Influence on the roof stability of EMU induced by welding deformation

The EMU roof with a thin plate structure is prone to buckling deformation during welding, which will affect its stability. Due to the complex structure, large size, and many types of welded joints, it is an urgent problem to solve the influence of different joint shapes on welding deformation and buckling stability in one model. Based on the inherent strain-temperature loading method, the inherent strain data of four kinds of local joint butt, lap, fillet, and plug welding were accurately obtained through joint welding deformation verification. Then the welding deformation simulation and buckling stability analysis were conducted. The results indicate that plug welding will have minimal impact on roof deformation. The roof buckling deformation cannot occur under the original and 1.2 times heat input conditions are selected within the range of the actual given heat source parameters. Under the 1.5 times heat input condition, the roof buckling deformation occurs. The results provide technical support for the selection of the welding process and the roof stability study of the EMU.


Introduction
The roof structure of the EMU is typically assembled by welding the roof frame and roof sheet.Due to its large curvature, it is prone to deformation during welding, assembly, and interior installation, affecting the appearance of the entire vehicle [1].Moreover, the thin sheet structure is susceptible to buckling instability damage due to the magnitude of welding heat input [2].Therefore, there are still urgent and important problems with weld deformation of large structures and buckling stability that need to be addressed in industrial production [3].
The roof structure of the EMU is large, and the cost of welding experiments is high.It is difficult to study the welding deformation through experiment methods for such big structures.With the development of computer technology, the use of welding numerical simulation instead of physical experiments can effectively predict and control the deformation.Wu and Kim [4] used the temperature loading method to investigate the welding deformation of the butt plate and summarized the relationship between the inherent strain and the plate thickness.By comparing the calculation results between the experimental and thermal elastic-plastic methods, it is found that the method can better predict the welding deformation of thin plates.Most of the roof panels adopt a thin plate structure, which is prone to buckling deformation during welding.To investigate the buckling stability of thin plates, Wang et al. [5] took thin plate reinforced structures with butt joints and fillet joints as the research object, explained the mechanism of buckling caused by welding, and discussed the applicability of calculation methods and inherent deformation methods in predicting buckling for welded joints.Zaeem et al. [6] investigated the local and global welding-induced buckling deformation of thin plate T joints during and after welding.
The studies above focus primarily on the inherent deformation of individual joints and the welding buckling deformation of simple structures.The EMU roof is comprised of a variety of welding joints, including butt and fillet welding between the longitudinal and bending beams, segmental welding between the longitudinal beams and roof panels, lap welding between the center and side roof panels, and plug welds between the bending beams, longitudinal beams, and roof panels.Currently, fewer people study the welding simulation with one model considering various welded joints, and even fewer people analyze the buckling stability of large structures with multiple welded joints.
Given the above problem, the thermal elastic-plastic finite element method was used to calculate the residual plastic strain of the four types of joints, and calibration also was done to extract the inherent strain value.Buckling deformation induced by welding was calculated based on actual clamping conditions, and the impact of varying heat input on roof stability was analyzed.This is useful to reduce welding deformation and provide technical support to enhance the overall stability of the roof.

Basic theories
Welding buckling deformation describes the deformation phenomenon that occurs in welded structures due to residual compressive stress from welding, where longitudinal shrinkage is the primary cause of buckling deformation [7].
The welding shrinkage load is determined by the equivalent shrinkage load APP F of the longitudinal residual stress on the central section of the weld.This stress is the total of the longitudinal residual stresses.
where N is the quantity of elements in the weld section, i  and i  are the mean longitudinal residual stress and strain of the i -th element on the intermediate weld section, measured in MPa, i A is the area of the i -th element (mm 2 ), and E is the elastic modulus in GPa.
To estimate the buckling behavior of the structure while welding, the critical buckling load is related to the shrinkage load of the equivalent welding stress, as defined in Equation ( 2) [8].
where CBL F is the crucial buckling load in N,  is the computed eigenvalues, weld A is the crosssectional area of the weld (mm 2 ), and  is the coefficient of linear expansion in 1/°C.

Introduction to welded joint forms
The roof welding joints consist of four types: butt, lap, fillet, and plug welding.The structure is simplified with a plate thickness of 2 mm.The material used is Q350, and the welding process parameters are shown in Table 1.The data in brackets is the best value after calibrating the heat source.

Inherent strain calculation of welded joints
Based on the thermal elastic-plastic method, the simulation calculation of four kinds of joints was carried out, the inherent strains of various joints were extracted, and the welding deformation of the three-dimensional thermal elastic solid model and the two-dimensional inherent strain shell model were compared.After data correction, the inherent strain magnitude and range in 2D shell elements were determined with high accuracy.
3.2.1.Lap joint.We took a 2+2 mm lap welding joint as an example, and similar validation processes were conducted for the remaining welding joints.A three-dimensional model of the lap welding joint, as depicted, was performed for thermal elastic-plastic analysis.Inherent strains in the model were extracted, and the average longitudinal and transverse inherent strain values were calculated.These values were then applied to the two-dimensional model weld by using the thermal expansion coefficient.
Through a comparison of the deformation curves obtained from the thermal elastic-plastic method and the inherent strain method (as shown in Figure 1), corrections were made to determine the magnitude and application scope of the inherent strain to maintain the consistent calculation result from the two methods.

Fillet and butt join.
The deformation curves for fillet and butt joints, obtained by using the same verification method, were shown in Figure 2.

Plug welding.
Currently, there is little information regarding the three-dimensional thermal elastic-plastic analysis of plug welds.To verify the plug welding, the relevant study in [9] was consulted to determine the plastic strain value for a plate thickness of 2+2 mm.The beam element was used to simulate plug welding and the extracted inherent strain was applied at the welding seam.The results obtained consistently align with the referenced deformation, demonstrating the accuracy of the plug welding simulation, as illustrated in Figure 3.

Establishment of roof finite element model
The total length of the roof measures 25, 500 mm, with a width of 3, 112 mm.The roof skeleton comprises 13 longitudinal beams and 45 curved beams.Plug welding is used to connect the bending beams with the roof panels.The positioning longitudinal beams are joined to the roof panel by using a two-sided segmental weld, while the remaining 11 longitudinal beams and the roof panel are connected through plug welding.Butt and fillet welding are employed to connect the bending beams and longitudinal beams.Conducting a 1:1 3D solid element numerical simulation is not realistic for a large and complex roof structure.Hence, it is necessary to develop a 2D shell finite element model using the inherent strain temperature loading method.
The roof consists of 350 butt welds, 1, 924 fillet welds, and 342 lap welds, all directly connected by shell meshes.Additionally, there are 4, 966 plug welds.The beam elements are chosen to simulate the plug welds, considering time efficiency and loading effects [10].The overall finite element model comprises 7, 582 welds with a total length of 122 m.The mesh size near the weld is refined to 5×5 mm, while the maximum mesh size away from the weld is 25×26 mm.The total number of elements is 456, 309 with 438, 696 nodes as shown in Figure 4.The X-axis is the longitudinal direction, the Yaxis is the vertical direction, and the Z-axis is the transverse direction.The naming of the longitudinal and bending beams is shown in Figure 5.

Welding deformation calculation
Based on the actual clamping conditions, vertical constraints were applied to the curved beams at the junctions between each longitudinal beam and bending beam.Constraints were also enforced at both roof ends to prevent rigid body displacement.The clamping conditions are illustrated in Figure 6.
Although the roof bending beams and a portion of the longitudinal beams are joined to the roof panel by plug welding, the influence of plug welding is often neglected in the numerical simulation of many welded structures.This paper first explored the inherent strain loaded by plug welding and examined the resulting deformation of the welding.Considering that the roof deformation occurred primarily in the vertical direction, this analysis focused on Y-direction deformation, as shown in Figure 7.  Figure 7 shows that the maximum roof deformation measured was 0.559 mm only considering plug welding.It was on the 11th longitudinal beam, located between the 26th and 27th bending beams, while other primary deformations were present on both sides of the roof.Considering all the different welding forms, the deformation cloud is shown in Figure 8.The maximum deformation of the skeleton was 3.865 mm, considering all types of welds, which occurred at the vertical fillet weld between the third longitudinal beam and the first bending beam, as shown in Figure 8.The maximum deformation of the roof panel was 3.445 mm, situated near the roof panel between the second longitudinal beam and the twenty-first bending beam.The influence of the plug welds on the deformation of the roof plate was relatively insignificant.In large structural welding simulations, the deformations caused by plug welds can be ignored to improve efficiency.

Analysis of roof welding buckling stability
If the heat input for the thin plate structure of the roof (plate thickness of 2 mm) is not properly selected, the combined effect of the residual compressive stresses from different welds can potentially cause the compressive stresses to exceed the critical instability stresses of the roof structure.This will cause buckling deformation of the roof plate, and it is necessary to analyze its stability.
Through the initial welding heat input and actual clamping conditions, the buckling factor of the first 50 modes of the roof was calculated, and the buckling factor and instability regions of the entire roof caused by welding were obtained, as shown in Table 2.Under the original welding heat input parameters, buckling deformation occurred only on the roof longitudinal beam, with a buckling factor of less than 1.However, the buckling factor of the roof plate was greater than 1, indicating that welding did not cause buckling instability failure in the roof plate.
Considering that welding deformations mainly arise near the welds connecting the side and middle roof plates, the effect of various welding heat inputs on the deformations in this region was investigated.So, the influence of different heat inputs on the stability of three joint types, butt, lap, and fillet joints, was mainly considered, as detailed in Table 3.
Table 3.We adjust the heat input parameters to 1.2 times and 1.5 times the original and the corresponding buckling factors and instability regions are shown in Table 4.  4, the buckling factor of the roof panel at 1.2 times the heat input was 1.026, indicating that the roof is in a critical condition.At 1.5 times the heat input, the buckling factor was 0.914, which was less than 1, indicating that the roof was in an unstable failure condition.Both the original heat input and 1.2 times the heat input were all within the range of welding parameters shown in Table 1, which suggests that only these welding process parameters were selected appropriately, instability damage to the roof panel could be avoided.

Conclusion
(1) Based on the inherent strain-temperature loading method, a large-scale welding deformation simulation model that considered four types of joint shapes simultaneously was established through welding deformation verification.
(2) Considering all weld joint forms under the original welding heat input and real clamping conditions, the maximum roof deformation was measured to be 3, 865 mm.This occurred at the fillet weld joint of the third longitudinal beam and the first bending beam of the skeleton.When only considering plug welding, the maximum deformation value was 0.559 mm, which was observed between the 11th longitudinal beam and the 26th and 27th bending beams.The total deformation due to plug welding was minimal.
(3) Under the original welding heat input, the roof panel did not experience buckling instability damage due to residual compressive stresses, with a buckling factor of 1.151.At 1.2 times the heat input, the buckling factor of the roof panel reached 1.026, indicating that the roof was in a critical condition.At 1.5 times the heat input, the buckling factor of the roof panel was 0.914, leading to instability damage.It was crucial to select appropriate clamping conditions and welding heat input in practical welding processes to ensure the quality of the roof welding.

Figure 2 .
Figure 2. Comparison of fillet and butt deformation curves.

Table 1 .
Welding process parameters

Table 2 .
Results of roof welding buckling analysis.
Table of various heat input parameters for each joint.

Table 4 .
Buckling analysis results for various heat inputs.