The Reconsitution of the Weld Pool Surface in Stationary TIG Welding Process With Filler Wire


 In order to study the dynamic characteristics of the weld pool surface during the TIG welding process of the filler wire, an observation test platform for the study of the three-dimensional surface behavior evolution of the TIG weld pool based on the grid structure laser was used to observe the weld pool surface and obtain the reflection grid laser image. The three-dimensional surface evolution of the fixed-point TIG welding pool is accurately restored by the three-dimensional recovery algorithm of the weld pool surface, so as to obtain the three-dimensional surface morphology of the weld pool. The difference between the obtained weld pool height and the experimental results is very small, and the results are basically the same.

TIG welding has many advantages, such as high weld quality, ease of control the base metal heat input, and use of simple equipment, and thus it is widely used in industrial production [1] . Because of the limit of the tungsten electrode, the weld penetration of TIG welding is shallow, which can easily result in incomplete penetration [2] . Incomplete penetration in the welding process has a strong negative influence on the weld mechanical properties. Therefore, penetration is usually the focus of attention in the arc welding process [3] .
The weld pool formed in welding contains a wealth of information that reveals the changing state, stability and penetration of the thermal process [4] . Observing the weld pool and obtaining its geometric information have become the key technologies in welding penetration control [5] . The ever-changing information of the relevant physical quantity in the welding process can be obtained effectively by sensing the information of the weld pool surface change [6] . For the welding process, this observation offers an effective method for monitoring the mechanical properties of weld, studying the complex welding thermal physical process, and ensuring control of the weld penetration [7] . Scholars have used different methods to study weld pool geometry, e.g., weld pool oscillation detection [8] , infrared sensing [9] , radiographic sensing [10] , and visual sensing [11] , among others. These methods mostly extract one-dimensional or two-dimensional geometric information from the surface of the weld pool and, only one or a few of the features for welding penetration control [12] . In further work, the researchers found that the three-dimensional geometric information of the weld pool can better reveal the penetration situation of the weld. Current methods for three-dimensional geometric measurement offer stereo vision [13] , shading recovery [14] and structured light [15] . Among these mothods, as a comparatively accurate method, structured light has attracted the attention of many researchers. The structured light method was first proposed by Zhang and Kovacevic [16] . The basic principle of the structured light method is, that with the use of reflection principle, the structured laser projects to the entire pool surface, and the reflection of the laser irradiates a screen. The images on the screen are captured by a CCD industrial camera, to collect images of the structured laser with the weld pool shape changes and extract the spatial geometric relationship between the projection point and the reflection point. According to selected mathematical computations, the surface morphology of the weld pool can be recovered. To obtain a better improvement in accuracy, Wang et al. [17] ameliorated structured light and collected better clear images under strong arc light. Liu et al. [18] proposed a phase change correction method based on a linear ratio for measurement of the surface depth of the TIG weld pool, and obtained satisfactory results. Wang [19] proposed a new system based on the structured light method that satisfactiorily measured the 3-D weld pool shapes. Our research group also performed certain preliminary studies on the structured light method [20] . The result shows that a certain relationship exists between the penetration of the weld and the concavity and convexity of the weld pool surface. Via the surface of the weld pool, the dynamic welding process and surface concavity or convexity can be studied. Therefore, the weld penetration state can be controlled according to the geometrical parameters and shape of the weld pool surface. This experimental design hardly recovers the geometrical parameters and shape of the weld pool surface accurately. Based on this observation, the experimental design is modified, and a new approximate mathematical algorithm is proposed to accuratdly obtain the geometrical parameters and shape of the weld pool surface.
Thus far, most research on the weld pool surface in TIG welding via the structured light method has not covered the addition of filler wire. Use of filler wire is common in TIG welding for industrial applications. The aim of this paper is to better study the dynamic behavior of the weld pool surface in TIG welding with filler wire. In this paper, a modified measurement system and the new proposed approximate algorithm were to observe and analyze the surface changes in stationary TIG welding with filler wire. The validity and accuracy of the new method were tested.

The fast algorithm of reconstruction
The measurement system with a grid laser is shown in Fig. 1. This system is established based on the light reflection law. The smooth weld pool surface conforms to the specular reflection, whereas the rough workpiece surface conforms to diffuse reflection. Based on the light reflection law, and the difference between the weld pool and the base material in diffuse reflection, the grid laser is projected onto the surface of the weld pool and reflected from the surface of the weld pool. The reflection is intercepted by a screen. The changing process of the laser grid on the screen is captured by a camera, and the images on the screen are analyzed and recorded. The three-dimensional weld pool surface can be recovered via an approximate algorithm. The following illustration of Fig. 2 presents the schematic diagram and parameter settings of the weld pool surface recovery process:

Fig. 2. Diagram of the reflection of the weld pool and calibration of its parameters.
A new algorithm for surface restoration of the weld pool is established, and its calculation flow is shown in the following Fig. 3:

Fig. 3. Flow chart of the algorithm.
In the process of recovering the weld pool surface, the following simplifications were applied: As shown in Fig. 4, the grid laser projects onto the surface of weld pool, and the reflection of the XZ section is shown in the diagram. The location of the reflection point in the center of the weld pool is different from that at the edge of the weld pool in the X direction, which is affected by the height of the weld pool. Because the pool height is noably small, this difference can be ignored.
In addition, the a is determined according to the actual size. The specific method of calculation is given as follows: after setting the projection point, which is obtained from the orthographic projection of the laser source to the plane of the weld pool surface, as the origin Oxyz (0, 0, 0), the three-dimensional Cartesian coordinate system is established. The coordinate of the grid laser source in the space is O(0, 0, z0) and the incident light projected onto the weld pool surface is described by: where ( , , ) x y z I I I I  is the direction vector of the incident light, and based on Fig. 2, z0 is the height d of the laser source.
The boundary of the weld pool contains abundant geometric information. The weld pool height is approximately 0, and the laser obeys the principle of specular reflection. The reflected long line of the laser projecting to the boundary of the weld pool is assigned given a point in the space, which can be treated as the focal point of the reflected ray. It is symmetrical to the plane of the laser source on the weld pool, and the focal point of the inverse ray is O' (0, 0, -z0). Thus, the reflected rayslaser counter rays at the boundary can be obtained as follows:  The coordinates of the endpoints of the grid on the screen plane are obtained through the transpose matrix B, and the coordinates are expressed as follows: where B is a matrix of 3*2, and its specific parameters are determined by the location of A(0,0) in the global coordinates of the space. The direction vector I` of the reflected light of the weld pool can be obtained by combining the focal coordinates and the coordinates of the points on the screen. The specific parameters of the laser reflection line at the weld pool boundary can be obtained. The intersection of the laser reflection line and the plane z=0 is the boundary of the weld pool, and the coordinates of the laser projected on the edge of the weld pool can be determined.
According to the first assumption, when the laser tilt angle α is large, the grid transverse line ci of the grid laser projecting to the weld pool surface is approximately the same in the X direction, i.e., the endpoint line lj of the grid transverse line has the same coordinates in the X direction.
The plane, formed by the grid transverse line Mi and the focus O' of the reflected laser, intersects with the surface of the weld pool, and the intersection line bi can be obtain. The end points of the intersection bi at the edge of the weld pool are tiU and tiD, and the endpoint connection mi can be approximated as the projection of the radiation bi on the plane z=0. Therefore, the intersection point between the connection lj and the connection Mi is the projection of the grid laser node a(i,j) on the plane z=0, and they have the same coordinates in the directions of X and Y.
On the screen P, the distance from node A(i,j) to the endpoint connection Lj is H(i,j), which is proportional to the height of a(i,j) at the corresponding node of the weld pool surface.
Because the reflection of the grid laser on the surface of the weld pool presents specular-like reflection, the height of the projecting point in the pool affects its position on the screen P, and the triangle similarity can prove the relationship.
The distance from the projection point A(i,j) to its corresponding auxiliary line Lj is H(i,j), the reflection point of the weld pool surface corresponding to A(i,j) is a(i,j), and the height of the weld pool is h(i,j).
According to the first assumption, when the incidence angle α is larger, the following relationship exists： ( , ) ( , ) i j i j h kH   (5) By combining the coordinates of a(i, j) in X and Y directions obtained in Formula 3, the coordinates of each reflection point a(i,j) in the global space can be determined.
According to the reconstruction principle of the three-dimensional surface of the weld pool, the known surfaces can be recovered to verify the accuracy and feasibility of the algorithm via a program. The laser beam is projected onto a known Gaussian surface, which has reflective properties. A screen with an angle of 45° to the X axis is placed on the path of the laser reflection line, and the reflected laser is projected onto the screen, as shown in Fig. 7. The data of the projected image on the screen can be measured and extracted, and the recovered surface can be calculated. Finally, by comparing the restored Gaussian surface with the known surface, we can obtain the error between them.

Fig. 7. Calibration of the grid laser on the screen.
The recovery processes of the Gaussian convex and concave surfaces, are shown in Fig. 8 and Fig. 9, respectively, where Fig. 8(a) is the position of the standard Gaussian convex surface in space. Fig.8(b) is the imaging of the laser beam reflected on the screen, and Fig.8(c) is a convex surface restored by the calculation. The Gaussian concave surface is verified and restored in a similar manner. The main steps are the same as described above. Fig. 9(a) is the position of the standard Gaussian concave surface in space. Fig.9 (b) is the imaging of the laser beam reflected on the screen, and Fig.  9 (c) is a concave surface restored by the calculation.  Table 1 shows the verification results of the Gaussian surface and their comparison with standard the surface. It can be observed from the results that the algorithm has a better effect on the recovery of convexity and concavity. The calculated results show good conformation to the actual value.  Fig.10 is a schematic diagram of TIG welding droplet transition, which describes the process of welding wire being heated by the arc to melt into droplets and enter the weld pool, and the process of weld pool surface changes after the droplets enter the weld pool.

Reconstruction of the weld pool surface
The surface of the weld pool can reflect the welding quality. To obtain high level of welding quality, we analyze the dynamic behavior of the pool surface in stationary TIG welding with filler metal. The most important and direct external performance aspect of TIG welding with filler wire is the impact action of the droplet on the weld pool. The droplet impact on the weld pool is a complex and multi-factorial process. Many types of forces act on droplets, including pressure, surface tension, and gravity. At the same time, the droplet transfers to the weld pool with high speed in the transient process, and a high speed camera is necessary to capture the real-time droplet transfer information. Based on the above experimental system, the reconstruction of weld pool surface in stationary TIG welding is studied. The grid laser is customized according to the test requirements, as shown in Fig. 11. The camer is a MV-GED30M CCD industrial camera, and 304 stainless steel with 125 × 50 × 30 mm 3 dimensions is used in the workpiece. The welding current is 40A, the flow rate of argon gas is 10 L/min, the diameter of the welding wire is 0.8 mm, and the size of experimental system is measured as d=11.32 mm and D=59.40 mm. In this experiment, only one droplet is studied. During stationary TIG welding, the welding wire is inserted by hand. After one drop falls, the welding wire is pulled out. The wire feed angle and the distance to the specimen are approximately 45°and ~2.5 mm, respectively.
The entire welding process was detected by the above experimental observation system. The three-dimensional information of the weld pool surface was obtained by analysis and measurement, and the weld pool surface is reconstructed in three dimensions. Fig. 11. Imaging of the grid laser: (a) T=0s (b) T=0.05s, and (c) T=0.13s. Fig. 12 shows the real-time reconstruction result of the three dimensional surface according to the reflection imaging of the grid laser. Fig. 12(a) presents the three-dimensional restoration of the weld pool surface when the welding wire is unfilled, which is a typical convex surface. Fig. 12(b) displays the morphology of the three-dimensional surface after the droplet enters the weld pool approximately 0.05 s. It can be observed that the center of the weld pool is severely deformed by the droplet impact. The center of the weld pool is depressed, the free surface height of the weld pool increases by approximately 0.0127 mm compared with that when the droplet enters, and the width of the weld pool increases about by approximately 0.09 mm. Fig. 12(c) shows the morphology of the three-dimensional surface after the droplet enters the weld pool approximately 0.13 s. Compared with the observation at 0.05 s, the surface center of the weld pool is restored to a convex shape, and the surface height and the width of the weld pool change minimally. The measured results are shown in Fig.13.

Conclusion
To study the dynamic weld pool surface in TIG welding with filler wire, an algorithm based on the mirror reflection principle is used to recover the free surface of the weld pool when the droplet falls into it. The following conclusions can be obtained in this work: (1) Through the TIG welding pool three-dimensional surface behavior evolution test platform, we collected the information about the change of the three-dimensional surface of the weld pool when the droplet entered the weld pool.
(2) Through three-dimensional recovery, it is observed that when the droplet enters the weld pool for 0.05 seconds, the center of the weld pool is sunken. When the droplet enters the weld pool for 0.13 seconds, the weld pool returns to a convex shape and the free surface rises by 0.0141mm, and the width increases by 0.11mm .
(3) The recovery results of the weld pool surface show that this algorithm can effectively reflect the change of concavity and convexity of the weld pool surface. A small error occurs between the experimental results and the recovery results of the weld pool morphology, and the overall morphology is consistent, which proves that the recovery method is feasible.

Declaration Ethics approval and consent to participate
The manuscript is ethically approved and all authors agree to participate.