Journal of Applied Mathematics and Physics, 2014, 2, 342-348
Published Online May 2014 in SciRes. http://www.scirp.org/journal/jamp
http://dx.doi.org/10.4236/jamp.2014.26041
How to cite this paper: Tang, W., Wang, W.J., Wang, Y. and Li, Q. (2014) Fatigue Strength and Modal Analysis of Bogie
Frame for DMUs Exported to Tunisia. Journal of Applied Mathematics and Physics, 2, 342-348.
http://dx.doi.org/10.4236/jamp.2014.26041
Fatigue Strength and Modal Analysis of
Bogie Frame for DMUs Exported to Tunisia
Wei Tang*, Wenjing Wang, Yao Wang, Qiang Li
School of Mechanical Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
Received January 2014
Abstract
The equivalent stress at key positions of Bogie Frame for DMUs Exported to Tunisia is obtained by
using simulation analysis. The evaluation of static strength and fatigue strength is checked refer-
ring to UIC specification and Goodman sketch for welding materials. In addition, the modal analy-
sis of the frame is made, and the vibrational modal of frame in given frequency domain is prede-
termined to evaluate the dynamical behavior of the frame in order to meet the dynamical design
requirements. The results show that the key points of the calculated frame of the equivalent stress
are less than allowable stress, and thus it could provide a theoretical foundation for the optimized
design of frame structure and safety of industrial production.
Keywords
Fatigue St reng th , Diesel Multiple Units, Frame, Finite Element, Modal An alysis
1. Introduction
The bogie frame is the main load bearing components and power transmission components of the vehicle, when
the vehicle is in motion the process, not only to the bogie frame to withstand loads, but also need to pass a va-
riety of forces between the body and the wheel. Due to the fatigue test costs are expensive, the fatigue strength
assessment of key components in the bogie frame using finite element model can find out the fatigue strength of
the weak parts, can reduce the risk of fatigue testing prototypes, shorten development cycles, reduce trial costs.
In addition, the current domestic commonly uses Electric Multiple Units [1], lacks of bogie products of Diesel
Multiple Units; Diesel Multiple Units still have a large market in many countries such as Tunisia for its poor line
conditions and economic factors. Therefore, strength analysis and dynamic assessment for the bogie frame of
Diesel Multiple Units is of great significance.
This paper is to understand the export Tunisia DMUs bogie basic components, infrastructure characteristics,
determined the type of bogie frame load sources and calculated in accordance with the relevant specifications to
determine the load; then to use the Hyper mesh software architecture network entities meshing, to re-use the
ANSYS finite element analysis software for finite element analysis of the bogie frame. The evaluation of static
strength and fatigue strength is checked referring to UIC specification and Goodman sketch for welding mate-
rials. In addition, the modal analysis of the frame is made [2].
*
Corresponding author.

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2. Bogie Frame Structure and Finite Element Modeling
2.1. Bogie Frame Structure
The bogie Frame for DMUs Exported to Tunisia is adopted by welded structure, Figure 1 demonstrates that the
main framework architecture is H-shaped in the horizontal plane, which is composed of two box-shaped side
sills, the overall composition of the box beam welding, by the central concave belly of the fish box structure
composed of a spring seat side beam welding, basic brake mounts, anti-roll torsion bar seat, etc., the cavity has a
thickness of 10 mm stiffener plate [3]. Box beam structure for the central opening, the transverse beam welding
has ended with stopper seat, traction rod seat, motor bracket, gearbox bracket and secondary lateral damper seat
and so on.
2.2. FEM Model of Bogie Frame
Considering calculating workload, precision and the actual situation in structure of the entire bogie frame, this
research selects 10-node solid element of solid 92. Based on the model, the entire bogie frame is discrete with
the software Hyper mesh and analyzed with the large generally used finite element software ANSYS [4]. In or-
der to simulate the real boundary conditions of the bogie frame, axle box spring in the bogie frame mount simu-
lated by a series of axle box spring unit Combine14 spring means, consistent with the axle box spring stiffness
of the spring element stiffness. In the end, the finite element discrete nodes of 110,368, the number of units to
341,334, finite element discrete model shown in Figure 2.
2.3. Evaluating Standard of Bogie Frame Strength
In the fatigue strength of welded bogie frame has now formed the international standard UIC 615-4 [5] as the
representative of the design, evaluation system. Bogie frame structure strength assessment generally includes
three aspects, namely, the role of analysis to determine the load, static strength analysis and assessment, analysis
and evaluation of the fatigue strength.
Figure 1. Welded bogie frame.
Figure 2. The FEM model of the bogie frame.

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According to the UIC 615-4 regulations, we can calculate the appropriate supernormal load, simulated opera-
tional load and special operational load. Supernormal load when the maximum load operations may occur; si-
mulate actual operating load refers to the load operations occur frequently; special operational load refers to the
load frame by a special device caused. In the practical constraints are consistent with the principles of the frame,
and the constraints of the axial knuckle arm spring constraints loads. Then, referring to the UIC 615-4 regula-
tions on load conditions are combined to get the final five groups exceptional load cases, four groups of special
load cases and 13 groups of operational load cases. Tables 1-3 lists the typical cases of supernormal loads and
operating loads.
3. Results and Analysis
3.1. Calculation and Analysis of Static Strength
The conditions of supernormal loads are used to verify that there is no permanent deformation when the bogie
frame experiences supernormal loads, which can be used to evaluate static strength of the bogie frame. In the
Table 1. Main extraordinary load case combinations table. KN
Loading point
Conditions
1 (K = 1.4) 2 (K = 2.0) 3 4 5
Left air spring vertical loads −168.3 −240.4 −168.3 −168.3 −168.3
Right air spring vertical loads −168.3 −240.4 −168.3 −168.3 −168. 3
Lateral load stopper 108.2 108.2
Air springs lateral load 16.4 16.4
The left side of the anti-roll load 79.6
The right side of the anti-roll load −79.6
Buckling load/mm +24.0 +24.0
A series of vertical damper load −9.0
Secondary lateral damper load 8.0
Anti-snake damper load 24.0
Note : K is a safety factor.
Table 2. Extraordinary special load case combinations table. KN
Loading point Emergency braking
condition
Shunting impact
conditions
Equipment inertia
conditions
Derailment
conditions
Left air spring vertical loads −168.3 −168.3 −168.3 −120.2
Right air spring vertical loads −168.3 −168.3 −168.3 −120.2
Traction rod seat longitudinal load 168.8 367.5
Thre e-point
support analog
derailment
1st gearbox reaction rod load Flank
2nd gearbox reaction rod load Flank
1st unit brake load 24.0
2nd unit brake load 24.0
Gearbox vertical vibration 47.6
Gearbox lateral vibration 9.2
Gearbox longitudinal vibration 9.2

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Table 3. Typical operating conditions load combination table. KN
Conditions
Vertical load Lateral
load
Longitudinal
load
Distorting
load
Braking
load z/y
Motor load
z/y/x
Gearbox
load
Two series
shock
absorb ers x/z
The left side
of the beam
The right side
of the beam
1 Fz Fz −mg
3 Fz (1 + α − β) Fz (1 − α − β) +Fy −15.5 27.4/61.2 31. 5/21/21 −27.7 8.7/5.63
7 Fz (1 − α − β) Fz (1 + α − β) −Fy −15.5 27.4/61.2 31.5/21/21 −27.7 8.7/5.63
8 Fz (1 – α + β) Fz (1 + α + β) 15.5 27.4/61.2 31.5/21/21 27.7 8.7/5.63
10 Fz (1 + α − β) Fz (1 – α − β) +Fy 15.5 5.75 27.4/61 .2 31.5/21/21 27.7 8.7/5.63
11 Fz (1 + α + β) Fz (1 − α + β) +Fy −15.5 −5.75 27.4/61.2 3 1.5/21/21 −27.7 8.7/5.63
12 Fz (1 – α − β) Fz (1 + α − β) −Fy 15.5 5.75 27.4/61.2 31.5/21/21 27.7 8.7/5.63
13 Fz (1 + α − β) Fz (1 + α + β) −Fy −15.5 −5.75 27. 4/61.2 31.5/21/21 −27.7 8.7/5.63
Note : α is roll coefficient is taken as 0.1; β coefficient for the ups and downs , taken as 0.2; m motor quality ; g is the gravitational acceleration.
supernormal main loads conditions, the maximum stress occurs at the welded joint of Cross-side beam connec-
tions under lateral beam support beams in the cover plate and cover plate in condition 5, and the maximum value
is 295.2 MPa; In the supernormal special loads conditions, the maximum stress occurs at the welded joint of
Cross -side beam connections under lateral beam support beams in the cover plate and cover plate when the bo-
gie derails, and the value is 256.5 MPa. All these stress analyzed above is less than the yield stress of P355NL1
steel (355 MPa), which satisfies the UIC standards static strength requirements [6].
3.2. Calculation and Analysis of Fatigue Strength
According to the framework structure and analysis of static strength, fatigue crack tends to happen on 13 major
parts that endure larger stress. Finite element analysis is carried out on these 13 major parts in different condi-
tions, as shown in Table 3. Corresponding maximum stress σmax and minimum stress σmin is found. The mean
stress σm can be found with the standards of UIC:
min maxmin max
,
22
ma
σσ σσ
σσ
+−
= =
(1)
Table 4 shows the calculation results of mean stress and dynamic stress amplitude in strong stress areas. Se-
lective analysis is carried out on critical points, which are selected according to the framework structure. Figure
3/Figure 4 show the overall architecture , and the high stress amplitude of dynamic stress nephogram when the
fatigue strength is of the greatest effect conditions, the maximum stress is found at the welded joint of Longitu-
dinal beams and beams, and the value is 79.5 MPa.
4. Evaluation of Fatigue Strength
Fatigue strength is evaluated with Goodman line. Import the mean stress and dynamic stress amplitude in strong
stress areas into the fatigue limit diagram of frame materials (Figure 5), we can find that all these representative
and dangerous points are located inside of the Goodman line, which means that all these mean stress and dy-
namic stress amplitude are less than the fatigue limit of P355NL1 steel. Therefore, the bogie frame meets the
design requirements of the fatigue strength.
5. Modal Analy sis
In consideration of the influence of practical operation constrains on the modal, we apply horizontal constraint
and vertical constraint on locating seat of axle box rotary arm, and we also apply vertical elastic constraint on
the bottom of the axle box. In order to determine whether there is resonance or other vibration mode that against
the operating of vehicles, we used the subspace iteration method provided by the ANSYS software to carry out
the modal analysis on the frame. In general, there is no high-frequency vibration during the operation of trains,

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Figure 3. Overall dynamic stress amplitude cloud.
Figure 4. Partial cloud dynamic amplitude stress in large
stress parts.
Table 4. Synthesis of the results mean stress/dynamic stress amplitude on the frame big stress area. MPa
Part name No. Location Average
stress
Dynamic stress
amplitude
Materials
area
Beam and
side beams
connecting
area
1 Within a support beam and side sill beam weld connection 47.4 6 4.3 Weld
2 beams and side beams connecting welds 66.4 51.6 Weld
3 Cover plate with the support of the beam connecting the beams
and side beams under three side beams connecting welds Department 116.1 58.5 Weld
Side sill
area
4 positioning seat upright plate portion of the opening arc bends 28.4 60.1 Base metal
5 positioning seat cover is connected with the lower side beam welds 67.6 47.6 Weld
6 Under positioning seat cover parts connected with the vertical plate welds 76.1 5 3.5 Weld
7 Anti-nake-seat legislature damper plate 0 51.0 Base metal
8 Anti-snake damper seat and side sill outer webs connecting portion 33.8 2 8.4 Weld
Beam
area
9 Brake bracket vertical plate 0 55.8 Base metal
10 Brake bracket and beam connection area 25.4 37.4 Weld
11 Anti-roll torsion bar seat ribs 0 78.1 Base metal
12 Longitudinal beams and beam weld connection 41.8 79.5 Weld
13 Gearbox boom stand upright plate 0 60.3 Base metal

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so when to analyze framework of free mode, only to take the first six modal characteristics. Table 5 shows the
inherent frequency and vibration shape for each modal.
From Table 5 we can find that the first-order characteristics is two side beams nod reversing, which means
that the torsional stiffness of the bogie frame is small; this helps trains to overcome the vertical irregularity of
lines. The six-order characteristic is that beams in the vertical plane of the first bending with a larger frequency,
which means that the stiffness of the beam is pretty big; this helps the beam to bear load and keep connection to
other parts. As a conclusion, the vertical stiffness and transverse stiffness of the bogie frame is ideal. Both of
them meet the design requirements and the smooth running of vehicles.
6. Conclusions
According to the UIC615-4 specification, this research analyzes the static strength and fatigue strength of bogie
frame for DMUs exported to Tunisia. The result shows that all the stress amplitudes are less than fatigue limit,
which means that the bogie frame meets the requirements of fatigue strength.
ANSYS software is used to calculate the inherent frequency and vibration shape of bogie frame, and the re-
sults reveal that the torsional stiffness of the bogie frame is small. Trains benefits from the low torsional stiff-
ness to come over lines with vertical irregularity, and bogie frame can avoid other excitation frequency.
With the help of CAD/CAE, people can do the simulation and analysis on bogie frame of high speed train ef-
fectively, which contributes a lot to shorten the development cycle, reduce cost and raise efficiency.
Acknowledgements
This research was financially supported by the National Natural Science Foundation of China (NO.51205017)
Figure 5. Fatigue limit diagram for base metal/welded joint of steel P355NL1.
Table 5. Frame modal analysis results.
Order Frequency/Hz Modal characteristics
1 43.3 Two side beams reverse nod
2 76.2 First bending of the frame beams
3 84.7 Two side beams reverse bend in the horizontal plane
4 87.0 Two side beams in the same direction in the horizontal plane first bending
5 102.3 Two side beams in the same direction in the horizontal plane of second-bending
6 103.2 Beams in the vertical plane of the first bending

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and the National High Technology Research and Development Program (863) Fund Project (Key technology
research lineage system of high-speed trains.NO.2012AA112001-01).
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