1. Introduction
During the operation of radio telescopes, a series of problems affecting the pointing accuracy of the azimuth tracks [
1], such as track wear, fatigue cracks, and impact damage to track welded joints, occur in the wheel–rail contact system. A lot of design optimizations and improvements to tracks have already been conducted [
2,
3,
4]. For the QiTai radio telescope (QTT) studied in this paper, the joints of the azimuth track are all welded. Since the welded joint is the weakest part of the entire track, most of the damage occurs in this zone. The welded joint of the azimuth track adopts an innovative multi-pass welding method of multi-layer and multi-pass due to the thick track. Therefore, it is significant to study the contact mechanical characteristics in the welded joint.
In the research of welded joints, there are four methods commonly used to obtain the local mechanical properties. The first method is based on hardness testing, characterizing the local constitutive behavior of the welded joint by the correlation between hardness values and strength, but the empirical hardness–strength relationship proposed by different researchers is only valid for the materials studied and lacks universality. The second method is to obtain the stress–strain constitutive relationship by cutting microscopic specimens and conducting tensile, shear, and impact tests. This method can provide a relatively accurate stress–strain constitutive relationship as long as the material in the specimen is uniform. However, it is difficult to ensure the uniformity of the material in the joint due to the presence of welding heat, especially in the heat-affected zone where material property gradients exist. The third method is to simulate the welding process through thermodynamic finite element analysis, but it is difficult to accurately reproduce the temperature history of the welded joint. The fourth method is the DIC technology approach. This method has made good progress. According to these methods, many scholars have conducted all kinds of experiments. Microscopically, Kumar et al. [
5] conducted micro-hardness, tensile, and impact tests on the welded joints and analyzed the microstructural properties of the multi-pass welded joints. Han [
6] explained the evolution of the microstructure and mechanical properties of welded joints. These studies focused on the microstructure of materials and achieved good results. Macroscopically, Saranath et al. [
7] conducted research on the welded joints by cutting microscopic samples and subjecting them to tension, shear, and impact tests, but it is difficult to ensure the uniformity of the materials due to the influence of thermal processes in the welded joint. Zhang et al. [
8] studied the welded joints by simulating the weld process through thermodynamic finite element analysis, but it is difficult to accurately reproduce the temperature history of the welded joint. However, with the widespread application of digital image correlation (DIC) technology, the aforementioned problems have been solved. Zhang et al. [
9] used DIC technology to analyze the strain field of the welded joint, which can effectively obtain the local constitutive relation of the nonuniform welded joint, but it also has a drawback in that it cannot obtain the complete stress–strain curve of the nonfracture position.
In the research on wheel–rail contact, there are already a sufficient theoretical foundation and technical methods for determining the wheel–rail contact of track vehicles. For the mechanical analysis and damage analysis of wheel–rail contact, the mainstream methods currently are finite element simulation analysis and numerical simulation analysis. Tan and Shi [
10] used numerical simulation to solve wheel–rail fatigue damage. Moreover, they [
11] also used the multi-finite-element coupling method and the multi-time-step solution method to solve the dynamics of wheel–rail contact. Many wheel–rail contact methods have been applied in azimuth tracks such as the finite element method. Arslan [
12] and Twllsikivi [
13] found that the track is more prone to significant plastic deformation during wheel–rail contact. Kuminek and Aniolek [
14] investigated the influence of computational accuracy. Tian et al. [
15] analyzed the deformation patterns during wheel–rail contact. Fu et al. [
16] obtained the maximum contact stress and contact width of the wheel–rail based on the Hertz elastic contact theory. Yang et al. [
17] discussed wheel–rail frictional rolling contact using the explicit finite element analysis method. However, these methods lack an experimental basis for material parameters, material properties, and track division. Moreover, the models established above are finite element models of the form “base metal–welded joint–base metal”. Although this method saves a lot of computation time, it ignores the influence of the heat-affected zone of the welded joint, leading to significant discrepancies between the simulation results and the actual test results.
In this paper, we conducted experiments at a macro level. We combined and improved existing methods to analyze the welded joint of the azimuth track by conducting tensile tests and Vickers hardness measurements based on digital image technology. Then, we fitted constitutive models of the welded joint by comparing and analyzing the experimental data, and a real finite element model of the azimuth track was established. Based on these, the Mises stress of welded joints during smooth operation under different loads and the distribution of stress on the welded joint surface during start-up and braking conditions were obtained by simulation.
4. Simulation and Discussion
4.1. The Mises Stress of Welded Joints during Ordinary Working Condition under Different Loads
The overall weight of the QTT is about 6000–7000 tons. It is supported by approximately 30 or more bearing wheels, with each wheel bearing a load of about 200–240 tons. In order to study the influence of the self-weight of the structure on the mechanical characteristics of the azimuth wheel–rail rolling contact, a simulation study for ordinary working condition was conducted to examine the variation in contact stress under five different loads: 200 t, 210 t, 220 t, 230 t, and 240 t.
Figure 17a–c shows the contour of Mises stress under partial loads at different depths of the azimuth track in the BM, HAZ, and WZ. Extracting the Mises stress along the depth direction, the trend of the Mises stress in the BM, HAZ, and WZ with different loads can be obtained in
Figure 17d–f. It can be seen that the Mises stress showed a trend of increasing first and then decreasing with the change in the contact surface depth, and the values of the Mises stress all reached the maximum at a subsurface depth of about 6 mm on the contact surface. For example, the Mises contour under 210 t at 6 mm depth in the HAZ was 375.2 MPa, and it was obviously higher than that at other depths in the same conditions.
Figure 18a shows a stress contour example of the Mises stress distribution in the BM under 200 t.
Figure 18b shows the situation of the maximum Mises stress in the different zones under different loads. It can be observed that the Mises stress on the wheel–rail gradually increased with the increase in load. Meanwhile, it also showed a trend of the stress field with “HAZ > WZ > BM”; it was fully and completely consistent with the distribution pattern of yield strength in the experiment.
Figure 19 shows the vertical deformation distribution of the azimuth track welding joints under different loads, with the vertical deformation of the HAZ being the largest, followed by the WZ, and that of the BM being the smallest.
Through simulation analysis in this part, we first predicted the overall stress field distribution of the QTT under the ordinary working condition with different pre-loads, and this verified the correctness of the experiment by the distribution of the stress in each zone. Secondly, the zone with the highest stress was located at 25–27 mm on both sides of the center of the weld in the track welding area, while the areas with lower stress were at 0–24 mm on both sides and 50 mm away. Thirdly, it was found that the most perilous points for the future operation of the QTT were 22 mm inward from both sides of the cross track and 6 mm vertically from the track. Finally, it was concluded that the maximum vertical deformation occurred in the HAZ zone when the design axle load was 230 t.
4.2. Formatting of Mathematical Components
This section conducts finite element simulations of the start-up and rapid braking of the large radio telescope to better understand the force conditions on the track. Based on the results, appropriate measures can be taken, such as limiting acceleration and velocity, to reduce damage to the track and ensure its safety and reliability.
4.2.1. Start-Up Working Condition
Simulation analysis of the mechanical response of the welded joint at various zones during the telescope start-up process under a 200 t load. The start-up speed is defined using the smooth step amplitude curve provided in ABAQUS, with an acceleration to 1 rad/s within 1 s. The start-up speed loading method is shown in
Figure 20a.
Figure 20b depicts the contact stress distribution on the surface of the welded joint under start-up conditions. It can be observed that the BM, HAZ, and WZ exhibited significant differences in contact stress, and there was also considerable fluctuation in the distribution of contact stress values within the same zone. However, the stress in each zone fluctuated within a fixed range. From a global perspective, under the operating conditions, the distribution of contact stress on the surface of the welded joint showed a W-like pattern.
Therefore, it can be seen that the contact stress amplification in the HAZ was the highest among the three different zones. This indicates that the start-up condition has the greatest impact on the contact stress of the HAZ, which may have a significant effect on the durability of the joint.
4.2.2. Braking Condition
To test the braking condition, we simulated the mechanical response of the welded joint in different zones under a 200 t load during the rapid braking process. In the rapid braking condition, the smooth step amplitude curve provided by ABAQUS was used to define the braking process, as shown in
Figure 21a, and it was set to decelerate to 0 rad/s within 1 s.
According to
Figure 21b, the contact stress distribution on the surface of the welded joint under braking conditions also showed a W-shaped distribution.
Under the start-up condition, the average contact stress at both ends of the BM contact area was approximately 750 MPa, while the average contact stress in the middle of the contact area was approximately 460 MPa; the average contact stress at both ends of the HAZ contact area was approximately 630 MPa, with the average stress in the middle of the contact area at approximately 430 MPa; the average contact stress at both ends of the WZ contact area was approximately 720 MPa, with the average stress in the middle of the contact area at approximately 450 MPa. A comparison with the mechanical parameters of the joint under steady conditions in the previous section revealed that the contact stress in the rail joint area under the start-up conditions was significantly higher than that under stable contact conditions. Specifically, in the HAZ contact area, the contact stress at both ends and in the middle increased by 161 MPa and 102 MPa. It can be seen that, among the three different areas, the HAZ contact area experienced the greatest increase in contact stress. This indicates that the start-up has the greatest impact on the contact stress of the HAZ, which may have a significant impact on the durability of the joint. Therefore, greater attention should be paid to the health of the HAZ. Meanwhile, compared to the distribution of contact stress on the surface of the welded joint in the start-up condition, the braking condition had a similar trend, and its HAZ was also weak.
5. Conclusions
This article experimentally investigated the position distribution and mechanical properties of the BM, HAZ, modified layer, overlay layer, and filling layer in the welded joint of a large azimuth track for the first time through the combination of image recognition with tensile and Vickers hardness tests macroscopically and explored the stress–strain relationship in each region.
By obtaining the tensile curve, image recognition strain field, Vickers hardness curve, and distribution of yield strength and tensile strength from the experiments, a constitutive equation for the elastic–plastic nonlinearity of the welded joint was fitted with the Ramberg–Osgood equation.
By combining experimental data and welding properties, a finite element model of the wheel–rail contact in the welded joint of the large azimuth track was established. The global stress field distribution under different design loads was obtained through simulation, and the weak points under the ordinary working condition, start-up conditions, and braking conditions were determined, providing a theoretical basis for the health monitoring of the track and research on wear and damage.