Fatigue Design Evaluation of Railway Bogie with Full-Scale

Research ArticleFatigue Design Evaluation of Railway Bogie withFull-Scale Fatigue Test

Jung-Won Seo Hyun-Moo Hur Hyun-Kyu Jun Seok-Jin Kwon and Dong-Hyeong Lee

Korea Railroad Research Institute Uiwang Gyeonggi-do 437-755 Republic of Korea

Correspondence should be addressed to Jung-Won Seo jwseokrrirekr

Received 12 October 2016 Accepted 22 December 2016 Published 8 February 2017

Academic Editor Paolo Ferro

Copyright copy 2017 Jung-Won Seo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The bogie frame of a railway is an important structural member for the support of vehicle loading In general more than 25 yearsrsquodurability is necessaryMuch study has been carried out in experimental and theoretical domains on the prediction of the structuralintegrity of the bogie frameThe objective of this paper is to estimate the structural integrity of the bogie frame of an electric railcarStrength analysis has been performed by finite element analysis From this analysis stress concentration areas were investigatedTo evaluate the loading conditions dynamic stress was measured by strain gauge It has been found that the stress and strain due tothe applied loads were multiaxial conditions according to the location of the strain gauge Fatigue strength evaluations of the bogieframe 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 framessuspensions axles and wheelsThe shapes of bogies as well asthe load conditions such as static load and dynamic load arecomplex Therefore various tests including static load testsfatigue tests and track tests are required for the design andthe strength evaluation of the bogie [1ndash4] The bogie frameis required to last 25 years or longer as the main structurethat supports loads of the vehicle body Although the UICEN and JIS standards [5ndash7] prescribe the strength evaluationmethods of bogie frames they do not define detailed fatiguelife assessment approaches

EN 13789 [5] defines the static load and the fatigue loadto evaluate the strength of bogie frames The fatigue test inthe laboratory requires the load magnitude and cycles toguarantee 30 years within an annual mileage of 200000 km[5] However the load magnitude may vary according to thevehicle type and track conditions Excessive definition of theload conditions in the fatigue testmaymakeweight reductionand the optimization of bogie frames difficult [8 9] If theload conditions of the fatigue test are lower than those ofthe in-service track the fatigue damage and the crack mayoccur during the operation of the railway vehicle The EN

standard requires the fatigue life to be evaluated by tracktest The fatigue life evaluation is required to be conducted inaccordance with the cumulative damage rule but the detailedevaluation method has not been specified In particular thefatigue life evaluation method for multiaxial load has notbeen defined Therefore a number of detailed studies on thefatigue life evaluation of bogie frames have been conducted[1 10 11] However there have been few studies on the fatiguelife evaluation method and the characteristics of the stresshistory that occur in the fatigue test and the track test

In this study the static load test fatigue test and tracktest were conducted to evaluate the fatigue strength of bogieframes that were used in electric railcars The characteristicsof the load history obtained on track test were evaluatedTheload conditions in Korea were compared to those of EN 13798and the fatigue damage was assessed by applying variousfatigue evaluation methods

2 Finite Element Analysis and Static Test ofBogie Frames

21 Finite Element Model Figure 1(a) shows a driving bogieused in an electric vehicle A rubber spring is used as theprimary suspension and an air spring is used as the secondary

HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 5656497 11 pageshttpsdoiorg10115520175656497

2 Advances in Materials Science and Engineering

Air spring

Air spring

1st spring

1st spring

(a) Driving bogie

H - beamVertical force

Boundary condition

Vertical force

Boundary condition

Boundary condition

Boundary condition

(b) Finite element model of bogie frame

Figure 1 Driving bogie and finite element model

Table 1 Load case for static test

Load case Load conditions Load (kN) Boundary conditionLoad point Support point

Exceptional load

Vertical force 1719 Air spring 1st springTransverse force 1276 Lateral buffer 1st springLongitudinal force 2310 Center pivot 1st springLozenging forces 421 Wheel point 1st spring + center pivot

Twist load 517 Air spring 1st springTraction motor 1275 Traction motor bracket 1st springInertia load

Traction motor load 1808 Traction motor bracket 1st springEmergency braking load 159 Braking bracket 1st spring

Normal service load

Vertical force 1000 Air spring 1st springTransverse force 693 Lateral buffer 1st springLozenging forces 139 Wheel point 1st spring + center pivot

Twist load 260 Air spring 1st spring

suspension As it is a driving bogie it has a tractionmotor anda disc brake is used as the brake system Figure 1(b) shows afinite element model of the bogie frame For the modelingshell elements were usedThe number of elements was 51811and the number of nodes was 47356

22 Load Conditions The static loads can be divided inaccordance with EN 13798 into the exceptional loads and thenormal service loads Table 1 shows the static loads calculatedaccording to EN 13798 The exceptional loads can be dividedinto nine cases and the normal service loads are dividedinto four cases Vertical forces were applied at the air springsand the 1st springs were constrained as boundary conditionsTransverse forces were applied at the lateral buffers and the1st springs were constrained Table 1 shows the boundaryconditions for each load

Table 2 shows the mechanical properties of the materialsused in the bogie frameThemain framematerial of the bogieis SM490A the transom pipe is STKM18B and the bracket ismade from SS400 The stress occurring in the bogie frameon exceptional loads should be less than the yield strength ofthe material used Under the normal service loads the mean

Table 2 Mechanical properties

MaterialYieldingstrength(MPa)

Tensilestrength(MPa)

Remark

SM490A 325 490Side frame TM mounting

bracket transom support gearmounting bracket

STKM18B 315 490 TransomSS400 245 400 Bracket

stress and the stress amplitude are calculated on each load andthey should be within the fatigue limit diagram

120590119898 = 120590max + 120590min2 120590119886 = 120590max minus 120590min2 (1)

where 120590max is the maximum stress 120590min is the minimumstress 120590119898 is the mean stress and 120590119886 is the stress amplitude

Advances in Materials Science and Engineering 3

Results 1- BC 1 Strees_1 verticalstress - Von mises min 0 max 125frame of REF part

125

113

100

88

75

62

50

37

25

12

0

Value option actualshell surface top

y

x z

Figure 2 Maximum stress of the bogie frame under vertical Load

zy

x

(a) Upper location

x

z y

(b) Lower location

Figure 3 Strain gauge location for static test

23 Static Load Test For the static load test the areas wherehigh stress occurred in each load condition should be pre-dicted Therefore the finite element analysis was conductedunder the same conditions as the static load test Figure 2shows the result of the finite element analysis when verticalload is applied The maximum stress occurred on the bracketattached under the side frame Figure 3 shows the locationswhere strain gauges were attached for the static load testThose locations were selected from the result of the finiteelement analysis for each load condition Strain gauges wereattached to a total of 44 locations

Table 3 shows the result of the static load test on theexceptional loads On the vertical load the compressive loadof minus127MPa occurred at the point (gauge location No 2) thatis located on the upper side frame and 113MPa occurred onthe connection (gage location No 37) between the side frameand the bracket The maximum stress of 125MPa from theresult of finite element analysis occurred on the connectionbetween the side frame and the bracket which was a similarresult On transverse load the maximum stress occurred atthe point (gauge location No 2) which is located on theupper side frame which was the compressive stress The


Table 3 Measured maximum stress for static test

Load case Load conditions Maximum stress (MPa) Yielding strength (MPa) Safety factor Material Gauge no

1 Vertical force minus127 325 256 SM490A 02113 325 287 SM490A 37

2 Transverse force minus114 325 285 SM490A 02104 325 313 SM490A 38

3 Longitudinal force 95 315 332 STKM18A 3284 325 386 SM490A 36

4 Lozenging forces minus87 325 374 SM490A 025 Twist load minus93 325 349 SM490A 42

6 Traction motor minus106 325 301 SM490A 10Inertia load

7 Traction motor load minus93 325 349 SM490A 018 Emergency braking load minus107 325 304 SM490A 029 Active steering force 140 315 225 STKM18A 3210lowast Vertical + transverse force 123 325 264 SM490A 3411lowast Vertical + transverse + twist force 135 325 241 SM490A 34lowastCombined load at normal service load

Mean stress (Nmm2)

0 50 100 150 200 250

0

20

40

60

80

100

120

140

160

180

DataT weldBase metal

Butt weld

Stre

ss am

plitu

de (N

mm

2)

minus200 minus150 minus100 minus50

Figure 4 Goodman diagram with the results of service static load

maximum tensile stress occurred on the connection betweenthe side frame and the bracket Under the normal serviceload conditions each load to be applied is combined Table 3shows that the load conditions ofNos 10 and 11 are the normalservice load conditions The maximum stress occurred onthe connection between the frame and the bracketThe stressthat occurred under exceptional loads was less than the yieldstrength which was considered to be safe

Figure 4 shows the result of evaluating the fatigue limitdiagram after the mean stress and the stress amplitude werecalculated under the normal service load conditions Thestress amplitude and the mean stress were calculated for each

2

Fz1

Fz2Ftw

Fx

Ftw

Ux = 0Uy = 0

Ux = 0Uy = 0

Ux = 0Uy = 0

Uz = 0

Ux = 0Uy = 0

Uz = 0

X

Y

Z

31

Figure 5 Load conditions and strain gauge locations

combined load Stresses of all areas where the strain gaugesare attached are within the safe area Therefore the fatiguestrength is assessed to be safe

3 Fatigue Test and Track Test

31 Fatigue Test The fatigue test of the bogie frame for elec-tric railcars was conducted according to EN 13749 Figure 5shows the load conditions consisting of the vertical load (119865119911)the transverse load (119865119909) and the twist load (119865tw) In thefatigue test the loads are composed of the static load thequasi-static load and the dynamic load

(i) a static part 1198651199111 = 1198651199112 = 1198651199112(ii) a quasi-static part 1198651199111 = 1198651199112 = plusmn1205721198651199112(iii) a dynamic part 1198651199111 = 1198651199112 = plusmn1205731198651199112

where 120572 is the roll coefficient which indicates the load at thecurve track and 01 was applied 120573 is the bounce coefficientwhich indicates the dynamic load and 02 was applied The


Step 1

Step 2

Step 3

100

Load

Cycles

Static vertical load Static verticalload

Static verticalload

120

140

Quasi-static and dynamicverticaland lateral

loads and twist

Quasi-staticand dynamicvertical andlateral loads

and twist


and twist

6 times 106 2 times 106

cycles2 times 106

cyclescycles

Figure 6 Step-by-step load conditions of fatigue test [6]

H-beam

Bogie frame

VerticalactuatorTwist

actuatorLateralactuator

Jig forvertical

stopper force

Figure 7 Equipment and specimen for fatigue test

strain gauges were attached to evaluate the characteristics ofthe stress history in the fatigue test The strain gauges wereattached to the areas where the maximum stress occurredfrom the result of the static load test

Figure 6 shows the load condition for fatigue tests accord-ing to EN 13749 In step 1 the fatigue test was conductedby applying an initial load up to 6 times 106 cycles In step 2the quasi-static load and dynamic load were increased by 12times and the fatigue test was conducted up to 2 times 106 cyclesIn step 3 the quasi-static load and the dynamic load wereincreased by 14 times and the fatigue test was conducted upto 2 times 106 cycles After the fatigue test in step 1 and 2 cracksshould not occur while very small cracks are permitted instep 3

Figure 7 shows the test equipment for the fatigue testTheequipment has two actuators for vertical load one actuatorfor transverse load and two actuators for twist load Figure 8shows a graph of the fatigue load history in step 1 The quasi-static load and the dynamic load were applied for the verticalload after the static loadwas appliedThe quasi-static load forthe curve track was applied differently to the left and right

The load magnitude changed every 10 cyclesThe quasi-staticload and the dynamic load were applied to the transverseload The twist load was applied every 10 cycles Figure 9shows the result of nondestructive testing (magnetic particleinspection) after the fatigue test The nondestructive testingwas conducted from steps 1 to 3 and no cracks were evident

32 Track Test To evaluate the fatigue life of bogie frames forelectric railcars a track test was conducted by using similarbogie frames on an in-service track The strain gauges wereattached to the same locations shown in Figure 5 to compareit with the fatigue test Figure 10 shows the test vehicle andthe data acquisition system for measuring the strain for thetrack test The test was performed with the data acquisitionsystem which is MGCplus made by HBM and the samplingrate was set to 600Hz The test distance was 30 km and thetrack test was conducted in the same conditions as in-serviceconditions

4 Test Results and Discussions

41 Stress Analysis This section assesses and compares thestress characteristics occurring in the fatigue test and thetrack test Figure 5 shows the location of Points 1 2 and 3for comparison of the fatigue test and track test results Straingauges were attached to the location where the stresses werelarge in the static load test Figure 11 shows the strain historythat occurs at Point 1 in the fatigue test In the fatigue testvertical load transverse load and twist load are applied withchanging every ten cyclesTherefore Figure 11 shows that thestrain repeats the identical shape every ten cycles Figure 12describes the strain history that occurs at Point 1 in the tracktest The strain history that occurs in the track test showsrandom shapes Since the static load is included in the fatiguetest the maximum strain that occurs is greater in the fatiguetest than in the track test However because the track test doesnot include static load the mean strain is close to ldquo0rdquo


Vertical force (right)Vertical force (left) Lateral force

Twist load

Time (second)

9995 kN

6397 kN

630 kN

8374 kN 6397 kN

13594 kN

8796 kN11195 kN

9995 kN13594 kN

11195 kN8796 kN

minus630kN

minus8374kN

Forc

e (kN

)

Figure 8 Load history of fatigue test in step 1

Figure 9 Nondestructive testing after fatigue test

The biaxiality ratio (120582) is applied as the parameter toevaluate the local stress conditions [13 14] 120582 is defined asfollows

120582 = 12059021205901 (2)

where 120582 is the biaxiality ratio and 1205901 is the maximumprincipal stresses while 1205902 is theminimumprincipal stresses

Figure 13 shows the changes in 120582 and its principal stressof Point 1 in the fatigue test 120582 for all principal stresses isdistributed around zero and the direction of the principalstress is distributed around 30∘ndash45∘ This is uniaxial andis the proportional loading condition Figure 14 shows thechanges in 120582 of Point 1 and its principal stress in the tracktest Although 120582 is generally distributed between minus1 and

1 the stresses with large principal stresses are distributedin ldquo0rdquo Moreover the direction of the principal stress withlarge stresses is fixed at 40∘ This is uniaxial and in thesame proportion as in the fatigue test Even though in thecase of Point 1 the stresses that occur in the fatigue testand the track test differ from each other in terms of thestress magnitude the stress conditions are uniaxial and thedirection of principal stresses is similar

Figure 15 shows the changes in 120582 of Point 3 and itsprincipal stress in the fatigue test 120582 varies from minus08 to 0and the direction of its principal stress changes from 20∘ to40∘ This is the multiaxial and the nonproportional loadingcondition Figure 16 shows the changes in 120582 of Point 3 andits principal stress in the track test 120582 is generally distributedbetween minus1 and 1 and the direction of the principal stresschanges from 0∘ to 90∘ This is the multiaxial and thenonproportional loading condition the same as in the fatiguetest

Therefore since the stresses of the bogie frame are themultiaxial and the nonproportional loading condition thefatigue life evaluation should be done by taking this intoaccount

42 Fatigue Life Evaluation Since the load characteristics canvary in accordancewith the vehicle type and track conditionsthe stresses characteristics of the bogie frames of electricrailcars running in Korea were investigated


(a) (b)

Figure 10 Test vehicle and data acquisition system for track test

6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)

Figure 11 Strain occurring in fatigue test (Point 1)

Figure 17 shows comparisons of the stress magnitudesoccurring in the fatigue test and the track test To comparewith the fatigue test the track test was presented by con-verting the cycle into the case of 30 years of running withinthe annual mileage of 200000 km To do this the rainflowcycle countingmethodwas used In both cases themaximummagnitude of the stress range appears similarly as shown inFigure 17 Nonetheless in the fatigue test the cycle of stresseswith a large stress range occurs often

It is difficult to directly compare both the fatigue test andthe track test with the result of cycle counting as shown inFigure 17 Therefore the equivalent stress range applied inIIW [15] was used and the formula is as follows

ΔSeq= 1198981radic 1119863 sum (119873119894 sdot Δ119878

1198981119894 ) + Δ119878(1198981minus1198982)119871119889

sdot sum (119873119895 sdot Δ1198781198982119895 )sum119873119894 + sum119873119895 (3)

Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25

minus100minus60minus20

2060

100

minus40minus20

0204060

minus40minus30minus20minus10

010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)

Figure 12 Strain occurring in track test (Point 1)

whereΔ119878eq is the equivalent stress range119863 is theMiner sum1198981 is the slope of the upper part of the knee point on the S-Ncurve 1198982 is the slope of the lower part of the knee point onthe S-N curve Δ119878119894 is the stress range of the upper part of theknee point at level 119894 of the S-N curve Δ119878119895 is the stress rangeof the lower part of the knee point at level j of the S-N curveΔ119878119871119889 is the stress range of the knee point on the S-N curve119873119894is the number of cycles of Δ119878119894 and119873119895 is the number of cyclesof Δ119878119895

Table 4 shows the stresses that occur in the fatigue testand the track test in the equivalent stress range In the case ofPoint 1 with the largest stress the equivalent stress range offatigue test with 2389MPa is much larger than that of tracktest with 421MPa In the case of Point 3 it is assessed thatthe equivalent stress range of the two tests is similar Sincethe fatigue test result is larger than the track test result the


Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)

minus08 minus06 minus04 minus02 00 02 04 06 08 10minus10Biaxiality ratio ()

0

50

100

Prin

cipa

l stre

ss (M

Pa)

minus60 minus30 0 30 60 90minus90Angle (degrees)

Y vehicle directionAngleX

Y 1

Figure 13 Changes in principal stress in fatigue test (Point 1)

Track measurement

AngleX

Y


minus08 minus06 minus04 minus02 00 02 04 06 08minus10 10

Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1

Figure 14 Changes in principal stress in track test (Point 1)

Table 4 Comparison of equivalent stress range in fatigue test andtrack test

Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)

Fatigue test 2389 978 414Track test 421 412 407

load conditions specified for the fatigue test in EN 13749 canbe evaluated to be sufficiently conservative compared to thedomestic track conditions

The fatigue life was evaluated based on the stresses occur-ring in the fatigue test and the track test For the fatigue lifeevaluation on welded joints the method by BS7608 [16] was

Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus08 minus06 minus04 minus02 00 02 04 06 08 10minus10

minus60 minus40 minus20 0 20 40 60 80minus80Angle (degrees)


Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1


used Under BS7608 the S-N curves are classified accordingto each class and the nominal stress is applied In the caseof tubular nodal joints the S-N curve to which the hot-spotstress is applied is given In addition according to weldingconfigurations the fatigue notch factors should be used andit is obtained through stress analysis or measurement Sincethe configuration of the bogie frame at the strain gauge pointfalls underClass F the S-N curve for the fatigue life evaluationthat was used was Class FWhen the measurement location isfar enough from the welded toe the measured stresses canbe assumed as the nominal stress When this is not the casesince the fatigue life is evaluated conservatively revisions tothis are needed Figure 18 shows the definition of stresses inwelded joints [17]

To take into account the stress concentration in weldedjoints finite element analysis was carried out and Figure 19


Table 5 Comparison of fatigue damage between lab test and track test

Location Fatigue test Track test Remark

Point 11st load step 007

002Track test in-service track

2nd load step 020 Distanceyear 2 times 1053rd load step 046 Life 30 years

Fatigue test Track measurement

102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)

Figure 17 Comparison of cycle counting results in fatigue test andtrack test (Point 1)

shows the finite element model Figure 20 shows the longi-tudinal stress distribution and the weld toe is the locationwhere the maximum stress occurs The hot spot stress can beobtained by extrapolating the stress of the location that is 05times t away from the welded end and the stress of the locationthat is 15times t away from thewelded end as shown in Figure 20In this case the hot spot stress is 1009MPa the nominalstress is 100MPa and the maximum stress is 2711MPa Themaximum stress by welded joint notch can be represented asfollows [17 18]

120590peak = 119870119905 times 120590119899 = (119870119904 times 119870119908) times 120590119899 = (119870119904 times 120590119899) times 119870119908= 120590ℎ119904 times 119870119908 (4)

where 120590peak is the maximum stress 120590119899 is the nominal stress120590ℎ119904 is the hot spot stress119870119905 is the stress concentration factor119870119908 is the stress concentration factor caused by the weld beadand119870119904 is the structural stress concentration factor

Thus the stress concentration factor can be obtained fromthe analysis as follows

119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)

Table 5 shows the results of calculating the fatigue damagein the fatigue test and the track test In the fatigue test the

Table 6 Material properties for fatigue analysis [12]

119864 (GPa) 120592 1205901015840119891 (MPa) 1205761015840119891 () 119887 119888209 03 927 0656 minus0084 minus073Table 7 Comparison of fatigue damage according to the fatigueevaluation method

Location Normalstrain SWT Remark

Point 1 100 098Normalization tocompare resultsPoint 2 100 095

Point 3 100 086

fatigue damagewas assessedwith each load step In the case ofthe fatigue test the least fatigue damage occurred in the firststep while the fatigue damage increased in the second andthe third steps Although the load magnitude in the secondstep increases to 12 times that of the first step the fatiguedamage increases to 29 times In the third step comparedto the first step the load magnitude increases to 14 times butthe fatigue damage increases to 66 times In the track testthe fatigue damage is 002 which is smaller than that of thefatigue testTherefore among the three steps under EN 13749it is determined that the load magnitude of the second andthe third steps is specified more conservatively than that ofin-service running conditions

As in the stress distribution in Figures 13ndash16 stress condi-tions of the bogie frame have multiaxial stress characteristicsaccording to the measurement locations in Figure 5 Toevaluate the fatigue damage in the multiaxial condition (6)of the normal strain and (7) of SWT were used [19ndash21]

Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)

where 1205901015840119891 and 119887 are the fatigue strength coefficient and thefatigue strength exponents and 1205761015840119891 and 119888 are the fatigueductility coefficient and the fatigue ductility exponentsrespectively and the values used for the analysis are as shownin Table 6 [12]

Table 7 contains the results of the fatigue damage inaccordancewith the evaluationmethods In the normal strainmethod the total strain amplitude is calculated withoutconsidering the multiaxial condition and the fatigue damageis calculated When the principal stress varies with time asin Point 3 it should be evaluated in consideration of the


ss

hs hs

x

Structuraldistribution(strain gauge or FE)

Notch stress distribution (FE)

Weld-toe radiusr

Linear extrapolation

d

Weld-toe d = f (thickness gauge length) asymp 1 to 2mm

Weld angle

Stress-concentrationfactor Kt = xhs

structural stresss hot-spot-stresshs maximum notch stressx weld geometry loading mode)f(

Figure 18 Stress definition in welded joints [17]

X

Y

Z

Figure 19 Weld toe configuration

Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t

Figure 20 Longitudinal stress distribution

multiaxial condition In the SWT method the normal strainamplitude and the maximum normal stress on the planeare calculated in each plane to account for the multiaxialconditions The accumulation of fatigue damage on allpossible planes is calculated and the critical plane with thelargest damage is selected By normalization based on thenormal strain method the fatigue damage is compared Inthe case of Point 1 since it is uniaxial and in the proportionalcondition as in Figure 14 the fatigue damages in both thenormal strain method and the SWT method are evaluatedsimilarly However as for Point 3 since it is multiaxial andin the nonproportional condition as in Figure 16 there aredifferences in the fatigue damage Therefore to evaluate thefatigue strength of the bogie frame it is determined that theappropriate fatigue evaluation methods should be applieddepending on the locations and stress conditions

5 Conclusion

In this paper to evaluate the fatigue strength of the bogieframes of electric railcars the static load test fatigue testand track test were performedThe load conditions occurringunder the track test of Korea and the load conditions specifiedunder the fatigue test of EN 13798 were compared and thedifferences between themwere examinedThe characteristicsof stress history in the fatigue test and the track test wereevaluated and various fatigue life evaluation methods wereapplied The following conclusions were obtained

(1) Since the stresses that occurred as a result of the staticload test on the bogie frame were within the yieldstrength of the materials the bogie frame satisfies therequirements for static strength safety

(2) The fatigue test was conducted and it was proven thatsince no cracks occurred until the third step load


the bogie frame has adequate strength against fatigueloads

(3) The stresses that occur on the bogie frame are mul-tiaxial and under nonproportional load accordingto their locations Therefore to evaluate the fatiguestrength of the bogie frame it is determined thatappropriate fatigue evaluation methods should beapplied depending on the locations and stress con-ditions

(4) The fatigue damage was evaluated with the stressesthat occurred in the fatigue test and the track test It isconsidered that among the three step loads under EN13749 the loadmagnitudes of the second and the thirdsteps are specified more conservatively than those ofthe in-service running conditions

Competing Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by a grant from the RampDProgram of the Korea Railroad Research Institute Republicof Korea

References

[1] M Kassner ldquoFatigue strength analysis of a welded railwayvehicle structure by different methodsrdquo International Journal ofFatigue vol 34 no 1 pp 103ndash111 2012

[2] J-W Han J-D Kim and S-Y Song ldquoFatigue strength evalua-tion of a bogie frame for urban maglev train with fatigue teston full-scale test rigrdquo Engineering Failure Analysis vol 31 pp412ndash420 2013

[3] H-K Jun J-W Seo S-J Kwon D-H Lee and S-H ParkldquoEffect of corrosion on the fatigue life of aged EMU underfatigue loadingrdquo International Journal of Precision Engineeringand Manufacturing vol 17 no 1 pp 73ndash79 2016

[4] W G Lee J S Kim H J Yoon K B Shin and S I SeoldquoStructural behavior evaluation of T-joints of the compositebogie frame under bendingrdquo International Journal of PrecisionEngineering and Manufacturing vol 14 no 1 pp 129ndash135 2013

[5] UIC Code 615-4 ldquoMovie power units bogies and running gearbogie frame structure strength testsrdquo International Union ofRailway 1994

[6] EN 13749 ldquoRailway applicationsmdashwheelsets and bogiesmdashmethods of specifying structural requirements of bogie framesrdquoEuropean Committee for Standardization 2011

[7] JIS E7105 ldquoTest methods for static load of body structures ofrailways rolling stockrdquo Japanese Industrial Standard 1994

[8] J-H Kim K-B Shin and J-S Kim ldquoOptimum design onsuspension joint parts of GFRP composite bogie frame withH-shaped side beams for urban railway trainsrdquo InternationalJournal of Precision Engineering and Manufacturing vol 13 no1 pp 71ndash76 2012

[9] H-J Kim H Cho H-S Jung T-S Kwon and M-W SuhldquoCrashworthiness design and evaluation on the leading-cab

structure of rolling stock using topology optimizationrdquo Interna-tional Journal of Precision Engineering and Manufacturing vol10 no 2 pp 79ndash85 2009

[10] A Esderts J Willen andM Kassner ldquoFatigue strength analysisof welded joints in closed steel sections in rail vehiclesrdquoInternational Journal of Fatigue vol 34 no 1 pp 112ndash121 2012

[11] K-W Jeon K-B Shin and J-S Kim ldquoEvaluation of tension-compression and tension-tension fatigue life of woven fabricglassepoxy laminate composites used in railway vehiclerdquo Inter-national Journal of Precision Engineering and Manufacturingvol 12 no 5 pp 813ndash820 2011

[12] J Seo S Kwon Y Ham and S Kwon ldquoThe Fatigue lifeevaluation and load history measurement for Bogie frame oflocomotiverdquo in Proceedings of the Autumn Conference of KoreanSociety of Mechanical Engineers vol 11 pp 378ndash383 2008

[13] M Quaresimin L Susmel and R Talreja ldquoFatigue behaviourand life assessment of composite laminates under multiaxialloadingsrdquo International Journal of Fatigue vol 32 no 1 pp 2ndash162010

[14] M Quaresimin and P A Carraro ldquoOn the investigation ofthe biaxial fatigue behaviour of unidirectional compositesrdquoComposites Part B Engineering vol 54 pp 200ndash208 2013

[15] A Hobbacher ldquoRecommendations for fatigue design of weldedjoints and componentsrdquo International Institute of Welding(IIW) Document XIII-2151r4XV-1254r4-07 WRC-Bulletin520 Welding Research Council 2009

[16] BS 7608 ldquoCode of practice for fatigue design and assessment ofsteel structuresrdquo British Standard 1993

[17] C M Sonsino and M Kueppers ldquoMultiaxial fatigue of weldedjoints under constant and variable amplitude loadingsrdquo Fatigueamp Fracture of Engineering Materials amp Structures vol 24 no 5pp 309ndash327 2001

[18] W Fricke and H Paetzoldt ldquoFatigue strength assessment ofscallops -an example for the application of nominal and localstress approachesrdquoMarine Structures vol 8 no 4 pp 423ndash4471995

[19] M Backstrom andGMarquis ldquoA review ofmultiaxial fatigue ofweldments experimental results design code and critical planeapproachesrdquo Fatigue and Fracture of Engineering Materials andStructures vol 24 no 5 pp 279ndash291 2001

[20] S Kang and W Kim ldquoA proposed S-N Curve for Welded shipstructures-a hot-spot stress-based design S-N curve for filletweld joints takes into account the effects of static cargo loadsrdquoWelding Journal vol 82 no 7 pp 161ndash169 2003

[21] B Atzori and G Meneghetti ldquoFatigue strength of fillet weldedstructural steels finite elements strain gauges and realityrdquoInternational Journal of Fatigue vol 23 no 8 pp 713ndash721 2001

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Air spring

Air spring

1st spring

1st spring

(a) Driving bogie

H - beamVertical force

Boundary condition

Vertical force

Boundary condition

Boundary condition

Boundary condition

(b) Finite element model of bogie frame

Figure 1 Driving bogie and finite element model

Table 1 Load case for static test

Load case Load conditions Load (kN) Boundary conditionLoad point Support point

Exceptional load

Vertical force 1719 Air spring 1st springTransverse force 1276 Lateral buffer 1st springLongitudinal force 2310 Center pivot 1st springLozenging forces 421 Wheel point 1st spring + center pivot

Twist load 517 Air spring 1st springTraction motor 1275 Traction motor bracket 1st springInertia load

Traction motor load 1808 Traction motor bracket 1st springEmergency braking load 159 Braking bracket 1st spring

Normal service load

Vertical force 1000 Air spring 1st springTransverse force 693 Lateral buffer 1st springLozenging forces 139 Wheel point 1st spring + center pivot

Twist load 260 Air spring 1st spring

suspension As it is a driving bogie it has a tractionmotor anda disc brake is used as the brake system Figure 1(b) shows afinite element model of the bogie frame For the modelingshell elements were usedThe number of elements was 51811and the number of nodes was 47356

22 Load Conditions The static loads can be divided inaccordance with EN 13798 into the exceptional loads and thenormal service loads Table 1 shows the static loads calculatedaccording to EN 13798 The exceptional loads can be dividedinto nine cases and the normal service loads are dividedinto four cases Vertical forces were applied at the air springsand the 1st springs were constrained as boundary conditionsTransverse forces were applied at the lateral buffers and the1st springs were constrained Table 1 shows the boundaryconditions for each load

Table 2 shows the mechanical properties of the materialsused in the bogie frameThemain framematerial of the bogieis SM490A the transom pipe is STKM18B and the bracket ismade from SS400 The stress occurring in the bogie frameon exceptional loads should be less than the yield strength ofthe material used Under the normal service loads the mean

Table 2 Mechanical properties

MaterialYieldingstrength(MPa)

Tensilestrength(MPa)

Remark

SM490A 325 490Side frame TM mounting

bracket transom support gearmounting bracket

STKM18B 315 490 TransomSS400 245 400 Bracket

stress and the stress amplitude are calculated on each load andthey should be within the fatigue limit diagram

120590119898 = 120590max + 120590min2 120590119886 = 120590max minus 120590min2 (1)

where 120590max is the maximum stress 120590min is the minimumstress 120590119898 is the mean stress and 120590119886 is the stress amplitude



125

113

100

88

75

62

50

37

25

12

0


y

x z


zy

x

(a) Upper location

x

z y

(b) Lower location













Mean stress (Nmm2)

0 50 100 150 200 250

0

20

40

60

80

100

120

140

160

180


Butt weld

Stre

ss am

plitu

de (N

mm

2)





2

Fz1

Fz2Ftw

Fx

Ftw

Ux = 0Uy = 0

Ux = 0Uy = 0

Ux = 0Uy = 0

Uz = 0

Ux = 0Uy = 0

Uz = 0

X

Y

Z

31








Step 1

Step 2

Step 3

100

Load

Cycles


Static verticalload

120

140


loads and twist


and twist


and twist


cycles2 times 106

cyclescycles


H-beam

Bogie frame



Jig forvertical

stopper force











Twist load

Time (second)

9995 kN

6397 kN

630 kN

8374 kN 6397 kN

13594 kN

8796 kN11195 kN

9995 kN13594 kN

11195 kN8796 kN

minus630kN

minus8374kN

Forc

e (kN

)




120582 = 12059021205901 (2)








(a) (b)


6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)





1198981119894 ) + Δ119878(1198981minus1198982)119871119889


Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25


2060

100

minus40minus20

0204060


010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)





Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





125

113

100

88

75

62

50

37

25

12

0


y

x z


zy

x

(a) Upper location

x

z y

(b) Lower location













Mean stress (Nmm2)

0 50 100 150 200 250

0

20

40

60

80

100

120

140

160

180


Butt weld

Stre

ss am

plitu

de (N

mm

2)





2

Fz1

Fz2Ftw

Fx

Ftw

Ux = 0Uy = 0

Ux = 0Uy = 0

Ux = 0Uy = 0

Uz = 0

Ux = 0Uy = 0

Uz = 0

X

Y

Z

31








Step 1

Step 2

Step 3

100

Load

Cycles


Static verticalload

120

140


loads and twist


and twist


and twist


cycles2 times 106

cyclescycles


H-beam

Bogie frame



Jig forvertical

stopper force











Twist load

Time (second)

9995 kN

6397 kN

630 kN

8374 kN 6397 kN

13594 kN

8796 kN11195 kN

9995 kN13594 kN

11195 kN8796 kN

minus630kN

minus8374kN

Forc

e (kN

)




120582 = 12059021205901 (2)








(a) (b)


6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)





1198981119894 ) + Δ119878(1198981minus1198982)119871119889


Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25


2060

100

minus40minus20

0204060


010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)





Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials












Mean stress (Nmm2)

0 50 100 150 200 250

0

20

40

60

80

100

120

140

160

180


Butt weld

Stre

ss am

plitu

de (N

mm

2)





2

Fz1

Fz2Ftw

Fx

Ftw

Ux = 0Uy = 0

Ux = 0Uy = 0

Ux = 0Uy = 0

Uz = 0

Ux = 0Uy = 0

Uz = 0

X

Y

Z

31








Step 1

Step 2

Step 3

100

Load

Cycles


Static verticalload

120

140


loads and twist


and twist


and twist


cycles2 times 106

cyclescycles


H-beam

Bogie frame



Jig forvertical

stopper force











Twist load

Time (second)

9995 kN

6397 kN

630 kN

8374 kN 6397 kN

13594 kN

8796 kN11195 kN

9995 kN13594 kN

11195 kN8796 kN

minus630kN

minus8374kN

Forc

e (kN

)




120582 = 12059021205901 (2)








(a) (b)


6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)





1198981119894 ) + Δ119878(1198981minus1198982)119871119889


Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25


2060

100

minus40minus20

0204060


010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)





Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Step 1

Step 2

Step 3

100

Load

Cycles


Static verticalload

120

140


loads and twist


and twist


and twist


cycles2 times 106

cyclescycles


H-beam

Bogie frame



Jig forvertical

stopper force











Twist load

Time (second)

9995 kN

6397 kN

630 kN

8374 kN 6397 kN

13594 kN

8796 kN11195 kN

9995 kN13594 kN

11195 kN8796 kN

minus630kN

minus8374kN

Forc

e (kN

)




120582 = 12059021205901 (2)








(a) (b)


6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)





1198981119894 ) + Δ119878(1198981minus1198982)119871119889


Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25


2060

100

minus40minus20

0204060


010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)





Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Twist load

Time (second)

9995 kN

6397 kN

630 kN

8374 kN 6397 kN

13594 kN

8796 kN11195 kN

9995 kN13594 kN

11195 kN8796 kN

minus630kN

minus8374kN

Forc

e (kN

)




120582 = 12059021205901 (2)








(a) (b)


6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)





1198981119894 ) + Δ119878(1198981minus1198982)119871119889


Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25


2060

100

minus40minus20

0204060


010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)





Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b)


6080

100120140

Time (sec)

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

020406080

100

100150200250300350

R-a(

)

R-b(

)

R-c(

)





1198981119894 ) + Δ119878(1198981minus1198982)119871119889


Time (sec)

0 5 10 15 20 25

0 5 10 15 20 25

0 5 10 15 20 25


2060

100

minus40minus20

0204060


010203040

times105

Time (sec) times105

Time (sec) times105

R-a(

)

R-b(

)

R-c(

)





Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Fatigue test

minus

0

50

100

Prin

cipa

l stre

ss (M

Pa)


0

50

100

Prin

cipa

l stre

ss (M

Pa)



Y 1


Track measurement

AngleX

Y



Biaxiality ratio ()


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)


0

10

20

30

Prin

cipa

l stre

ss (M

Pa)

Y vehicle direction

1



Case Point 1(MPa)

Point 2(MPa)

Point 3(MPa)




Fatigue test

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)

minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)




Y 1

Biaxiality ratio ()


Track measurement

minus20

minus10

0

10

20Pr

inci

pal s

tress

(MPa

)


minus20

minus10

0

10

20

Prin

cipa

l stre

ss (M

Pa)



Y 1











102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










102 103 104101 106105 107 109108 1010

Cycles

1

10

100

Stre

ss ra

nge (

MPa

)






119870119905 = 2711100 = 271119870119908 = 27111009 = 269

(5)






Point 3 100 086



Δ1205762 = 1205901015840119891119864 (2119873119891)119887 + 1205761015840119891 (2119873119891)119888 (6)

120590maxΔ12057612 = (1205901015840119891)2119864 (2119873119891)2119887 + 12059010158401198911205761015840119891 (2119873119891)119887+119888 (7)




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




ss

hs hs

x



Weld-toe radiusr


d


Weld angle




X

Y

Z


Weld-toe

Hot spot stress

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3013

Distance (mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

05 t 15 t



5 Conclusion








Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







Competing Interests


Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Documents

Fatigue Design Evaluation of Railway Bogie with Full-Scale