Scholar]
- Saxena, T.; Karsai, G. Towards a generic design space exploration framework. In Proceedings of the 10th International Conference on Computer and Information Technology, Kanpur, India, 6–8 July 2010; pp. 1940–1947. [Google Scholar] [CrossRef]
- Sandberg, M.; Tyapin, I.; Kokkolaras, M.; Lundbladh, A.; Isaksson, O. A knowledge-based master model approach exemplified with jet engine structural design. Comput. Ind.
**2017**, 85, 31–38. [Google Scholar] [CrossRef] - Forslund, A.; Söderberg, R.; Lööf, J. Multidisciplinary robustness evaluations of aero engine structures. In Proceedings of the 20th ISABE Conference, Gothenburg, Sweden, 12–16 September 2011. [Google Scholar]
- Landahl, J.; Madrid, J.; Levandowski, C.; Johannesson, H.; Söderberg, R.; Isaksson, O. Mediating constraints across design and manufacturing using platform-based manufacturing operations. In Proceedings of the 21st International Conference on Engineering Design (ICED 17) Vol 6: Design Information and Knowledge, Vancouver, BC, Canada, 21–25 August 2017; pp. 179–188, ISBN 978-1-904670-94-0. [Google Scholar]
- Madrid, J.; Landahl, J.; Söderberg, R.; Johannesson, H.; Lööf, J. Mitigating risk of producibility failures in platform concept development. In Proceedings of the 31st Congress of the International Council of the Aeronautical Sciences, Belo Horizonte, Brazil, 9–14 September 2018. [Google Scholar]
- Srinivasan, V. Role of statistics in achieving global consistency of tolerances. In Global Consistency of Tolerances; Springer: Dordrecht, The Netherlands, 1999; pp. 395–404. [Google Scholar]
- Söderberg, R.; Lindkvist, L.; Wärmefjord, K.; Carlson, J.S. Virtual geometry assurance process and toolbox. Proc. CIRP
**2016**, 43, 3–12. [Google Scholar] [CrossRef] - Runnemalm, H.; Tersing, H.; Isaksson, O. Virtual manufacturing of light weight aero engine components. In Proceedings of the XIX International Symposium on Air Breathing Engines 2009, Montreal, QC, Canada, 7–11 September 2009. [Google Scholar]
- Choudhury, B.; Chandrasekaran, M. Investigation on welding characteristics of aerospace materials—A review. Mater. Today
**2017**, 4, 7519–7526. [Google Scholar] [CrossRef] - Chaturvedi, M.C. Welding and Joining of Aerospace Materials; Elsevier: Amsterdam, The Netherlands, 2011; ISBN 978-1-84569-532-3. [Google Scholar]
- De Filippis, L.; Serio, M.; Facchini, F.; Mummolo, G.; Ludovico, A. Prediction of the vickers microhardness and ultimate tensile strength of AA5754 H111 friction stir welding butt joints using artificial neural network. Materials
**2016**, 9, 915. [Google Scholar] [CrossRef] [PubMed] - Nandan, R.; DebRoy, T.; Bhadeshia, H. Recent advances in friction-stir welding–process, weldment structure and properties. Prog. Materials Sci.
**2008**, 53, 980–1023. [Google Scholar] [CrossRef] - Pahkamaa, A.; Wärmefjord, K.; Karlsson, L.; Söderberg, R.; Goldak, J. Combining variation simulation with welding simulation for prediction of deformation and variation of a final assembly. J. Comput. Inf. Sci. Eng. JCISE
**2012**, 12, 021002. [Google Scholar] [CrossRef] - Kazemi, K.; Goldak, J.A. Numerical simulation of laser full penetration welding. Comput. Mater. Sci.
**2009**, 44, 841–849. [Google Scholar] [CrossRef] - Madrid, J.; Forslund, A.; Söderberg, R.; Wärmefjord, K.; Hoffenson, S.; Vallhagen, J.; Andersson, P. A welding capability assessment method (WCAM) to support multidisciplinary design of aircraft structures. Int. J. Interact. Des. Manuf. IJIDeM
**2018**, 12, 1–19. [Google Scholar] [CrossRef] - Tasalloti, H.; Eskelinen, H.; Kah, P.; Martikainen, J. An integrated DFMA–PDM model for the design and analysis of challenging similar and dissimilar welds. Mater. Des.
**2016**, 89, 421–431. [Google Scholar] [CrossRef] - O’Brien, A.; Guzman, C. Welding Handbook. Welding Processes Part 1; American Welding Society: Miami, FL, USA, 2007. [Google Scholar]
- Benyounis, K.; Olabi, A.-G. Optimization of different welding processes using statistical and numerical approaches—A reference guide. Adv. Eng. Softw.
**2008**, 39, 483–496. [Google Scholar] [CrossRef] - Manonmani, K.; Murugan, N.; Buvanasekaran, G. Effects of process parameters on the bead geometry of laser beam butt welded stainless steel sheets. Int. J. Adv. Manuf. Tech.
**2007**, 32, 1125–1133. [Google Scholar] [CrossRef] - Nagaraju, U.; Gowd, G.H.; Vardan, T.V. An integrated approach for optimization of pulsed ND: YAG laser beam welding PROCESS. Mater. Today Proc.
**2017**, 5, 7991–8000. [Google Scholar] [CrossRef] - Caiazzo, F.; Alfieri, V.; Sergi, V.; Schipani, A.; Cinque, S. Dissimilar autogenous disk-laser welding of Haynes 188 and Inconel 718 superalloys for aerospace applications. Int. J. Adv. Manuf. Tech.
**2013**, 68, 1809–1820. [Google Scholar] [CrossRef] - Kanigalpula, P.; Pratihar, D.; Jha, M.; Derose, J.; Bapat, A.; Pal, A. Experimental investigations, input-output modeling and optimization for electron beam welding of Cu-Cr-Zr alloy plates. Int. J. Adv. Manuf. Tech.
**2016**, 85, 711–726. [Google Scholar] [CrossRef] - Siddaiah, A.; Singh, B.; Mastanaiah, P. Prediction and optimization of weld bead geometry for electron beam welding of AISI 304 stainless steel. Int. J. Adv. Manuf. Tech.
**2017**, 89, 27–43. [Google Scholar] [CrossRef] - Casalino, G.; Minutolo, F.M.C. A model for evaluation of laser welding efficiency and quality using an artificial neural network and fuzzy logic. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2004**, 218, 641–646. [Google Scholar] [CrossRef] - Prakash, C.; Singh, S.; Singh, M.; Gupta, M.; Mia, M.; Dhanda, A. Multi-objective parametric appraisal of pulsed current gas tungsten arc welding process by using hybrid optimization algorithms. Int. J. Adv. Manuf. Tech.
**2019**, 101, 1107–1123. [Google Scholar] [CrossRef] - Shanmugam, N.S.; Buvanashekaran, G.; Sankaranarayanasamy, K. Some studies on weld bead geometries for laser spot welding process using finite element analysis. Mater. Des.
**2012**, 34, 412–426. [Google Scholar] [CrossRef] - Ai, Y.; Jiang, P.; Shao, X.; Li, P.; Wang, C. A three-dimensional numerical simulation model for weld characteristics analysis in fiber laser keyhole welding. Int. J. Heat Mass Transf.
**2017**, 108, 614–626. [Google Scholar] [CrossRef] - Hernando, I.; Arrizubieta, J.; Lamikiz, A.; Ukar, E. Numerical model for predicting bead geometry and microstructure in laser beam welding of Inconel 718 sheets. Metals
**2018**, 8, 536. [Google Scholar] [CrossRef] - Lindgren, L.-E.; Lundbäck, A.; Malmelöv, A. Thermal stresses and computational welding mechanics. J. Therm. Stresses
**2019**, 42, 107–121. [Google Scholar] [CrossRef] [Green Version] - Xu, K.; Cui, H.; Li, F. Connection mechanism of molten pool during laser transmission welding of T-joint with minor gap presence. Materials
**2018**, 11, 1823. [Google Scholar] [CrossRef] [PubMed] - Shanmugam, S.; Buvanashekaran, G.; Sankaranarayanasamy, K.; Kumar, R. A transient finite element simulation of the temperature and bead profiles of T-joint laser welds. Mater. Des.
**2010**, 31, 4528–4542. [Google Scholar] [CrossRef] - Kumar, N.; Mukherjee, M.; Bandyopadhyay, A. Study on laser welding of austenitic stainless steel by varying incident angle of pulsed laser beam. Opt. Laser Technol.
**2017**, 94, 296–309. [Google Scholar] [CrossRef] - Goos, P.; Jones, B. Optimal Design of Experiments: A Case Study Approach; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- Jenney, C.L.; O’Brien, A. Welding Handbook, Volume 1—Welding Science and Technology, 9th ed.; American Welding Society (AWS): Miami, FL, USA, 2001. [Google Scholar]
- NASA. NASA. NASA Technical Standard. In General Welding Requirements for Aerospace Materials; National Aeronautics and Space Administration: Washington, DC, USA, 2016. [Google Scholar]
- Forslund, A.; Madrid, J.; Söderberg, R.; Isaksson, O.; Lööf, J.; Frey, D. Evaluating how functional performance in aerospace components is affected by geometric variation. SAE Int. J. Aerosp.
**2018**, 11, 5–26. [Google Scholar] [CrossRef] - Forslund, A.; Lorin, S.; Lindkvist, L.; Wärmefjord, K.; Söderberg, R. Minimizing weld variation effects using permutation genetic algorithms and virtual locator trimming. J. Comput. Inf. Sci. Eng. JCISE
**2018**, 18, 041010. [Google Scholar] [CrossRef] - Goldak, J.A.; Akhlaghi, M. Computational Welding Mechanics; Springer Science & Business Media: Berlin, Germany, 2006. [Google Scholar]
- ASM. Handbook Volume 6: Welding, Brazing and Soldering; Olson, D.L., Siewert, T.A., Liu, S., Edwards, G.R., Eds.; ASM International: Materials Park, OH, USA, 1993. [Google Scholar]
- Lindgren, L.-E. Computational Welding Mechanics; Elsevier: Amsterdam, The Netherlands, 2014; ISBN 978-94-007-2739-7. [Google Scholar]
- Lindgren, L.-E. Modelling for residual stresses and deformations due to welding: “Knowing what isn’t necessary to know”. In Proceedings of the International Seminar on Numerical Analysis of Weldability, Graz, Austria, 1–3 October 2001; Maney Publishing (for The Institute of Materials, Minerals and Mining): London, UK, 2002. [Google Scholar]
- Pavelic, V. Experimental and computed temperature histories in gas tungsten arc welding of thin plates. Weld J. Res. Suppl.
**1969**, 48, 296–305. [Google Scholar] - Lorin, S.; Madrid, J.; Söderberg, R.; Wärmefjord, K. A new heat source model for keyhole mode laser welding. Sci. Technol. Weld. Join.
**2019**. submitted. [Google Scholar] - Montgomery, D.C. Design and Analysis of Experiments; John Wiley & Sons: Hoboken, NJ, USA, 2017. [Google Scholar]
- Box, G.E.; Draper, N.R. Empirical Model-Building and Response Surfaces; John Wiley & Sons: Hoboken, NJ, USA, 1987. [Google Scholar]
- Myers, R.H.; Montgomery, D.C. Response Surface Methodology: Process and Product Optimization Using Designed Experiments; Wiley: New York, NY, USA, 1995; Volume 4. [Google Scholar]
- Meyer, R.K.; Nachtsheim, C.J. The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics
**1995**, 37, 60–69. [Google Scholar] [CrossRef] - JMP. 2019. Available online: https://www.jmp.com/en_us/home.html (accessed on 31 January 2019).
- RD&T, RD&T Software Manual. Mölndal, 2009. Available online: http://rdnt.se (accessed on 31 January 2019).
- Milickovic, N.; Lahanas, M.; Balstas, D.; Zamboglou, N. Comparison of evolutionary and deterministic multiobjective algorithms for dose optimization in brachytherapy. In Proceedings of the International Conference on Evolutionary Multi-Criterion Optimization, Zurich, Switzerland, 7–9 March 2001; Springer: Berlin/Heidelberg, Germany, 2001. [Google Scholar]
- Fraser, K.; St-Georges, L.; Kiss, L. Optimization of friction stir welding tool advance speed via monte-carlo simulation of the friction stir welding process. Materials
**2014**, 7, 3435–3452. [Google Scholar] [CrossRef]

**Figure 2.**Case study parameters: (

**a**) laser beam incident angle, joint thickness, and 12 points to measure distortion (X:[0,75,150]; Y:[0,5,35,40]; Z:[0]); (

**b**) laser weld bead geometry showing incomplete joint penetration (in which C = 0) and complete joint penetration.

**Figure 4.**Experimental region noncubic: (

**a**) linear constraint expressed as a plane; (

**b**) the 16 experiments distributed along the plane that defines the feasible experimental region.

**Figure 6.**(

**a**) Cross sections of the four BOP-welds. Each cross section has been replicated twice. (

**b**) Generic representation of a laser weld bead, which can be divided in two main areas: conduction area (A

_{C}) and keyhole area (A

_{K}).

**Figure 7.**Relationship between the laser beam incident angle (degrees) and the total, conduction, and keyhole areas of the weld bead (mm

^{2}), as described in Figure 6b. Image produced in JMP

^{®}.

**Figure 8.**Combined heat source model with geometrical parameters as proposed in the work of [46]. P = placement of the cone. D = depth of the cone. r

_{1}and r

_{2}are the radii of Gaussian and cone heat sources, respectively.

**Figure 9.**Validation of the simulation with the physical welds for the different beam incident angles and thicknesses.

**Figure 11.**Contour plot for bottom width C on the two-dimensional space formed by the parameters thickness and beam angle. Infeasible region for complete penetration are coloured in light red.

**Figure 12.**Profiles of the response surface for optimizing bottom width C (penetration) for two different thickness values: (

**a**) 6 mm thickness; (

**b**) 10 mm thickness. Image taken from JMP

^{®}prediction profile.

**Figure 13.**Response surface distortion in the Z direction. (

**a**) Actual response surface for specific values of power and beam angle. (

**b**) Sections of the response surface for thicknesses of 3 mm and 8 mm.

Level −1 | Level +1 | |
---|---|---|

Power, P (W) | 2100 | 5100 |

Speed, s (mm/min) | 40 | 900 |

Thickness, t (mm) | 3 | 15 |

Beam angle, α (°) | 0 | 25 |

Experiment (Run) | Speed (mm/min) | Power (W) | Beam Angle (°) | Thickness (mm) |
---|---|---|---|---|

1 | 40 | 3582.4 | 25 | 9.5 |

2 | 40 | 5100 | 0 | 1.9 |

3 | 40 | 5100 | 25 | 14.9 |

4 | 536.3 | 5100 | 0 | 11.95 |

5 | 40 | 5064.9 | 12.5 | 15 |

6 | 900 | 3270.3 | 0 | 3 |

7 | 40 | 2100 | 0 | 3.8 |

8 | 470 | 5100 | 25 | 12.35 |

9 | 900 | 5100 | 25 | 9.97 |

10 | 900 | 5100 | 0 | 9.97 |

11 | 370.3 | 3808.2 | 12.5 | 8.17 |

12 | 456.6 | 2497.2 | 25 | 3 |

13 | 40 | 3582.4 | 0 | 9.5 |

14 | 40 | 2100 | 25 | 3.8 |

15 | 642.1 | 2798.1 | 0 | 3 |

16 | 900 | 3270.3 | 25 | 3 |

Bead Parameters | Sum of Squares | Degrees of Freedom | F-Ratio | R^{2} | Model Adequacy | ||
---|---|---|---|---|---|---|---|

Regression | Residual | Regression | Residual | ||||

Bottom width C | 49.74 | 12.73 | 3 | 12 | 15.6242 | 0.80 | Adequate |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Madrid, J.; Lorin, S.; Söderberg, R.; Hammersberg, P.; Wärmefjord, K.; Lööf, J.
A Virtual Design of Experiments Method to Evaluate the Effect of Design and Welding Parameters on Weld Quality in Aerospace Applications. *Aerospace* **2019**, *6*, 74.
https://doi.org/10.3390/aerospace6060074

**AMA Style**

Madrid J, Lorin S, Söderberg R, Hammersberg P, Wärmefjord K, Lööf J.
A Virtual Design of Experiments Method to Evaluate the Effect of Design and Welding Parameters on Weld Quality in Aerospace Applications. *Aerospace*. 2019; 6(6):74.
https://doi.org/10.3390/aerospace6060074

**Chicago/Turabian Style**

Madrid, Julia, Samuel Lorin, Rikard Söderberg, Peter Hammersberg, Kristina Wärmefjord, and Johan Lööf.
2019. "A Virtual Design of Experiments Method to Evaluate the Effect of Design and Welding Parameters on Weld Quality in Aerospace Applications" *Aerospace* 6, no. 6: 74.
https://doi.org/10.3390/aerospace6060074