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Fatigue life prediction based on the rainflow cycle
counting method for the end beam of a freight ca
机械
International Journal of Automotive Technology, Vol. 9, No. 1, pp. 95??101 (2008)DOI
10.1007/s12239??008??0012??y
Copyright?2008KSAE1229??9138/2008/038??12
FATIGUE LIFE PREDICTION BASED ON THE RAINFLOW CYCLE COUNTING METHOD FOR THE END BEAM
OF A FREIGHT CAR BOGIE
S. H. BAEK1), S. S. CHO2) and W. S. JOO3)*
2)
School of Mechanical Engineering, Dong-A University, Busan 604-714, Korea
Department of Vehicle Engineering, Kangwon National University, Gangwon 245-711,
Korea
3)
Department of Mechanical Engineering, Dong-A University, Busan 604-714, Korea
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(Received 17 May 2007; Revised 15 December 2007)
1)
ABSTRACT??This paper presents a system for treating of the actual measured data for
load histories. The approach consistsof two steps: stress analysis and fatigue damage
prediction. Finite element analysis is conducted for the component in questionto
obtain
detailed
stress-strain
resphttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7onses.
A
significant number of failures occurred in a brake end beam which led to
economiclosses and disruption of service. The cracks appeared to be fatigue cracks
caused by the dynamic load produced in the loadedbogie frame. Strain gauge data were
analyzed, and fatigue cycles were calculated from this data. Rainflow cycle counting
wasused to estimate cumulative damage of the end beam under in-service loading
conditions. The fatigue life calculated with therainflow cycle counting method, the
P-S-N curve, and the modified Miner’s rule agreed well with actual fatigue life
withinan error range of 2.7%~31%.
KEY WORDS : Fatigue life prediction, Rainflow cycle counting, Cumulative damage,
Miner’s rule, P-S-N curve, Censoredstrain data
1. INTRODUCTION
In the beginning of 2001, cracks were found in the brakeend beam of the bogie frame
of
freight
cars
in
a
particularrunning
section
of
the
South
Korean
railway.http://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7 The end beamof
a freight car is a structural element that supports thebogie frame and braking system.
The location and connec-tion method of the end beam should be considered in viewof
structural design, because the end beam is built into thelower part of the side frame
of the bogie.
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Usually, important parts such as the bogie frame and carbody etc. are designed to
last more than 25 years (Goo andSeo, 2003; Baek et al., 2005). In the case of a
fracturedbogie frame, service life can be affected because themaximum stress is lower
than the fatigue limit. However,two-thirds of the total number of end beams failed
inservice via fatigue cracking in this particular running section.The cracked end
beams had either two years (240,000 km)or three years (360,000 km) of service. The
cracks appearto be fatigue cracks caused by the dynamic load producedin the loaded
bogie frame.
In
the
time-domain
analysis
of
structures
subjhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7ected
torandom
loading, an appropriate cycle counting technique(Matsuishi and Endo, 1968; Downing
and Socie, 1982;Nagpal and Kuo, 1996; Wang et al., 2006; Haq et al., 2007)and a fatigue
cumulative
damage
rule
(Fatemi
and
Yang,*Corresponding
author.
e-mail:
wsjoo@dau.ac.kr
95
1998; Barboza et al., 2005; Kang et al., 2007) are used toestimate the fatigue service
life. The bogie frame of freightcars has been evaluated by endurance test
standards.However, because the South Korean railway has manymore curved tracks than
railways abroad, there is a highbraking load during operation. A design specification
thatreflects the domestic track in the existing endurance teststandard must be
developed.
In the present paper, the load history was obtained fromstrain measurements on a bogie
frame. A three-dimen-sional finite element model of a simplified bogie frame
wasdeveloped
for
static
stress
analysis.
Miner’s
rule
http://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7was com-bined with a
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probabilistic S-N curve (Murty et al., 1995;Zheng and Wei, 2005) and stress results
to develop a stress-based fatigue life prediction for the brake end beam of thebogie
frame.
2. FATIGUE DAMAGE APPROACH FOR FATIGUE LIFE PREDICTION
A general method for fatigue life estimation of railwayvehicles is required, as
evidenced by cracking that occurredin the end beams of freight cars. As illustrated
in Figure 1,by collecting different load amplitudes using the rainflowcycle counting
method, the fatigue damage is linearlyaccumulated, as is proposed by Miner’s rule.
96S. H. BAEK, S. S. CHO and W. S. JOO
Figure 1. Flow chart for fatigue life prediction.
2.1. Rainflow Cycle Counting Method
The end beam of a freight car bogie is subjected to variableamplitude service loading.
To predict the fatigue life of theend beam in a freight car bogie, service stress
(or strain)http://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7history is
measured by a uniaxial strain gauge.
Signal processing uses a cycle counting algorithm toextract stress-strain hysteresis
loops quickly and accurately.In this study, rainflow cycle counting was used as a
signalprocessing method for fatigue analysis.
Figure 2 shows the procedure for the cycle countingmethod as demonstrated by Downing
and Socie (1982).(i) Consider the following sequence of peaks/valleys.The notation
uses point A as the most recent data point,point B as the previous point, and so
on.Range A to B > Range B to C
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(ii) Becausethe range from A to B is greater than therange from B to C, a cycle is
closed, and is represented bythe range from B to C.
(iii) Figure 2 (b) shows a new cycle. As before, the rangefrom A to B is greater than
that from B to C, so B to C isone cycle. This procedure is repeated until no more
cyclesare closed by this point.
The fatigue cumulativhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7e
damage rule for the actual runn-
Figure 2. Rainflow cycle counting procedure.
ing environment is needed for improving the safety of rail-way vehicles. The extracted
cycle produces stress ampli-tude and mean stress. Cumulative damage D and numberof
fractures to cycle N are determined using a histogram ofcycle ranges and Miner’s
rule.
For infinite life design for very high mean stresses, theBuch mean stress correction
is selected. Miner’s rule isexpressed as follows. Failure is expected to occur
if:D=-n1N----- -n---2-- -n---3
-- =(1)
f?
-ni
1Nf2Nf3
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i
N----t1fi
where ni is the number of applied cycles and Nfi is thenumber of cycles to failure at a specified stress amplitudeVi,
respectively. In this study, the critical cumulative dam-age value of D is chosen to be 1 in Eq. (1). The fatigue
lifein
the
repeated
signal
is
expressed
as
follows:Lhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7ife=-?--------1
-----------
(2)
ni/Nfi
i
Since, in many cases, the Palmgren-Miner theory (Singh,2002) leads to non-conservative life predictions, the
lineardamage rule associated with a critical damage sum D,different from one, has been proposed in many design
codesfor fatigue damage assessment of structures subjected tovariable amplitude loading.
2.2. P-S-N Curve
Because of the scatter in fatigue life data at any given stresslevel, it must be recognized that there is not only one
S-N
Figure 3. Photograph of a fractured end beam.
Figure 4. Bogie frame model with coupled effect, load, andboundary conditions.
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FATIGUE LIFE PREDICTION BASED ON THE RAINFLOW CYCLE COUNTING METHOD97
Figure 5. Distribution of stresses in the bogie frame.curve for a given material, but instead, a family of S-Ncurves
with probability of failure as the variabhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7le
parameter.These curves are called the P-S-N curves (Zheng and Wei,2005). A P-S-N curve can be obtained from
JSME S002.Fatigue data displayed on a log-log plot of stress versus lifefor finite life can be expressed as follows
for an end beam:logN=D
? E?log'S¡À1.64V???logN?? (3)
8
1/2
V
???logN??=1-6
-?logNi????D
? E?log
S??
(4)
1where V
???logN?? is the standard deviation of the number ofcycle to fracture obtained by the staircase test. S-N
curveswith failure probability 5% or 95% are determined bytranslating the S-N curve with failure probability of
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50% tothe coordinate axis (¡À1.64V).
3. FATIGUE LIFE PREDICTION FOR A BRAKE END BEAM OF A FREIGHT CAR BOGIE
3.1. Visual Examination of the End Beam
The fractured end beam was first subjected to visual exami-nation. The failure location of the end beam is
presehttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7nted inFigure 3. As seen from this figure,
the end beam firstfractured in the welding zone between the C shape beamand the gusset plate.
3.2. Finite Element Analysis
A geometric model of the freight car bogie was developedusing CATIA and ANSYS. The finite element model of
thebogie frame presented in Figure 4 consists of a 10-nodetetrahedral element and a 2-node beam element. The
coupl-ing element was selected to model the load applied to thebracket hinge of the end beam. Since geometrical
shape,load, and boundary conditions are symmetrical, we use thehalf-model as the effective model. The load
condition wasdetermined through JIS E4207 (1984). The end beam andside frame are manufactured out of SS400
and SM490A,respectively. In this analysis, a vertical load of 17,000 kgand a braking load of 2,875 kg were
applied to the center
Figure 6. Distribution of stresses of the end beam withbraking load.
http://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7Figure 7. Strain gauge layout for the end beam.
pivot and end beam, respectively.
Figure 5 shows that the von-Mises stress for the bogieframe (243.5 MPa) is located on the center pivot. Figure
6shows that the maximum von-Mises stress for the endbeam (75.4 MPa) is located on the corner of the
weldedgusset plate. These results are particularly interesting fromthe viewpoint of the fatigue strength, because
tensile stressesalone contribute the most to the fatigue crack initiation andpropagation. The location of the stress
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peak in Figure 6overlaps the fracture region presented in Figure 3. How-ever, the location of the stress peak in
Figure 6 does notoverlap with the fracture region.
The high level of stress in the end beam area was themain cause of crack initiation. The fatigue load (a
combi-nation of the self weight and braking load) caused thesuccessive propagation of the crack to critical size
and thenrhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7esulted in rupture at the welded gusset
plate. A consider-ably lower stress value in the region of the side frame canbe observed in Figure 5. The center
frame, except for thecenter pivot, isn¡¯t as highly loaded as the end beam. Themaximum von-Mises stress in the
region of the centerframe is only 243.5 MPa, whereas in the side frame thestresses are around 112.2 MPa (Figure
5).
3.3. Estimation of Load History
To determine whether the fatigue life is accurately predict-ed by the measured stress, it is necessary to compare
thefatigue life as calculated by the rainflow cycle countingmethod with that observed in experimental fatigue
dataattained under in-service loading.
Figure 7 shows attachment locations of six strain gauges
98S. H. BAEK, S. S. CHO and W. S. JOO
Figure 8. Blocks of strain-time history.
Figure
9.
Comparison
of
measured
stress
and
FEA
result.with
direction
perpendihttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7cular to the fatigue crack. In thisstudy,
we assumed that the direction perpendicular to crackpropagation is the principal stress direction. A one axisstrain
gauge (KFG-5-128) was installed on the end beambefore loading, and the test track was the
Donghae-Jecheonsection. The load history in the test track was measuredthrough 60 km/hr over 25 min, from
starting to braking.Figure 8 shows the results of the test series with the loadhistory based on six strain gauges. The
stresses resultingfrom the strain measurement are 48.3 MPa and 72 MPa,respectively. The stress ratios at the
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region are ??0.75.Figure 9 shows maximum principal stresses plotted as ex-perimental data and finite element
analysis (FEA) results.Compared to the FEA results, the experimental stresses atlocations of G2 and G5 are
measured within an error rangeof 12% as compared with analytical stresses. However,experimental stress at
location G4 is lower than the analy-tihttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7cal stress.
The measured stress at this location is very highdue to track vibration and braking load.
3.4. Fatigue Life Prediction
Knowledge of the material properties at the most criticalpoint of the end beam is needed for correct evaluation
ofthe integrity of the bogie frame. For this reason, 10 mmthick flat specimens were taken from a broken end beam
ofSS400 steel and investigated under alternating bendingstresses (R=??1). Test results for fatigue life given in
Baeket al. (2005) were obtained by flat specimens on a Scenk
Figure 10. Apparatus for the Scenk type fatigue test.
Figure 11. P-S-N curve for SS400 steel.
type twisting and bending fatigue testing machine (Figure10), and then plotted on the S-N curves with 5%, 50%,
and95% failure probabilities.
Figure 11 shows a P-S-N curve for SS400 steel. Theexpression of the P-S-N curve with 50% failure
probabilitycan
be
given
ashttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7
follows.logN=6.728??0.0094'S/2¡À0.405
(5)
The mean of the fatigue limit by the JSME statistical S-N testing method is 52.8 MPa.
A commercial fatigue analysis program, Fe-safe (2003),is used to calculate fatigue life of the end beam.
Miner¡¯srule was used as the fatigue cumulative damage rule. The
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first counting data for stress level was determined within
FATIGUE LIFE PREDICTION BASED ON THE RAINFLOW CYCLE COUNTING METHOD99
Figure 12. Rainflow cycle counting histogram.
Figure 13. Result of the damage histogram.
the confidence interval of the P-S-N curve by a correctionmethodfor the curve that considers stresses under
fatiguelimit.
Figure 12 shows the distribution of the stress range andmean stress at the location of G4. Figure 13 shows
fatiguedamage at each stress cycle using Miner¡¯s rule. It can benoted that although the high amplitude stress
cycle hhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7as lowfrequency, fatigue damage is
relatively large. Figure 14 showsthe damage histories over running time. Damage does notoccur during running
but most damage occurs during brak-ing.
Figure 15 shows fatigue life prediction by the S-N curveswith a given failure probability. The fatigue life
predictionby the S-N curves with 50% failure probability agrees wellwith actual fatigue life. In contrast, the
fatigue life predic-tions by the S-N curves with 5% or 95% failure probabi-lities were underestimated or
overestimated, respectively.Figure 16 shows fatigue life prediction at failure locationG2 using Miner¡¯s and
Modified Miner¡¯s rules. Miner¡¯s ruleoverestimates fatigue life, but the modified Miner¡¯s rulewhich considers
the stress state under the fatigue limitprovides an accurate fatigue life prediction within an errorrange of
2.7%~31%.
Figure 14. Time-correlated fatigue damage.
Figure
15.
Fatigue
confidence region.
life
disthttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7ribution
for
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Figure 16. Comparison of experimental fatigue life byMiner¡¯s rule and predicted fatigue life.
Table 1 shows the fatigue life and damage at all straingauge locations using modified Miner¡¯s rules. The
shortestfatigue life and damage are expected to occur at 1,410cycles and 7.14¡Á10-5 at the location of G4.
Considering that one cycle of the load history is 25 min,
the fatigue life of end beam is predicted to be 5,837.5 hrs. If
100S. H. BAEK, S. S. CHO and W. S. JOO
Table 1. Fatigue life and damage prediction by Miner¡¯s and modified Miner¡¯s rule.
Location numberMean stress correctionG1G2G3G4G5G6G1G2G3G4G5G6
LifeNo
damage2,533,0001,015,000545,80017,190,0001,100¡Á106120,000,00081,64080,90027,040113,80052,130,000
Miner¡¯s
ruleDamage03.95u10??79.85u10??71.83u10??65.82u10??89.09u10??108.33u10??91.22u10??51.24u10??53.7u10
??58.79u1http://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b70??61.92u10??8
YearUnlimited120.4848.2825.96817.63752,32125,0001716.855.6323.7110,860
LifeNo damage983,700360,400209,8005,146,000170,000,00023,200,00035,35036,55014,01050,78011,510,000
Modified Miner¡¯s rule
Damage01.02u10??62.77u10??64.77u10??61.94u10??75.88u10??94.31u10??82.83u10??52.74u10??57.14u10??5
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1.97u10??58.69u10??8
YearUnlimited46.7917.147.98244.788,0864,8337.367.612.9210.582,397
None
Goodman
a freight car speed is 60 km/hr, its life expectancy is350,250 km. This corresponds to 2.92 years, assuming
theendurance life of a freight car as 25 years (3¡Á106 km). But,because the location of G4 is fixed at the center
beam, andstress intensity is concentrated at the welded gusset plate,discussion in regard to twisting shear stress is
needed. Formore accurate fatigue life prediction, further research isrequired for stress concentration at the welded
gusset of http://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7theend beam.
5. CONCLUSIONS
The present work proposed a fatigue life estimation methodfor freight cars based on the rainflow cycle counting
method,P-S-N curve, and modified Miner¡¯s rule. Further improve-ments may be made to the procedure by
incorporating amore representative hazard function with cumulative failureprobability rather than the cumulative
damage rule used inthis paper.
(1) The measured stress at the end beam agrees well with
the FEA result, within a 12% error range.
(2) Fatigue data displayed on a log-log plot of stress versus
life for finite life can be expressed as follows:logN=6.728??0.094'S/2¡À0.405
(3) The fatigue damage and life calculated with the stress
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spectrum during 25 min are 7.14¡Á10??5, and 2.92 years,on the basis of rainflow cycle counting method,
P-S-Ncurve, and modified Miner¡¯s rule.
ACKNOWLEDGEMENT??This
paper
was
supporhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7ted by Dong-A university research fund
in 2006.
REFERENCES
Barboza, W., Raminelli, L. F. and Antonelli, J. (2005).Cumulative fatigue damage in the diesel engines appli-
cation. SAE Paper No. 2005-01-4110.
Baek, S. H., Jeon, J. H., Lee, K. Y., Cho, S. S. and Joo, W.S. (2005). Reliability analysis and preventive
mainten-ance for fatigue life of end beam for un-covered freightcar. Trans. Korean Society Mechanical
Engineers29,3,495??502.
Downing, S. D. and Socie, D. F. (1982). Simplified rain-flow cycle counting algorithms. Int. J. Fatigue4,1,
31??40.
Fatemi, A. and Yang, L. (1998). Cumulative fatiguedamage and life prediction theories: A survey of the stateof the
art for homogeneous materials. Int. J. Fatigue20,1, 9??34.
Fe-safe (2003). Software Package, Ver. 5: Volume3-SignalProcessing Reference Manual. Section 7. Safe
Techno-logy Limited. 1??14.
Goo, B. C. anhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7d Seo, J. W. (2003). Probabilistic
fatigue lifeevaluation of rolling stock structures. Trans. KoreanSociety Automotive Engineers11,5, 89??94.
文档下载 免费文档下载
http://www.mianfeiwendang.com/
Haq, S., Lee, Y., Larsen, J. L., Frinkle, M. and Akkala, B.(2007). Reliability-based test track schedule
developmentfor a vehicle suspension system. SAE Paper No. 2007-01-1653.
Japanese Industrial Standard (JIS) E4207 (1984). TruckFrames for Railway Rolling Stock-General Rules
forDesign. Japanese Standards Association.
Kang, B. J., Sin, H. C. and Kim, J. H. (2007). Optimalshape design of the front wheel lower control arm
con-sidering dynamic effects. Int. J. Automotive Technology8,3, 309??317.
Matsuishi, M. and Endo, T. (1968). Fatigue of metalssubjected to varying stress-fatigue lives under
randomloading.Proc. Kyushu District Meeting, JSEM, Fukuoka,Japan, 37??40.
Murty,
A.
S.
R.,
Gupta,
U.
C.
and
Krishna,
R.
(1995).
Anew
approach
to
fatigue
strhttp://www.mianfeiwendang.com/doc/50dfc296011fbf07750549b7ength distribution for fatigue
FATIGUE LIFE PREDICTION BASED ON THE RAINFLOW CYCLE COUNTING METHOD101
reliability evaluation. Int. J. Fatigue17,2, 85??89.
Nagpal, R. and Kuo, E. Y. (1996). A time-domain fatiguelife prediction method for vehicle body structures.
SAEPaper No. 960567.
Singh, A. (2002). The nature of initiation and propagationS-N curves at and below the fatigue limit. Fatigue
Fract.Eng. Mater. Struct.,25, 79??89.
Wang, H., Kim, N. H. and Kim, Y. J. (2006). Safety
envelope for load tolerance and its application to fatiguereliability design. ASME J. Mech. Des.128,4,
919??927.Zheng, X. and Wei, J. (2005). On the prediction of P-S-Ncurves of 45 steel notched elements and
probabilitydistribution of fatigue life under variable amplitudeloading from tensile properties. Int. J. Fatigue,27,
文档下载 免费文档下载
http://www.mianfeiwendang.com/
601??609.