Fatigue Resistance of Fillet Welds of Traction Rod Brackets on a Locomotive Bogie Based on International Union of Railways Standards and Improvement Measures Adopted

Abstract

To solve the problem of fatigue failure in fillet welds of traction rod brackets on locomotive bogies of a given model, the cause for failure and the improvement method were studied. The results show that when there is maximum clearance at weld roots, maximum incomplete fusion of sidewalls, maximum incomplete fusion at weld roots, and maximum pores allowable in the ISO 5817 standard, the stress amplitude separately increases by 70~97%, 53~55%, 40~46%, and 19~34%. Despite this, when various types of defects of the maximum size are present in the weld alone, the static and fatigue strengths of fillet welds with a throat depth of 6 mm on the traction rod bracket can still meet the requirements in the UIC615-4 standard. In practical fillet welds, defects including clearance at weld roots, incomplete fusion, and pores are very likely to occur at the same time, which may induce fatigue failure in fillet welds of traction rod brackets within the original design life. According to the size of the frame and the traction rod brackets, a strengthening scheme for increasing the throat depth of fillet welds of traction rod brackets to 8 mm was designed. Calculation results of the strengthening scheme show that for new structures subjected to overall post-weld stress-relief thermal treatments, the maximum stress amplitude decreases by 5~29% when increasing the throat depth of fillet welds from 6 to 8 mm. For structures in service with the throat depth of fillet welds increased from 6 to 8 mm through repair welding, peak residual stress at the weld root after repair welding can reach 383 MPa. Because overall stress-relief thermal treatments cannot be performed on repair-welded structures, the fatigue strength of repair-welded fillet welds cannot meet the requirements of UIC615-4; therefore, local stress-relief treatments have to be performed in the welded zone. The results are of guiding significance for the treatment of locomotives in service and performance improvement of new locomotives and suggest that the current standard is relatively conservative.

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. Material parameters.

	Material	Elastic Modulus/MPa	Poisson’s Ratio	Yield Strength/ MPa	Ultimate Strength/ MPa	Coefficient of Thermal Expansion/°C	Specific Heat kJ/kg °C	Thermal Conductivity W/m °C	Surface Coefficient of Heat Transfer W/m2 °C
Frame	S355J2	2 × 105	0.3	355	470	1.1 × 10−5	460	50	100
traction rod bracket	E300-520-MS C2	2 × 105	0.3	300	520	1.1 × 10−5	460	50	100

. 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. Combined conditions of supernormal loads (unit: N).

Load Conditions	Vertical Forces in Each Side of the Frame		Transverse Load	Longitudinal Load	Loads of Driving Devices			Load of Brake Carrier
	Left Side Sill	Right Side Sill			Dead Load	Vibration	Motor Torque
1.1	159,412.5	159,412.5	0	0	35,580	0	0	0
1.2	111,589	111,589	193,500	0	35,580	0	0	0
1.3	111,589	111,589	193,500	0	35,580	0	0	0
1.4	111,589	111,589	−193,500	0	35,580	0	0	0
1.5	111,589	111,589	0	0	35,580	0	0	0
1.6	111,589	111,589	0	47,500	35,580	10 g	11,389	0
1.7	111,589	111,589	0	47,500	35,580	−10 g	11,389	0
1.8	111,589	111,589	0	−47,500	35,580	10 g	−11,389	0
1.9	111,589	111,589	0	−47,500	35,580	−10 g	−11,389	0
1.1	111,589	111,589	0	−10,025	35,580	10 g	0	26,025
1.11	111,589	111,589	0	−10,025	35,580	−10 g	0	26,025
1.12	111,589	111,589	0	10,025	35,580	10 g	0	26,025
1.13	111,589	111,589	0	10,025	35,580	−10 g	0	26,025
1.14	111,589	111,589	0	47,500	35,580	10 g	45,556	0
1.15	111,589	111,589	0	47,500	35,580	−10 g	45,556	0
1.16	111,589	111,589	0	−47,500	35,580	10 g	−45,556	0
1.17	111,589	111,589	0	−47,500	35,580	−10 g	−45,556	0
1.18	111,589	111,589	0	0	35,580	10 g	45,556	0
1.19	111,589	111,589	0	0	35,580	−10 g	45,556	0
1.2	111,589	111,589	0	0	35,580	10 g	−45,556	0
1.21	111,589	111,589	0	0	35,580	−10 g	−45,556	0
1.22	85,837.50	85,837.50	0	0	35,580		0	0
1.23	79,706.50	79,706.50	0	128,756.25	35,580		0	0
1.24	79,706.50	79,706.50	0	−128,756.25	35,580		0	0

,

Table A3. Combined conditions of operational loads (unit: N).

Load Conditions	Vertical Forces in Each Side of the Frame		Transverse Load	Twisting Load
	Left Side Sill	Right Side Sill
2.1	79,707	79,707	0	0
2.2	71,735.625	55,794.375	0	0
2.3	71,735.625	55,794.375	122625	0
2.4	103,618.125	87,676.875	0	0
2.5	103,618.125	87,676.875	122,625	0
2.6	55,794.375	71,735.625	0	0
2.7	55,794.375	71,735.625	−122,625	0
2.8	87,676.875	103,618.125	0	0
2.9	87,676.875	103,618.125	−122,625	0
2.1	71,735.625	55,794.375	122,625	5‰ track twist
2.11	71,735.625	55,794.375	122,625	−5‰ track twist
2.12	103,618.125	87,676.875	122,625	5‰ track twist
2.13	103,618.125	87,676.875	122,625	−5‰ track twist
2.14	55,794.375	71,735.625	−122,625	5‰ track twist
2.15	55,794.375	71,735.625	−122,625	−5‰ track twist
2.16	87,676.875	103,618.125	−122,625	5‰ track twist
2.17	87,676.875	103,618.125	−122,625	−5‰ track twist

,

Table A4. Combined condition 1 of special operational loads (unit: N).

Load Conditions	Vertical Forces in Each Side of the Frame		Longitudinal Load	Loads of Driving Devices		Damper Load	Load of Secondary Vertical Damper
	Left Side Sill	Right Side Sill		Load of Vertical Acceleration of the Motor	Counter-Force of Motor Suspender
3.1	79,707	79,707	138,500	43,560	39,816	−108,000	20,445
3.2	79,707	79,707	138,500	−43,560	39,816	−108,000	−20,445
3.3	79,707	79,707	−138,500	43,560	−39,816	108,000	20,445
3.4	79,707	79,707	−138,500	−435,560	−39,816	108,000	−20,445

,

Table A5. Combined condition 2 of special operational loads (Unit: N).

Load Conditions	Vertical Forces in Each Side of the Frame		Longitudinal Load	Load of Driving Device	Damper Load	Load of Secondary Vertical Damper	Normal Force on Each Unit of the Brake	Frictional Force of Each Unit of the Brake
	Left Side Sill	Right Side Sill
4.1	79,707	79,707	−38,500	43,560	108,000	20,445	−38,500	11,435
4.2	79,707	79,707	−38,500	−43,560	−108,000	−20,445	−38,500	11,435
4.3	79,707	79,707	38,500	43,560	108,000	20,445	−38,500	−11,435
4.4	79,707	79,707	38,500	−43,560	−108,000	−20,445	−38,500	−11,435

and

Table A6. Combined condition 3 of special operational loads (unit: N).

Load Condition	Vertical Forces in Each Side of the Frame		Longitudinal Loads of Wheels
	Left Side Sill	Left Side Sill	Left	Right
5.2	79,707	79,707	24,525	−24,525
5.3	79,707	79,707	−24,525	24,525

(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.

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

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:

$${\sigma }_e=\sqrt{\frac{1}{2}\left[{\left({\sigma }_1-{\sigma }_2\right)}^2+{\left({\sigma }_2-{\sigma }_3\right)}^2+{\left({\sigma }_3-{\sigma }_1\right)}^2\right]}\le \left[\sigma \right]$$

(1)

In Equation (1), ${\sigma }_e$ is the von Mises equivalent stress; ${\sigma }_1$, ${\sigma }_2$, and ${\sigma }_3$ are the first, second, and third principal stresses, respectively; $\left[\sigma \right]$ is the allowable stress, where $\left[\sigma \right]={\sigma }_s/n$; ${\sigma }_s$ is the yield strength of the material; and $n$ is the safety factor. The yield limit $\sigma$ 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. Coordinates for inflection points on the enclosed outline in the Goodman diagram of fatigue limit.

Inflection Point	Mean Stress σm	Stress Amplitude σa
A	0	${\sigma }_{-1N}$
B	$\frac{{\sigma }_{yt}-{\sigma }_{-1N}}{{\sigma }_b-{\sigma }_{-1N}}{\sigma }_b$	${\sigma }_{yt}$
C	${\sigma }_{yt}$	${\sigma }_{yt}$
D	$\frac{{\sigma }_{yt}-{\sigma }_{-1N}}{{\sigma }_b-{\sigma }_{-1N}}{\sigma }_b$	$\frac{\left({\sigma }_b+{\sigma }_{-1N}\right){\sigma }_{yt}-{2\sigma }_b{\sigma }_{-1N}}{{\sigma }_b-{\sigma }_{-1N}}{\sigma }_b$
E	0	${-\sigma }_{-1N}$
F	${{\sigma }_{-1N}-\sigma }_{yc}$	${-\sigma }_{yc}$
G	${-\sigma }_{yc}$	${-\sigma }_{yc}$
H	${{\sigma }_{-1N}-\sigma }_{yc}$	${{2\sigma }_{-1N}-\sigma }_{yc}$

. Therein, ${\sigma }_{-1N}$ is the fatigue strength in symmetrical cycling under the given fatigue life N; $\sigma$ denotes the ultimate tensile strength; $\sigma$ is the tensile yield limit; and $\sigma$ is the compressive yield limit.

Step 2: The maximum principal stress σ_max, minimum principal stress σ_min, mean stress $\sigma$, and stress amplitude ${\sigma }_a$ under operational loads are calculated.

The minimum and maximum working stresses, ${\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}$, 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 ${\sigma }_m$ and stress amplitude $\sigma$ are calculated using Equation (2).

$${\sigma }_m=\frac{{\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}+{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}}{2} \mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}{\sigma }_a=\frac{{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}}{2}\mathrm{}$$

(2)

Step 3: If the mean stress σ_m, maximum principal stress σ_max, and minimum principal stress σ_min 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.

3. Results and Discussion

3.1. Analysis of the Static Strength under Supernormal Loads

The combined conditions of supernormal loads in Table 3 were applied to the FEM model of the bogie frame. Results show that under the combined conditions of supernormal loads, the maximum equivalent stress on the attachment weld of the type A traction rod brackets in each model is found under Condition 5(1.5) and the maximum stress is 123.12 MPa; the maximum equivalent stress on the attachment weld of the type B traction rod brackets is observed under Condition 15(1.15) and the maximum stress is 148.72 MPa, as shown in Figure 10. Under conditions of supernormal loads, the calculated maximum equivalent stress of traction rod brackets is always lower than the allowable stress of 215.15 MPa, showing that fillet welds of traction rod brackets always meet requirements for the static strength in the UIC615-4 standard under the 24 combined conditions of supernormal loads.

3.2. Analysis Results of the Fatigue Strength under Operational Loads

All root nodes of fillet welds of traction rod brackets were taken as stress measuring points, and the stress of all models under each condition of operational loads was calculated. The mean stress and stress amplitude were calculated (

Table 4. Maximum stress amplitudes at root nodes of fillet welds of traction rod brackets of the frame (unit: MPa).

	Model	Type A Traction Rod Brackets	Type B Traction Rod Brackets
1	Fillet weld A6 of the existing welded structure	42.68	30.49
2	Clearance (h = 1.7 mm)	72.63	60.02
3	Incomplete fusion of sidewalls (l = 10 mm, h = 2 mm)	65.28	47.27
4	Incomplete penetration of weld roots (l = 10 mm, h = 2 mm)	59.82	44.41
5	Pores (d = 2 mm, s = 20 mm)	50.95	40.91

).

Goodman diagrams of fatigue strength curves were drawn for the calculation results of all models, and the results are illustrated in Figure 11 and Figure 12. The strengths of fillet weld roots in all models were found to meet the design requirements for fatigue strength.

The calculated results show that when various defects allowable in the UIC standard are present in the welds, the strengths at the fillet weld roots of traction rod brackets all meet the design requirements for fatigue strength; because locations with the maximum stress amplitude are locations most prone to failure of welds, influences of various defects on the fatigue strength were compared from the perspective of stress amplitudes.

It can be seen from Figure 13 that if the maximum clearance at weld roots, maximum incomplete fusion of side walls, maximum incomplete fusion at weld roots, and maximum pores allowable in the ISO 5817 standard are present, the maximum stress amplitude of the fillet welds of type A traction rod brackets separately increases by 70%, 53%, 40%, and 19%; meanwhile, that of the type B traction rod bracket increases by 97%, 55%, 46%, and 34%. This indicates that among the four types of defects allowable in the ISO 5817 standard, clearance exerts the greatest influences on the fatigue strength of fillet welds of the two traction rod brackets, while pores show the lowest influences thereon.

Analysis indicates that fatigue cracks occurred in the locomotive bogie before the driving mileage probably reached the design value because of the following reasons: (1) locomotives observed to have fatigue cracks operate on railway lines under poor conditions; and (2) different types of defects are present in practical fillet welds at the same time. In practice, dozens of locomotives of this model were produced in the same batch and multiple locomotives in which fatigue cracks occurred in traction rod brackets before the accumulated mileage driven reached the design value all operated on the same railway line in the mountainous area. In comparison, fatigue cracks were not found on other locomotives operating on railway lines beyond mountainous areas before the mileage reached its design value. Dissection of fatigue cracks shows that defects, including the large assembly clearance at weld roots, pores, and incomplete fusion, occur simultaneously in the crack initiation zone.

To guarantee the safety of locomotives that have operated, and will operate, on a railway line, defects in fillet welds need to be controlled on the one hand; on the other, the throat depth of fillet welds can be increased to enlarge the bearing area of weld metal, thus prolonging fatigue life.

3.3. Simulation Results for Influences of the Increased Throat Depth of Fillet Welds Due to Repair Welding

3.3.1. Influences of Changes in the Throat Depth of Fillet Welds

Calculated results under combined conditions of supernormal loads suggest that the fillet welds A8 of traction rod brackets on the bogie frame satisfy requirements for the static strength in UIC615-4. Calculated results under combined conditions of operational loads indicate that except for models with cracks, the maximum stress and minimum stress in calculation results of other models are both in the Goodman diagrams, meeting the requirements for fatigue strength. The maximum stress amplitudes at weld roots in models of fillet welds A6 and A8 of the first and second traction rod brackets are separately illustrated in Figure 14 and Figure 15.

When the throat depth of fillet welds increases from 6 to 8 mm, the maximum stress amplitudes of defect-free welds of type A and type B traction rod brackets separately decrease by 5% and 14%, respectively. As the throat depth increases from 6 to 8 mm, if the welds contain the maximum clearance at weld roots, maximum incomplete fusion of side walls, maximum incomplete fusion at weld roots, and the maximum porosity permissible in ISO 5817, the maximum stress amplitude of the type A traction rod bracket separately decreases by 13%, 29%, 24%, and 25%; meanwhile, that of the type B traction rod bracket separately reduces by 17%, 18%, 11%, and 1%. This can be explained as follows: fillet welds with a greater throat depth are more tolerant of defects. It is worth noting that when throat depth enlarges, the maximum stress amplitude of fillet welds with incomplete fusion of side walls exhibits the maximum decrease.

3.3.2. Influences of Residual Stress Induced by Repair Welding

This research first simulated the temperature field during repair welding of fillet welds without defects in the traction rod brackets on the bogie frame (Figure 16). At the initial temperature of room temperature (22 °C), a volumetric heat source of 13 W/mm³ was applied to the fillet welds for 1 s, which were then cooled to room temperature. Taking the transient temperature field as the load for structural analysis, the stress field was simulated. After calculating the residual stress distribution induced by welding, the models with residual stress were solved under the UIC standard conditions; thus, the fatigue strength of the repair-welded structure was measured.

Calculation results of the temperature field during repair welding are shown in Figure 17. Results of the residual stress field induced by overall welding of the bogie frame are displayed in Figure 18. Results relating to the fillet welds of the first and second traction rod brackets are shown in Figure 19 and Figure 20, respectively. Goodman diagrams for calculation results under UIC conditions with residual stress induced by welding are illustrated in Figure 21. Goodman diagrams demonstrate that the calculation results under UIC standard conditions with residual stress induced by welding do not meet the requirements for the fatigue strength of the bogie frame.

To verify the reliability of the repair schemes for defects in the attachment welds of existing welded structures on the type B traction rod brackets of the locomotive bogie, the fillet welds of failed traction rod brackets were repair-welded, and the results were combined with data-processing output from the test railway line, followed by stress-relief treatments after welding. Fatigue tests were conducted on repair-welded fillet welds of traction rod brackets on existing welded structures under equivalent loads on the test railway line. Test results prove that the fatigue life of the repair-welded fillet welds of traction rod brackets reached 10 million cycles. The simulations and practical fatigue tests differ in the following aspect: the welds in simulations incur residual stress, while the fillet welds of traction rod brackets in the practical fatigue tests are subjected to stress-relief treatment. The difference indicates that the residual stress induced by welding affects the fatigue strength of welds. In practice, that is, after repair welding, stress-relief treatments need to be performed to guarantee the safety of the components. Considering that fillet welds cannot be subjected to thermal treatment after repair welding, measures are suggested after welding to eliminate or reduce residual stress.

4. Conclusions

Focusing on the fatigue failure of the fillet weld of the tie rod seat of a locomotive bogie during its design life, the causes of failure and methods of improvement were studied according to UIC615-4 standard load conditions and the Goodman fatigue limit diagram. The main results can be summarized as follows:

(1)

When there are the maximum clearance at weld roots, maximum incomplete fusion of sidewalls, maximum incomplete fusion at weld roots, and maximum porosity allowable in ISO 5817, the stress amplitude separately increases by 70~97%, 53~55%, 40~46%, and 19~34%;

(2)

When various types of defects with the maximum size allowable in the ISO 5817 standard are present in the weld alone, the static and fatigue strengths of fillet welds with a throat depth of 6 mm of the traction rod bracket can still meet the requirement codified in the UIC615-4 standard. The reasons for fatigue failure of fillet welds of the tie rod seat during the design life are complex; analysis shows that in actual fillet welds, defects such as root gap, a lack of fusion, and porosity may occur at the same time, which is one of the possible reasons for fatigue failure of fillet welds during their design life;

(3)

According to the size of the frame and the traction rod brackets, a strengthening scheme for increasing the throat depth of fillet welds of traction rod brackets to 8 mm was presented. Calculations show that for new structures subjected to overall post-weld stress-relief thermal treatment, the maximum stress amplitude decreases by 5~29% when increasing the throat depth of fillet welds from 6 to 8 mm;

(4)

For structures in service, when the throat depth of fillet welds increases from 6 to 8 mm through repair welding, the peak residual stress at the weld root after repair welding can reach 383 MPa; because overall stress-relief thermal treatments cannot be performed on repair-welded structures, the fatigue strength of repair-welded fillet welds cannot meet the requirements codified in the UIC615-4 standard, so local stress-relief treatments must be applied in the welded zone.