Modelling the Weld Cladding Process to Predict Weld Clad Position and Shape Error

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One of its most promising applications holds in manufacturing of difficult-to-cut materials where production costs can be reduced with minimizing the time of machining and total tool costs. To develop a correct WAAM technological process for manufacturing complex shaped components welding torch path corrections and welding power corrections have to be made especially in critical sections such as corners and sharp edges. A predictive mathematical model of the material cladding during WAAM process has been developed for the purposes of generating an optimal toolpath of the WAAM clads. This predictive mathematical model is simplified to reflect the important physical phenomena in the weld pool but also to optimize computing time. In this paper the principle of the mathematical model is described and its functionality is verified by the welding experiments with five different welding power settings. 3D scans of welded samples are used for the verification. Wire Arc Additive Manufacturing Simulation Toolpath Cold metal transfer 3D scanning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 1 Introduction A subtype of metal Additive Manufacturing (AM) which combines wire as a feedstock and electric arc as a heat source is called Wire arc additive manufacturing (WAAM) [ 1 ][ 2 ]. High deposition rates and low equipment costs are the main advantages of WAAM over other metal AM methods such as Laser Metal Deposition (LMD) and Selective Laser Melting (SLM) [ 2 ]. However precision and possible geometrical complexity of manufactured parts are higher when using LMD or SLM [ 3 ]. Manufacturing complex shapes that are not possible to be machined in a conventional way is a suitable application for WAAM, especially when WAAM is combined with milling. Inter-operational milling during WAAM process greatly increase the precision which otherwise might not be sufficient when using WAAM. So far, our experience shows that manufacturing inner cooling channels in thermally stressed components is the application in which the industrial companies are greatly interested. This type of geometry can be manufactured using hybrid WAAM as it is shown in the paper [ 4 ]. Techniques used for WAAM can be further categorized by the type of arc welding process. Three basic techniques are gas tungsten arc welding (GTAW), gas metal arc welding (GMAW) and plasma arc welding (PAW)[ 5 ]. According to the current state of the art discussed also in [ 5 ][ 6 ] a GMAW modification, known as Cold Metal Transfer (CMT) should be the most effective and suitable method for 5-axis WAAM. Nevertheless, different approaches to the WAAM where only 3-axis motions are used suggest PAW as the optimal method [ 2 ]. The disadvantages of PAW are most significant when manufacturing complex shapes which is the main reason this research relies on GMAW CMT. Numerous research papers deal with simulation of WAAM process with majority of them focusing on thermal phenomena (for example: [ 7 ][ 8 ][ 9 ]). However, there are not many published papers about weld clad position error during WAAM. An approach to the weld clad position simulation using machine learning principle is presented in [ 10 ]. Weld clad shape cross-section prediction is presented in [ 11 ] but the study does not deal with the 3D shape of the weld clad including start and end section. It is usual that WAAM produces blanks that are further machined [ 2 ]. However, increasing the precision of WAAM can save costs spent on further machining and allow possibility of manufacturing more complex shapes like the ones mentioned in [ 12 ]. To increase the position accuracy of the weld clads it is necessary to study the physical phenomena in the weld pool like metal transfer and forces acting on the metal droplet. From this knowledge a rather simplified mathematical model of weld cladding was developed because using a full-scale FEM simulation is very demanding on a computing power and also very complex to use [ 13 ]. The simplified mathematical model is designed to predict a portion of weld clad position error. The position error prediction may be further used to generate corrected WAAM toolpath. 1.1 Analysis of the main physical phenomena affecting the weld clad position In the CMT welding process metal droplet is transferred in the modified (controlled wire retraction movement) short-circuit transfer mode [ 14 ][ 15 ]. In addition, welding parameters used in the study (127–176 A, 15,4–17,4 V) correspond to the short-circuit transfer mode as shown in Fig. 1 [ 16 ]. During the short-circuit metal transfer various forces affects the liquid metal droplet [ 17 ]. These forces are shown in Fig. 2 [ 17 ]. The study [ 18 ] shows the shape of the weld pool during WAAM. In Fig. 3 it is clearly visible that the liquid metal solidifies at the distance ‘behind’ the axis of the welding torch. This distance depends on the welding method and welding parameters [ 18 ][ 19 ]. 2 Design of a mathematical model for predicting weld clad position error In Fig. 4 the scheme explains the difference between the full-scale FEM simulation [ 20 ] and the simplified mathematical model used in this study. For simplified mathematical model of WAAM cladding it is assumed that the welding torch is always normal to the substrate. During welding the torch is moving only in the plane parallel to the substrate (xy). A preview is shown in Fig. 5 . This simplification eliminates most of the forces affecting the liquid metal droplet shown in Fig. 2 as their acting vector is normal to the substrate leaving the surface tension force the only one which affects the XY position. Next phenomenon affecting the XY position of the weld clad is the weld pool length which causes the metal to solidify in a distance ‘behind’ the axis of the welding torch. This can also be seen in Fig. 3 . According to the authors, two phenomena, which are the surface tension force acting on the liquid metal droplet and the weld pool length, are considered to have the main effect on the weld clad position error. These phenomena were incorporated into the simplified mathematical model of weld cladding. The basic interface of the simplified mathematical model of weld cladding was designed in Matlab software. The substrate is defined by two-dimensional matrix M (Fig. 6 - left). The two dimensions of matrix M represent the X and Y dimensions in the workspace. Matrix values represent the Z dimension. The shape of the substrate is obtained by creating a surface chart of the M matrix. The 110 x 110 mm substrate is represented by 1100 x 1100 matrix meaning the smallest distinguishable element is 0.1 x 0.1 mm. In the simulation the weld clad is created by adding a ‘droplet element’ (Fig. 6 - right) along the defined trajectory. Droplet element is also a two-dimensional matrix, size of this matrix corresponds to the welding parameters (circa 6 x 6 mm). The ‘droplet element’ matrix is added to substrate matrix M in every step (0.01 s) of the simulation along the defined trajectory. The result of the successive addition is a final matrix describing a weld clad on the substrate. Final shape is obtained by creating a surface chart of the final matrix (Fig. 6 - bottom). Size and shape of the ‘droplet element’ has to be obtained from the shape of the real weld seam and it is also inspired by the shape of the heat source model for welding [ 21 ]. Values of the ‘’droplet element matrix’’ were defined in a way that simulated weld seam shape match the experimental weld seam shape. The deposition process in the simulation is split in two different steps. In the first step 35% of volume is cladded exactly along the NC code toolpath. In second step 65% of volume is cladded according to the phenomena known from the physical behaviour of the melt pool – these are (i) the effect of the weld pool length and (ii) the surface tension force acting on the liquid metal droplet. This split in the simulated cladding process allows to create weld clads that have almost equal shape as the real weld clads and also as the shape described in [ 22 ] where the first step of cladding represents the partial melting of the substrate. To create a weld clad shape (also used in [ 23 ]) shown in Fig. 7 basic parameters for setting the size of the droplet element and simulated cladding are needed to be set in the simulation – see Table 1 . The torch speed is not involved by these parameters because it would be redundant for the simulation which works in step-by-step manner. It is assumed that welding process with wire feed/power 6 m/min and torch speed of 0,6 m/min will behave the same as welding process with wire feed/power 10 m/min and torch speed of 1 m/min as the calculated volume of the droplet elements are equal (the equation of continuity applies). However, the width and height of the weld clads will be different. Table 1 Basic parameters of the simplified mathematical model of weld cladding Parameter name Explanation Dw [mm] Feedstock wire diameter used in the welding process s [m/min] Wire feed speed which corresponds to the welding power. This is internally measured by Fronius unit. Real wire feed speed differs from the set value. rw [mm] Width of the weld clad have to be obtained experimentally. Height of the weld clad is then calculated from the total wire feedstock input (Dw and s) H [vector] Torch toolpath vector. This can be obtained from the NC code. Ws [%] Volume increase in the first second of welding process caused by cladded material before the torch starts moving. Weld initiation process. This has to be obtained experimentally. Wf [-] Number of droplet elements missing in the end of the weld clad when the torch finishes the movement. Weld termination process. This has to be obtained experimentally. (i) Effect of the weld pool length As shown in Fig. 3 according to study [ 16 ], the length of the weld pool depends on the welding parameters and it is clear that this phenomenon is present in the WAAM process. It was decided that this phenomenon would be incorporated in the mathematical model using a simplification is inspired by a ‘ball pulled on astring’. The principle is shown in Fig. 8 . As the weld pool length could not be calculated precisely because it depends on many variables, it is necessary to determine the weld pool length experimentally. (ii) Surface tension force acting on the liquid metal droplet Assuming that during welding a substrate is partially melted and a part of metal droplets do not solidify until an emission of next liquid metal droplet from the electrode happens – this means that the position of the depositing liquid metal droplet is affected by the recently deposited material and the substrate shape. According to these assumptions a function which scans a close surroundings of an actual droplet deposition was designed. In this area a XY position of mass center is calculated. Deposited droplet is than translated in the direction of this mass center vector multiplied by the sF parameter. This simplification is an compensation of a surface tension force acting on the liquid metal droplet effect and it is also explained in Fig. 9 . Simplified mathematical model of the weld cladding contains parameters which aredependent on the welding parameters and materials used but their values are unknown. To calibrate this simplified mathematical model an experimental weld clads should be made. From the comparison of the experimental and the simulated weld clads positions above mentioned mathematical model parameters can be obtained. An overview of weld pool parameters used in the simplified mathematical model of weld cladding is shown in Table 2 . The scheme of an experimental calibration process is shown in Fig. 10 . Table 2 Weld pool parameters of the simplified mathematical model of weld cladding Parameter The meaning in the mathematical model The meaning in the real welding process D [mm] The length of the ‘string’ guide between torch centerpoint and weld cladding centerpoint The distance between torch centerpoint and the spot where liquid metal solidifies. sF [-] Correction factor which is used to calculate translation of deposited droplet along the vector directed to the center of mass of the scanned area. Defines the total effect of surface tension force acting on the deposited droplet. So a sH [mm] Define a size of the scanned area in which an actual center of mass is calculated Defines a size of area where the substrate and deposited material are partially melted thus surface tension force is in effect. 3 Experimental setup The experimental welds were manufactured on the 5-axis welding machine equipped with Fronius TPS 320i welding source. For the experiments only 3-axis operations were used. Toolpath deviations (because of the actuators and interpolation control) could be significant when using serial kinematics (e.g. industrial robot) [ 24 ]. However, when using standard CNC kinematics and actuators and if the toolpath is trivial these deviations are much smaller. Complete welding equipment is shown in Fig. 11 . Substrate material for welding was S235JRG1 (EN10025) 110 x 110 x 40 mm plates. As a welding wire Voestalpine Böhler X70-IG Ø 1 mm was used together with shielding gas mixture from Messer – 18% CO 2 in Argon. For the 1st set of experiments five different settings of welding power was used to prove that model is functional for different welding parameters. Welding parameters are shown in Table 3 . Table 3 Welding parameters for experimental clads welding strategy MIG CMT wire feed [m/min] 5.0–5.9–6.8–7.7–8.6 torch travel speed [m/min] 0.6 current [A] 127–146 – 155–162–176 voltage [V] 15.4–16.4–16.8–17.1–17.4 shielding gas flow [l/min] 15 For 3D scanning (which was also used in [ 25 ]) of experimental welds an optical 3D scanner Atos Capsule by GOM was used (shown in Fig. 13 ). The output from the GOM software is a STL file. This STL file is loaded into the mathematical model using a Matlab function called ‘stlread’. When the origin and the scale are set correctly it is possible to project both simulated and experimental welds in one surface chart to detect the deviation between them. For easier evaluation of the deviation between simulated and experimental weld a Rhinoceros software was used. Rhinoceros has a function to calculate the chart of deviation between two surfaces so it is not necessary to program this function as a script in Matlab. The purpose of this set of 3 experimental samples is to obtain the basic parameters to create simple line weld clad. Different welding power settings were used in a way that for each weld clad it is possible to find optimal size of the droplet element. For optimal settings of the D , sF and So , sH further experiments have to be conducted. It was necessary to add features for establishing a correct zero points of the coordinate systems, otherwise the measurement accuracy would be unsatisfying. Also, the substrate plates have to be minimum 20 mm thick otherwise the plate would be heat deformed which disrupts measurement accuracy. A set of three experimental samples were manufactured. Each sample contains 5 weld clads with same welding strategy but different welding power – Fig. 14 . The samples were sanded after welding which made them suitable for 3D scanning. Two 6 mm holes for centre pins were used as an establishment of the XY of the coordinate system. Top and bottom surface were face-milled. Top surface works as Z level establishment of the coordinate system. Side walls of the substrate plate were not machined and neither involved in the 3D scan because their geometry is not accurate – Fig. 15 . 4 Results and discussion 4.1 Calibration procedure After 3 samples were 3D scanned and converted to the STL file format it was possible to start the calibration of the basic model parameters of the simplified model of weld cladding in Matlab. To correctly specify the deviation between simulated and real/3D scanned weld clad Rhinoceros 7 software function called surface deviation was used. Basic model parameters were obtained/calibrated by the following procedure. (i) Dw Voestalpine Böhler X70-IG Ø 1 mm was used. (ii) s Real wire feed internally measured by Fronius welding unit. Measured wire feed differs from the set wire feed. It is necessary to use the measured average values rather than the set ones so the simulation fit the experiment – Table 4 . The measured wire feed values are noisy so standard deviation for each weld clad measured values from all 3 samples are also included in Table 4 . Table 4 Wire feed measured internally by Fronius Set wire feed [m/min] 5,0 5,9 6,8 7,7 8,6 Measured average wire feed [m/min] 5,6 6,6 7,4 7,9 8,5 Standard deviation [m/min] 0,3 0,4 0,3 0,3 0,3 (iii) rw The width of the weld clads have been measured from the STL files using Rhinoceros 7 software. (iv) Ws and Wf Both of these parameters have been obtained by manual calibration using the Rhinoceros 7 software. The goal was so the simulated weld clad shape is fitted to overlay with the 3D scanned weld clad shape as ideally as possible. 4.2 Calibration results Using the experiments, it was possible to calibrate the simplified model of weld cladding for 5 different welding powers. To calibrate the simplified model for different materials or welding strategies, more experiments would have to be conducted. The results are summed up in Table 5 . and are valid for weld clads made using: (i) Voestalpine Böhler X70-IG Ø 1 mm wire (ii) 18% CO2 in Argon shielding gas with flow of 15 l/min (iii) MIG CMT welding strategy (iv) Torch travel speed of 0,6 m/min Table 5 Calibration results of basic parameters of the simplified model of the weld cladding Weld clad [-] welding power 1 welding power 2 welding power 3 welding power 4 welding power 5 Set wire feed [m/min] 5,0 5,9 6,8 7,7 8,6 Set current [A] 127 146 155 162 176 Set voltage [V] 15,4 16,4 16,8 17,1 17,4 Dw [mm] 1 1 1 1 1 s [m/min] 5,6 6,6 7,4 7,9 8,5 rw [mm] 5,8 6,1 6,4 6,8 7,1 Ws [%] 125 126 130 132 135 Wf [-] 65 75 85 85 90 With these calibrated parameters simplified mathematical model of weld cladding could simulate weld clad that differs circa 0,20 mm and at the starting segments circa 0,30 mm from the real 3D scanned weld clads – see Fig. 16 , Fig. 17 , Fig. 18 . Coordinate systems synchronization was done as explained in Fig. 15 . Side walls of the substrate plate were not machined so they are not fitting the ideal shape of substrate from the simulation. 5 Conclusions The aim of this study was to develop a simplified mathematical model of weld cladding which could predict weld clad position error. The simplified mathematical model of weld cladding was designed according to the physical phenomena affecting the weld clad position. Matlab software was used to create an interface for the simulation. The simplified mathematical model contains variables describing the weld cladding behaviour. In the study values of these variables have been determined by experimental calibration process where welded samples were 3D scanned and compared with the simulated weld clads. For further calibration weld pool parameters of the simplified model of weld cladding have to be investigated. For that kind of calibration experimental samples with curvaceous weld clads and substrate with geometrical elements will be necessary. These experiments will be the subject of further work. In the current state the simulation is able to predict the precise shape with maximum deviation circa 0,20 mm. The starts of weld clads is a more complex problem where the deviation is circa 0,30 mm. These are valuable results as the WAAM technology is generally considered to be reasonably rough. The simplified model is a promising method to predict position and shape errors of the WAAM weld clads. Further experiments with more complex toolpaths and substrate geometry will show if the simplification of the weld cladding was sufficiently accurate. The simplified simulation model of the weld cladding will be extended with the function to recalculate the welding torch NC code toolpath based on the simulation results. These corrections will improve the weld clad position for some cases of the curved path weld clads. This function will also be the subject of further work and it is planned to validate it experimentally as well. In this study the knowledge of the WAAM process was improved in the field of weld pool and weld clad position by the simplified mathematical model of weld cladding that was developed and calibrated. Declarations Acknowledgments This work was supported by the Grant Agency of the Czech Technical University in Prague, grant no. SGS22/159/OHK2/3T/12. Availability of data and material The authors confirm that the data and material supporting the findings of this work are available within the article. Author contribution Not applicable. Funding will be added Ethics approval The article follows the guidelines of the Committee on Publication Ethics (COPE) and involves no studies on human or animal subjects. Consent to participate Not applicable. The article involves no studies on humans. Consent for publication Not applicable. The article involves no studies on humans. Competing interests The authors declare no competing interests. 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Int J Adv Manuf Technol 103. 10.1007/s00170-019-03706-1 Cite Share Download PDF Status: Published Journal Publication published 05 Apr, 2024 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Reviewers agreed at journal 30 Dec, 2023 Reviewers invited by journal 30 Dec, 2023 Editor assigned by journal 23 Nov, 2023 First submitted to journal 21 Nov, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3645070","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":264505497,"identity":"e74970b9-c340-4712-98f3-8c482e378868","order_by":0,"name":"Vojtěch 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Fornůsek","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Tomáš","middleName":"","lastName":"Fornůsek","suffix":""},{"id":264505499,"identity":"7c6121dc-b1c0-41aa-8b17-117a10d59653","order_by":2,"name":"Tomáš Havlan","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Tomáš","middleName":"","lastName":"Havlan","suffix":""},{"id":264505500,"identity":"81046db4-b2b8-429b-8c73-39bb355190b2","order_by":3,"name":"Tomáš Kratěna","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Tomáš","middleName":"","lastName":"Kratěna","suffix":""},{"id":264505501,"identity":"9d54f78a-f7d2-4270-9e3e-a542ca4949bc","order_by":4,"name":"Jan Smolík","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"Smolík","suffix":""}],"badges":[],"createdAt":"2023-11-21 16:50:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3645070/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3645070/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-024-13481-3","type":"published","date":"2024-04-05T15:00:52+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":49128753,"identity":"05d83dc9-ce00-4e35-80ba-fb8633d459be","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68767,"visible":true,"origin":"","legend":"\u003cp\u003eMetal transfer mode: a – short circuit, b – globular, c – spray, d – streaming, e – streaming rotating \u0026nbsp;[16]\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/b63fccad64f6ca59a0e70e42.png"},{"id":49129606,"identity":"f5dca0d9-e313-4652-8c77-c7e041084219","added_by":"auto","created_at":"2024-01-03 15:16:57","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":187152,"visible":true,"origin":"","legend":"\u003cp\u003eForces on the metal droplet during welding process [17]\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/d136860725884c4d370fd88b.png"},{"id":49130246,"identity":"3dda77ff-f96e-4fa2-a0c8-ebcad5dccea0","added_by":"auto","created_at":"2024-01-03 15:32:57","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":599593,"visible":true,"origin":"","legend":"\u003cp\u003eWeld pool length: left – high welding power, right – low welding power [18]\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/2ba0b7ae9b1d00a4c299c35a.png"},{"id":49128754,"identity":"cd738a43-fcf8-48e5-9f14-1ce691167529","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":37499,"visible":true,"origin":"","legend":"\u003cp\u003eScheme of the simplified mathematical model for predicting weld clad position\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/4494716e891938f8128cb63d.png"},{"id":49128756,"identity":"0912d713-a9ea-4258-a6a4-4cd9b9aae0f7","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":35800,"visible":true,"origin":"","legend":"\u003cp\u003eConsidered weld cladding situation\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/e0b8f1cf26429cdece5aa6f7.png"},{"id":49130052,"identity":"4a3e7a79-531c-422c-9adc-7498939e7f6f","added_by":"auto","created_at":"2024-01-03 15:24:57","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":118580,"visible":true,"origin":"","legend":"\u003cp\u003eInterface of the mathematical model shown in Matlab representing one weld clad on the substrate plate\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/b06ea6e179cde724cbb97932.png"},{"id":49128762,"identity":"bd2542cc-9d36-48bc-8f76-a17134df46a4","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":72950,"visible":true,"origin":"","legend":"\u003cp\u003eThe split of the cladding process into two steps\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/814d2efdebb9d0eb577b679e.png"},{"id":49129607,"identity":"ecf5d955-60fb-4e15-8886-8165918907e9","added_by":"auto","created_at":"2024-01-03 15:16:57","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":43441,"visible":true,"origin":"","legend":"\u003cp\u003eModel for simulating the weld pool length phenomenon\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/d22e9d9bd86f9a2f7eb0503f.png"},{"id":49129609,"identity":"5847ddf2-14f3-4590-9c53-b0250c1846cd","added_by":"auto","created_at":"2024-01-03 15:16:57","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":68841,"visible":true,"origin":"","legend":"\u003cp\u003eModel for simulating surface tension force acting on liquid metal droplet in the weld pool\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/7aa8a75ff878646f4e93e892.png"},{"id":49128760,"identity":"6e821317-4a2f-4314-babb-23b3832f800b","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":28166,"visible":true,"origin":"","legend":"\u003cp\u003eThe scheme of the calibration process\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/5fe029b50ec8aa2727a2903c.png"},{"id":49128764,"identity":"6908f0d2-8f47-4c20-b570-8d0696061fcf","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":928558,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental WAAM machine setup\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/f559404988d7bc1b0d782582.png"},{"id":49129611,"identity":"6d978488-d761-4073-b519-d61517bac53c","added_by":"auto","created_at":"2024-01-03 15:16:57","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":31617,"visible":true,"origin":"","legend":"\u003cp\u003eComplete diagram of the model functionality\u003c/p\u003e","description":"","filename":"image12.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/d51b81d685ea43a27bb1aec1.png"},{"id":49128766,"identity":"08b1afe8-659f-4186-80a1-31dfb75b8661","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":278844,"visible":true,"origin":"","legend":"\u003cp\u003eAtos Capsule by GOM (left) is able to create a STL model (right) of the experimental sample\u003c/p\u003e","description":"","filename":"image13.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/d71f94b6bdfac8ae75ee9f6a.png"},{"id":49128767,"identity":"53ed0197-7432-49c2-a6c5-1c5c4e66034f","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"jpeg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":81707,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental weld clads samples - sanded for 3D scanning\u003c/p\u003e","description":"","filename":"image14.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/79b91773acd6c14ea96d7050.jpeg"},{"id":49128769,"identity":"4a1db00d-0691-4aec-aeb1-0fd7c48f1141","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":334444,"visible":true,"origin":"","legend":"\u003cp\u003eCoordinate system of the samples STL file obtained from 3D scanning\u003c/p\u003e","description":"","filename":"image15.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/79f1bee089e73c3f5aec0116.png"},{"id":49129612,"identity":"cf66876a-ee88-4c36-9f08-e5803edd0ff0","added_by":"auto","created_at":"2024-01-03 15:16:57","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":324769,"visible":true,"origin":"","legend":"\u003cp\u003eSurface deviation between sample 1 and simulation\u003c/p\u003e","description":"","filename":"image16.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/08ec71cfb70c6e93428e079d.png"},{"id":49128763,"identity":"439b1e0c-8c54-4244-bc52-4b6ae3690354","added_by":"auto","created_at":"2024-01-03 15:08:57","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":350105,"visible":true,"origin":"","legend":"\u003cp\u003eSurface deviation between sample 2 and simulation\u003c/p\u003e","description":"","filename":"image17.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/ed1945224703eb419ba4c61b.png"},{"id":49128771,"identity":"a36cfdbb-239a-49a7-9c5e-c1d760b57289","added_by":"auto","created_at":"2024-01-03 15:08:58","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":340628,"visible":true,"origin":"","legend":"\u003cp\u003eSurface deviation between sample 3 and simulation\u003c/p\u003e","description":"","filename":"image18.png","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/186acc9854e4c335f15732d4.png"},{"id":54303722,"identity":"328e083b-16e2-4a86-b4c8-563681e0e114","added_by":"auto","created_at":"2024-04-08 15:09:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3382436,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3645070/v1/bd77b426-5a14-49b6-84ef-71bf26856045.pdf"}],"financialInterests":"","formattedTitle":"Modelling the Weld Cladding Process to Predict Weld Clad Position and Shape Error","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eA subtype of metal Additive Manufacturing (AM) which combines wire as a feedstock and electric arc as a heat source is called Wire arc additive manufacturing (WAAM) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e][\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. High deposition rates and low equipment costs are the main advantages of WAAM over other metal AM methods such as Laser Metal Deposition (LMD) and Selective Laser Melting (SLM) [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. However precision and possible geometrical complexity of manufactured parts are higher when using LMD or SLM [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Manufacturing complex shapes that are not possible to be machined in a conventional way is a suitable application for WAAM, especially when WAAM is combined with milling. Inter-operational milling during WAAM process greatly increase the precision which otherwise might not be sufficient when using WAAM. So far, our experience shows that manufacturing inner cooling channels in thermally stressed components is the application in which the industrial companies are greatly interested. This type of geometry can be manufactured using hybrid WAAM as it is shown in the paper [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTechniques used for WAAM can be further categorized by the type of arc welding process. Three basic techniques are gas tungsten arc welding (GTAW), gas metal arc welding (GMAW) and plasma arc welding (PAW)[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. According to the current state of the art discussed also in [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e][\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] a GMAW modification, known as Cold Metal Transfer (CMT) should be the most effective and suitable method for 5-axis WAAM. Nevertheless, different approaches to the WAAM where only 3-axis motions are used suggest PAW as the optimal method [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The disadvantages of PAW are most significant when manufacturing complex shapes which is the main reason this research relies on GMAW CMT.\u003c/p\u003e \u003cp\u003eNumerous research papers deal with simulation of WAAM process with majority of them focusing on thermal phenomena (for example: [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e][\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e][\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]). However, there are not many published papers about weld clad position error during WAAM. An approach to the weld clad position simulation using machine learning principle is presented in [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Weld clad shape cross-section prediction is presented in [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] but the study does not deal with the 3D shape of the weld clad including start and end section. It is usual that WAAM produces blanks that are further machined [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. However, increasing the precision of WAAM can save costs spent on further machining and allow possibility of manufacturing more complex shapes like the ones mentioned in [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo increase the position accuracy of the weld clads it is necessary to study the physical phenomena in the weld pool like metal transfer and forces acting on the metal droplet. From this knowledge a rather simplified mathematical model of weld cladding was developed because using a full-scale FEM simulation is very demanding on a computing power and also very complex to use [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The simplified mathematical model is designed to predict a portion of weld clad position error. The position error prediction may be further used to generate corrected WAAM toolpath.\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Analysis of the main physical phenomena affecting the weld clad position\u003c/h2\u003e \u003cp\u003eIn the CMT welding process metal droplet is transferred in the modified (controlled wire retraction movement) short-circuit transfer mode [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e][\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. In addition, welding parameters used in the study (127\u0026ndash;176 A, 15,4\u0026ndash;17,4 V) correspond to the short-circuit transfer mode as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. During the short-circuit metal transfer various forces affects the liquid metal droplet [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. These forces are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe study [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] shows the shape of the weld pool during WAAM. In Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e it is clearly visible that the liquid metal solidifies at the distance \u0026lsquo;behind\u0026rsquo; the axis of the welding torch. This distance depends on the welding method and welding parameters [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e][\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"2 Design of a mathematical model for predicting weld clad position error","content":"\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e the scheme explains the difference between the full-scale FEM simulation [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] and the simplified mathematical model used in this study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor simplified mathematical model of WAAM cladding it is assumed that the welding torch is always normal to the substrate. During welding the torch is moving only in the plane parallel to the substrate (xy). A preview is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. This simplification eliminates most of the forces affecting the liquid metal droplet shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e as their acting vector is normal to the substrate leaving the surface tension force the only one which affects the XY position. Next phenomenon affecting the XY position of the weld clad is the weld pool length which causes the metal to solidify in a distance \u0026lsquo;behind\u0026rsquo; the axis of the welding torch. This can also be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the authors, two phenomena, which are the surface tension force acting on the liquid metal droplet and the weld pool length, are considered to have the main effect on the weld clad position error. These phenomena were incorporated into the simplified mathematical model of weld cladding.\u003c/p\u003e \u003cp\u003eThe basic interface of the simplified mathematical model of weld cladding was designed in Matlab software. The substrate is defined by two-dimensional matrix M (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e - left). The two dimensions of matrix M represent the X and Y dimensions in the workspace. Matrix values represent the Z dimension. The shape of the substrate is obtained by creating a surface chart of the M matrix. The 110 x 110 mm substrate is represented by 1100 x 1100 matrix meaning the smallest distinguishable element is 0.1 x 0.1 mm.\u003c/p\u003e \u003cp\u003eIn the simulation the weld clad is created by adding a \u0026lsquo;droplet element\u0026rsquo; (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e - right) along the defined trajectory. Droplet element is also a two-dimensional matrix, size of this matrix corresponds to the welding parameters (circa 6 x 6 mm). The \u0026lsquo;droplet element\u0026rsquo; matrix is added to substrate matrix M in every step (0.01 s) of the simulation along the defined trajectory. The result of the successive addition is a final matrix describing a weld clad on the substrate. Final shape is obtained by creating a surface chart of the final matrix (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e - bottom).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSize and shape of the \u0026lsquo;droplet element\u0026rsquo; has to be obtained from the shape of the real weld seam and it is also inspired by the shape of the heat source model for welding [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Values of the \u0026lsquo;\u0026rsquo;droplet element matrix\u0026rsquo;\u0026rsquo; were defined in a way that simulated weld seam shape match the experimental weld seam shape.\u003c/p\u003e \u003cp\u003eThe deposition process in the simulation is split in two different steps. In the first step 35% of volume is cladded exactly along the NC code toolpath. In second step 65% of volume is cladded according to the phenomena known from the physical behaviour of the melt pool \u0026ndash; these are (i) the effect of the weld pool length and (ii) the surface tension force acting on the liquid metal droplet. This split in the simulated cladding process allows to create weld clads that have almost equal shape as the real weld clads and also as the shape described in [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] where the first step of cladding represents the partial melting of the substrate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo create a weld clad shape (also used in [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]) shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e basic parameters for setting the size of the droplet element and simulated cladding are needed to be set in the simulation \u0026ndash; see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The torch speed is not involved by these parameters because it would be redundant for the simulation which works in step-by-step manner. It is assumed that welding process with wire feed/power 6 m/min and torch speed of 0,6 m/min will behave the same as welding process with wire feed/power 10 m/min and torch speed of 1 m/min as the calculated volume of the droplet elements are equal (the equation of continuity applies). However, the width and height of the weld clads will be different.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBasic parameters of the simplified mathematical model of weld cladding\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExplanation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDw\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[mm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFeedstock wire diameter used in the welding process\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003es\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[m/min]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWire feed speed which corresponds to the welding power. This is internally measured by Fronius unit. Real wire feed speed differs from the set value.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003erw\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[mm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWidth of the weld clad have to be obtained experimentally. Height of the weld clad is then calculated from the total wire feedstock input (Dw and s)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eH\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[vector]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTorch toolpath vector. This can be obtained from the NC code.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eWs\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[%]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVolume increase in the first second of welding process caused by cladded material before the torch starts moving. Weld initiation process. This has to be obtained experimentally.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eWf\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[-]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of droplet elements missing in the end of the weld clad when the torch finishes the movement. Weld termination process. This has to be obtained experimentally.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e(i) Effect of the weld pool length\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e according to study [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], the length of the weld pool depends on the welding parameters and it is clear that this phenomenon is present in the WAAM process. It was decided that this phenomenon would be incorporated in the mathematical model using a simplification is inspired by a \u0026lsquo;ball pulled on astring\u0026rsquo;. The principle is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the weld pool length could not be calculated precisely because it depends on many variables, it is necessary to determine the weld pool length experimentally.\u003c/p\u003e \u003cp\u003e(ii) Surface tension force acting on the liquid metal droplet\u003c/p\u003e \u003cp\u003eAssuming that during welding a substrate is partially melted and a part of metal droplets do not solidify until an emission of next liquid metal droplet from the electrode happens \u0026ndash; this means that the position of the depositing liquid metal droplet is affected by the recently deposited material and the substrate shape. According to these assumptions a function which scans a close surroundings of an actual droplet deposition was designed. In this area a XY position of mass center is calculated. Deposited droplet is than translated in the direction of this mass center vector multiplied by the sF parameter. This simplification is an compensation of a surface tension force acting on the liquid metal droplet effect and it is also explained in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSimplified mathematical model of the weld cladding contains parameters which aredependent on the welding parameters and materials used but their values are unknown. To calibrate this simplified mathematical model an experimental weld clads should be made. From the comparison of the experimental and the simulated weld clads positions above mentioned mathematical model parameters can be obtained. An overview of weld pool parameters used in the simplified mathematical model of weld cladding is shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The scheme of an experimental calibration process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWeld pool parameters of the simplified mathematical model of weld cladding\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe meaning in the mathematical model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe meaning in the real welding process\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eD\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[mm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe length of the \u0026lsquo;string\u0026rsquo; guide between torch centerpoint and weld cladding centerpoint\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe distance between torch centerpoint and the spot where liquid metal solidifies.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003esF\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[-]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCorrection factor which is used to calculate translation of deposited droplet along the vector directed to the center of mass of the scanned area.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDefines the total effect of surface tension force acting on the deposited droplet.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSo a sH\u003c/b\u003e\u003c/p\u003e \u003cp\u003e[mm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDefine a size of the scanned area in which an actual center of mass is calculated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDefines a size of area where the substrate and deposited material are partially melted thus surface tension force is in effect.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3 Experimental setup","content":"\u003cp\u003eThe experimental welds were manufactured on the 5-axis welding machine equipped with Fronius TPS 320i welding source. For the experiments only 3-axis operations were used. Toolpath deviations (because of the actuators and interpolation control) could be significant when using serial kinematics (e.g. industrial robot) [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. However, when using standard CNC kinematics and actuators and if the toolpath is trivial these deviations are much smaller. Complete welding equipment is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. Substrate material for welding was S235JRG1 (EN10025) 110 x 110 x 40 mm plates. As a welding wire Voestalpine B\u0026ouml;hler X70-IG \u0026Oslash; 1 mm was used together with shielding gas mixture from Messer \u0026ndash; 18% CO\u003csub\u003e2\u003c/sub\u003e in Argon. For the 1st set of experiments five different settings of welding power was used to prove that model is functional for different welding parameters. Welding parameters are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWelding parameters for experimental clads\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ewelding strategy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMIG CMT\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ewire feed [m/min]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.0\u0026ndash;5.9\u0026ndash;6.8\u0026ndash;7.7\u0026ndash;8.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003etorch travel speed [m/min]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecurrent [A]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e127\u0026ndash;146 \u0026ndash; 155\u0026ndash;162\u0026ndash;176\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003evoltage [V]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15.4\u0026ndash;16.4\u0026ndash;16.8\u0026ndash;17.1\u0026ndash;17.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eshielding gas flow [l/min]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor 3D scanning (which was also used in [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]) of experimental welds an optical 3D scanner Atos Capsule by GOM was used (shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e). The output from the GOM software is a STL file. This STL file is loaded into the mathematical model using a Matlab function called \u0026lsquo;stlread\u0026rsquo;. When the origin and the scale are set correctly it is possible to project both simulated and experimental welds in one surface chart to detect the deviation between them. For easier evaluation of the deviation between simulated and experimental weld a Rhinoceros software was used. Rhinoceros has a function to calculate the chart of deviation between two surfaces so it is not necessary to program this function as a script in Matlab.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe purpose of this set of 3 experimental samples is to obtain the basic parameters to create simple line weld clad. Different welding power settings were used in a way that for each weld clad it is possible to find optimal size of the droplet element. For optimal settings of the \u003cb\u003eD\u003c/b\u003e, \u003cb\u003esF\u003c/b\u003e and \u003cb\u003eSo\u003c/b\u003e, \u003cb\u003esH\u003c/b\u003e further experiments have to be conducted. It was necessary to add features for establishing a correct zero points of the coordinate systems, otherwise the measurement accuracy would be unsatisfying. Also, the substrate plates have to be minimum 20 mm thick otherwise the plate would be heat deformed which disrupts measurement accuracy.\u003c/p\u003e \u003cp\u003eA set of three experimental samples were manufactured. Each sample contains 5 weld clads with same welding strategy but different welding power \u0026ndash; Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. The samples were sanded after welding which made them suitable for 3D scanning.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTwo 6 mm holes for centre pins were used as an establishment of the XY of the coordinate system. Top and bottom surface were face-milled. Top surface works as Z level establishment of the coordinate system. Side walls of the substrate plate were not machined and neither involved in the 3D scan because their geometry is not accurate \u0026ndash; Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4 Results and discussion","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Calibration procedure\u003c/h2\u003e\n\u003cp\u003eAfter 3 samples were 3D scanned and converted to the STL file format it was possible to start the calibration of the basic model parameters of the simplified model of weld cladding in Matlab. To correctly specify the deviation between simulated and real/3D scanned weld clad Rhinoceros 7 software function called surface deviation was used. Basic model parameters were obtained/calibrated by the following procedure.\u003c/p\u003e\n\u003cp\u003e(i) \u003cstrong\u003eDw\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eVoestalpine B\u0026ouml;hler X70-IG \u0026Oslash; 1 mm was used.\u003c/p\u003e\n\u003cp\u003e(ii) \u003cstrong\u003es\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eReal wire feed internally measured by Fronius welding unit. Measured wire feed differs from the set wire feed. It is necessary to use the measured average values rather than the set ones so the simulation fit the experiment \u0026ndash; Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. The measured wire feed values are noisy so standard deviation for each weld clad measured values from all 3 samples are also included in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eWire feed measured internally by Fronius\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSet wire feed\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[m/min]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e5,0\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e5,9\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e6,8\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e7,7\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e8,6\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMeasured average wire feed\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[m/min]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5,6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6,6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7,4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7,9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8,5\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eStandard deviation\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[m/min]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,3\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e(iii) \u003cstrong\u003erw\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe width of the weld clads have been measured from the STL files using Rhinoceros 7 software.\u003c/p\u003e\n\u003cp\u003e(iv) \u003cstrong\u003eWs\u003c/strong\u003e and \u003cstrong\u003eWf\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBoth of these parameters have been obtained by manual calibration using the Rhinoceros 7 software. The goal was so the simulated weld clad shape is fitted to overlay with the 3D scanned weld clad shape as ideally as possible.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 Calibration results\u003c/h2\u003e\n\u003cp\u003eUsing the experiments, it was possible to calibrate the simplified model of weld cladding for 5 different welding powers. To calibrate the simplified model for different materials or welding strategies, more experiments would have to be conducted. The results are summed up in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. and are valid for weld clads made using:\u003c/p\u003e\n(i) \u003cstrong\u003eVoestalpine B\u0026ouml;hler X70-IG \u0026Oslash; 1 mm wire\u003c/strong\u003e\u003c/p\u003e\n\n\u003cp\u003e(ii) \u003cstrong\u003e18% CO2 in Argon shielding gas with flow of 15 l/min\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(iii) \u003cstrong\u003eMIG CMT welding strategy\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(iv) \u003cstrong\u003eTorch travel speed of 0,6 m/min\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCalibration results of basic parameters of the simplified model of the weld cladding\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eWeld clad\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[-]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ewelding power 1\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ewelding power 2\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ewelding power 3\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ewelding power 4\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ewelding power 5\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSet wire feed\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[m/min]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5,0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5,9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6,8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7,7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8,6\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSet current\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[A]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e127\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e146\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e155\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e162\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e176\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSet voltage\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[V]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e15,4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e16,4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e16,8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e17,1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e17,4\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"\" /\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eDw\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[mm]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[m/min]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5,6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6,6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7,4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7,9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8,5\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003erw\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[mm]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5,8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6,1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6,4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e6,8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e7,1\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eWs\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[%]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e125\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e126\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e130\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e132\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e135\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eWf\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[-]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e75\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e85\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e85\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e90\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eWith these calibrated parameters simplified mathematical model of weld cladding could simulate weld clad that differs circa 0,20 mm and at the starting segments circa 0,30 mm from the real 3D scanned weld clads \u0026ndash; see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e18\u003c/span\u003e. Coordinate systems synchronization was done as explained in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e. Side walls of the substrate plate were not machined so they are not fitting the ideal shape of substrate from the simulation.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Conclusions","content":"\u003cp\u003eThe aim of this study was to develop a simplified mathematical model of weld cladding which could predict weld clad position error. The simplified mathematical model of weld cladding was designed according to the physical phenomena affecting the weld clad position. Matlab software was used to create an interface for the simulation.\u003c/p\u003e \u003cp\u003eThe simplified mathematical model contains variables describing the weld cladding behaviour. In the study values of these variables have been determined by experimental calibration process where welded samples were 3D scanned and compared with the simulated weld clads.\u003c/p\u003e \u003cp\u003eFor further calibration weld pool parameters of the simplified model of weld cladding have to be investigated. For that kind of calibration experimental samples with curvaceous weld clads and substrate with geometrical elements will be necessary. These experiments will be the subject of further work.\u003c/p\u003e \u003cp\u003eIn the current state the simulation is able to predict the precise shape with maximum deviation circa 0,20 mm. The starts of weld clads is a more complex problem where the deviation is circa 0,30 mm. These are valuable results as the WAAM technology is generally considered to be reasonably rough. The simplified model is a promising method to predict position and shape errors of the WAAM weld clads. Further experiments with more complex toolpaths and substrate geometry will show if the simplification of the weld cladding was sufficiently accurate.\u003c/p\u003e \u003cp\u003eThe simplified simulation model of the weld cladding will be extended with the function to recalculate the welding torch NC code toolpath based on the simulation results. These corrections will improve the weld clad position for some cases of the curved path weld clads. This function will also be the subject of further work and it is planned to validate it experimentally as well.\u003c/p\u003e \u003cp\u003eIn this study the knowledge of the WAAM process was improved in the field of weld pool and weld clad position by the simplified mathematical model of weld cladding that was developed and calibrated.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgments \u0026nbsp; \u0026nbsp;This work was supported by the Grant Agency of the Czech Technical University in Prague, grant no. SGS22/159/OHK2/3T/12.\u003c/p\u003e\n\u003cp\u003eAvailability of data and material \u0026nbsp; \u0026nbsp; The authors confirm that the data and material supporting the findings of this work are available within the article.\u003c/p\u003e\n\u003cp\u003eAuthor contribution \u0026nbsp; Not applicable.\u003c/p\u003e\n\u003cp\u003eFunding \u0026nbsp; \u0026nbsp;will be added\u003c/p\u003e\n\u003cp\u003eEthics approval \u0026nbsp; The article follows the guidelines of the Committee on Publication Ethics (COPE) and involves no studies on human or animal subjects.\u003c/p\u003e\n\u003cp\u003eConsent to participate \u0026nbsp; Not applicable. The article involves no studies on humans.\u003c/p\u003e\n\u003cp\u003eConsent for publication \u0026nbsp; Not applicable. The article involves no studies on humans.\u003c/p\u003e\n\u003cp\u003eCompeting interests \u0026nbsp; The authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAcheson R (1990) Automatic welding apparatus for weld buildup and method of achieving weld build-up; US patent no. (4) 952\u0026ndash;76917\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWilliams SW, Martina F, Addison AC, Ding J, Pardal G, Colegrove P (2016) Wire + arc additive manufacturing. 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Int J Adv Manuf Technol 103. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s00170-019-03706-1\u003c/span\u003e\u003cspan address=\"10.1007/s00170-019-03706-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Wire Arc Additive Manufacturing, Simulation, Toolpath, Cold metal transfer, 3D scanning","lastPublishedDoi":"10.21203/rs.3.rs-3645070/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3645070/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWire Arc Additive Manufacturing (WAAM) is one of the most productive metal additive manufacturing methods. One of its most promising applications holds in manufacturing of difficult-to-cut materials where production costs can be reduced with minimizing the time of machining and total tool costs. To develop a correct WAAM technological process for manufacturing complex shaped components welding torch path corrections and welding power corrections have to be made especially in critical sections such as corners and sharp edges. A predictive mathematical model of the material cladding during WAAM process has been developed for the purposes of generating an optimal toolpath of the WAAM clads. This predictive mathematical model is simplified to reflect the important physical phenomena in the weld pool but also to optimize computing time. In this paper the principle of the mathematical model is described and its functionality is verified by the welding experiments with five different welding power settings. 3D scans of welded samples are used for the verification.\u003c/p\u003e","manuscriptTitle":"Modelling the Weld Cladding Process to Predict Weld Clad Position and Shape Error","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-03 15:08:52","doi":"10.21203/rs.3.rs-3645070/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2023-12-30T22:37:45+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-12-30T20:30:27+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-11-23T06:56:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2023-11-22T03:28:33+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"84e56b90-e046-45de-bf31-ccc8e499c644","owner":[],"postedDate":"January 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-04-08T15:02:54+00:00","versionOfRecord":{"articleIdentity":"rs-3645070","link":"https://doi.org/10.1007/s00170-024-13481-3","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2024-04-05 15:00:52","publishedOnDateReadable":"April 5th, 2024"},"versionCreatedAt":"2024-01-03 15:08:52","video":"","vorDoi":"10.1007/s00170-024-13481-3","vorDoiUrl":"https://doi.org/10.1007/s00170-024-13481-3","workflowStages":[]},"version":"v1","identity":"rs-3645070","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3645070","identity":"rs-3645070","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}