1. Introduction
A locomotive bogie generally comprises the primary suspension, secondary suspension, wheelset axle box, traction device, brake, and frame [
1,
2,
3]. To ensure a light-weight ensemble, bogie frames are generally welded structures. The fatigue failure of each component relates to the safety of personnel and locomotives and therefore has long been of concern among researchers [
4,
5,
6,
7,
8].
In an entire bogie, the frame is the skeleton that plays important roles in supporting the car body, ensuring safe operation of locomotives, easing interactions between locomotives and tracks, braking, and steering. In view of this, problems pertaining to locomotive bogie frames remain key topics of research. Based on the DVS 1612 and JIS 4270 standards, Zhang et al. [
9] assessed the fatigue strength of the bogie frame of a certain model. The results show that the bogie frame meets the requirements for fatigue strength in both standards. Under the JIS 4270 standard, welds of the motor cabinet and gearbox bracket are more remarkably loaded, while welds of joints between sill and side sills, and at the transverse stop base, are more significantly loaded under the DVS 1612 standard. Liu et al. [
10] assessed and compared the fatigue strength of welded frames of a certain model separately based on the UIC and JIS standards. The results indicate that the weld toe at the side sills of the frame meets the requirements for fatigue strength when it is evaluated using the UIC standard, while the weld root at side sills of the frame does not meet the requirements for fatigue strength when it is assessed using the JIS standard. Fan et al. [
11], Wang et al. [
12], and Lu et al. [
13] separately evaluated the static and fatigue strengths of different bogie frames based on UIC615-4 and EN13749 standards. They found that the static strengths at key locations of the frames and the fatigue strengths at important locations of welds all meet codified requirements. According to JIS E 4207 and UIC 515/615-4, Jeon et al. [
14] evaluated the fatigue strength of a bogie make of GFRP composites based on the S-N curves and Goodman diagrams of GEP224 glass/epoxy resin composites. Their results indicate that the fatigue strength of the bogie made of GFRP composites satisfies the design requirements; compared with traditional metallic bogies, the bogie fabricated using GFRP composites shows better fatigue performance considering its weight. According to the UIC615-4 and EN13749 standards, Liu et al. [
15] performed static strength, fatigue strength, and modal analysis of a bogie frame fabricated using carbon fiber composites on a subway locomotive through simulation. The calculated results show that the strength of the frame meets working requirements. Mozafari et al. [
16,
17] proposed a novel fatigue-life-prediction theory based on microplasticity and conducted finite element simulation on this basis. Computation indicates that the theory can predict the fatigue life of several selected metallic alloys under multiaxial loads and is accurate. The aforementioned research into bogie frames mainly assesses fatigue strength by combining the standard loads and Goodman diagrams. Considering that the UIC standard can meet stress conditions of various bogie frames, the standard has also been widely used.
Meanwhile, many scholars have also studied the failure of welded frames. Taking the Ti6Al4V/nickel-chromium-iron alloy 625 dissimilar joints obtained by intermediate inserts of vanadium and AISI 304 as a case study, Carone et al. [
18] explored fatigue behaviors of joints using a scanning electron microscope and a confocal microscope. Fracture analysis revealed that the failure mode is mainly related to the presence of multiple pores on crack paths. Xie et al. [
19] experimentally studied the fatigue performance of 2205 two-phase stainless-steel cross-type welded joints, and the results show that fatigue failure of the 2205 steel cross-type welded joints is influenced by material inhomogeneity and welding defects. Wang et al. [
20] conducted finite element simulation and structural dynamic response analysis on the load spectra of hydraulic damper for the axle box of a certain electric locomotive. The results show that if the damper contains welding defects, it is prone to premature failure. Cao et al. [
21] conducted a series of physical and chemical tests and finite element simulation on the failure of girth joints at a natural gas station inspected via X-rays, and the results show that welding defects are original failure factors that induce crack initiation and propagation through walls. For fatigue cracks in fillet welds of traction rod brackets on multiple electric locomotives of a certain model in service before reaching the design life, Ma et al. [
22] experimentally observed the failure thereof and found that fatigue cracks are related to pores in welds, incomplete fusion, and assembly clearance at the root of the fillet welds. Seo Jung-Won et al. [
23] investigated the influences of repair welding on fatigue strength of bogie frames of railway locomotives and compared the fatigue performance of fillet joints not subjected to repair welding and repair-welded fillet joints of SM490A steel. Fatigue test results imply that the S-N curves of repair-welded fillet joints are lower than those of the joints without repair welding. Moreover, they also compared changes in residual stress and the results indicate that the residual stress of repair-welded samples is much greater than that of samples not subjected to repair by welding. For medium-strength welded structural steel widely used in practice, Goo et al. [
24] studied influences of post-weld thermal treatments on materials, and the results indicate that post-weld thermal treatments remove the residual stress and slightly improve the fatigue strength of samples. This all shows that welding defects significantly affect the fatigue strength of bogie frames; therefore, research into the influences of welding defects on welding residual stress is justified.
The aforementioned research reveals that welding defects are key factors that influence the strength of bogie frames. At present, influences of welding defects on the fatigue performance of bogie frames have been extensively studied, while influences of defects on fatigue performance of welded bogie frames remain a focus of much research due to the complexity of such defects and their influences. Therefore, the finite element method (FEM) was adopted to explore influences of defects (assembly clearance, incomplete fusion, incomplete penetration, and pores) according to the International Union of Railways (UIC) standard UIC 615-4. It also developed and evaluated the effect of increasing weld thickness on the fatigue reliability of the bogie frame, formulated a repair plan for in-service equipment based on the new manufacturing plan and evaluated the influence of repair welding stress. Research results are of guiding significance for maintaining locomotives in service and improving new locomotives and provide reference for the assessment of fatigue performance of other welded structures.
2. Methodology
As shown in
Figure 1, the locomotive bogie frame is a welded structure composed of a front sill, a central sill, a rear draft sill, and two bilaterally symmetric side sills. Traction rod brackets in two different shapes (four for each) are mounted on the side sills of the bogie, i.e., the type A traction rod bracket is relatively small, while type B is relatively large. The traction rod brackets are linked with side sills through fillet welds. The material trademarks and physical parameters of the bogie frame and traction rod brackets are listed in
Table 1. The plastic theory used in the research mainly includes three aspects as follows: von Mises yield criterion; correlated flow criterion; and bilinear kinematic hardening criterion. The stress-strain relationships are displayed in
Figure 2 (key technical drawings and calculation parameters are provided in
Appendix A). The established model has fillet welds with failure in the operation process, while other fillet welds without failure on the bogie frame are simplified. Unless otherwise specified below, the throat depth of fillet welds on traction rod brackets is 6 mm.
2.1. Bogie Frame Model and Its Mesh Generation Scheme
Figure 3 shows that tetrahedron elements were used for the mesh generation of the bogie frame model. In the calculation process, an overall model with a coarser mesh was used at first, then sub-models with a more refined mesh were established in regions near the fillet welds of traction rod brackets. Taking the model without defects as an example, the grid size of the overall bogie model was 15 mm, and the model contained 905,282 elements and 278,475 nodes. Elements with a side length of 4 mm were applied to the region around the welds in the sub-models, while those measuring 0.5 mm were used to represent defects and weld roots.
2.2. Boundary Conditions of Bogie Frames and Load Application Locations
According to the actual installation and usage of the bogie frame, the following boundary conditions and loads were applied to the FEM models:
A vertical constraint was applied to the rolling circle of the simulated wheelset;
A transverse constraint was applied to the rolling circle on one side of the wheelset;
A longitudinal constraint was applied to the traction pin;
The vertical load acting on the side sills was applied to the base plate of the secondary rubber-metal pad of the frame;
The transverse load acting on the side sills was applied to the base plate of the secondary rubber-metal pad and the secondary transverse stop of the frame;
The vertical displacement caused by a track twist of either 10‰ or 5‰ was applied at the rolling circle of the wheels in the diagonal simulation.
The 100% load shedding of a wheel was simulated by not applying any constraint to the rolling circle of the simulated wheel. Boundary conditions under Condition 1 of operational loads are displayed in
Figure 4.
2.3. Calculated Basic Loads on the Bogie Frame According to the UIC Standard
The supernormal load, operational load, and special operational load of the bogie were calculated according to the UIC615-4 standard. The loading conditions were combined by referring to the standard, finally obtaining 24 combined conditions of supernormal load, 17 combined conditions of operational load, and 10 combined conditions of special operational load.
Table A2,
Table A3,
Table A4,
Table A5 and
Table A6 (
Appendix A) show the combined conditions of supernormal loads and operational loads. The schematic diagram of one typical operating load condition is shown in
Figure 5. The calculation results under combined conditions of supernormal loads in
Table 2 were used to assess the static strength, while those under 27 combined conditions of operational loads shown in
Table A3,
Table A4,
Table A5 and
Table A6 were adopted to estimate fatigue strength.
2.4. Research Scheme Used to Assess the Influences of Fillet Weld Defects of Traction Rod Brackets
The fatigue strengths of fillet welds of traction rod brackets on the bogie in six weld defect states shown in
Table 2 were calculated. Combining observations from the fracture tests of fillet welds of traction rod brackets on the locomotive bogie and definitions for the types and degrees of weld defects in international standard ISO 5817, the calculation scheme for weld defects was determined by referring to the maximum defect size in the standard. Defects considered in the calculation included the following: assembly clearance; incomplete fusion of sidewalls; incomplete penetration of weld roots; and pores. The defect distribution is illustrated in
Figure 6. Through calculation of various conditions in
Table 2 according to the aforementioned boundary conditions and 27 operational loads, the influences of defects on the fatigue strength of fillet welds were estimated. Unless otherwise stated, fillet welds on traction rod brackets in the present research are defect-free.
Table 2.
Types, sizes, and distribution of defects considered in the calculation.
Table 2.
Types, sizes, and distribution of defects considered in the calculation.
Serial Number | Type of Weld Defect | Distribution of Defects Loci | Defect Size |
---|
Attachment Weld of Traction Rod Brackets | Cross-Section of Welds |
---|
1 | No defects (Figure 6a) | / | / | / |
2 | Clearance at weld roots (Figure 6b) | A clearance of 1.7 mm outside the traction rod brackets on the bogie frame | / | Clearance h = 1.7 mm |
3 | Incomplete fusion of sidewalls (Figure 6c) | Bottom arc corner and midline of the traction rod brackets (Figure 6f) | Incomplete fusion near the weld root in the side of the fusion surface of the traction rod brackets | Length l = 10 mm along the weld length direction and height h = 2 mm |
4 | Incomplete penetration at weld roots (Figure 6d) | Bottom arc corner and midline of the traction rod brackets (Figure 6f) | Incomplete penetration near the weld root in the side of the fusion surface of the cover plate | Length l = 10 mm along the weld length direction and height h = 2 mm |
5 | Pores (Figure 6e) | Two pores are set along the weld length direction at bottom arc corner and midline of the traction rod brackets | Pores near the weld root in the side of the fusion surface of the traction rod brackets | Diameter d = 2 mm and clearance s = 20 mm |
2.5. Research Scheme for Influences of the Throat Depth of Fillet Welds
The throat depth of fillet welds is defined in
Figure 7. The throat depth was increased by 2 mm based on the original fillet weld with the thickness of 6 mm (A6), thus building the fillet weld model of traction rod brackets with a throat depth of 8 mm (A8) containing a single defect separately in different types. The same constraints and operational loads were used in FEM calculations and the results were compared with those arising from use of the original fillet welds.
2.6. Research Scheme for Influences of Residual Stress
It is necessary to perform repair welding on fillet welds with a throat depth of 6 mm on locomotives that have operated and will continue to operate on railway lines under potentially poor conditions, thus increasing the throat depth; because assembly surfaces of bogies on these locomotives have been fine-finished and reached the final size, stress-relief thermal treatments are not allowed after repair welding of the fillet welds. Otherwise, deformation caused by thermal treatments increases the size of the assembly surfaces of traction rod brackets beyond the allowable range. Residual stress is generated in the weld zone after making a welded repair. The actual stress in the weld zone of the repair-welded bogie in service includes the working stress induced by external loads and the residual stress induced by welding. Therefore, influences of residual stress induced by repair welding on the fatigue strength of fillet welds of traction rod brackets should be studied. In the present research, the thermo-dynamic coupling calculation in the repair welding process was performed to ascertain the residual stress distribution in the weld zone. The fatigue strength under constraints and operational loads identical to those mentioned was then calculated using the residual stress model.
2.7. Strength Evaluation of Frame
- 1.
Evaluation of the static strength
Due to the various complex stresses that the locomotive bogie frame is subjected to, strength theory can be adopted to determine whether the material is damaged. The materials used in this article are elastic-plastic materials, so the fourth strength theory is used for static strength verification and evaluation. According to the fourth strength theory, the conditions for the material structure of the frame to not fail under any stress state are as follows:
In Equation (1), is the von Mises equivalent stress; ,
, and
are the first, second, and third principal stresses, respectively; is the allowable stress, where ;
is the yield strength of the material; and is the safety factor. The yield limit of the frame material is 355 MPa and the allowable safety factor S of the base metal of the bogie frame is 1.65, so the allowable stress on the frame is 215.15 MPa.
- 2.
Evaluation of the fatigue strength based on Goodman diagrams
To assess the fatigue strength of frames, Goodman diagrams of fatigue strength curves recommended by the International Union of Railways (UIC) were adopted.
The methods and criterions for evaluating the fatigue performance are described as follows:
Step 1: Goodman diagrams of fatigue limit are drawn. A Goodman diagram is composed of an enclosed octagon ABCDEFGH (
Figure 8) and coordinates for the inflection points are listed in
Table 3. Therein,
is the fatigue strength in symmetrical cycling under the given fatigue life N;
denotes the ultimate tensile strength;
is the tensile yield limit; and
is the compressive yield limit.
Step 2: The maximum principal stress σmax, minimum principal stress σmin, mean stress , and stress amplitude under operational loads are calculated.
The minimum and maximum working stresses,
and
, respectively, are calculated under 27 combinations of operational loads (
Appendix B,
Table A3,
Table A4,
Table A5 and
Table A6).
Figure 9 shows the method of determination of σ
max and σ
min, which mainly involves the following steps: (a) the value and direction of principal stresses at each node on welds under different loading conditions are determined; (b) the direction of the maximum principal stress at each node on welds under all load conditions is set as the basic stress distribution direction, and the corresponding value is the calculated maximum principal stress σ
max; and (c) principal stresses under other load conditions are transformed in the direction of the determined direction of the maximum principal stress and the minimum stress value is ascertained as the calculated minimum principal stress σ
min.
The mean stress and stress amplitude are calculated using Equation (2).
Step 3: If the mean stress σm, maximum principal stress σmax, and minimum principal stress σmin of the bogie frame are all within the enclosed outline (ABCDEFGHA) in the Goodman diagram of fatigue limit of the materials, the fatigue strength of the frame meets the requirements.