Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Summary

A process is described for acquiring near-real-time metrology of weld beads and prepare the resulting geometry automatically for finite element analysis.

Abstract

Fusion welding for high-value manufacturing requires strict process controls on component distortion and ascertaining levels of residual stress imparted to the completed component. The process is dependent on controlling a myriad of parameters, focusing predominantly on ensuring adequate fusion of parent material and consumables. High thermal gradients that are imparted during the process can result in significant distortion if left unchecked, and high levels of residual stress if the component is completely restrained. Finite element analysis is commonly applied in fusion welding processes to predict distortion. These models, however, almost exclusively use an idealized or simplified geometry defined before the start of the process, which can be unrepresentative of the final component. A protocol is described for capturing the true shape of a single weld bead deposition within a unique coordinate system using a laser scanning system and converting this captured geometry into a form that can immediately be incorporated into finite element analyses. This allows the finite element model to be rapidly populated with a geometry representative of the true deposition with limited user input.

Introduction

Fusion welding is used for the permanent bonding of metallic components through localized melting of parent and filler materials. These filler materials are in the form of a wire or rod. The heat source to effect this melting can vary¹, but in all cases, both the parent and filler are exposed to high temperatures and gradients. These thermal excursions can result in significant distortion, changes to the material properties, and induce residual stresses within the component during both the welding process and during cooling. As these side effects can be extremely detrimental to the lifespan or viability of high-value components, welding processes are often modeled by the finite element (FE) method to determine thermal history, distortion, and residual stress². Such models generally use simplified or idealized geometry of the weld and parent material, which is determined before any welding takes place, rather than using a geometry based on the full 3D deposition, including welding start and stop locations. Reproducible multi pass welding can be achieved using automated systems where the welding torch is manipulated by a robotic arm. It should be noted that some apparatus used for automated arc welding can also be used for direct energy deposition additive manufacturing, which is known as directed energy deposition-arc (DED-Arc) or wire arc additive manufacturing³ (WAAM). The same predictive modelling approaches are typically also employed for WAAM as for joining⁴.

WAAM can produce 3D components in a near-net shape by selectively combining many layers of deposited material. WAAM has been used in the past to create walls and other geometric shapes⁵, pipes⁶, as well as components with more complicated topologies, such as turbine blades⁷. Due to the increased number of thermal cycles as compared to joining and the increase in deposited material, the distortion of such WAAM components can become significant. As such, any FE model implemented reflecting this process may have its accuracy undermined by the idealized or presumed print geometry. Distortion of the substrate can be limited during deposition by increased mechanical restraint. However, this will also increase the level of residual stress in the final component, which is also undesirable.

Traditionally, post weld geometry inspection can be manually achieved with inspection tools⁸ or by cross sectioning the deposition and substrate to reveal the profile of the weld, including the deposited material, the melted region of the parent material, and the heat-affected zones⁹. Manual geometric inspection tools, though good for providing information on the extents of the deposition, require the operator to interrupt the automated routine to conduct any measurements and transcribe any data obtained. Similarly, cross sectioning provides a very accurate representation of the weld but is destructive and requires multiple preparation steps, which must be carried out externally to manufacturing locations. Both approaches only provide information about the bead profile in specific locations measured, which, for cross sectioning, may be a single profile. In contrast, laser scanners have the advantage of rapidly assessing the weld profile without the need to remove the sample from the weld cell and have the potential for high-resolution capture of the entire deposition. Monitoring of the real bead geometry during welding with laser systems has been employed^10,11 much in the same way that it is commonly employed in metal forming¹². Laser systems have also been used to capture WAAM geometry¹⁰. However, the specific steps taken to process this data to be included or compared to FE analysis have not been well described. The present work presents a new protocol for using an automated laser scanner to monitor the evolution of weld geometry between deposition passes and integrate the recorded geometry to update a finite element analysis (FEA), as realized with the commercial package ABAQUS. The ability to automatically capture the weld bead in situ and convert the weld bead into an FE input geometry with limited user input is a step towards intelligent manufacturing.

The geometry capture employed in the present work is a full scan of a weld, facilitated by the scanner being integrated with a robotic arm with six degrees of freedom that is distinct and separate from the robotic arm controlling the deposition. This is a departure from previous implementation of laser scanning systems, which were designed to probe the geometry at specific locations, either by handheld means¹³, fixed but limited by the extent of a sample stage^10,11, or where the laser scanner is attached to the same robotic arm as the welding torch⁸. The present approach allows the full geometry of the bead to be captured regardless of the deposition location within the cell, in the coordinate system of the welding cell, without the need for customized fixtures or complicated algorithms.

The captured geometry can then be used to predict important factors such as the temperature history during deposition. When combined with suitable thermocouple data, distortion and residual stress can also be simulated, which is adjacent to the present work. This has the potential to improve manufacturing by allowing rapid process modelling of real-world welding. The automated nature of the geometry capture provides an avenue to link welding parameters to the resultant geometry. This, in turn, can be used for the development of improved process control and path planning. Current manual welding relies on the operator's skill to control the output. The robotic welding adds consistency but limits the opportunity for on-the-fly decision making. Capturing the bead profile between passes will allow for the programming of the next bead pass to be altered if desired, and combined with process modeling, has the potential to improve production rates, material properties, and part lifetimes. The present protocol is exemplified by a single bead-on-plate example case to demonstrate the workflow developed.

Setup of the welding cell and equipment used
The subject welding cell consists of robotic arms with the necessary attachments to conduct welding (referred to as the welding robot) and laser scanning (referred to as the scanning robot). The subject cell is shown in Figure 1. These robots can be controlled through a programming interface that understands KUKA Robot Language (KRL)¹⁴, a functional programming language that gives the robot the necessary instructions, which are interpreted by the robots as joint and motor movements. The welding system operates in cold metal transfer (CMT) mode and is equipped with TouchSense, a form of electronic point finding. The consumable used was a G3Si-120n 1.2 mm diameter steel wire in the presence of argon/carbon dioxide gas mixture (80/20%). The substrate employed was a G43 mild steel plate that was fixed by clamps. The deposition imposed was a bead-on-plate with parameters given in Table 1. This combination of welding parameters was selected as it was known to create an industrially representative deposition. The laser scanner employed is capable of scanning a line of 2048 points simultaneously, which was used to acquire data at a frequency of 100 Hz. Additionally, a coordinate measurement machine (CMM) was used to provide the dimensions of a calibration component.

Metrology data obtained from laser scanners require calibration. This need for calibration is even more important when the scanner must be moved to capture a large region with overlapping scans. Were the laser scanner skewed relative to the substrate or the motion not to be smooth, there would be distortion in the resultant geometry, as illustrated in Figure 2. Additionally, the scanner only records information for light, which returns to the sensor; it is common, therefore, in welding, which produces a highly reflective, non-uniform, curved surface as the melt pool solidifies, that much of the spatial information can be lost. To improve the likelihood that the shape being recorded represents the true bead shape, some level of curve fitting is therefore required. In the simplest case, a single weld bead shape can be well approximated by a parabola¹⁵. This approach has been used by Hu et al. with laser scanning type systems to calculate bead overlaps¹³. The following protocol will employ this fitting technique to the single bead example case to create a digital representation within the selected FE package.

Protocol

It is assumed that both robots have been activated and undergone any setup diagnostics to confirm positional compliance, such as brake tests, and have been homed.

1. Perform calibration

NOTE: Before the laser scanner can be used, it must be calibrated to ensure that the distances it perceives are representative of true distances. This may not be the case by default, as if the scanner is at an angle to the plate, this will create a trigonometric change in distance (Figure 2).

1. To calibrate, scan a component of known dimensions, which is rigid and preferably metallic, with fiducial points added to it in the form of spheres.
   NOTE: These spheres provide an easy-to-identify shape that can be fitted to reliably find the center of the fiducial sphere with a low number of data points and high precision. An example component is shown in the weld cell in Figure 3A. The summary workflow used for the calibration steps 1.1-1.13 is shown in Figure 4.
2. Place a minimum of three fiducial spheres randomly across different locations, for example, standard ball bearings larger than 10 mm from low- to medium-grade ABEC ratings (e.g., 15.875 mm diameter ball bearings [0.625 ± 0.0001 inches]). Attach them to the component with a suitable medium such as a conductive epoxy resin to ensure good conductivity between the sphere and the calibration part. Use washers of suitable radius (e.g., 10 mm) to support the spheres to improve the surface area contact between the sphere and the component.
3. Locate the coordinates of a number of points on the surface of the fiducial spheres with a Coordinate Measurement Machine (CMM) as in Figure 3C. These coordinates will be used to generate a virtual datum corresponding to the center of each of the fiducial spheres (Figure 3B).
   1. Before measuring the fiducial spheres, first calibrate the CCM by affixing a calibration benchmark with known dimensions into the CMM bay. This calibration benchmark takes the form of a ceramic sphere of radius 29.993 mm embedded onto a rod with a threaded bottom so it can be screwed into the CMM bay and held rigidly.
   2. Screw the calibration benchmark into the CMM bay.
   3. With the tip of the CMM in the same orientation as will be used to measure the fiducial spheres for the welding cell calibration component, run the calibrate automatically function within the appropriate software. To begin running the calibration of the CMM tip, with the CMM set to measure mode, move the tip into contact with the top surface of the calibration benchmark. The program will then take control, automatically mapping the benchmark sphere and calibrating the CMM tip for the current orientation.
   4. Once the calibration of the tip has been completed, save the calibration to a chosen tip number, for example, tip number 1.
   5. Remove the calibration benchmark from the CMM.
   6. Place the calibration component with the attached fiducial spheres into the CMM bay. Choose an orientation and note the orientation for future reference, such as by using an annotated photograph with each fiducial sphere numbered.
   7. Create a program to identify points on each of the fiducial spheres.
      1. Select the tip using probe | change probe.
      2. Select the contour | measure CNC point and bring the tip into contact with the first fiducial sphere. Repeat for many points across the top hemisphere of the first fiducial sphere.
      3. Do the same for each fiducial sphere, creating a point cloud for each of the surface of the sphere.
         NOTE: In principle, a minimum of three points per sphere is required to locate the center; however, many more are preferred. Here, a minimum of 12 points located over the entirety of one half was employed, as illustrated by the fitted sphere from the CMM points in Figure 3D. Aspects involving CMM operation to obtain surface points on the fiducial sphere will vary based on the equipment used.
4. Calculate the coordinates of the center of the fiducial spheres by fitting the surface points to a sphere by a least-squares fitting approach. For example, this could be achieved using the Numpy least squares solver¹⁶.
5. Choose one of the fiducial spheres to act as the origin of the calibration coordinate system. Subtract this coordinate from each of the fiducial spheres to create a part coordinate system.
   NOTE: Assuming the calibration component is rigid, once the CMM procedure is complete and the centers of the fiducial spheres are known, future implementations of this protocol can skip steps 1.2-1.5 as the calibration component dimensions and associated coordinate system are already known.
6. Place the calibration component in the welding cell in the same orientation relative to the origin when measured in the CMM.
   NOTE: Orientation is not theoretically important but replicating the original orientation allows any errors to be more easily identified.
7. Set up the scan of the calibration component with the laser scanner as shown in Figure 5A. The output is in the form of an x,y,z coordinate file.
   CAUTION: The laser scanner is the source of laser radiation and can therefore be hazardous if laser safety protocols are not followed. The use of class 2M and below lasers is necessary as these can fulfil the required role and an open beam is often required.
8. For the illustrative laser system employed, measure each 15.875 mm diameter fiducial sphere, and scan across each fiducial sphere with the laser scanner to measure the component (Figure 5A). Truncate the output of these line scans to remove any information originating from the substrate, using a combination of circles in x and y around the known ball positions and z value thresholds. Use the remaining points to fit a sphere (Figure 5B) using the same least-squares fitting procedure as in step 1.4 to obtain a central coordinate.
   NOTE: The surface finish of the fiducial spheres may interact poorly with the laser scanner employed. An aerosolized dye-penetrant developer can be used to coat and matte the surface as in Figure 5A.
9. Return the scanning robot to its home position.
10. Locate the calibration component with the welding robot using electronic point finding. Use a metallic tip that is integrated into the welding torch with known dimensions. Bring this tip into contact with the fiducial sphere at a number of points around the surface (Figure 6), similar to the CMM approach. When the tip contacts the fiducial sphere, a low-voltage circuit is completed, and the current robot location is recorded directly by the robot system.
    NOTE: A similar effect can be achieved using other types of electronic edge finders fitted to the welding robot, which rely on physical contact.
11. Use these points to fit a sphere and locate the central position of each fiducial sphere in the deposition robot coordinates system.
12. Return the welding robot to its home position and remove the calibration component from the welding cell.
13. Use the CMM coordinate system to calibrate the weld cell coordinates through single value decomposition. An outline of the process to create the required affine transformation matrices is given in Figure 7.
    NOTE: The resulting affine transformation matrix transforms the position of each of the fiducial sphere centers from the measured coordinates to true distances. This will correct for any misalignment of the laser scanner to the direction of scanning.

2. Locate the build plate position

1. Place the substrate or parent material to receive a deposition into the welding cell.
   1. Run the laser scanner over the corners of the build area such that it overhangs the edge of the plate, starting completely off the plate and ending partially on the plate as in Figure 8A. Ensure that this is done as a continuous motion at a constant speed, with the frequency of the data recording being known. Use the time of acquisition of a particular scan along with the start and end points of the path to assign a position in space to each scan recorded at a particular time. Record the locations of the corners of the build plate, which will be used to acquire geometry suitable for FE analysis.
      NOTE: Performing step 2.1.1 allows the corners of the plate to be located in the laser scanner coordinate system as there will be a step function with the height significantly changing as the laser arrives over the plate (Figure 8B).
   2. Identify the substrate in the scanning robot coordinate system by transforming the corners found in Step 2.1.1 into the welding robot's coordinate system via the transformation matrix calculated in Step 1.13.
2. As a check, with the welding robot, bring the tip of the welding head to each corner of the plate and record the locations as shown in Figure 8C and confirm these locations are as expected.

3. Conduct the deposition

1. With the plate located, program the welding robot to produce the desired path in the correct position relative to the position of the plate in the welding robot's coordinates.
2. Initiate a weld pass resulting in a deposition of a bead of material as shown in Figure 9.
3. After the pass is completed, retract the welding robot head to a safe distance to prevent collisions with the scanning robot.

4. Scan the bead and generate FE geometry

NOTE: See Figure 10 for a summary of the workflow for scanning the bead geometry and using the scan data to create a 3D point cloud, which can be solidified and meshed for FEA. The following steps describe how each part of the workflow is conducted.

1. Program the scanning robot to follow a path that will allow the bead to be scanned. For simple lines, use similar start and end points as the welding robot or for a more robust method, conduct a scan of the full plate.
   NOTE: This will use the same scanning requirements used to locate the plate position initially.
2. Take measurements as the scanner is moved over the workpiece as per Figure 11. Note the start and end points of the path, the robot movement speed, and acquisition frequency. Ensure that the frequency of acquisition corresponds to distance intervals no less than the minimum element size intended for use in the subsequent FEA.
3. If the bead profile cannot be captured in one pass, do multiple parallel passes with an overlap corresponding to at least 10% of the laser scanner's field of view.
4. Once the scans are completed, retract the laser scanner robot to prevent collisions with the welding robot in any subsequent weld pass.
5. Fit the bead output with an appropriate analytical function, facilitated through a series of commands coded in Python. For the example deposition of a single bead, a parabolic function is used for the fitting.
   NOTE: The Python code used to undertake steps 4.5.1-4.5.10 is available in the supplementary repository¹⁷. Step 4.5.10 requires an additional software package FreeCAD¹⁸, as well as a Python installation, to function.
   Figure 10 shows the workflow outlined in this section. An example output at each of the following stages is provided in Figure 12A-J. An example script used for the bead scanned in Figure 11 along with the scanned geometry used to produce Figure 12 is also available in the supplementary repository¹⁷.
   1. Before attempting to manipulate or use the point cloud data from the laser scanner in any way, apply the same affine transformation matrix to the laser output as was found the calibration step 1.13.
   2. Crop the scanned data to the rough area of a single bead to be fitted. Be sure to include some of the plate around the bead, effected by some percentage of the bead width for windowing. At this stage, remove any scanning artifacts stemming from reflections by using height filters.
   3. Flatten the local plate within the cropped section of the scan by solving for the normal for the plate and applying a rotation matrix such that the data are now in a coordinate system where the plate normal is parallel to the vertical axis.
   4. Locate the orientation of the bead on the plate by applying a height filter threshold just above the height of the base plate, then fit the remaining data points with a 1^st order polynomial. This will give a vector for the direction of the bead. If the bead is known not to be straight, split the bead up into smaller sections that can be approximated by straight sections
   5. Rotate the bead so that it is parallel with the y-axis for ease of manipulation.
   6. Crop the rotated section to remove the extremities of the plate but leave a small amount (~5 mm) on either side of the bead to allow for fitting.
   7. Select the center of the bead section to be fitted and perform a parabolic fit to the cross section of the data at this y position. The program workflow for this step is given in Figure 13.
   8. Using the fit, extract the extents of the bead by evaluating the fit at the x coordinates corresponding to the maximum height of the plate-where the bead begins.
      1. Evaluate the maximum y position of the bead using the same thresholding.
      2. Create bead termination profiles using the same parabolic shape but transposed into the x-y plane at each end of the bead.
      3. Record the points that would make up the outline by evaluating all the parabola at a series of x and y coordinates that span the full extents of the bead.
   9. Translate the domain of the points back into the original coordinates by first starting the bead at the origin of a new co-ordinates system, then transforming it to the original welding robot co-ordinate system.
   10. Using meshing tools, fill in the surface of the points and make a solid surface that can be imported into an FE analysis. To do this, use the FreeCAD¹⁸ program to combine the series of parabolas to create a full 3D solid that is suitable for importing into the FEA preprocessor.
       1. Add a substrate at this point by defining either the true base plate extents or other dimensions as needed.
       2. Use macros to generate STL (Standard Tessellation Language) and STEP (Standard for the Exchange of Product Data) files using the points calculated in Step 4.5.9.
       3. Once the solid geometry is produced, it is exported in a file format suitable for FE analysis, in this case, an ".inp" (input) format. If desired, the finite element mesh can be created directly, facilitated by another FreeCAD macro. For this example, the Netgen mesh FEM tool plugin to FreeCAD is used. The example bead mesh was generated using moderate fineness within Netgen mesh, a defined maximum element size of 0.5 mm, and a minimum element size of 0.1 mm.
          NOTE: At this stage the real geometry can now be successfully imported into an FE analysis processor.

Results

The calculated radii and distances between fiducial spheres for the calibration component in each of the coordinate systems are shown in Table 2. The error between the CMM and the electronic point finding for each fiducial sphere position is small, under 0.1 mm. Both of these techniques rely on physical contact between the fiducial sphere and the stylus. The error induced by the laser scanner when locating the spheres is somewhat large in comparison and dominates at 1-2 mm. The application of the transfo...

Discussion

Capture quality
The dimensional accuracy and precision of the laser scanning system were investigated by the positions and radii of the fiducial spheres in Table 2. The accuracy of each system is determined by the positional difference of the fiducial spheres as measured by the robot systems (laser scanner and electric edge finding) as compared to the CMM data when transformed into the welding robot's coordinate system. The CMM is known to have both high accuracy and precision,...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
3 mm diameter ruby CMM stylus	Renishaw		Stylus used on the CMM machine (A-5004-0422)
80% Argon 20% CO2 gas	BOC		Gas mix for shielding gas (Argosheild)
Crysta-Apex 776	Mitutoyo		Co-ordinate measurement machine, quoted precition 10 µm
FK 1000 MIG 1.2 mm welding wire	Iabco		Welding wire consumable
FreeCAD 1.0	FreeCAD		Software for veiwing geometrties and creating stl, step and FE files from the point cloud. Used version 1.0
Fronius CMT 4000 GMAW welder	Fronius		Welding torch
G43 mild steel plate 50 cm x 50 cm x2.5 cm	Smiths Metal		Substrate metal used as the build plate
GEOPAK/MCOSMOS	Mitutoyo		Software for controlling the CMM. Used version 4.0
KUKA KR20	KUKA		Robotic arm used as scanning robot
KUKA KR70	KUKA		Robotic arm used as welding robot
LAZ3RUS	University of Manchester		LAZer-based 3d Rendering in Universal Scene: for creating the FE geometry for the laser scan. Used version 1.0
Micro Epsilon LLT3010-100	Micro Epsilon		Laser scanner, quoted precition 9 µm
Mitutoyo 30 mm dimater calibration sphere	Mitutoyo		Fused silica CMM calibration sphere
ScanCONTROL3000_100	Micro Epsilon		Software for capturing and processing the information from the laser scanner
TouchSense	Fronius		System for electronic edge/feature finding in a roboticized welding implementation