aerospace

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

Julia Madrid 1,* , Samuel Lorin 2, Rikard Söderberg 1, Peter Hammersberg 1, Kristina Wärmefjord 1 and Johan Lööf 3 1 Department of Industrial and Materials , Chalmers University of Technology, SE-412 96 Gothenburg, Sweden; [email protected] (R.S.); [email protected] (P.H.); [email protected] (K.W.) 2 Fraunhofer-Chalmers Research Centre for Industrial , SE-412 88 Gothenburg, Sweden; [email protected] 3 GKN Aerospace Engine Systems, SE-461 38 Trollhättan, Sweden; [email protected] * Correspondence: [email protected]; Tel.: +46-31-722-1344

 Received: 29 April 2019; Accepted: 14 June 2019; Published: 20 June 2019 

Abstract: During multidisciplinary design of welded aircraft components, are principally optimized upon component performance, employing well-established modelling and simulation techniques. On the contrary, because of the complexity of modelling welding process phenomena, much of the welding experimentation relies on physical testing, which welding producibility aspects are considered after the design has already been established. In addition, welding optimization research mainly focuses on welding process parameters, overlooking the potential impact of product design. As a consequence, redesign loops and welding rework increases product cost. To solve these problems, in this article, a novel method that combines the benefits of design of experiments (DOE) techniques with welding simulation is presented. The aim of the virtual design of experiments method is to model and optimize the effect of design and welding parameters interactions early in the design process. The method is explained through a , in which weld bead penetration and distortion are quality responses to optimize. First, a small number of physical welds are conducted to develop and tune the welding simulation. From this activity, a new combined heat source model is presented. Thereafter, the DOE technique is employed to design an experimental matrix that enables the conjointly incorporation of design and welding parameters. Welding simulations are then run and a response function is obtained. With virtual experiments, a large number of design and welding parameter combinations can be tested in a short time. In conclusion, the creation of a meta-model allows for performing welding producibility optimization and robustness analyses during early design phases of aircraft components.

Keywords: welding producibility; welding simulation; design of experiments; aerospace design for manufacturing

1. Introduction The development of aircrafts is driven by a complex business-to-business market, in which suppliers and sub-suppliers need to work with a wide variety of design solutions in order to be adaptive to requirement changes from the OEMs (original equipment manufacturers) [1]. In the early stages of development, aero-engine manufacturers need to quickly evaluate the feasibility of a large number of design variants to give a rapid response to OEMs in regards to potential performance quality, producibility, and component cost [2,3]. Established approaches begin

Aerospace 2019, 6, 74; doi:10.3390/aerospace6060074 www.mdpi.com/journal/aerospace Aerospace 2019, 6, 74 2 of 23 by parametrizing component concept and setting a large design space defined by a broad number of design parameters [4]. Multidisciplinary optimization in combination with modelling and simulation techniques are then employed to find optimal designs to fulfil high performance requirements such as aerodynamics, extreme temperatures, or safety aspects [5,6]. While designs are principally optimized upon component performance, producibility aspects have been considered lately [7,8]. However, producibility is also an important constraint to the design space because all manufactured and assembled products are afflicted by variation [9]. Geometrical variation at a part level can propagate and accumulate throughout the assembly process, resulting in products that do not fulfil assembly, functional, or esthetical conditions. In the context of assembled products, Söderberg et al. [10] proposes virtual geometry assurance as a process to foresee geometrical variation from early design stages. Virtual geometry assurance is a set of activities and tools needed to analyse and control the effect of geometrical variation with the use of variation simulation and practices, which allows giving an early response to the OEMs concerning the assembly feasibility and robustness of the component design. In the last decade, a common approach to the manufacture of aero-engine components has been the fabrication of small parts that are joined together into the final component by employing fusion welding [11]. For this type of application, laser beam welding (LBW) has played an integral role. LBW is a high energy density beam welding method, which has lately been considered as a promising alternative to the conventional arc welding methods [12,13]. This welding method produces welds with high depth-to-width aspect ratios, small heat affected zones, and reduced distortion due to the heat source being a high-energy density beam. Thus, it is an advantageous solution to welding nickel-based super alloy components [12]. When it comes to weld titanium alloy components, a competitive technology to laser welding is friction stir welding (FSW). FSW is a solid-state joining process that produces a joint without melting the workpiece material. The absence of melting enables very low welding temperatures. As a consequence, mechanical distortion is nearly reduced and the heat affected zone is minimal [14]. The surface finish quality also increases considerably according to Nandan et al. [15]. Nevertheless, to perform variation simulation of a welded component, Pahkamma et al. [16] stated that besides assembly variation, it is necessary to also model the joining process because of the combinatory effect between part variation, assembly variation, and welding deformation. However, modelling welding processes is not an easy task because it involves the of complex thermal, mechanical, and metallurgical phenomena [17]. In addition, distortion and geometrical variation are not the only characteristics determining the final weld quality. In aerospace applications, weld quality criteria also include weld bead geometry, microstructure, metallurgical discontinuities, and residual stresses [18]. Therefore, current needs in the field of virtual geometry assurance rely on the capacity of evaluating in a virtual asset whether certain design geometries and parameters can be welded to specific weld quality levels in order to ensure component functionality. The quality of a welded aero-component can be affected by multiple factors such as welding process parameters and set-up, materials composition, weld joint design, fixture design, product form division, and product geometry [19,20]. The interaction of product geometry and welding process causes welding engineers to struggle because they need to find a new optimal set of process parameters for every new component geometry and material to produces a good welded joint. In the literature, studies can be found that use design of experiments (DOE) and other statistical and numerical approaches to predict and optimize weld quality for different welding methods [14,21–28]. Nevertheless, few studies can be found that optimize the interaction of product geometry and welding process. For example, Casalino et al. [27] employs neural networks, including joint thickness, as a parameter to predict weld bead geometry. Caiazzo et al. [24] emphasized that understanding the effect of laser beam incident angle is required for real application in commercial turbine engines. However, the majority of the studies only include conventional welding process parameters such as power and speed in the optimization. Aerospace 2019, 6, 74 3 of 23

In addition, these welding–DOE studies are performed via physical experiments. The lack of virtual analysis for welding producibility makes the design longer and more costly when compared with other disciplines such as aerodynamics that have a strong simulation capability. The evaluation time and cost increment even more as more parameters are considered in the DOE. As a consequence, less parameter combinations are physically tested and less information is gained.

Scope and Structure of the Paper To rapidly evaluate the welding producibility of all geometrical variants considered within the design space, and to be able to gain more welding capability information, there is a need to incorporate virtual approaches that investigate and optimize potential combinations of design and welding parameters. The objective of this study is to propose a method that combines DOE techniques with welding simulation. The use of DOE techniques will allow exploring a big part of the design space, formed by selected design and welding parameters, requiring a minimal number of experiments. Welding simulations will be conducted as virtual experiments to shorten the evaluation time. The aim is to be able to quickly evaluate the effect of the different product geometries on weld quality during early phases of the multidisciplinary design of aerospace components. In this manner, a rapid answer can be provided to the OEM about the design and manufacture feasibility of a component variant. The virtual and design of method is presented in the Material and Methods section of this article. First, a brief description of the method steps is given. Further on, an industrial case study is employed to give a more detailed explanation of each of the steps in the method. Thus, in the subsections of Section2, the reader can find descriptions of the experimentation, welding simulation, and DOE techniques employed. In Section3, the results obtained from applying the proposed method in the case study are presented. Section4 presents the discussion with regards to the industrial case results and the proposed method. Section5 presents the conclusions of the study.

2. Materials and Methods The steps of the method proposed in this article are illustrated in Figure1. The objective of the virtual design of experiments method is to investigate the effect of the interaction between welding and design parameters on weld quality by combining specific DOE techniques with welding simulation. The method was divided into three main blocks containing a number of steps that will lead to three types of analyses. The first block is the identification of design and welding process parameters (considered as control factors) together with the identification of weld quality criteria (responses). After the first block, the method was divided into Blocks 2 and 3, named as “Case Specific—Development of Welding Simulation” and “Virtual Design of Experiments”, respectively. Block 2 focuses on preparing welding simulation to the specifics of the case study under consideration. To date, welding simulations are validated and employed in industrial applications to study macro-level product deformation (distortion) and residual stresses. However, the simulation of other aspects of weld quality such as weld bead geometry, microstructure, and formation of metallurgical discontinuities such as cracks and pores are at a research stage [29–33]. Additional aspects of welding simulation that are under investigation are the effects of welding set-up parameters such as gun-to-workpiece distance and beam incident angle [34,35]. Thus, Block 2 of the method (see Figure1) aims at evaluating whether the current case lies inside the welding simulation validation zone. In the event that the application under consideration is outside the validation zone and the welding simulation is not mature, there is a need for input from physical experiments. Therefore, prior to jumping into the design of the simulation experiment matrix, a number of physical experiments are required in order to understand the case-based welding phenomenon. The physical experiments’ results will serve to develop the simulation by tuning the simulation parameters. These physical experiments will also serve to validate the developed simulation model as Aerospace 2019, 6, x FOR PEER REVIEW 4 of 23

Aerospace 2019, 6, 74 4 of 23 The physical experiments’ results will serve to develop the simulation by tuning the simulation parameters. These physical experiments will also serve to validate the developed simulation model wellas well as to as find to find reasonable reasonable values values for the for input the parametersinput parameters to the DOE.to the In DOE. an industrial In an industrial context, physicalcontext, experimentsphysical experiments are usually are limited usually as alimited result ofas costa result and time.of cost Thus, and thetime. ultimate Thus, the aim ultimate would be aim to reducewould thebe to number reduce of the physical number tests of physical and leave tests the and load leave of experimentation the load of experimentation to simulation. to simulation.

FigureFigure 1.1. Virtual designdesign ofof experimentsexperiments methodmethod toto optimizeoptimize designdesign andand weldingwelding parameters.parameters.

Once the welding simulation capability has been expanded to simulate the study phenomena, Once the welding simulation capability has been expanded to simulate the study phenomena, the execution phase “Virtual Design of Experiments” starts (see Block 3 in Figure1). This is the block the execution phase “Virtual Design of Experiments” starts (see Block 3 in Figure 1). This is the block in which DOE is applied. First, the matrix of experiments is designed following an optimal design in which DOE is applied. First, the matrix of experiments is designed following an optimal design approach [36], which can integrate design and welding parameters in the same experimental design. approach [36], which can integrate design and welding parameters in the same experimental design. Thereafter, the simulation experiments are conducted. The final step in Block 3, after having obtained Thereafter, the simulation experiments are conducted. The final step in Block 3, after having obtained the simulation results table, is to build a meta-model, understood as a that is based on the simulation results table, is to build a meta-model, understood as a statistical model that is based virtual experiments. This meta-model represents the response function embodying the effect of input on virtual experiments. This meta-model represents the response function embodying the effect of design and process parameters on the system output responses. From this meta-model, actions can be input design and process parameters on the system output responses. From this meta-model, actions performed such as optimization, robustness analysis, and definition of unfeasible regions. can be performed such as optimization, robustness analysis, and definition of unfeasible regions. The proposed virtual design of experiments method presented in Figure1 is designed to be valid The proposed virtual design of experiments method presented in Figure 1 is designed to be valid in an aerospace industrial context. Aerospace products in general, and aircraft engines in particular, in an aerospace industrial context. Aerospace products in general, and aircraft engines in particular, are constituted of components with complex and highly integrated geometries. Questions related to are constituted of components with complex and highly integrated geometries. Questions related to the producibility of component geometries that are raised during design phases concern, for example, the producibility of component geometries that are raised during design phases concern, for example, welding gun accessibility and the ability to weld different thicknesses. welding gun accessibility and the ability to weld different thicknesses.

Aerospace 2019, 6, 74 5 of 23

Aerospace 2019, 6, x FOR PEER REVIEW 5 of 23 From this context description, a simplified case consisting of test forged plates made of nickel-based super alloyFrom (Inconel this context 718) welded description, with a laser simplified beam case welding consisting (LBW) of aretest considered forged plates as made a case of study nickel- to test based super alloy (Inconel 718) welded with laser beam welding (LBW) are considered as a case study the proposed method. to test the proposed method. Forged nickel-based superalloys are materials commonly employed in the hot section of aircraft Forged nickel-based superalloys are materials commonly employed in the hot section of aircraft enginesengines owing owing to their to their high high strength strength at at elevated elevated temperaturestemperatures [12]. [12 ].LBW LBW produces produces welds welds with with a high a high depth-to-widthdepth-to-width aspect aspect ratio, ratio, small small heat heat a affectedffected zones,zones, and and reduced reduced distortion distortion as the as theheat heat source source is a is a high-energyhigh-energy density density beam. beam. Thus, Thus, laser laser hashas beenbeen cons consideredidered lately lately as asa promising a promising alternative alternative to the to the conventionalconventional arc weldingarc welding methods methods in in the the aerospace aerospace industry [12,13]. [12,13 ]. The applicationThe application of the of methodthe method steps steps for thisfor particularthis particular case case study study are detailedare detailed in the in comingthe coming sections. sections. 2.1. Identifying Responses and Control Factors 2.1. Identifying Responses and Control Factors The first block in Figure1 is the identification of the welding responses that wanted to be controlled and the correspondingThe first block in control Figure factors.1 is the Theidentification weld quality of the criteriawelding in responses this case that study wanted is covered to be by controlled and the corresponding control factors. The weld quality criteria in this case study is the responses: complete penetration and minimum distortion. Complete penetration is one of the covered by the responses: complete penetration and minimum distortion. Complete penetration is parametersone of the that parameters defines weld that defines bead geometry weld bead (see geom Figureetry (see2b). Figure Weld 2b). bead Weld geometry bead geometry is an important is an aspectimportant of weld aspect quality of because weld quality it can because affect product it can affect performance product performance [37]. For example, [37]. For in example, aircraft in engine components,aircraft engine welds components, must achieve welds complete must achieve penetration complete with penetration a minimum with bead a minimum bottom bead width bottom to ensure life andwidth safety to ensure requirements life and safety [38]. requirements This means [38]. that This the weldmeans metal that the must weld extend metal throughmust extend the joint thickness,through achieving the joint thickness, a minimum achieving bead bottoma minimum width; bead see bottom C in width; Figure see2b. C Anotherin Figure 2b. aspect Another of weld qualityaspect is geometrical of weld quality distortion, is geometrical which isdistortion, a consequence which is of a theconsequence built up stressesof the built and up shrinkages stresses and caused duringshrinkages welding caused heating during and coolingwelding cyclesheating [37 and]. Geometricalcooling cycles distortion [37]. Geometrical needs todistortion be controlled needs to within tolerances,be controlled otherwise within it can tolerances, cause decrement otherwise init productcan cause performance decrement in [ 39product] or misalignments performance [39] in theor next misalignments in the next assembly level [40]. assembly level [40].

t

C=0 Incomplete Penetration

t

C

(a) (b)

FigureFigure 2. Case 2. Case study study parameters: parameters: (a(a)) laserlaser beambeam incident incident angle, angle, joint joint thickness, thickness, and and12 points 12 points to to measuremeasure distortion distortion (X:[0,75,150]; (X:[0,75,150]; Y:[0,5,35,40]; Y:[0,5,35,40]; Z:[0]); Z:[0]); (b) laser (b) weldlaser beadweld geometrybead geometry showing showing incomplete joint penetrationincomplete joint (in penetration which C = (in0) andwhich complete C = 0) and joint complete penetration. joint penetration.

The responses’The responses’ complete complete penetration penetration and distortionand distortion will bewill obtained be obtained through through welding welding simulation. simulation. Welding simulation using finite element analysis (FEA) calculates temperature, Welding simulation using finite element analysis (FEA) calculates temperature, distortion, and stress for distortion, and stress for the geometry under consideration [41]. Thus, a way to calculate complete the geometrypenetration under is by consideration employing the [temperature41]. Thus, a field way an tod calculatemeasuring complete the width penetration of the fusion is area by employingat the the temperaturebottom of the field joint and (see measuring weld bead thedimension width of C thein Figure fusion 2b). area Distortion at the bottom will be of measured the joint (seein Z weld beaddirections dimension forC 12in different Figure 2points,b). Distortion indicated willas dots be in measured Figure 2a.in Z directions for 12 di fferent points, indicatedTwo as dots conventional in Figure welding2a. parameters considered to have an effect on the complete penetration Twoand distortion, conventional and weldingthat can be parameters found in laser considered welding toarticles have and an eweldingffect on handbooks the complete [23,42], penetration are and distortion,welding speed and and that welding can be foundpower. in An laser ideal welding approach articles is to and weld welding with a handbooks laser beam [23angle,42], are welding speed and welding power. An ideal approach is to weld with a laser beam angle perpendicular to the joint and to consider the same joint thickness in order to have a more efficient and homogeneous Aerospace 2019, 6, x FOR PEER REVIEW 6 of 23

perpendicular to the joint and to consider the same joint thickness in order to have a more efficient and homogeneous heat transfer. However, in this aerospace context, different component geometries Aerospace 2019, 6, 74 6 of 23 incorporating different thickness values will give different accessibilities to the weld, and thus will require welding with different beam angles. heat transfer.The material However, type inand this composition aerospace context,are also di criticalfferent factors component affecting geometries the welding incorporating process diparametersfferent thickness and thus values the response will give penetration. different accessibilities Each material to the has weld, different and prop thuserties will require such as welding thermal withconductivity different beamthat will angles. affect the nature of heat transfer [37]. In this study, the material is fixed to InconelThe material718. However, type and the composition reasoning are throughout also critical the factors case a ffstudyecting can the weldingbe applied process for parametersany giving andmaterial. thus the response penetration. Each material has different properties such as thermal conductivity that willHence, affect the the control nature factors of heat affecting transfer the [37 ].responses’ In this study, complete the materialpenetration is fixed and distortion to Inconel were 718. However,identified the as reasoninglaser beam throughout power (P), theweld caseing study speed can (s),be laser applied beam for incident any giving angle material. (α), and joint/plate thicknessHence, (t). the The control last two factors parameters affecting are the deriv responses’ed from complete the component penetration variant and geometries. distortion wereOther identifiedwelding process as laser parameters beam power such (P), as welding shielding speed gas (s),flow laser rate beamand focus incident are kept angle constant. (α), and joint/plate thicknessA representation (t). The last twoof input parameters and output are parameters derived from to the the welding component process variant and geometries.their units is Othershown weldingin Figure process 3. To study parameters the effect such of asthe shielding input parameters gas flow rateon the and responses, focus are keptplates constant. of forged Inconel 718 (IN718)A representation with dimensions of input of 40 and × 300 output mm parametersand different to thicknesses the welding will process be laser and theirwelded, units varying is shown the inparameters’ Figure3. To speed, study power, the e ff ectand of beam the input incident parameters angle, as on shown the responses, in Figure plates2a. of forged Inconel 718 (IN718) with dimensions of 40 300 mm and different thicknesses will be laser welded, varying the × parameters’ speed, power, and beam incident angle, as shown in Figure2a.

] °

[ ]

α ] W mm/s Power, P [ Beam angle, Joint thickness, t [mm] Speed, s [ x1 x2 x3 x4 y1 Forged IN718 plates Laser Beam Bottom width C [mm] y2 Welding Distortion Z [mm]

Figure 3. Input parameters (control factors) vs. output parameters (responses). IN718—Inconel 718. Figure 3. Input parameters (control factors) vs. output parameters (responses). IN718—Inconel 718. 2.2. Case Specific—Conducting Physical Experiments to develop Welding Simulation 2.2. Case Specific—Conducting Physical Experiments to develop Welding Simulation The effect of tilting the laser beam and how to represent this in the simulation needs to be studied. Therefore,The effect the of purposetilting the of thelaser first beam step and within how the to block represent “Case Specific—Developmentthis in the simulation needs of Welding to be Simulation”studied. (see Figure1) is to perform physical welding experiments with di fferent beam angles. TheTherefore, objective the when purpose developing of the the first welding step with simulationin the isblock to get “Case the correct Specific—Development heat input. Thus, the of gapWelding identified Simulation” concerns (see modelling Figure the1) is e fftoect perform that tilting physical the beam welding angle experiments has on the heatwith input.different In orderbeam toangles. model this effect, there is a need to understand how the weld bead geometry changes according to differentThe beam objective angles. when The developing physical experiments the welding were simulation conducted is to forget thisthe correct purpose. heat input. Thus, the gap Theidentified materials concerns employed modelling for the the physicaleffect that experiments tilting the beam were angle two has plates on the of forged heat input. IN718 In withorder 10to model40 300 this mm effect,dimensions. there is a need To cut to downunderstand on the how cost the of theweld experiment, bead geometry two bead-on-platechanges according welds to × × (BOP-welds)different beam were angles. performed The physical in each plate.experiments A BOP-weld were conducted is a weld run for performed this purpose. on the top surface of a plateThe [37 materials]. The objective employed of the for physical the physical experiments experiment wass towere observe two plates the varying of forged weld IN718 bead with shapes 10 × depending40 × 300 mm on dimensions. the beam angles. To cut Thus, down several on the BOP cost weldsof the experiment, could be performed two bead-on-plate in the same welds plate. (BOP- welds) were performed in each plate. A BOP-weld is a weld run performed on the top surface of a The first weld was performed with a laser beam perpendicular to the plate surface (α = 0◦). The commonplate [37]. practice The objective in industry of the is to physical weld perpendicular, experiments orwas close to observe to perpendicular, the varying so thatweld less bead energy shapes is dissipateddepending from on the the beam laser angles. rays reflection. Thus, several The welding BOP welds parameter could be values performed for power in the (P) same and plate. speed (s) were realisticThe first values weld was employed performed to achieve with completea laser beam penetration perpendicular according to the to plate aerospace surface standards (α = 0°). [ PThe= 4000common W; s =practice140 mm in/ min].industry The is second,to weld third,perpendicula and fourthr, or weldsclose to were perpendicular, run with laser so that beam less incident energy is dissipated from the laser rays reflection. The welding parameter values for power (P) and speed angles (α) of 10◦, 15◦, and 19◦, respectively, as shown in Figure2a. The values of the welding speed and power were the same as those employed in the first weld. Aerospace 2019, 6, 74 7 of 23

BOP-welds were preferred in this study in order to remove any error or noise coming from the misalignment of the joint. The welding parameter values for speed and power were kept constant in the four welds to remove the effect of these parameters. A plate thickness of 10 mm was chosen to be thick enough in order to force incomplete joint penetration and observe this phenomenon in at least one of the weld cases. In addition to these four BOP-welds, historical on welds with different joint thickness (3, 6, and 8 mm) were gathered in order to support the next step, welding simulation development.

2.3. Case Specific—Developing Welding Simulation Once physical welds have been performed, the results will serve as input to develop the welding simulation, which is the second step of Block 2 in the method (See Figure1). Welding simulation is not an easy task because welding is a complex multi-physical process involving many phenomena such as heating, liquefaction, solidification, and vaporization. Thus, weld pool dynamics; heat transfer; micro-structure dynamics; and structural mechanics including stress, strain, and deformation need to be considered. In order to simulate the welding process in an industrial setting, it is typically necessary to focus on the phenomena that are most important for the scope of the analysis [43,44]. In this case, the scope is to model the effect of tilting the beam angle and to achieve the correct heat input to calculate penetration (through temperature distribution) and distortion (deformation). A standard industrial welding simulation for analysing temperature distribution, deformation, plastic strain, and stress is a thermomechanical problem, which is typically solved using the finite element method (FEM). In this study, FEM will be employed instead of analysing the dynamics of the melt pool, which would require computational fluid dynamics (CFD) using finite difference or finite volume methods. The reason for using FEM is that combining FEM and CFD is a complex problem requiring a very long simulation time, and is thus often infeasible for some industrial designs. The FEM simulation consists of three steps: first, modelling of the heat transfer; second, obtaining the transient temperature field; and third, determining the micro-structure dynamics and structural response [41,43]. To start with, some idealization needs to be made to model the heat source for taking into account the effect of tilting the beam angle. There are a number of standard heat source models including the Gaussian surface flux model proposed by Pavelic [45], the double ellipsoid model proposed by Goldak et al. [41], and the Gaussian cone heat source model [43]. The welding technology considered in this case study is laser beam welding, which produces weld beads with a “nail head” shape, as seen in Figure2b. Therefore, a combination of a Gaussian surface heat source and a cone heat source that accounts for the digging and stirring effect of the weld is considered as a potential solution to model this case [42]. Because of this idealization of the heat source, the parameters of the heat model need to be tuned with input from physical experiments. According to Goldak et al. [41], the most stringent test of the heat model is its ability to predict the fusion zone and peak temperature. Thus, the output expected from the physical experiments is the change on the weld bead geometries for different laser beam angles. In this work, the aim is to develop the welding simulation capability to cover the effect of the beam angle. Nevertheless, the goal is not to give a physical account or model for the phenomenon, but rather to give an approach on how to employ welding simulation as a design tool to provide directions to designers and manufacturing engineers. A more detailed explanation of the development of the welding simulation and the proposed heat source model is given by the authors of [46]. The potential parameters selected to define the combined heat source model are the following: 1. Efficiency: how much energy gets into the material in comparison with the exiting weld gun energy. 2. 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. 3. Depth of cone. 4. Placement of the cone. Aerospace 2019, 6, 74 8 of 23

5. Radius of the Gaussian heat source. 6. Radius of the cone heat source. The first step is to find the parameters of the heat model by fitting the model to the physical experiment for an angle of 0◦. Here, a steady state simulation of the heat transfer is employed. One assumption made is that the temperature distribution surrounding the weld gun is constant after a certain time duration once the weld starts. This enables the temperature distribution, and hence an approximation of the cross section geometry of the fusion zone, in one simulation step. The next step consists of incorporating hypotheses based on physical considerations on how the heat source would change as a function of beam angle. These are as follows: 1. 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. 2. The percentage of fusion area with respect to keyhole area changes with the parameter beam angle. The 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. 3. The decrement of efficiency is based on the growth of the fusion area as the beam angle increases. Using these considerations as the starting point, the heat model parameters would be tuned based on the results obtained from the physical experiments with different tilted angles (see step 3 in Block 2, Figure1). Once the welding simulation is validated and ready, it will be employed to perform the runs or virtual experiments designed by employing design of experiments techniques, as indicated by the steps in Block 3, see Figure1.

2.4. Virtual Design of Experiments—Designing the Experiment Matrix As described by Montgomery [47], design of experiments (DOE) is a statistical approach that allows for the determination of individual and interactive effects of various factors that can influence the output-responses. The idea is to maximize information with a minimum number of experiments. Thus, in DOE, extreme values (the so-called factor levels 1 and +1) are selected for each variable to − create the matrix of experiments. Once the experimental data were obtained, modelling techniques are applied with the objective of optimizing and analysing the robustness of the process. Within DOE, response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for modelling and optimization [48,49]. A standard RMS method used for the formation is the classical (CCD) method [48,49]. However, the problem of this case study design is that certain factor-level combinations are known in advance to be infeasible. For low thicknesses, combinations of low speed and high power values are undesirable and for high thicknesses, combinations of high speed and low power values are also undesirable, as these combination do not achieve complete penetration. The experimental regions are neither a perfect cube nor a sphere. The input values (or factor levels) of three of the factors considered cannot be varied independently. This condition makes the application of the standard CCD method unfeasible, because this method assumes that all the factors can be varied independently. Thus, with CCD, there will be factor combinations that are nonviable to perform. Therefore, to solve this problem, the optimal design approach [36,50] was proposed as a part of the virtual design of experiment method in order to find an experimental design that satisfies all constraints on the factor values (see step 1 of Block 3 in Figure1). More specifically, the custom design platform provided by the statistical data analysis software JMP® [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. Aerospace 2019, 6, x FOR PEER REVIEW 9 of 23 constraints on the factor values (see step 1 of Block 3 in Figure 1). More specifically, the custom design platform provided by the statistical data analysis software JMP® [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. By specifying linear constraints in the custom design platform, it is possible to determine the Aerospaceboundaries2019, 6of, 74 the experimental region, that is, the region of all factor-level combinations that9 of are 23 feasible. Therefore, in order to specify the linear constraint between the three input parameters (power, speed, and thickness), a regression model was built using historical data from previous By specifying linear constraints in the custom design platform, it is possible to determine the welding tests. Six different combinations of thickness, power, and speed values were used to build boundaries of the experimental region, that is, the region of all factor-level combinations that are the model. The regression model obtained is expressed in Equation (1) and represented in Figure 4a. feasible. Therefore, in order to specify the linear constraint between the three input parameters (power, The model has a coefficient of determination of R2 = 0.7, that is, adequate accuracy. The plane shown speed, and thickness), a regression model was built using historical data from previous welding tests. in Figure 4a represents the linear constraint between speed, power, and thickness, which illustrates Six different combinations of thickness, power, and speed values were used to build the model. The the experimental region. It can be observed that when thickness increases, power increases and speed regression model obtained is expressed in Equation (1) and represented in Figure4a. The model has decreases. a coefficient of determination of R2 = 0.7, that is, adequate accuracy. The plane shown in Figure4a The regression model expression connected to the plane shown in Figure 4 is as follows: represents the linear constraint between speed, power, and thickness, which illustrates the experimental region. It can be observed thatspeed when = −603.33 thickness + 0.67 increases, * power power– 166.67 increases * thickness. and speed decreases. (1)

(a) (b)

FigureFigure 4. 4.Experimental Experimental region region noncubic: noncubic: (a) linear (a) linear constraint constraint expressed expressed as a plane; as ( ba) theplane; 16 experiments (b) the 16 distributedexperiments along distributed the plane along that the defines plane the that feasible defines experimental the feasible region.experimental region.

TheOnce regression the experimental model expression region has connected been defined, to the plane the factor shown levels in Figure for 4each is as of follows: the four input parameters need to be determined. See Table 1. Factor levels are defined by extreme values (+1 and speed = 603.33 + 0.67 power 166.67 thickness. (1) −1 as coded values) representing− the of value∗ over− which these∗ parameters (or factors) will be varied. In this study, the thickness and beam angle factor levels were the first to be determined. Once the experimental region has been defined, the factor levels for each of the four input Thicknesses from 3 mm up to 15 mm are commonly employed in the geometry of aerospace parameters need to be determined. See Table1. Factor levels are defined by extreme values ( +1 and 1 components. The range of the parameter laser beam incident angel was determined from accessibility− as coded values) representing the range of value over which these parameters (or factors) will be varied. . The levels for power and welding speed represent typical values employed to weld the In this study, the thickness and beam angle factor levels were the first to be determined. Thicknesses preselected thickness range. All values presented in Table 1 were corroborated with welding from 3 mm up to 15 mm are commonly employed in the geometry of aerospace components. The range engineers. of the parameter laser beam incident angel was determined from accessibility evaluations. The levels for power and welding speed represent typical values employed to weld the preselected thickness Table 1. Factor levels for design and welding parameters. range. All values presented in Table1 were corroborated with welding engineers. Level −1 Level +1 Table 1. FactorPower, levels P (W) for design and 2100 welding 5100 parameters. Speed, s (mm/min) 40 900 Level 1 Level +1 Thickness, t (mm) − 3 15 Power, PBeam(W) angle, α (°) 2100 0 25 5100 Speed, s (mm/min) 40 900 Thickness, t (mm) 3 15 Beam angle, α (◦) 0 25

The input parameter values or factor levels shown in Table1 together with the linear constraint expressed in Equation (1) were added to the custom design platform at JMP. The resulting design matrix is shown in Table2 and contains 16 runs, that is, experiments. Figure4b shows how the di fferent Aerospace 2019, 6, x FOR PEER REVIEW 10 of 23

The input parameter values or factor levels shown in Table 1 together with the linear constraint expressed in Equation (1) were added to the custom design platform at JMP. The resulting design matrix is shown in Table 2 and contains 16 runs, that is, experiments. Figure 4b shows how the Aerospacedifferent2019 experiments, 6, 74 are spread in the experimental design space according to the linear constraint,10 of 23 which illustrates the design matrix in a 3D model. experiments are spread in the experimental design space according to the linear constraint, which illustrates the design matrix inTable a 3D 2. model. Design matrix containing the 16 runs. Experiment (Run) Speed (mm/min) Power (W) Beam Angle (°) Thickness (mm) 1 Table40 2. Design matrix3582.4 containing the 16 runs.25 9.5 2 40 5100 0 1.9 Experiment (Run) Speed (mm/min) Power (W) Beam Angle (◦) Thickness (mm) 3 40 5100 25 14.9 1 40 3582.4 25 9.5 24 40536.3 5100 0 011.95 1.9 35 4040 5064.9 5100 12.5 25 15 14.9 46 536.3900 3270.3 5100 0 0 11.953 57 4040 5064.92100 12.50 3.8 15 6 900 3270.3 0 3 8 470 5100 25 12.35 7 40 2100 0 3.8 89 470900 5100 25 25 9.97 12.35 910 900900 5100 0 25 9.97 9.97 1011 900370.3 3808.2 5100 12.5 0 8.17 9.97 1112 370.3456.6 2497.2 3808.2 25 12.5 8.173 12 456.6 2497.2 25 3 1313 4040 3582.4 0 09.5 9.5 1414 4040 2100 25 25 3.8 3.8 1515 642.1642.1 2798.1 0 03 3 1616 900900 3270.3 25 25 3 3

2.5. Virtual Design of Experime Experiments—Performingnts—Performing Welding Simulations The 16 runs runs (see (see Figure Figure 4b4b and Table Table 22),), whichwhich areare the result of of applying applying the the optimal optimal design design of ofexperiments experiments approach, approach, will will be performed be performed with with weld weldinging simulations simulations (see (seesecond second step stepof Block of Block 3 in 3Figure in Figure 1). BOP-welds1). BOP-welds will be will simulated be simulated in comput in computerer aided aideddesign design (CAD) (CAD) plate models plate models with similar with similardimensions dimensions as the plates as the employed plates employed in the physical in the experiments. physical experiments. The CAD Theplates CAD are 40 plates × 150 are mm 40 as × 150width mm × length as width dimensions,length dimensions, varying the varying plate thickne the platess according thickness to according the values to thein Table values 2. inHaving Table2 a. × Havingplate CAD a plate model CAD of half-length model of half-length (physical (physicalplate leng plateth was length 300 mm) was 300did mm)not affect did not the aresults,ffect the because results, becausethe interest the interestwas to wascompare to compare the weld the weld bead bead geom geometriesetries between between simulation simulation results results and and physical welds—instead, it saved computational time.time. The CAD models were createdcreated usingusing anan FEFE softwaresoftware andand variationvariation simulationsimulation RD&TRD&T®® [[52].52]. In Figure5 5,, anan exampleexample ofof aa 99 mmmm plateplate modelmodel andand itsits corresponding corresponding meshmesh isis shown. shown. TheThe elementelement sizesize around the weld pathpath isis approximatelyapproximately 11 × 1 × 11 mm. mm. For For every every CAD CAD model, model, the the elements elements are adjusted × × for the didifferentfferent thicknessesthicknesses so thatthat eacheach layerlayer ofof thethe meshmesh hashas thethe samesame dimension.dimension. The elements further away from the weld path are larger elements,elements, asas nono big gradients are expected.expected. The mesh size was validatedvalidated usingusing aa smaller smaller mesh, mesh, in in which which each each element element was was approximately approximately 0.5 0.5 times times the the size size of the of originalthe original mesh. mesh. No No significant significant change change was was observed. observed.

® FigureFigure 5.5. Example of a 9 mm plate modelmodel andand meshmesh withwith fixturefixture points.points. Image fromfrom RD&TRD&T® [52].[52].

The welding simulation is a transient simulation. First, the temperature history is calculated and then the mechanical response is calculated. In this work, microstructure dynamic has not been considered because it is assumed to have only a minor effect on the result [43]. Adaptive time stepping Aerospace 2019, 6, x FOR PEER REVIEW 11 of 23

The welding simulation is a transient simulation. First, the temperature history is calculated and then the mechanical response is calculated. In this work, microstructure dynamic has not been Aerospaceconsidered2019 , because6, 74 it is assumed to have only a minor effect on the result [43]. Adaptive11 time of 23 stepping is employed with a minimum time step of 0.1 s. This means that during welding, the time isstep employed is forced with to be a minimum0.1 s, and timegrows step after of 0.1the s. weld This is means finished that when during temperature welding, the gradients time step are is forceddecreasing. to be 0.1 s, and grows after the weld is finished when temperature gradients are decreasing.

3. Results The description and analysis of the experimental and virtual results from applying the virtual design of of experiment experiment method method in in the the aerospace aerospace case case are are provided provided in this in thissection. section. There There are three are threemain mainresults: results: (1) physical (1) physical welding welding experiments experiments (see block (see 2 block in Figure 2 in Figure1); (2) 1a); new (2) acombined new combined heat source heat sourcemodel modelto cover to coverthe effect the eofffect tilting of tilting the beam the beam angle angle (see (see block block 2 in 2 inFigure Figure 1);1); and and (3) the weldingwelding simulation results and the subsequent meta-modelmeta-model andand analysesanalyses (see(see blockblock 33 inin FigureFigure1 1).).

3.1. Physical Experiments Results Physical welding tests were performed as described in Section 2.2 (see also step 1 of Block 2 in Figure1 1)) in in order order to to develop develop the the welding welding simulation simulati andon tuneand tune the parameters the paramete of thers of heat the source heat modelsource tomodel cover to the cover effect the of tiltingeffect theof lasertilting beam the incidentlaser beam angle. incident The results angle. from The the results welding from experiments the welding are shownexperiments in Figure are6 shown. An etch in Figure test has 6. been An etch applied test ha tos the been BOP-welds applied to to the reveal BOP-welds the weld to bead reveal geometries. the weld Thisbead testgeometries. involved This cutting test each involved specimen cutting transverse each sp toecimen the weld transverse axis and to applying the weld an axis etching and applying solution withan etching oxalic acidsolution at 6 Vwith over oxalic 20 s, whichacid at allowed 6 V over inspecting 20 s, which the exposeallowed surface. inspecting This the method expose is adequate surface. forThis determining method is adequate the fusion for area, determining thus assessing the fusion incomplete area, thus penetration. assessing Two incomplete transversal penetration. cross sections Two weretransversal made forcross each sections of the were four BOP-welds,made for each which of the can four be BOP-welds, seen in Figure which6a. can be seen in Figure 6a.

Power = 4000 W; Speed = 140 mm/min Weld 0° Weld 10° Weld 15° Weld 19°

AC

A K Weld 0° Weld 10° Weld 15° Weld 19°

(a) (b)

Figure 6. (a(a) )Cross Cross sections sections of of the the four four BOP-welds. BOP-welds. Each Each cross cross section section has hasbeen been replicated replicated twice. twice. (b) (Genericb) Generic representation representation of a oflaser a laser weld weld bead, bead, which which can canbe divided be divided in two in twomain main areas: areas: conduction conduction area

area(AC) and (AC )keyhole and keyhole area (A areaK). (AK).

Looking at the cross sections in Figure6 6a,a, itit cancan bebe observedobserved thatthat thethe weldweld beadbead geometrygeometry ofof thisthis type ofof laserlaser weldweld can can be be divided divided into into two two main main areas, areas, named named in thisin this article article as the as conductionthe conduction area (AareaC) and(AC) keyholeand keyhole area (AareaK); (A seeK); Figure see Figure6b. 6b. The conduction area is similar to the weld bead geometry that is obtained when welding is run in conduction . The The keyhole keyhole area area represents represents the the actual effect effect of the keyhole, when material is vaporized andand the the energy energy from from the the laser laser is directly is dire deliveredctly delivered into the into material. the material. These two These areas two together areas representtogether represent the “nail the head” “nail shape head typical” shape of typical laser welds. of laser welds. In order to know how these two areas change in relation to the laser beam incident angle, the total, conduction, and keyhole areas of the eight cross sections shown in Figure6a were measured three times each. The relation of each of these areas to the beam incident angle is shown in Figure7. Aerospace 2019, 6, x FOR PEER REVIEW 12 of 23

In order to know how these two areas change in relation to the laser beam incident angle, the total, conduction, and keyhole areas of the eight cross sections shown in Figure 6a were measured Aerospace 2019, 6, 74 12 of 23 three times each. The relation of each of these areas to the beam incident angle is shown in Figure 7.

Figure 7. RelationshipRelationship between between the the laser laser beam beam incident incident angle angle (degrees) (degrees) and the total, conduction, and keyhole areas of the weld bead (mm2),), as as described described in in Figure Figure 66b.b. Image producedproduced inin JMPJMP®. .

In Figure Figure 77,, thethe graphgraph showsshows thethe regressionregression lineslines andand confidenceconfidence intervalsintervals (CI)(CI) forfor thethe weldweld beadbead 2 total areas, as well as the key hole andand fusionfusion areas.areas. The values of R2 indicate good adequacy of of the models. Looking at thethe regressionregression lines, lines, it it can can be be observed observed that that the the larger larger the the beam beam incident incident angle, angle, the thelarger larger the conductionthe conduction area andarea theand smaller the smaller the keyhole the keyhole area. However, area. However, there is there a distinction is a distinction between betweenthe effect the of the effect angle of onthe bothangle areas. on both The areas. conduction The conduction area increases area linearly increases from linearly angle 0from◦, whereas angle the0°, whereaskeyhole areathe keyhole starts to area decrease starts quadratically to decrease quadratically from angle 5–10 from◦. angle 5–10°.

3.2. Heat Source Model to Cover the E ect of the Laser Beam Angle 3.2. Heat Source Model to Cover the Effectff of the Laser Beam Angle On the basis of the experiment results (see Figure 66a)a) andand inin keepingkeeping withwith thethe initialinitial hypothesishypothesis Aerospace 2019, 6, x FOR PEER REVIEW 13 of 23 given in in the the end end of of the the Subsection Section 2.3 2.3,, a a new new combined combined heat heat model model was was proposedproposed (see(see FigureFigure8 8)) toto reproduce the the fusion fusion zone zone according according to to the the observ observeded “nail “nail head” head” shape. shape. The Theproposed proposed combined combined heat generic heat model (see Figure 8), and functions relating these parameters with beam incident angle modelheat model is the is result the result of the of thesecond second step step of ofBloc Blockk 2 2in in Figure Figure 1,1, called “Developing thethe weldingwelding were included in the simulation code. simulation capability”. The solution adopted in order to get a reasonable fit of the model was to reverse the cone and employ the placement of this cone as a parameter, as shown in Figure 8. Above and below the cone, the heat input is set to 0. Additional parameters that also relate to the heat model geometry such as depth of cone, radii of the Gaussian and cone heat sources, as well as the parameters’ and percentage of energy were been tuned. The weld bead shapes shown in Figure 6a and the analysis obtained from the graph in Figure 7 supported the tuning process. An extended description of this process can be found in the work of [46]. During the tuning process (step 3 of Block 2 in Figure 1), parameter values for the nominal case (angle 0°) were first obtained. Thereafter, the parameter values for the angle tilted cases were fitted, employing the nominal case values as a starting point. From this tuning process, it can be concluded that the first hypothesis presented in the end of Section 2.2 with regards to changing the radii parameters values had no significant effect on penetration. Instead, it was found that the parameters that led to major changes on penetration were the placement and depth of the cone, and the efficiency. Therefore,FigureFigure to 8.8. Combinedcapture the heat effect source of model the beam with geometrical angle, these parameters parameters as proposed were incorporatedin the work of [46]. [into46]. the

PP == placement of thethe cone.cone. D == depth of the cone.cone. r1 and r 2 are the radii of Gaussian and conecone heatheat sources,sources, respectively.respectively.

The same procedure was repeated in order to capture the effect of increasing the thickness. A set of experiments performed with the weld gun perpendicular to the base metal for different thicknesses was employed to fit the parameters. The result showed that by varying the efficiency, the depth, and the placement of the cone, it was possible to reproduce the experimental results in simulation. The dependency of these parameters on plate thickness and tilted angle was modeled by heuristic mathematical models. To validate the simulation model (last step of Block 2 in Figure 1), seven simulations with the same input values as the physical experiments described in the Section 2.2 were conducted. The results of the validation process can be observed in Figure 9.

Thickness validation (Angle 0°)

Thickness 3 mm Thickness 6 mm Thickness 8 mm

Angle validation (Thickness 10 mm)

Angle 0° Angle 10° Angle 15° Angle 19°

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

According to Goldak et al. [41] (p. 122), the most stringent test of a heat model is its ability to predict the fusion zone. Thus, looking at Figure 9, it can be observed that the simulated fusion zones match the real test fusion zones. It can be noted that the simulation model proposed was based upon eight experimental results and re-used historical results. However, this is typically the case in industry, in which there is a need

Aerospace 2019, 6, x FOR PEER REVIEW 13 of 23 generic heat model (see Figure 8), and functions relating these parameters with beam incident angle were included in the simulation code. Aerospace 2019, 6, 74 13 of 23

The solution adopted in order to get a reasonable fit of the model was to reverse the cone and employ the placement of this cone as a parameter, as shown in Figure8. Above and below the cone, the heat input is set to 0. Additional parameters that also relate to the heat model geometry such as depth of cone, radii of the Gaussian and cone heat sources, as well as the parameters’ efficiency and percentage of energy were been tuned. The weld bead shapes shown in Figure6a and the analysis obtained from the graph in Figure7 supported the tuning process. An extended description of this process can be found in the work of [46]. During the tuning process (step 3 of Block 2 in Figure1), parameter values for the nominal case (angle 0◦) were first obtained. Thereafter, the parameter values for the angle tilted cases were fitted, employing the nominal case values as a starting point. From this tuning process, it can be concluded that the first hypothesis presented in the end of Section 2.2 with regards to changing the radii parameters values had no significant effect on penetration. Instead, it was found that the parameters that ledFigure to major8. Combined changes heat on source penetration model with were geometrical the placement parameters and depth as proposed of the cone, in the and work the of e[46].fficiency. Therefore,P = placement to capture of the the cone. effect D of = thedepth beam of the angle, cone. these r1 and parameters r2 are the radii were of incorporated Gaussian and into cone the heat generic sources, respectively. heat model (see Figure8), and functions relating these parameters with beam incident angle were included in the simulation code. The same procedure was repeated in order to capture the effect of increasing the thickness. A The same procedure was repeated in order to capture the effect of increasing the thickness. A set set of experiments performed with the weld gun perpendicular to the base metal for different of experiments performed with the weld gun perpendicular to the base metal for different thicknesses thicknesses was employed to fit the parameters. The result showed that by varying the efficiency, the was employed to fit the parameters. The result showed that by varying the efficiency, the depth, depth, and the placement of the cone, it was possible to reproduce the experimental results in and the placement of the cone, it was possible to reproduce the experimental results in simulation. simulation. The dependency of these parameters on plate thickness and tilted angle was modeled by The dependency of these parameters on plate thickness and tilted angle was modeled by heuristic heuristic mathematical models. mathematical models. To validate the simulation model (last step of Block 2 in Figure 1), seven simulations with the To validate the simulation model (last step of Block 2 in Figure1), seven simulations with the same input values as the physical experiments described in the Section 2.2 were conducted. The same input values as the physical experiments described in the Section 2.2 were conducted. The results results of the validation process can be observed in Figure 9. of the validation process can be observed in Figure9.

Thickness validation (Angle 0°)

Thickness 3 mm Thickness 6 mm Thickness 8 mm

Angle validation (Thickness 10 mm)

Angle 0° Angle 10° Angle 15° Angle 19°

FigureFigure 9. ValidationValidation of the simulation with with the the physical physical welds welds for for the the different different beam incident angles andand thicknesses. thicknesses.

AccordingAccording to to Goldak et et al. [41] [41] (p. 122), 122), the the most most stringent stringent test test of of a a heat heat model model is is its ability to predict the fusion zone. Thus, Thus, looking looking at at Figure Figure 99,, itit cancan bebe observedobserved thatthat thethe simulatedsimulated fusionfusion zoneszones matchmatch the real test fusion zones. ItIt can can be be noted that the simulation model prop proposedosed was based upon eight experimental results andand re-used re-used historical results. results. Howe However,ver, this this is is typically typically the the case case in in industry, industry, in which there there is a a need need to make the best assumption based on the data available. The same applies to the expression of uncertainties and the measurements required to get high fidelity in the virtual results. Aerospace 2019, 6, x FOR PEER REVIEW 14 of 23 Aerospace 2019, 6, 74 14 of 23

to make the best assumption based on the data available. The same applies to the expression of 3.3.uncertainties Virtual Experiments and the measurements Results and Meta-Model required to get high fidelity in the virtual results.

3.3. VirtualIn this Experiments section, the Results statistical and Meta-Model analysis and modelling from the virtual experiment’s (welding simulations) results will be presented (see last step of Block 3 and analyses in Figure1). The complete tableIn containing this section, all the the simulation statistical resultsanalysis can and be foundmodelling in Appendix from theA .virtual experiment’s (welding simulations)The first results step of will modelling be present is toed determine (see last step which of areBlock the 3 main and an factorsalyses and in Figure interactions 1). The that complete do not havetable acontaining significant all eff theect simulation on the responses, results andcan removingbe found in them Appendix from the A. model. UsingThe first the step statistical of modelling software is JMPto determine® [51], the whic responseh are functionthe main (meta-model)factors and interactions for the weld that bead do dimensionnot have a Csignificant was obtained effect after on the reducing responses, the modelsand removing and can them be expressed from the asmodel. in Equation (2): Using the statistical software JMP® [51], the response function (meta-model) for the weld bead dimension C was obtainedC = 0.9 after0.62 reducing thickness the mode0.096ls beam and can angle be +expressed0.002 power. as in Equation (2): (2) − − C = 0.9 – 0.62 thickness – 0.096 beam angle + 0.002 power. (2) The bottom width response function, C = f (thickness, beam angle, power), is a first order polynomialThe bottom equation. width Thus, response no interaction function, is significant.C = f (thickness, Significant beam factors angle, are power), beam angle,is a first thickness, order andpolynomial power. equation. In this case, Thus, the no speed interaction is not a is significant significant. factor Significant because factors it is determinedare beam angle, by the thickness, values ofand thickness power. In and this power case, accordingthe speed is to not the a constraint significan expressedt factor because in Equation it is determined (1), which by represents the values the of experimentalthickness and region. power according to the constraint expressed in Equation (1), which represents the experimentalThe analysis region. of of the mathematical model is presented in Table3. The values of F ratio and RThe2 assess analysis the adequacyof variance of of the the model, mathematical indicating model that is this presented model is in adequate. Table 3. The values of F ratio and R2 assess the adequacy of the model, indicating that this model is adequate. Table 3. (ANOVA) for testing the adequacy of models. Table 3. Analysis of variance (ANOVA) for testing the adequacy of models. Sum of Squares Degrees of Freedom Bead Parameters F-Ratio R2 Model Adequacy RegressionSum of Squares Residual Regression Degrees of ResidualFreedom Bead Parameters F-Ratio R2 Model Adequacy Bottom width C Regression49.74 Residual 12.73 Regression 3 Residual 12 15.6242 0.80 Adequate Bottom width C 49.74 12.73 3 12 15.6242 0.80 Adequate

Figure 10 shows the actual versus predicted plot. This plot works as a visual aid to also understand Figure 10 shows the actual versus predicted plot. This plot works as a visual aid to also the accuracy of the model by relating observed (actual) values to predicted values. Ideally, the points understand the accuracy of the model by relating observed (actual) values to predicted values. should be close to the red diagonal line. The red band represents the confidence intervals. The blue line Ideally, the points should be close to the red diagonal line. The red band represents the confidence indicates the average. The coefficient of determination R2 = 0.80 (RSq in graph legend) and p-value = intervals. The blue line indicates the average. The coefficient of determination R2 = 0.80 (RSq in graph 0.0002 indicate adequate accuracy of the model. legend) and p-value = 0.0002 indicate adequate accuracy of the model.

Figure 10. Actual by predicted for bottom width C (penetration).(penetration).

The firstfirst analysisanalysis that that can can be be derived derived from from the the weld weld bead bead dimension dimension response response function, function, Equation Equation (2), regards(2), regards the significance the significance of the of beam the anglebeamparameter. angle parameter. From the From case the results case and results meta-model, and meta-model, designers designers and process engineers can know that beam angle has an effect on joint penetration (represented by the parameter bead bottom width C).

Aerospace 2019, 6, 74 15 of 23

andAerospace process 2019 engineers, 6, x FOR PEER can know REVIEW that beam angle has an effect on joint penetration (represented by 15 the of 23 parameter bead bottom width C). Therefore,Therefore, the the upcoming upcoming questions questions designers designers might migh raiset raise related related to to thickness thickness and and beam beam angle, angle, whichwhich aff ectsaffects component component accessibility, accessibility, are are as follows:as follow Whichs: Which combinations combinations of of joint joint thicknesses thicknesses and and beambeam angles angles do do not not achieve achieve complete complete penetration? penetration? Which Which values values of of these these parameters parameters give give a morea more stablestable result? result? Which Which are are the the optimal optimal values? values? These These threethree questionsquestions concernconcern analysesanalyses with regards to toinfeasible regions, robustness,robustness, andand optimizationoptimization (see(see last last part part of of the the virtual virtual design design of of experiment experiment methodmethod presented presented in Figurein Figure1). 1).

3.3.1.3.3.1. Infeasible Infeasible Region Region for for Complete Complete Penetration Penetration ToTo represent represent the the infeasible infeasible region,region, the the graphical graphical technique technique contour contour plot plot was was applied. applied. The contour The contourplot in plot Figure in Figure 11 represents 11 represents the isolines the isolines of the of response the response surface surface bead bead bottom bottom width width C onC onthe the two- two-dimensionaldimensional plane plane defined defined by by the the para parametersmeters beambeam angleangle andand thickness. thickness.C Cvalues values approximately approximately belowbelow 2 mm2 mm can can be be considered considered unacceptable, unacceptable, that that is, is, requirements requirements on on complete complete penetration penetration are are not not fulfilled.fulfilled. Thus, Thus, all all the the isolines isolines with with values values below below 2 mm2 mm are are coloured coloured in in red. red. The The rest rest of of the the isolines isolines areare blue, blue, which which represents represents the the combination combination of thicknessof thickness and and beam beam angle angle values values that that fulfil fulfil penetration penetration requirements.requirements. On On the the basis basis of of these these requirements, requirements, the th infeasiblee infeasible region region has has been been marked marked by by colouring colouring it init lightin light red. red.

Figure 11. Contour plot for bottom width C on the two-dimensional space formed by the parameters 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. thickness and beam angle. Infeasible region for complete penetration are coloured in light red. For example, thickness values between 12 and 15 mm cannot be welded with angles above For example, thickness values between 12 and 15 mm cannot be welded with angles above approximately 13◦. Thus, all aero component geometries containing these thickness values will have approximately 13°. Thus, all aero component geometries containing these thickness values will have accessibility problems, because only low beam angles will be feasible to perform the weld and achieve accessibility problems, because only low beam angles will be feasible to perform the weld and achieve complete penetration. complete penetration. 3.3.2. Robustness and Optimization of Input Parameters towards Penetration 3.3.2. Robustness and Optimization of Input Parameters towards Penetration Profiles of the response surface for bottom width C were employed to analyse robustness and performProfiles optimization, of the response following surface the gradient for bottom descent width algorithm C were employed implemented to analyse in JMP ®robustness. Figure 12 and ® showsperform these optimization, profiles with blackfollowing straight the lines, gradient which descent represent algorithm cross sections implemented of the response in JMP surface. Figure for 12 twoshows different these thickness profiles with values, black 6 mm straight (Figure lines, 12 a)whic andh represent 10 mm (Figure cross sections12b). The of greythe response areas around surface thesefor crosstwo different sections thickness represent values, statistical 6 mm errors. (Figure 12a) and 10 mm (Figure 12b). The grey areas around these cross sections represent statistical errors. To optimize the input parameters beam angle and power for each of the thicknesses, an optimization criterion needs to be defined for the response bottom width C (representing joint penetration).

AerospaceAerospace 20192019,, 66,, x 74 FOR PEER REVIEW 1616 of of 23 23

(a)

(b)

FigureFigure 12. ProfilesProfiles ofof the the response response surface surface for optimizingfor optimizing bottom bottom width widthC (penetration) C (penetration) for two for diff erenttwo ® differentthickness thickness values: ( avalues:) 6 mm (a thickness;) 6 mm thickness; (b) 10 mm (b) thickness. 10 mm thickness. Image taken Image from taken JMP from® prediction JMP prediction profile. profile. To optimize the input parameters beam angle and power for each of the thicknesses, an optimization criterionThe straight needs to green be defined lines “Upper” for the response and “Lower” bottom that width appearC (representing in Figure 12 represent joint penetration). the upper and lowerThe specification straight green limits lines set “Upper”for the dimension and “Lower” bottom that width appear C in. In Figure this example, 12 represent the objective the upper is and to matchlower a specification target around limits 4 mm set in for order the dimensionto achieve a bottom reasonable width penetration.C. In this example, the objective is to matchThe a targetoptimized around values 4 mm for in the order input to parameters achieve a reasonable appear in penetration.each of the thickness graphs in Figure 12 in Thered optimizedcolour. These values values for the are input based parameters on the optimization appear in each criterion of the and thickness the predictive graphs in response Figure 12 functionin red colour. already These built. values For example, are based if on considering the optimization a geometry criterion with and a thethickness predictive of 6 response mm (see function Figure 12a),already the built.optimal For beam example, angle ifand considering power are a 16.51° geometry and with4408 aW, thickness respectively. of 6 mmThus, (see the Figure bottom 12 widtha), the Coptimal optimal beam value angle is 4.5 and mm, power also indicated are 16.51◦ inand red 4408 colour. W, respectively. Thus, the bottom width C optimal valueIn is addition, 4.5 mm, a also robustness indicated analysis in red colour.can be performed by examining either the slope of these profile responsesIn addition, or the purple a robustness triangles analysis that appear can be performedin the graphs. by examining The desirabilit eithery thegraphs slope (graphs of these located profile inresponses the second or therow purple of each triangles Figure that12a,b) appear also ingive the a graphs.sense of The robustness. desirability Desirability graphs (graphs graphs located are a piecewisein the second function row generated of each Figure by the 12 statisticala,b) also givesoftware a sense JMP of® that robustness. pass through Desirability three control graphs points are a definedpiecewise by functionthe optimization generated criterion. by the statistical Looking softwareat these indicators, JMP® that passit can through be observed, three controlfor example, points thatdefined for the by 6 the mm optimization thickness graph criterion. in Figure Looking 12a atand these optimal indicators, values it of can power be observed, and beam for angle, example, the response C is more robust towards beam angle than towards power. This conclusion could support

Aerospace 2019, 6, x FOR PEER REVIEW 17 of 23

Aerospace 2019, 6, 74 17 of 23 the designers’ and welding engineers’ decision regarding which parameters can be stricter and which can be more flexible. that for the 6 mm thickness graph in Figure 12a and optimal values of power and beam angle, the 3.3.3.response Response C is more Surface robust for towards Distortion beam angle than towards power. This conclusion could support the designers’In the andsame welding way as engineers’for joint penetration, decision regarding a response which surface parameters for distortion can be in stricter the Z anddirection which was can obtainedbe more flexible.from the virtual experiment results. In this particular case, the significant individual factors were thickness, beam angle, power, and Coord_PX (representing the position along the X axis of the 3.3.3. Response Surface for Distortion points selected to measure distortion). Figure 13a shows the 3D representation of the response surface for a constantIn the same beam way angle as for and joint power. penetration, The dots a repr responseesent surfacethe actual for virtual distortion experiment in the Z results.direction From was thisobtained figure, from it can the virtualbe observed experiment that there results. are In two this particulardifferent distortion case, the significant modes depending individual on factors the thicknesswere thickness, values. beam angle, power, and Coord_PX (representing the position along the X axis of the pointsThis conclusion selected to can measure serve designers distortion). and Figure welding 13a engineers shows the in 3D knowing representation that for of low the thickness response values,surface the for adistortion constant beamin the angle middle and of power. the plat Thee dots(Coord_PX represent = the0.75 actual mm) virtualis positive experiment and for results. high thicknessFrom this values, figure, it it is can negative. be observed that there are two different distortion modes depending on the thickness values.

(a) (b)

FigureFigure 13. Response surfacesurface distortion distortion in in the theZ direction.Z direction. (a) Actual(a) Actual response response surface surface for specific for specific values valuesof power of power and beam and angle.beam (angle.b) Sections (b) Sections of the response of the response surface surface for thicknesses for thicknesses of 3 mm of and 3 mm 8 mm. and 8 mm. This conclusion can serve designers and welding engineers in knowing that for low thickness values,A key the distortionfinding was in thethat middle the standard of the plate model (Coord_PX assumption= 0.75 of quadratic mm) is positive terms and for forresponse high thickness surface didvalues, not itcapture is negative. all distortion modes. Thus, a screening in JMP [51] of higher order needed to be performed.A key findingThis screening was that revealed the standard that the model inte assumptionractions between of quadratic quadratic terms terms for responseand individual surface factorsdid not are capture significant. all distortion By adding modes. these Thus, terms a screeningto the model, in JMP it was [51] ofpossible higher to order capture needed the totwo be distortionperformed. modes, This screeningas shown in revealed Figure 13a. that the interactions between quadratic terms and individual factorsThe are graphs significant. in Figure By adding 13b show these sections terms to of the the model, response it was surface possible (profiles) to capture for the3 mm two and distortion 8 mm thicknesses.modes, as shown In thein 3 Figuremm thickness 13a. graph, it is possible to find values of beam angle and power that can compensateThe graphs the in Figuredistortion 13b along show the sections X axisof almost the response to zero. However, surface (profiles) for higher for thickness 3 mm and values, 8 mm asthicknesses. shown in the In thegraph 3 mm for thickness8 mm, it is graph, not possible it is possible to compensate to find values the distortion, of beam angle but it and is possible power that to minimizecan compensate it. the distortion along the X axis almost to zero. However, for higher thickness values, as shown in the graph for 8 mm, it is not possible to compensate the distortion, but it is possible to 4.minimize Discussion it.

4. DiscussionThe results of this article can be discussed in regards to two findings. The first finding involves the results of the aerospace case investigation, that is, the results from the physical welding tests, creationThe of results a new of heat this articlesource can model, be discussed simulation in regards results, to and two subsequent findings. The statistical first finding modelling involves and the analysis.results of The the second aerospace finding case investigation,involves the proposed that is, the virtual results design from theof experiments physical welding method. tests, creation of a new heat source model, simulation results, and subsequent statistical modelling and analysis. The second finding involves the proposed virtual design of experiments method.

Aerospace 2019, 6, 74 18 of 23

4.1. Discussion of the Results A simplified case was employed to investigate the main and interaction effects of a number of design and welding parameters that are relevant within an aerospace welding context. Physical welding tests, more precisely, four bead-on-plate welds (BOP), were performed to understand the effect of tilting the laser beam with different angles into the weld bead geometry. The objective was to cover this phenomenon with the welding simulation. An angle of 5◦ was known in advance to give an acceptable and similar behavior as an angle of 0◦ from welding expert knowledge. Thus, the interest was to test angles over 10◦. Limited resources and high costs permitted the making of only four BOP-welds. In addition, the experimental set-up, because of safety reasons, only allowed programming of the robot to weld at a maximum angle of 19◦. These conditions represent limitations when developing the welding simulation. At the same time, the robot safety limitation leads to virtual experiments and simulation as the way to move forward in order to understand the capability of the welding technology and to be able to explore angles above 19◦. The downside is that simulation does not represent a complete answer to reality. Nevertheless, there is the potential to gain more fidelity in the simulation model by, for example, incorporating fluid dynamics into the weld pool. Besides the absolute values of virtual experiments’ results, the main finding in this study is how these results served to demonstrate that a statistical model can be built with welding simulation to understand the effect of the interaction between design and welding parameters. With this meta-model at hand, infeasible regions for welding producibility can be found and an optimization and robustness analysis can be performed during the design phases.

4.2. Discussion of the Method The virtual design of experiments method was proposed to model the effect of design and welding parameter combinations (see Figure1). In the method, DOE techniques are combined with welding simulation. The DOE technique optimal design was selected instead of the classical central composite design (CCD), as the experimental region is constrained. Certain combinations of design and welding parameters are known in advance to be unfeasible. This is a common case in aerospace components that are welded, for which a strong interaction between product geometry and welding process exists. Thus, the incorporation of the thickness parameter into the design matrix together with the rest of factors was possible with optimal design. Otherwise, a CCD would have been needed for each of the thicknesses that required investigation. Suppose that three thicknesses were included in the analysis; thus, three design matrices with 16 runs each would have been needed. Instead, with the proposed approach, the total number of runs decreased by more than 50%, and the thickness factor interactions were taken into consideration. The optimization technique applied in this article is the gradient descent algorithm. This is the algorithm implemented in the statistical software used (JMP®). 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. In the case presented in this research, because the response function is already determined using the response surface methodology, the gradient descent algorithm can be applied. As a result, the global optimum can be found for a low calculation cost. A similar approach was presented by Fraser et al. [54]. In this study, the exterior penalty method was applied after having applied the response surface method. Nevertheless, future work can compare the performance of evolutionary optimization algorithms to the optimization presented in this article for the same case study. Aerospace 2019, 6, 74 19 of 23

Moreover, the benefits of combining DOE with welding simulation are multiple. One advantage is that simulation allows for performance of a larger number of runs (or virtual experiments) in a very short time in comparison with physical testing. Modelling welding also gives more extended and detailed information concerning welding phenomena, such as the heat distribution and the relationship with welding process parameters. Thus, more information is gained at a lower cost, as also argued by Goldak et al. [41]. In addition, with welding simulation, virtual experiment runs are performed with the exact numbers given in the design matrix, thus removing input factors’ variation. Errors in the responses and measurement uncertainties also disappear. On the other hand, there is the gap between simulation and reality. As discussed earlier, the simulation results in this article do not represent a complete answer to reality. Nevertheless, the aim was to present an engineering method to solve these related problems that appear in this type of industrial context. Still, there is room for improvement, which justifies further research by, for example, incorporating more physics into the simulation model. Future research can also take into consideration input material variation. Currently, the simulation considers nominal plate dimensions. However, it is possible to add variation to the input parameters and analyse the effect on the responses. With regards to validation, future work can incorporate additional physical welds of some of the 16 runs defined in the experimental matrix, which were performed with simulation.

5. Conclusions The key contribution of this article is the proposed virtual design of experiment method presented in Figure1. By applying this method in the aero-context case, it was possible to build a statistical meta-model employing welding simulation that has allowed the following:

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.

The virtual design of experiments method proposed in this article combines the benefits of experimental design and DOE with the benefits from simulation. The incorporation of DOE techniques allows for the modelling of the effects of input factors (design and welding parameters) into responses (weld quality criteria), as well as the study of possible interactions between input factors with a minimum number of experiments. The objective in DOE is to maximize information while minimizing efforts. Applying optimal design as a DOE technique leads to custom-built experimental designs for specific settings and constraints, which allows the adaptation of the experimental design to the specific characteristics of the study problem and not vice versa. With optimal design, experimental regions that are constrained because of dependencies between input factors can be investigated, which is a common scenario when investigating product design–welding systems interactions. The incorporation of simulation into the method enables the capacity for gaining an understanding of the welding process during the product design phases, thus supporting decision making. Executing experimental design with virtual experiments allows for a larger number of runs and factor combinations than when doing physical testing. Welding simulation can also provide detailed representation of welding phenomena, that is, the heat distribution. Thus, this meta-model approach allows access to more results and information, reducing evaluation time and cost. In conclusion, the virtual design of experiment method proposed in this article will bring the benefit of performing fast evaluations concerning the welding producibility of a number of design variants during early phases of multidisciplinary design of aerospace components. In this manner, a rapid answer can be provided to the OEM about the design and manufacture feasibility of a component variant. Aerospace 2019, 6, 74 20 of 23

An additional contribution to the welding simulation field is the application of the combined heat Aerospace 2019, 6, x FOR PEER REVIEW 20 of 23 source model to cover the effect of tilting the laser beam incident angle. welding experiments were designed by J.M. with support from S.L. and were conducted at the industrial partner. Author Contributions: The conceptualization of the paper and the method proposed were carried out and The development of the simulation was done and lead by S.L. in collaboration with J.M. The virtual experiments outlined by J.M. under the supervision of R.S. and K.W. J.M. wrote the majority of the paper. The physical welding wereexperiments done by wereS.L., who designed also contributed by J.M. with to support writing fromparts S.L.of the and Sections were conducted 2.3, 2.5, and at 3.2. the P.H. industrial played partner. the role The of DOEdevelopment expert by of contributing the simulation together was done with and J.M. lead to bythe S.L. design in collaboration and analysis with of the J.M. virtual The virtual experiments. experiments R.S. wereand K.W.done reviewed by S.L., who the final also contributeddraft of the manuscript. to writing parts J.L. re ofviewed the Sections the manuscript 2.3, 2.5 and from 3.2. an P.H. industrial played theperspective. role of DOE expert by contributing together with J.M. to the design and analysis of the virtual experiments. R.S. and K.W. Funding:reviewed This the finalresearch draft was of the funded manuscript. by the Swedish J.L. reviewed Govern themental manuscript Agency from of Innovation an industrial Systems perspective. (VINNOVA) and the NFFP7 program, and has also been part of the Centre for Additive Manufacturing–Metal (CAM2). Funding: This research was funded by the Swedish Governmental Agency of Innovation Systems (VINNOVA) Acknowledgments:and the NFFP7 program, This study and has was also carried been out part at of the the Wingquist Centre for La Additiveboratory Manufacturing–Metal VINN Excellence Center (CAM2). within the AreaAcknowledgments: of Advance ProductionThis study at Chalmers was carried University out at the of WingquistTechnology, Laboratory Sweden. The VINN welding Excellence tests Centerwere performed within the atArea the ofwelding Advance research Production department at Chalmers at GKN University Aerospace, of Technology, Trollhätan. Sweden.Their support The welding is gratefully testswere acknowledged. performed at the welding research department at GKN Aerospace, Trollhätan. Their support is gratefully acknowledged. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publishpublish the the results. results.

AppendixAppendix A A ThisThis appendix appendix contains contains the results ofof thethe 1616 virtual virtual experiments. experiments. The The responses responses are are as as follows: follows: (1) (1)bottom bottom width width [mm], [mm], which which represents represents the penetration the penetration (see Figure (see Figure2b); and 2b); (2) distortionand (2) distortion in Z direction in Z direction[mm] for [mm] the 12 for points the 12 indicated points indicated in Figure2 ina. Figure Images 2a. of theImages fusion of zonethe fusion or weld zone bead or areweld also bead shown are alsofor eachshown run. for each run.

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