Numerical Simulation and Test Study on Track Welding of QTT

. Considering the stringent requirement of the pointing accuracy up to 2.5 ″ of the world’s largest full steerable radio telescope, this paper studies the welding experiment of the azimuth track of the antenna. First, the opposite deformation jig and welding process were designed for the QTT’s azimuth track. Ten, the welding process was numerically simulated using a fnite element model. Te simulation results show that a better welding efect will be obtained by appropriately reducing the opposite force on the basis of the original. Te three deformation processes of the track are regulated by the opposite deformation jig. Te results show that the opposite deformation jig designed for QTT’s azimuth track can make the amount of deformation and fatness meet the design requirements. Finally, nondestructive testing was carried out to check the welding quality of the track surface and interior. Te results show that there are no obvious defects in the welds of the azimuth track. Te constraint jig and welding processes designed for QTT are efective and feasible.


Introduction
Te world's largest fully steerable radio telescope (Qitai Radio Telescope, QTT), which will be built in Qitai County, Xinjiang, China, has a diameter of 110 m, an observation frequency band of 150 MHz to 115 GHz, an overall antenna weight of about 6000 t, and a pointing accuracy of 2.5 arc seconds (arcsec) [1,2]. Tis places extremely high demands on the load-bearing properties of the azimuth track [3]. In the actual construction of a high-precision, large aperture antenna azimuth track using integral welding technology instead of the common splicing track technology for small and medium-diameter antennas [4,5]. However, the sectional welding technique requires flling the weld groove with a large amount of welding material, and this method will cause welding distortion. Terefore, it is necessary to analyze and study the deformation and weld quality of azimuth track. Tis will reduce the infuence of the azimuth track on the pointing accuracy and even the stability of the antenna.
Tere are some classical solutions at home and abroad in the welding design of the azimuth track of large radio telescopes. Te Mexico 50 m Radio Telescope (LMT) uses a narrow-band clearance groove welding process [6,7]. Each of the two sections of the track is fxed to the base plate by fllet welding, and a suitable amount of opposite deformation is given by bending the base plate so that the fatness of the entire track is within 0.3 mm after the welding is fnished. Te 100 m radio telescope (GBT) in the USA uses the same welding process as the LMT for its composite track [8][9][10]. After welding, the fatness of the entire track was controlled to within 0.127 mm. Te Italian 64 m Radio Telescope (SRT) uses a symmetrical welding process [11]. Tis type of welding requires two people to perform the top and back welding simultaneously, which can better ofset the thermal deformation of the welding. However, this welding process has high requirements for overhead position welding technology. In China, the Shanghai 65 m Radio Telescope uses the narrow-clearance groove section welding method to complete the welding of the whole track [12,13]. In this method, the entire track is manufactured in 30 sections, of which 15 segments are welded together at the construction site. Te fnal fatness of the track reaches 0.5 mm. Te above several classic track welding schemes provide a good reference for the track welding of QTT. In addition, it is necessary to perform a fnite element simulation of the QTT track welding process prior to welding to avoid costly waste.
Using numerical simulation to analyze the welding process of large structural parts, the advantages of fnite element simulation in calculating the hardening properties of elastoplastic materials can be efectively used [14][15][16]. In practical engineering applications, welding deformation will often accompany the welding process [17,18]. Uncontrollable-welding deformation will also lead to complex straightening processes and expensive subsequent machining costs. Based on this, many scholars use professional welding simulation software to improve the quality and performance of welded components and optimize the welding process [19,20]. Yang reviewed recent advances in mitigation techniques that have been applied in the structural design, manufacturing, and postweld stages and analyzed the residual stress relief method of each stage [21,22]. Ma et al. conducted a quantitative study on the efect of jig constraints on welding deformation. Te efects of the jig on longitudinal shrinkage, transverse shrinkage, and angular deformation were discussed in detail [23]. Napitupulu et al. simulated welding joints and compared the simulation results [24]. Yi et al. simulated the welding process of the stifened plate structure of a large container ship using the fnite element analysis method, and the test validated the applicability of the simulation results to its prediction [25]. Akbari and Asadi used the thermo-mechanically coupled three-dimensional fnite element method model to numerically simulate the FSP process and studied the material fow and particle distribution in the base metal and improved the properties of the A356 cast alloy [26].
Based on the abovementioned analysis, it can be seen that the combination of fnite element simulation and welding experiments has been widely used. However, as the diameter of the QTT's azimuth track reaches 76 m, the width of each track is 630 mm, the thickness is 240 mm, and the overall fatness of the track is required to be 0.3 mm (peak to peak value) [2]. Such high precision requirements pose a signifcant challenge for track to be welded in the feld. At present, there are no welding experiments and welding data related to it. Terefore, obtaining welding data for the azimuth track is crucial for the construction of QTT. In the preconstruction phase of the QTT, this study designed an opposite deformation jig for the QTT's azimuthal track and carried out welding experiments for the QTT's azimuthal track. Combined with the results of fnite element analysis, the welding deformation of the QTT's azimuthal track was accurately measured. Trough the designed opposite deformation jig, the welding deformation of the QTT's azimuth track is controlled within the design range. Tis provides data to support the feld welding of the QTT's azimuth track at a later stage.

Modeling and Simulation
According to the characteristics of the azimuth track welding process, the following assumptions are made: (1) Te initial temperature of the track is the preheating temperature.
(2) Te heat source moves at a constant rate, and the temperature in the center of the molten pool is uniform load. (3) Te convection and radiation efects between the track and the environment will be loaded in the form of heat fux density. (4) Factors such as chemical reactions, stirring, convection, and radiation inside the molten pool are not taken into account.

Governing Equation and
Boundary Conditions. Te heat input and heat transfer processes during the welding of the azimuth track have a great infuence on both the solid-state phase transition and the microstructure properties. Tis process is a typical nonstationary heat transfer process, and its control equation is [27] z zx Tere are three types of boundary conditions for the welding temperature feld: (1) Te temperature values on the boundary are specifed as follows: (2) Te heat fux density values on the boundary are specifed as follows: (3) Te surface heat transfer coefcient between the object on the boundary and the surrounding fuid and the temperature of the surrounding fuid are specifed as follows [27,28]: In equations (1)-(4), λ (T) is the material thermal conductivity (W·(m·°C) −1 ); C p (T), the specifc heat (kJ·(kg·°C) −1 ); ρ (T), the density (kg·m −3 ); τ, the time(s); h, the heat convection coefcients (W·(m 2 ·°C) −1 ); T W , the ambient temperature (°C); T F , the peripheral temperature (°C). In this study, the frst type of boundary condition is loaded onto the two side surfaces of the track. Te second type of boundary condition is loaded onto the upper surface of the track.

Heat Source Models.
Te choice of heat source model has a crucial infuence on welding. Te double ellipsoidal heat source takes into account the distribution of heat fow density in the thickness direction and the simulation results have the characteristics of large melting depths [29,30]. Terefore, the double ellipsoidal heat source is suitable for the numerical simulation of thick plate welding process [31]. Te double ellipsoidal heat source model was chosen for the numerical simulations in this study. Te intermediate temperature in the simulations was set to 280°C.
Te expression for the heat fux density distribution in the front half of the heat source model is as follows: Te expression for the heat fux density distribution in the rear half of the heat source model is as follows: In equations (5) and (6), Q (x, y, z) is heat density at a point (x, y, z) (J/mm 3 ); a, b, c f , and c r are geometric parameters that defne the size and shape of the ellipses and, consequently, the distribution of the heat source; f f and f r are fractions of the heat fux imposed in the front and rear quadrants, respectively. Te relationship between the two parameters is shown in equation (7). q 0 is the efective energy input of the heat source, which can be obtained by equation (8).where η is the thermal efciency; U is the welding voltage and I is the welding current.

Meshing.
In order to more realistically simulate the force state of the azimuth track, the constraint force and the opposite force are applied separately in the 3D model, as shown in Figure 1. Te overall dimensions of the two tracks are 2600 × 630 × 240 mm. Te cross-section of the track to be welded is U-shaped. Te cross-section has an upper width of 55 mm, a lower width of 26 mm, and a depth of 90 mm. Te height of the boss, where the track is in contact with the antenna roller, is 10 mm.
Given the large number of meshes and computational efciency, it is necessary to adjust the density of the meshes. In areas near the welds, a fne mesh is used to improve the accuracy of the calculation. In areas farther from the welds, a coarse mesh is used to improve computational efciency, as shown in Figure 2.
Te number of adjusted meshes is about 109,500, accounting for 91.6% of the fne meshes in the welds area. Te number of layers and passes of the weld is set by the heat source trajectory. To reduce the amount of calculation and improve the calculation efciency, the weld is set to 11 layers and 37 passes.
Te force state of the track model is set in the simulation software, as shown in Figure 3. Te forces on the track model include gravity, support, constraint, and opposite forces. Te constraint force acts vertically downward on the surface of the track, and the opposite force acts vertically upward on the stressed plate at the bottom of the track. Te stressed plate can evenly distribute the opposite force near the welds.
In simulations where no opposite force is applied, welding deformation occurs in the heat-afected zone of the track. Terefore, in this welding simulation, the local opposite force is added to cause the welding heat-afected zone of the track to produce opposite deformation before welding. Tis amount of opposite deformation is the same as the amount of welding deformation without applying opposite force, which counteracts the deformation caused by the welding process.

Experiment Procedures
An opposite deformation jig was designed for the welding of the QTT's azimuth track, and welding tests on the track were carried out. Te test process can be divided into three stages: opposite deformation before welding, preheating and welding, and measurement after welding.

Opposite Deformation.
Te azimuth track of the antenna to be welded is hoisted onto the opposite deformation jig, and a downward constraint force is applied to the track. Te fatness of the track is controlled to within 0.01 mm by continuously adjusting the size of the constraint force at 12 positions. Te process requires real-time measurements using a laser theodolite. After leveling the azimuth track, an upward opposite force is applied to the stress plate to cause upward opposite deformation near the welds, as shown in Figure 4.

Preheating and Welding.
Te preheating temperature is related to factors such as the size of the base material, the chemical composition, the shape of the zone to be welded, and the hydrogen content of the fller metal. Te calculation formula is as follows: where T 0 is the preheating temperature (°C); c is the carbon content of the base material (%); h is the thickness of the base material (mm).

Advances in Astronomy
Te fller material used in this experiment is J607Ni (AWS: E9015-G). Te weld base material is 42CrMo(ASTM: 4140). Te chemical composition and mechanical properties of the two materials are shown in Tables 1 and 2, respectively. Based on the thickness of the track in Figure 1 and the carbon content of 42CrMo in Table 1, T 0 is calculated to be 281°C.
Te welding process and parameters can have a signifcant impact on the quality of the welds. Referring to the relevant literature [34], choose the welding method as SMAW, set the welding voltage to 25 V, welding current to 190 A and welding speed to 20 cm/min. Heat the area to be welded to 280°C and hold for 3 hours, then start welding, as shown in Figure 5.
In Figure 5, the red part in (a) is the heating and insulation area around the welds. (b) collect the temperature of the welding area with an infrared thermal imager. (c) manual welding of azimuth track, the whole process lasts about 14 h. Te surface of the weld is continuously struck with a pneumatic hammer during welding to remove the coating and release the stress.

Numerical Study.
Te total deformation cloud and the residual stress cloud of the azimuth track are obtained by numerical simulation, as shown in Figures 6 and 7, respectively. Te y axis represents the track length and the z axis represents the track height.
As can be seen in Figure 6, the total deformation near the welds after the simulation is completed is the largest, about  Due to the constraint force and the opposite force near the welds, the deformation originally generated during the welding process is efectively suppressed by the opposite      Figure 7 shows the residual stresses of the track model after simulation. It can be seen that after the cooling is complete, the residual stress near the welds is 47.8 MPa and the residual stress away from the welds is gradually decreasing. Te trend of residual stresses perpendicular to the welds' direction has been shown to be strongly related to the constraint conditions [35]. Residual stress can be efectively reduced by heat treatment and surface treatment methods [36], such as tempering treatment, which can reduce residual stresses by 65% [37]. Terefore, in welding experiments, heat treatments such as tempering and holding are adopted for the welded track.

Nondestructive Testing (NDT).
After welding, the welds are inspected on-site for NDT. Magnetic particle testing [38] and ultrasonic testing [39] are widely used for inspection of welds quality due to their respective advantages. Terefore, we choose magnetic particle testing and ultrasonic testing to inspect the quality of the polished track, as shown in Figure 8. Figure 8(a) shows the grinding of the uppermost welds of the azimuth track. In multilayer, multipass welding of azimuth track, the latter weld has a heat treatment efect on the previous weld. Tis is equivalent to normalizing the previous weld and improving the secondary crystallization of the previous weld [40]. Terefore, after welding is completed, weld a layer on the track surface to improve the quality of the welds. (b) shows the magnetic particle testing of the weld on the azimuth track. Te results show that there are multiple path lines on the surface of the track. Tese path lines are not necessarily welding cracks, they may be caused by poor manual grinding precision or a mesh residual of austenite [41]. (c) shows the ultrasonic testing of the welds on the azimuth track. Te presence of clutter in the instrument indicates the presence of microcracks within the welds of the track. However, the position of the microcrack is at a depth of 40 cm∼50 cm in the track, which is basically not afected by the antenna load, so it will not have a substantial impact on the life of the azimuth track.

Measurement of Flatness.
During the welding process of the azimuth track, the height values at 12 positions on the track surface are measured several times using a laser theodolite. Te results of multiple measurements are compared as shown in Figure 9. A represents the measured value before welding; B represents the measured value after welding; C represents the measured value after manual adjustment after welding.
Te azimuth track was deformed three times during the welding process, which included the opposite deformation caused by the jig (before A), the deformation caused by welding (from A to B), and the deformation caused by manual adjustment (from B to C).
Te deformation process from A to B shows that the relative height of the track near the welds is signifcantly reduced after welding. Te deformation decreases from 2.25 to 0.375 mm and the fatness decreases from 2.25 to 0.375 mm. Tis indicates that the opposite deformation jig and the opposite deformation before welding ofset some of the deformation during the welding process.
Even if the welding deformation of the track is efectively controlled, it is still very difcult to completely eliminate it. To make the fatness of the track meet the design requirements, it is also necessary to manually adjust the fatness of the track again by using the opposite deformation jig. Te deformation process from B to C shows that the deformation of the azimuth track is reduced from 0.375 to 0.175 mm after manual adjustment. Te fatness of the manually adjusted track was 0.225 mm measured with a laser theodolite. Te result met the design requirements.

Measurement of Side Clearance.
During the welding of the azimuth track, the side clearance of the track was measured several times. Tis clearance is located below the welds and the stress relief hole. Figure 10 Advances in Astronomy clearance was about 2.5 mm before the opposite force was applied. After applying the opposite force, the upper part of the side clearance expanded to 2.97 mm and the lower part reduced to 2.04 mm. Combined with the simulation results and related studies [36,37], the track was maintained at 280°C for 3 hours to reduce residual stress after welding was complete. When the temperature of the track returns to room temperature, the side clearance is measured, and the results are shown in Figure 11. (a) indicates the size of the side clearance before welding and (b) indicates the size of the side clearance after welding.
Comparing Figures 10(b) and 11(a), it can be seen that the side clearance of the azimuth track changes before and after heating. Due to the thermal expansion during the heating process, the side clearance of the track shrinks by 1 mm. Since the track is heated evenly, the degree of shrinkage is also relatively uniform.
From Figures 11(a) and 11(b), it can be seen that the upper part of the side clearance is reduced by 1.39 mm and the lower part is reduced by 0.45 mm. We analyze that the phenomenon is caused by a combination of thermal expansion of the azimuth track and welding deformation during the welding process. Although side clearance of the azimuth track is not used as an evaluation indicator of welding quality, recording the variation value of the side clearance throughout the welding process will provide experience for welding on-site the QTT's azimuth track.

Conclusions
In order to obtain the experimental data of welding applicable for QTT's azimuth track, and study and improve the feasibility of welding process applicable for QTT's azimuth track, experiments were performed. After welding, the welds of the track with 42CrMo as the base material were inspected by magnetic particle testing and ultrasonic testing. Te fatness of the track was measured with a theodolite. In addition, an opposite deformation jig was designed for the QTT's track. Te welding process of the track under the constraint of the opposite deformation jig was simulated using the fnite element method. Te conclusions can be summarized as below.
After the opposite deformation process constrained by the jig and the deformation process of welding, the clearance located under the stress relief hole of the track shrinks by about 2 mm.
Tere are three deformations of the azimuth track that occurred during the welding process. Te opposite deformation jig designed for the QTT reduces the welding deformation of the track by 1.4 mm. Finally, the fatness of the two tracks was reduced from 2.2 mm to 0.3 mm.
Te numerical simulation shows that the opposite deformation generated by the opposite deformation jig ofsets the welding deformation of the track to 0.33 mm, and the residual stress after welding is 47.8 MPa. Te heat treatment Advances in Astronomy after welding and appropriate reduction of the opposite force applied to the track will obtain better welding results.
NDT shows that although there are microcracks at a depth of 40 cm∼50 cm in the track, this position does not bear the main load of the antenna, so it does not afect the life of the azimuth track.
Te track used in this experiment is the same as the QTT's azimuth track, which will provide experience and data to support the construction of the QTT.

Data Availability
Some standard data for the metallic materials used in this study were obtained from the ASTM publicly accessible website (https://www.astm.org/products-services/bos.html). Other data that support the fndings of this study are available from the corresponding author (xuqian@ xao.ac.cn) upon reasonable request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.