Abstract
The bogie frame of a railway is an important structural member for the support of vehicle loading. In general, more than 25 years’ durability is necessary. Much study has been carried out in experimental and theoretical domains on the prediction of the structural integrity of the bogie frame. The objective of this paper is to estimate the structural integrity of the bogie frame of an electric railcar. Strength analysis has been performed by finite element analysis. From this analysis, stress concentration areas were investigated. To evaluate the loading conditions, dynamic stress was measured by strain gauge. It has been found that the stress and strain due to the applied loads were multiaxial conditions according to the location of the strain gauge. Fatigue strength evaluations of the bogie frame were performed to investigate the effect of a multiaxial load through the employment of a critical plane approach.
1. Introduction
The bogies of railway vehicles consist of bogie frames, suspensions, axles, and wheels. The shapes of bogies as well as the load conditions, such as static load and dynamic load, are complex. Therefore, various tests including static load tests, fatigue tests, and track tests are required for the design and the strength evaluation of the bogie [1–4]. The bogie frame is required to last 25 years or longer as the main structure that supports loads of the vehicle body. Although the UIC, EN, and JIS standards [5–7] prescribe the strength evaluation methods of bogie frames, they do not define detailed fatigue life assessment approaches.
EN 13789 [5] defines the static load and the fatigue load to evaluate the strength of bogie frames. The fatigue test in the laboratory requires the load magnitude and cycles to guarantee 30 years within an annual mileage of 200,000 km [5]. However, the load magnitude may vary according to the vehicle type and track conditions. Excessive definition of the load conditions in the fatigue test may make weight reduction and the optimization of bogie frames difficult [8, 9]. If the load conditions of the fatigue test are lower than those of the in-service track, the fatigue damage and the crack may occur during the operation of the railway vehicle. The EN standard requires the fatigue life to be evaluated by track test. The fatigue life evaluation is required to be conducted in accordance with the cumulative damage rule, but the detailed evaluation method has not been specified. In particular, the fatigue life evaluation method for multiaxial load has not been defined. Therefore, a number of detailed studies on the fatigue life evaluation of bogie frames have been conducted [1, 10, 11]. However, there have been few studies on the fatigue life evaluation method and the characteristics of the stress history that occur in the fatigue test and the track test.
In this study, the static load test, fatigue test, and track test were conducted to evaluate the fatigue strength of bogie frames that were used in electric railcars. The characteristics of the load history obtained on track test were evaluated. The load conditions in Korea were compared to those of EN 13798 and the fatigue damage was assessed by applying various fatigue evaluation methods.
2. Finite Element Analysis and Static Test of Bogie Frames
2.1. Finite Element Model
Figure 1(a) shows a driving bogie used in an electric vehicle. A rubber spring is used as the primary suspension and an air spring is used as the secondary suspension. As it is a driving bogie, it has a traction motor and a disc brake is used as the brake system. Figure 1(b) shows a finite element model of the bogie frame. For the modeling, shell elements were used. The number of elements was 51,811, and the number of nodes was 47,356.
(a) Driving bogie
(b) Finite element model of bogie frame
2.2. Load Conditions
The static loads can be divided in accordance with EN 13798 into the exceptional loads and the normal service loads. Table 1 shows the static loads calculated according to EN 13798. The exceptional loads can be divided into nine cases and the normal service loads are divided into four cases. Vertical forces were applied at the air springs and the 1st springs were constrained as boundary conditions. Transverse forces were applied at the lateral buffers, and the 1st springs were constrained. Table 1 shows the boundary conditions for each load.
Table 2 shows the mechanical properties of the materials used in the bogie frame. The main frame material of the bogie is SM490A, the transom pipe is STKM18B, and the bracket is made from SS400. The stress occurring in the bogie frame on exceptional loads should be less than the yield strength of the material used. Under the normal service loads, the mean stress and the stress amplitude are calculated on each load and they should be within the fatigue limit diagram.where is the maximum stress, is the minimum stress, is the mean stress, and is the stress amplitude.
2.3. Static Load Test
For the static load test, the areas where high stress occurred in each load condition should be predicted. Therefore, the finite element analysis was conducted under the same conditions as the static load test. Figure 2 shows the result of the finite element analysis when vertical load is applied. The maximum stress occurred on the bracket attached under the side frame. Figure 3 shows the locations where strain gauges were attached for the static load test. Those locations were selected from the result of the finite element analysis for each load condition. Strain gauges were attached to a total of 44 locations.
(a) Upper location
(b) Lower location
Table 3 shows the result of the static load test on the exceptional loads. On the vertical load, the compressive load of −127 MPa occurred at the point (gauge location No. 2) that is located on the upper side frame, and 113 MPa occurred on the connection (gage location No. 37) between the side frame and the bracket. The maximum stress of 125 MPa from the result of finite element analysis occurred on the connection between the side frame and the bracket, which was a similar result. On transverse load, the maximum stress occurred at the point (gauge location No. 2) which is located on the upper side frame, which was the compressive stress. The maximum tensile stress occurred on the connection between the side frame and the bracket. Under the normal service load conditions, each load to be applied is combined. Table 3 shows that the load conditions of Nos. 10 and 11 are the normal service load conditions. The maximum stress occurred on the connection between the frame and the bracket. The stress that occurred under exceptional loads was less than the yield strength, which was considered to be safe.
Figure 4 shows the result of evaluating the fatigue limit diagram after the mean stress and the stress amplitude were calculated under the normal service load conditions. The stress amplitude and the mean stress were calculated for each combined load. Stresses of all areas where the strain gauges are attached are within the safe area. Therefore, the fatigue strength is assessed to be safe.
3. Fatigue Test and Track Test
3.1. Fatigue Test
The fatigue test of the bogie frame for electric railcars was conducted according to EN 13749. Figure 5 shows the load conditions consisting of the vertical load (), the transverse load (), and the twist load (). In the fatigue test, the loads are composed of the static load, the quasi-static load, and the dynamic load:(i)a static part ,(ii)a quasi-static part ,(iii)a dynamic part ,where α is the roll coefficient, which indicates the load at the curve track, and 0.1 was applied. β is the bounce coefficient, which indicates the dynamic load, and 0.2 was applied. The strain gauges were attached to evaluate the characteristics of the stress history in the fatigue test. The strain gauges were attached to the areas where the maximum stress occurred from the result of the static load test.
Figure 6 shows the load condition for fatigue tests according to EN 13749. In step 1, the fatigue test was conducted by applying an initial load up to 6 × 106 cycles. In step 2, the quasi-static load and dynamic load were increased by 1.2 times and the fatigue test was conducted up to 2 × 106 cycles. In step 3, the quasi-static load and the dynamic load were increased by 1.4 times and the fatigue test was conducted up to 2 × 106 cycles. After the fatigue test in step 1 and 2, cracks should not occur, while very small cracks are permitted in step 3.
Figure 7 shows the test equipment for the fatigue test. The equipment has two actuators for vertical load, one actuator for transverse load, and two actuators for twist load. Figure 8 shows a graph of the fatigue load history in step 1. The quasi-static load and the dynamic load were applied for the vertical load, after the static load was applied. The quasi-static load for the curve track was applied differently to the left and right. The load magnitude changed every 10 cycles. The quasi-static load and the dynamic load were applied to the transverse load. The twist load was applied every 10 cycles. Figure 9 shows the result of nondestructive testing (magnetic particle inspection) after the fatigue test. The nondestructive testing was conducted from steps 1 to 3, and no cracks were evident.
3.2. Track Test
To evaluate the fatigue life of bogie frames for electric railcars, a track test was conducted by using similar bogie frames on an in-service track. The strain gauges were attached to the same locations shown in Figure 5, to compare it with the fatigue test. Figure 10 shows the test vehicle and the data acquisition system for measuring the strain for the track test. The test was performed with the data acquisition system which is MGCplus made by HBM, and the sampling rate was set to 600 Hz. The test distance was 30 km, and the track test was conducted in the same conditions as in-service conditions.
(a)
(b)
4. Test Results and Discussions
4.1. Stress Analysis
This section assesses and compares the stress characteristics occurring in the fatigue test and the track test. Figure 5 shows the location of Points 1, 2, and 3 for comparison of the fatigue test and track test results. Strain gauges were attached to the location where the stresses were large in the static load test. Figure 11 shows the strain history that occurs at Point 1 in the fatigue test. In the fatigue test, vertical load, transverse load, and twist load are applied, with changing every ten cycles. Therefore, Figure 11 shows that the strain repeats the identical shape every ten cycles. Figure 12 describes the strain history that occurs at Point 1 in the track test. The strain history that occurs in the track test shows random shapes. Since the static load is included in the fatigue test, the maximum strain that occurs is greater in the fatigue test than in the track test. However, because the track test does not include static load, the mean strain is close to “0”.
The biaxiality ratio is applied as the parameter to evaluate the local stress conditions [13, 14]. is defined as follows:where is the biaxiality ratio, and is the maximum principal stresses, while is the minimum principal stresses.
Figure 13 shows the changes in and its principal stress of Point 1 in the fatigue test. for all principal stresses is distributed around zero and the direction of the principal stress is distributed around 30°–45°. This is uniaxial and is the proportional loading condition. Figure 14 shows the changes in of Point 1 and its principal stress in the track test. Although is generally distributed between −1 and 1, the stresses with large principal stresses are distributed in “0”. Moreover, the direction of the principal stress with large stresses is fixed at 40°. This is uniaxial and in the same proportion as in the fatigue test. Even though in the case of Point 1, the stresses that occur in the fatigue test and the track test differ from each other in terms of the stress magnitude, the stress conditions are uniaxial, and the direction of principal stresses is similar.
Figure 15 shows the changes in of Point 3 and its principal stress in the fatigue test. varies from −0.8 to 0, and the direction of its principal stress changes from 20° to 40°. This is the multiaxial and the nonproportional loading condition. Figure 16 shows the changes in of Point 3 and its principal stress in the track test. is generally distributed between −1 and 1, and the direction of the principal stress changes from 0° to 90°. This is the multiaxial and the nonproportional loading condition, the same as in the fatigue test.
Therefore, since the stresses of the bogie frame are the multiaxial and the nonproportional loading condition, the fatigue life evaluation should be done by taking this into account.
4.2. Fatigue Life Evaluation
Since the load characteristics can vary in accordance with the vehicle type and track conditions, the stresses characteristics of the bogie frames of electric railcars running in Korea were investigated.
Figure 17 shows comparisons of the stress magnitudes occurring in the fatigue test and the track test. To compare with the fatigue test, the track test was presented by converting the cycle into the case of 30 years of running within the annual mileage of 200,000 km. To do this, the rainflow cycle counting method was used. In both cases, the maximum magnitude of the stress range appears similarly, as shown in Figure 17. Nonetheless, in the fatigue test, the cycle of stresses with a large stress range occurs often.
It is difficult to directly compare both the fatigue test and the track test with the result of cycle counting as shown in Figure 17. Therefore, the equivalent stress range applied in IIW [15] was used, and the formula is as follows:where is the equivalent stress range, is the Miner sum, is the slope of the upper part of the knee point on the S-N curve, is the slope of the lower part of the knee point on the S-N curve, is the stress range of the upper part of the knee point at level of the S-N curve, is the stress range of the lower part of the knee point at level j of the S-N curve, is the stress range of the knee point on the S-N curve, is the number of cycles of , and is the number of cycles of .
Table 4 shows the stresses that occur in the fatigue test and the track test in the equivalent stress range. In the case of Point 1 with the largest stress, the equivalent stress range of fatigue test with 23.89 MPa is much larger than that of track test with 4.21 MPa. In the case of Point 3, it is assessed that the equivalent stress range of the two tests is similar. Since the fatigue test result is larger than the track test result, the load conditions specified for the fatigue test in EN 13749 can be evaluated to be sufficiently conservative compared to the domestic track conditions.
The fatigue life was evaluated based on the stresses occurring in the fatigue test and the track test. For the fatigue life evaluation on welded joints, the method by BS7608 [16] was used. Under BS7608, the S-N curves are classified according to each class and the nominal stress is applied. In the case of tubular nodal joints, the S-N curve to which the hot-spot stress is applied is given. In addition, according to welding configurations, the fatigue notch factors should be used and it is obtained through stress analysis or measurement. Since the configuration of the bogie frame at the strain gauge point falls under Class F, the S-N curve for the fatigue life evaluation that was used was Class F. When the measurement location is far enough from the welded toe, the measured stresses can be assumed as the nominal stress. When this is not the case, since the fatigue life is evaluated conservatively, revisions to this are needed. Figure 18 shows the definition of stresses in welded joints [17].
To take into account the stress concentration in welded joints, finite element analysis was carried out and Figure 19 shows the finite element model. Figure 20 shows the longitudinal stress distribution and the weld toe is the location where the maximum stress occurs. The hot spot stress can be obtained by extrapolating the stress of the location that is 0.5 × t away from the welded end, and the stress of the location that is 1.5 × t away from the welded end as shown in Figure 20. In this case, the hot spot stress is 100.9 MPa, the nominal stress is 100 MPa, and the maximum stress is 271.1 MPa. The maximum stress by welded joint notch can be represented as follows [17, 18]:where is the maximum stress, is the nominal stress, is the hot spot stress, is the stress concentration factor, is the stress concentration factor caused by the weld bead, and is the structural stress concentration factor.
Thus, the stress concentration factor can be obtained from the analysis as follows:
Table 5 shows the results of calculating the fatigue damage in the fatigue test and the track test. In the fatigue test, the fatigue damage was assessed with each load step. In the case of the fatigue test, the least fatigue damage occurred in the first step, while the fatigue damage increased in the second and the third steps. Although the load magnitude in the second step increases to 1.2 times that of the first step, the fatigue damage increases to 2.9 times. In the third step, compared to the first step, the load magnitude increases to 1.4 times but the fatigue damage increases to 6.6 times. In the track test, the fatigue damage is 0.02, which is smaller than that of the fatigue test. Therefore, among the three steps under EN 13749, it is determined that the load magnitude of the second and the third steps is specified more conservatively than that of in-service running conditions.
As in the stress distribution in Figures 13–16, stress conditions of the bogie frame have multiaxial stress characteristics according to the measurement locations in Figure 5. To evaluate the fatigue damage in the multiaxial condition, (6) of the normal strain and (7) of S.W.T were used [19–21].where and are the fatigue strength coefficient and the fatigue strength exponents and and are the fatigue ductility coefficient and the fatigue ductility exponents, respectively, and the values used for the analysis are as shown in Table 6 [12].
Table 7 contains the results of the fatigue damage in accordance with the evaluation methods. In the normal strain method, the total strain amplitude is calculated without considering the multiaxial condition and the fatigue damage is calculated. When the principal stress varies with time as in Point 3, it should be evaluated in consideration of the multiaxial condition. In the SWT method, the normal strain amplitude and the maximum normal stress on the plane are calculated in each plane to account for the multiaxial conditions. The accumulation of fatigue damage on all possible planes is calculated and the critical plane with the largest damage is selected. By normalization based on the normal strain method, the fatigue damage is compared. In the case of Point 1, since it is uniaxial and in the proportional condition as in Figure 14, the fatigue damages in both the normal strain method and the SWT method are evaluated similarly. However, as for Point 3, since it is multiaxial and in the nonproportional condition, as in Figure 16, there are differences in the fatigue damage. Therefore, to evaluate the fatigue strength of the bogie frame, it is determined that the appropriate fatigue evaluation methods should be applied, depending on the locations and stress conditions.
5. Conclusion
In this paper, to evaluate the fatigue strength of the bogie frames of electric railcars, the static load test, fatigue test, and track test were performed. The load conditions occurring under the track test of Korea and the load conditions specified under the fatigue test of EN 13798 were compared and the differences between them were examined. The characteristics of stress history in the fatigue test and the track test were evaluated and various fatigue life evaluation methods were applied. The following conclusions were obtained:(1)Since the stresses that occurred as a result of the static load test on the bogie frame were within the yield strength of the materials, the bogie frame satisfies the requirements for static strength safety.(2)The fatigue test was conducted and it was proven that since no cracks occurred until the third step load, the bogie frame has adequate strength against fatigue loads.(3)The stresses that occur on the bogie frame are multiaxial and under nonproportional load, according to their locations. Therefore, to evaluate the fatigue strength of the bogie frame, it is determined that appropriate fatigue evaluation methods should be applied, depending on the locations and stress conditions.(4)The fatigue damage was evaluated with the stresses that occurred in the fatigue test and the track test. It is considered that, among the three step loads under EN 13749, the load magnitudes of the second and the third steps are specified more conservatively than those of the in-service running conditions.
Competing Interests
The authors declare that they have no conflict of interests regarding the publication of this paper.
Acknowledgments
This research was supported by a grant from the R&D Program of the Korea Railroad Research Institute, Republic of Korea.