2.1 Heat source calibration
The side-wall of a high-speed EMU welded from five pieces of 6005A aluminum alloy with extruded profiles was considered. Two types of welding joints were considered, namely, butt and lap joints. Heat source calibration was carried out on both to develop a heat source model for simulation calculations.
The actual side-walls were welded using MIG welding, thus the double ellipsoidal heat source model proposed by Goldak [25] was selected for simulation. The forming of the weld was controlled by the shape parameters of the double ellipsoidal heat source model. Changing these parameters enabled calculation of different heat source shapes, resulting in the formation of different welds and diverse temperatures of the melt pool, which affected the temperature field of the welded component and caused deviations in the calculated stress field, and deformation. The relevant parameters of the heat source model were constantly adjusted after the process parameters were determined, and the heat source shape consistent with the actual molten pool shape was obtained. In [26], the relationship between plate thickness and double ellipsoid heat source model was provided, and the shape parameters was calculated using Eq. (1) to check the heat source.
Table 1 Welding and heat source parameters of butt and lap joints
Welding parameter
|
Butt joint
|
Lap joint
|
Welding speed V
|
12 mm/s
|
13 mm/s
|
Welding current I
|
210 A
|
260 A
|
Welding voltage U
|
22 V
|
25 V
|
Heat source efficiency
|
75%
|
75%
|
Total energy input Qz
|
385 J/mm
|
480 J/mm
|
Net energy input
|
289 J/mm
|
360 J/mm
|
The welding process parameters are presented in Table 1; as shown in Eq. (1), double ellipsoidal heat source shape parameters were adjusted for the two types of welding joints. The calculated heat source cross section was compared with the joint heat source model obtained after physical experiment corrosion. The simulated heat source was close to the actual heat source result, as shown in Fig.1, which satisfied the molten pool boundary criterion. The measured molten pool area was also consistent with the actual heat source. Therefore, the established double ellipsoid heat source was suitable for using as a heat source model for MIG welding. The final determined parameters of the double ellipsoid heat source model are shown in Table 2.
Table 2 Heat source parameters
Heat source parameter
|
Butt joint
|
Overlap joint
|
Width a
|
3 mm
|
3.5 mm
|
Depth b
|
4 mm
|
5 mm
|
Front half-axle length cf
|
3 mm
|
3.5 mm
|
Rear half-axle length cr
|
12 mm
|
14 mm
|
Front half-axis energy distribution ff
|
0.8
|
0.8
|
Rear half-axis energy distribution fr
|
1.2
|
1.2
|
2.2 Local model introduction
To improve the accuracy of the simulation, the inherent strain database for the local model is typically calculated using three methods, namely, the thermal elastic-plastic method [27,28], thermal cyclic curve method [29,30], and shrinkage force method [31,32]. In this study, these three methods were used to simulate and analyze the local model using Simufact software; simulation and experimental results were compared to identify the best simulation calculation method, and then, the inherent strain database of the two types of welding joints was established.
A small part between the upper and middle window panels was selected as a local model (dimensions = 1000 mm × 600 mm). There were two butt joints in the local model (Figure 2(a)) which used the heat source model presented in Table 2. 3D Solid elements were used to simulate the local model, with 424,705 nodes and 370,800 elements.
Five measurement points A–E were selected on the workpiece transverse centerline; these were located on the weld, on the edge of the weld, on the heat-affected zone (near the weld), on the heat-affected zone (away from the weld), and on the base material, respectively, and were 3 mm, 8 mm, 23 mm, 36 mm, and 280 mm, respectively, away from the center line of the weld. These were also the measurement points of residual stresses as well as simulation model tracking points, as shown in Figure 2(b).
During the actual processing, combination clamping conditions of the supporting platform and square blocks were used, as shown in Figure 3 (a). The simulation analysis was therefore based on the actual processing, and the restraints considered the same clamping conditions, as shown in Figure 3 (b); the welding was done along the X-direction.
2.3 Validation analysis of residual stresses
Residual stresses in the butt joint structure, determined by simulation, were mainly attributed to longitudinal residual stress. To better compare the accuracy of the results obtained using the three methods, the residual stresses calculated at five points (shown in Figure 2(b)) were selected. Comparison of simulated and measured values including longitudinal residual stress and relative error was shown in Figure 4. Furthermore, Table 3 provided a comprehensive explanation of each of the three methods. X-ray diffraction (XRD) was used for testing the residual stress of the joints. Because the test depth was only 20 µm, the additional stress layer on the surface was stripped by electrolytic polishing, and then, the actual distribution of the residual stress for welding was accurately measured. This mainly comprised five steps, namely, inspection, grinding, polishing, cleaning, and testing.
As shown in Fig. 4, the thermal elastic-plastic method had high calculation accuracy, and its curve was the closest to the measured curve, and the relative error was very small. The calculation results of the thermal cycle curve were also closer to the measured results, but the relative errors were large in the position away from the weld, while the calculation results of the shrinkage force method were the farthest from the measured curve, and the relative errors of each measuring point were large. This was because the thermal elastic-plastic method adopts a typical nonlinear process, which requires multiple iterations and is time consuming; however, it has high calculation accuracy. Furthermore, the thermal cycle curve method is based on the thermal elastic-plastic method, which further simplifies the moving heat source of the thermal elastic-plastic method. The shrinkage force method is based on the calculation theory of empirical accumulation and has poor accuracy. Therefore, this method will not be considered in the following discussion.
The simulated results of points A and B near the weld were far from each other from a single curve. This was because welding heat was most concentrated at the center of the weld, and the working conditions were complex and varied. Therefore, the absolute error of the numerical value on the center of the weld obtained by simulation calculation was larger than that in other regions, but it did not exceed 10% and the relative error was small. Except for shrinkage force method, the simulated results of points C–D were close to measured results and had low relative error based on the thermal elastic-plastic method and the thermal cycle curve method. The absolute error was only approximately 5%. The simulated results of point E was close to measured results although high relative error, this was because point E was far away from the weld, the temperature gradient was small, resulting in a small residual stress value, so a small absolute error would induce a large relative error at point E.
As shown in Table 3, under the same computer configuration, the same model, and the same mesh size and number, the calculation time of the three methods varied considerably, and the calculation error was also large. The thermal elastic-plastic method had high calculation accuracy and long calculation time, which made it suitable for small models that require high calculation accuracy. The thermal cycling curve method had relatively high calculation accuracy, and its calculation time was significantly smaller than that of the thermal elastic-plastic method, making it suitable for models of medium and large structures with high calculation accuracies. The shrinkage force method had lower calculation accuracy, making it suitable for models of large structures with low calculation accuracies. Thus, the thermal elastic-plastic method was used to simulate local models for obtaining high precision results of inherent strain values.
Table 3 Comparison of three methods
Methods
|
Thermal elastic-plastic method
|
Thermal cycling curve method
|
Shrinkage force method
|
Computer configuration
|
CPU: Intel(R) i9-11900K @ 3.50 GHz; Memory: 3000 MHz 64 GB
|
Model size.
|
1000 mm × 600 mm × 50 mm
|
Model scale
|
Nodes: 424,705 Elements: 370,800
|
Calculation time
|
72 h 10 min
|
43 h 20 min
|
25 min
|
Residual stresses error
|
Minimal
|
Smaller
|
Larger
|
Range of application
|
Small structure
|
Medium and large structure
|
Large structure
|
2.4 Inherent strain database establishment
In several studies, longitudinal and transverse shrinkage are only considered when using the inherent strain method, and angular deformation is not taken into account. The influence of transverse, longitudinal, and angular deformation should be considered for such large structures of EMU side walls, with >20 m of welds with butt and lap welding joints [33]. Structural welding deformation simulations therefore require a database of inherent strains in all welding joints.
Main steps for establishing the inherent strain database.
(1) Two welding joints were extracted from the overall model, and a 3D solid mesh was created, as shown in Figure 2(a).
(2) Based on the thermal elastic-plastic method, the two welding joints were simulated considering the temperature, material, and non-linearity of heat transfer.
(3) There were significant temperature changes between the arc starting and arc stopping stages of the weld, so the intermediate weld area was selected to extract the relevant data, and it was summarized to obtain the inherent strain database.
The inherent strain databases of the two welding joints are presented in Table 4.