Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

52, 3, pp. 745-755, Warsaw 2014

AN INNOVATIVE METHOD FOR STRESS ANALYSIS OF Y25 BOGIE
UNDER OSCILLATING LOADS DUE TO TANK WAGON FLUID SLOSHING

Mohammad Ali Rezvani, Mohammad Mahdi Feizi, Morad Shadfar

School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran

e-mail: rezvani ma@iust.ac.ir; mmfeizi@yahoo.com; morad.shadfar@gmail.com

Freight wagons carry higher axle loads and may travel along tracks of lower quality. This
can be interpreted as higher dynamic loading of freight bogies especially for tanker cars
that are subjected to sloshing loading. Rail irregularities, particularly during braking and
running on curved tracks initiate the fluid sloshing. This article is about introducing an
innovative method for analyzing bogie stresses of tanker cars while in travel and under
critical circumstances. The effect of the vehicle speed of travel, its liquid filling ratio, track
quality and fluid density are also investigated in terms of stress results of bogies.

Keywords: Y25 bogie, dynamic modeling, FEM, stress analysis, longitudinal sloshing

1. Introduction

Bogies are major parts in the configuration of railway vehicles that directly interact with the
rail and track irregularities. While in motion bogies tolerate severe dynamic loadings. Fatigue
in bogie axles, center bowls and frames is unavoidable. As a consequence of fatigue, safety in
travel is jeopardized and the cost of maintaining the fleet increases. There are a few research
papers concerned with the issue of fatigue in bogie frames. Most of such researches are focused
on passenger coaches. The reason for that is higher speed of travel in passenger trains. There is
also the need to improve safety aspects of the trip. This leads to higher forces and impact loads
on bogie frames.
Kim (2006) reported a research on high speed passenger trains in Korea. Kim and Kim

(2005) and Kim (2005) also reported on fatigue life estimations of articulated bogies according
to UIC615-4. Park (2006) examined the fatigue life of passenger bogies with the finite element
method.Younesian et al. (2009) estimated the fatigue life of passenger bogiesMD36 andMD523
in both time and frequency domain by introducing an innovativemethod. They also determined
sensitivity of the frame fatigue life on the track quality.
Although freight bogies travel at lower velocities, but the higher axle loads lead to higher

levels of static stresses. Locovei et al. (2010) examined fatigue of axles in tank wagons with the
finite element method considering thermal effects and the residual stresses in the axle box in
both tangent and curved tracks. However, the effect of sloshingwas ignored. The tanker wagons
carrying fluids are subjected to fluid sloshing while this does not exist for other types of freight
wagons.
Liquid sloshing can be examined with analytical, experimental and numerical methods in

order to calculate the forces due to liquid-solid interactions. Simulation of the sloshing mostly
falls into two groups (Badran et al., 2012; Cherna et al., 2012). The first group considers a
continuummediumfor thefluid (finite element)while the latter focuses on thediscrete equivalent
dynamic model. Aliabadi et al. (2003) studied a 3D sloshing of a tank vehicle in braking with
the finite element model. By using 250000 hex elements, they modeled an elliptic tank at the
speed of travel of 10m/s and braking acceleration of 0.2g. Lateral sloshing was also modeled
with the equivalent pendulum and finite element. Comparisons between the outcomes of the



746 M.A. Rezvani et al.

twomethods prove good agreement. However, the amplitude of the oscillations predicted by the
pendulummethod is higher.

The modeling tools such as the ADAMS/RAIL engineering software were used in order to
study the derailment behavior of a tanker wagon along a curved track. The effects of the para-
meters such as the fluid density, vehicle speed of travel and track irregularities were considered.
Lateral sloshing was also considered by using the assumption of the equivalent pendulum. The
effects of sloshing on other directions were neglected. 18% and 25% differences in the results for
the derailment and unloading of the wheel at the presence of the lateral sloshing were reported
(Younesian et al., 2010).

Vera et al. (2005) also simulated a dynamic model of 4 tanker wagons in SIMPACK. They
modeled the longitudinal sloshing by using the equivalent mass – the spring model, and an
equivalent pendulumwas used for the lateral sloshing. In the longitudinal model both braking
and acceleration was studied and the results were examined in couplers. They also conside-
red 4 simple baffles inside the tankers. Beside many tasks have been done on sloshing, many
scientists worked on ways to avoid failures caused by sloshing (Koh et al., 2013; Biswala and
Bhattacharayyab, 2010).

In this study, by combination of the method introduced by Younesian et al. (2009) and
implementing longitudinal sloshing into it, the effects of the longitudinal sloshing generated
during the braking process and its effect on the structural stresses of the bogie frame is studied.
It needs tobe reminded that simultaneous application of track irregularities and oscillatory loads
due to fluid sloshing have severe effects on the freight bogie stresses. This was not considered in
prior researches. The Y25 bogie is the subject of interest for this research. Initially, in order to
determine the dynamic forces, themodel for the selected wagon is developed in ADAMS/RAIL
engineering software. In this part, sloshing ismodeledwith the equivalentmass – a spring. In the
next step, the dynamic forces and the track irregularities are applied to themodel in LS-DYNA,
and the stress history of the critical points is extracted. This time signal gives a very important
required data for further analysis.

2. The Y25 bogie and its characteristics

The freight bogies in Iranian railway aremainly divided into two groups of solid and three pieces
frames. The bogies with solid frames are used for axle loads up to 20 tonnes and the three pieces
bogies are used for axle loads of up to 23.5 tonnes. The bogies with solid frames have more
stable behavior during operation. Besides, the limit tolerances in these bogies prevent warping
during operation. The wagon union bogie type Y25 is of the solid frame type. It is equipped
with the primary suspension and can carry the axle load of 20 tonnes. Y25 is widely in use for
freight transportation throughout the world. Figure 1 is for a tank wagon equipped with Y25
bogies manufactured byWAGON PARS in Iran.

Fig. 1. Tank wagon equipped with Y25 bogies



An innovative method for stress analysis of Y25 bogie... 747

While in motion, the common problemwith such tanker cars is the change in the axle load
due to longitudinal sloshing during braking that can increase the axle load of the bogies. This
phenomenonhas anegative effect on the fatigue life of bogies. In thispaper,byusing thedynamic
model of a tank wagon on Y25 bogies, the dynamic forces are calculated. These forces are used
in the stress analysis of the FE model of the frame and, finally, the effect of the longitudinal
sloshing in generating the structural stresses is studied.

3. The modeling of Y25 bogie

This bogie consists of a solid frame and the primary suspension that includes helical springs and
friction elements. The friction elements causenon-linear behavior of thebogie.This non-linearity
ismodeled by using the hysteresis loop reported byMolatefi et al. (2006). The schematic of such
a loop is presented in Fig. 2.

Fig. 2. Schematic of the hysteresis loopmodeled for the primary suspension system of Y25 bogie
(Molatefi et al., 2006)

The specifications for the primary suspension and the hysteresis loops are presented in Ta-
ble 1.

Table 1.Parameters of the primary suspension system of Y25 bogie (Molatefi et al., 2006)

Vertical direction Lateral direction Longitudinal direction

Ch Cg FD Ch Cg FD Ch Cg FD
[N/m] [N/m] [kN] [N/m] [N/m] [kN] [N/m] [N/m] [kN]

1.3 ·107 8.9 ·105 2.5 2.2 ·106 4.3 ·105 5.0 1.7 ·107 8.5 ·105 4.0

The schematic of the center bowl and its friction components that are also used for the
modeling purposes are presented in Fig. 3. The side bearers are also modeled.

3.1. The dynamic modeling

In order to estimate the sloshing loads, the dynamic model of Y25 bogie is modeled in
ADAMS/RAIL engineering software. Some details for the bogie are provided in Tables 1 and 2
from the report by Molatefi et al. (2006). The model is presented in Fig. 4. The calculated
inertial properties for different parts of this bogie are presented in Table 2.
The index x denotes the longitudinal axis, y lateral and z represents the vertical axis. The

liquid in the tank is subdivided into two components including a fixed mass mo and a moving
mass mfluid (Abramson and Silverman, 1966), see Fig. 5. There is no sloshing in the fixedmass.
Sloshing happens within the moving mass. The mass-spring system is used for the modeling of
the longitudinal sloshing of the liquid in the tank.



748 M.A. Rezvani et al.

Fig. 3. The center bowl of Y25 bogie (Molatefi et al., 2006)

Fig. 4. The 3D dynamic model of Y25 bogie in ADAMS/RAIL

Table 2. Inertial properties of Y25 bogie

Body M [kg] Ixx [kgm
2] Iyy [kgm

2] Izz [kgm
2]

Bogie frame 1990 1188 1484 2582

Axle box 20 5 5 5

Side bearer 25 10 10 10

Wheelset 1.380 902 108 906

Fig. 5. Modeled tank wagonwith longitudinal sloshing in ADAMS/RAIL

The specifications for the mass-spring system for partially filled tanks containing water of
different filling percentages are calculated and presented in Table 3.

Later on in this article, the sulfuric acid that is 1.83 timesdenser thanwater is also considered
as the content of the tank.

In order to verify the dynamic model, the hunting velocity of the vehicle is also calculated.
The result is presented in Fig. 6. The calculated hunting velocity is equal to 17.7m/s. It is



An innovative method for stress analysis of Y25 bogie... 749

Table 3.Mass and stiffness of the longitudinal mass-spring system (water content)

Filling ratio 30% 50% 80%

mfluid [kg] 1.3857 ·10
4 2.2684 ·104 3.4803 ·104

mo [kg] 3.3983 ·10
3 6.0748 ·103 1.1210 ·104

K [kN/m] 6.3291 ·103 1.6961 ·104 3.9926 ·104

hfluid [m] 0.0017 0.0079 0.0319

ho [m] 1.6762 2.5861 3.5294

comparable to the hunting velocity of 17m/s for the same vehicle that was reported byMolatefi
et al. (2006). The difference comes from the effect of neglecting structural clearances. It is
concluded that the dynamic model is reliable and can be used for further processing.

Fig. 6. Non-linear hunting velocity of Y25 bogie (output fromADAMS/RAIL)

3.2. The analysis

The Iranian freight tankers have been equipped withWagon Union (Y25) bogies since 1982
(Reports on the Technical Specifications of the Freight wagons, Freight Division, 2010). The
wheel profile for the fleet running over Iranian National tracks is S1002. The track inclination
angle is 1:20.With the simulatedmodel provided in theprior sections of this article, thepartially
filled tanker carswere testedduringthebrakingprocess. It is assumedthat thevehicledecelerates
at 1m/s2. Three scenarios including the tanker cars with 30%, 50% and 80% filling ratios are
examined. The results of the simulation for the vertical forces on the bogie centre bowl are
presented in Fig. 7. It is observed that during braking, the amplitude of fluctuation of the
vertical loads on the bogie decreases as the filling ratio increases.

Fig. 7. A comparison of the vertical forces on the bogie centre bowl during braking



750 M.A. Rezvani et al.

The calculated forces and track irregularities applied to a model of the frame in Ansys-LS-
-DYNAFEMengineering software. To speed up the calculations, the framemodel is divided into
several smaller parts. Consequently, the new parts are meshed by using 350243 Hexa meshes.
Figure 8 (right) illustrates the bogie centre bowl that is meshedmonotonously.

Fig. 8. Partitioning of the bogie to smaller parts (left), meshed view of the bogie in FEMsoftware (right)

In order to consider the effect of track irregularities on the bogie structure, the suspension
system is modeled by a set of the damper and spring. Irregularities act as displacements on the
end of the suspension system (Frýba, 1996; Wiriyachai et al., 1982).
The power spectral density (PSD) functions were used to generate track irregularities with

random nature. The Federal Railroad Administration of US (FRA) classifies the railway tracks
from 1 (the worst) to 6 (the best) in view of surface irregularities. The following PSD functions
provided byFRA represent Sc,g cross and gauge and Se,a elevation and alignment irregularities.

Sg(Ω)=
AΩ22

(Ω2+Ω21)(Ω
2+Ω22)

Se(Ω)=
AΩ22(Ω

2+Ω21)

Ω4(Ω2+Ω22)
(3.1)

S(Ω) is the PSD of irregularities versus wavelength (Ω=2π/(vω)), while v is the wagon speed
of travel and A,Ω1 and Ω2 are constant coefficients shown in Table 4.

Table 4.Railway track characteristics specified by FRA

Irregularity Parameter Unit
Track class
1 3 6

A 108m3 15.53 4.92 0.98
Elevation Ω1 10

3m−1 23.3 23.3 23.3
Ω2 10

3m−1 13.1 13.1 13.1

A 108m3 9.83 3.15 0.59
Gauge Ω1 10

3m−1 29.2 29.2 29.2
Ω2 10

3m−1 23.3 23.3 23.3

Using a Monte Carlo algorithm, the irregularities r(x) are calculated for the rail classes of
1, 3 and 6

r(x)=
N
∑

k=1

αk cos(ωkx+ϕk) (3.2)

where αk is the amplitude and ωk is the frequency in the range of (ω1,ω2). The calculations
were carried out in these intervals. ϕk is a random value with normal distribution in the range



An innovative method for stress analysis of Y25 bogie... 751

of (0,2π). X and N are the position on the track and the number of the divided intervals,
respectively. The values of αk and ωk are calculated as

αk =2
√

S(ωk)∆ω ωk =ω1+
(

k−
1

2

)

∆ω k=1,2, . . . ,N

∆ω=
ω2−ω1
N

(3.3)

The vertical and horizontal components of the irregularities calculated for the railway tracks of
1, 3 and 6 classes are presented in Fig. 9.

Fig. 9. Vertical and horizontal components of the rail track irregularities

It is intended to identify the critical points within the bogie structure while it is under the
influence of track irregularities of statistical nature. The size and the history of the stresses
on such points are extracted. The most critical point lies on the bogie centre bowl. The stress
contour for this zone is indicated inFig. 10. This case belongs to a filling ratio of 50%, the initial
velocity of 20m/s, the track of class 6, and the fluid content is water. All the results are plotted
for this point.

Fig. 10. Stress concentration in the bogie centre bowl

3.3. The effect of vehicle speed of travel on the bogie stresses

In Fig. 11, it is shown that by varying the vehicle speed of travel from 20 to 30m/s, the
stresses in the bogie center bowl grow approximately by 1.5%. By further increasing the speed,
the amplitude can growbymore than 10%.Themaximum stresses at the speed of 20 and30m/s
are 93.7 and 94.5MPa, respectively.
It is observed that there are two types of fluctuations in the calculated stress histories.

The track irregularities cause fluctuations in the forces with smaller amplitudes and higher



752 M.A. Rezvani et al.

Fig. 11. Calculated stresses in the bogie centre bowl at different speeds of travel (rail irregularity type 3)

frequencies. The oscillating loads due to sloshing cause fluctuations with higher amplitudes and
smaller frequencies.

3.4. The effect of track irregularities on the bogie stresses

Figure 12 indicates the effects of quality of the railway track on stressing out the bogie
structure. As the quality of the track worsens, the amplitude of the corresponding stresses
increases. The maximum stresses in tracks of the 1st, 3rd and 6th classes are 95, 93.6 and
92.8MPa, respectively.

Fig. 12. Themaximum calculated stresses in the bogies versus different classes of tracks

3.5. The effect of the fluid tank filling ratio on the bogie stresses

Clearly, as the liquid filling ratio increases, the vehicle axle load raises. Consequently, the
average stress loaded on the bogies grows. Figure 13 illustrates the stress loading on the bogie
at different filling ratios. The maximum stresses at the filling ratios of 30%, 50% and 80% are
90.5, 94.1 and 96.5MPa, respectively. It is worth to notice that the stresses at the filling ratio of
50% rather than others are highly sensitive to track irregularities. This can be associated with
the larger free surface at such a filing ratio.

3.6. The effect of fluid density on the bogie stresses

The simulated model of the vehicle was also used to study the effect of density of the liquid
content of the tanker car on the stresses generated within the bogie. Water was replaced with
sulfuric acid that is 1.83 times denser. As a result, the average stresses in the bogie structure
increased. Themaximumcalculated stress in the case of water is 93.8, and in the case of sulfuric
acid is 95MPa, Fig. 14.



An innovative method for stress analysis of Y25 bogie... 753

Fig. 13. Themaximum calculated stresses in the bogies versus different filling ratios

Fig. 14. The maximum calculated stresses in the bogies versus different liquids

4. Conclusions

This paper by employing a new combinedmethod, presents the stress behavior ofWagon Union
type Y25 bogie in the tanker wagon subjected to random and oscillating loads due to track
irregularities and by liquid sloshing. Using a number of numerical models, including the Finite
Element Method and the multi body dynamic techniques, the following important conclusions
are drawn:

• Thestudyof the stresshistoryof thebogie indicated two typesoffluctuations. Irregularities
of the track cause stresseswith smaller amplitudesathigher frequencies.The liquid sloshing
causes stresses of higher amplitudes and smaller frequencies.

• By increasing the speed of travel from 20 to 30m/s, the peak stresses rise up. At higher
speeds, the stress amplitude grows by more than 10%. The maximum stresses at 20 and
30 m/s are 93.7 and 94.5MPa, respectively.

• The type of the track has a noticeable effect on the stress amplitude within the bogie
structure. As the quality of the track worsens, the amplitude of the stress increases. In
this case, the maximum stresses for the tracks of the 1st, 3rd and 6th classes are 95, 93.6
and 92.8MPa, respectively.

• Themaximum stresses in the case of tanker wagons with 30%, 50% and 80% filling ratios
are 90.5, 94.1 and 96.5MPa, respectively. In addition, the stress at the 50% filling ratio,
rather than others, is highly sensitive to track irregularities. This can be attributed to the
larger free surface that becomes available for this case.

• At similar filling ratios, the maximum calculated stresses are 93.8 and 95MPa, while
carrying water or sulfuric acid, respectively.



754 M.A. Rezvani et al.

• The discussed/developed methodology could apply to any type of bogie under live or
random loads in order to extract stress history signals of the critical points.

Acknowledgements

The authors of this article would like to thank the office of research of IranUniversity of Science and

Technology for continuous support during the course of this research.

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Manuscript received October 30, 2013; accepted for print February 21, 2014