B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

Internat ional Journal of

Vehicle Structures & Systems Available online at www.ijvss.maftree.org

ISSN: 0975-3060 (Print), 0975-3540 (Online)

doi: 10.4273/ijvss.1.4.05

© 2009. MechAero Foundation for Technical Research & Education Excellence

85

Evaluation of Railway Vehicle Car Body Fatigue Life and Durability using

Multi-disciplinary Analysis Method

Bingrong Miaoa, Weihua Zhang

b, Jihui Zhang

b, and Dingchang Jin

b

State Key Laboratory of Traction Power,

Southwest Jiaotong University, Chengdu 610031 Sichuan, P.R. China aCorresponding Author, Email: brmiao@home.swjtu.edu.cn

bEmail: tpl@home.swjtu.edu.cn

ABSTRACT:

In this paper, a multi-disciplinary analysis method is proposed for evaluating the fatigue life and durability of railway

vehicle car body structure under random dynamic loads. The whole analysis involves the following steps: (1) Multibody

dynamics Simulation (MBS) and Finite Element Analysis (FEA), which derives the load time histories for durability

analysis, are performed to model the full vehicle complex system and simulate the rigid or flexible dynamic property of

the car body. (2) Car body durability analysis involving a definition of the useful life and damage distribution of car

body structure, including the stress or strain rainflow cycle counting, damage prediction, and remaining life estimation.

(3) Multi-Disciplinary Optimization (MDO) method, an iterative procedure incorporated with several kinds of analysis

results, is performed in a batch manner using some standard softwares, such as SIMPACK, ANSYS, FE-FATIGUE and

modeFRONTIER. The methodology is also illustrated for handling conflicting problems of railway car body design for

lightweight and fatigue requirements. Finally, the methodology and its detailed steps are discussed using a locomotive

car body structure. A comparison of analysis results with experimental test results and the necessary car body structure

fatigue design considering full vehicle dynamic property are also detailed.

KEYWORDS:

Multibody dynamic simulation, Finite element analysis, Railway car body structure, Fatigue life prediction, Durability

analysis, Multi-disciplinary optimization

CITATION:

B. Miao, W. Zhang, J. Zhang, and D. Jin. 2009. Evaluation of Railway Vehicle Car Body Fatigue Life and Durability

using Multi-disciplinary Analysis Method, Int. J. Vehicle Structures & Systems, 1(4), 85-92.

NOMENCLATURE:

M Mass matrix.

C Damp matrix.

K Stiffness matrix.

vf External force vector.

u Matrix of modal degrees of freedom of flexible car

body.

iΦ Matrix with static eigen mode.

iq Modal coordinate which defines the flexible

displacement corresponding to ith mode.

xiσ Stress influence coefficients in X direction.

yiσ Stress influence coefficients in Y direction.

xyiτ Stress influence coefficients in XY direction.

( )tFi Applied load histories (including force,

displacement, acceleration, etc.), [ ]ni ,1∈ .

1. Introduction

The rolling stock car body structure is facing severe

problems on wear and reliability with continuously

improving operational speed of trains. Most of the works

are aimed for lightweight structures, improved running

service safety, and reduced product design cycle. At the

same time, the fatigue life prediction and durability

design method for railway vehicle car body structure requires exploitation of the multi-disciplinary

optimization techniques to solve some conflict problems,

such as the structure lightweight and fatigue design

requirements.

With the increase of commercial speeds of railway

vehicles on conventional tracks in China, the car body

structures of these vehicles are subject to serious fatigue

problems. In the past years, the general strength

evaluation method of a car body was usually performed

by a static load test and finite element analysis (FEA).

However, the evaluation of fatigue strength of railway vehicle components could not be performed well due to

the fact that the structural failure is mainly caused by the

dynamic random loads. Moreover, the research on the

car body fatigue design is very limited. Possible reasons

can be that the car body structure is large and complex,

and requires expensive field dynamic stress/strain tests

to underpin the fatigue issues. In order to predict the

possible fatigue failures beforehand and during early

stages of car body structure design, effective simulation

technologies and methodology are indispensable such

that the estimation of fatigue property takes into account

of full vehicle dynamic property.

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

86

There is a strong need for research into the fatigue

life simulation methods for railway car body structure.

The dynamics simulation and finite element analysis had

been used to perform vehicle structure fatigue design in

many engineering fields. Luo [1] proposed a design

method for metro vehicles bogie fatigue life prediction

combined with the dynamic analysis and fatigue life

prediction. Dietz [2] used an integrated Computer Aided

Engineering (CAE) method based on time and frequency domains to predict the fatigue life of a railway bogie

under dynamic loads. Kim [3] proposed a

computationally viable durability prediction method for

prototype vehicle body structures. Haiba [4] has

published a detailed review of fatigue life assessment

techniques applied to dynamically loaded automotive

components. Sigmund [5] discussed a simulation method

to estimate the fatigue life of aluminium automotive

structures.

James [6] developed a fatigue life calculation for the

High Mobility Military Trailers using multibody analysis

and verified his results with experimental tests data. Most of the railway vehicle fatigue studies mainly focus

on key structural components of railway vehicle, such as

bogie frame, axles and other small components. It is

clear that the railway vehicle car body fatigue life and

durability prediction methods are relatively insufficient.

The main reason may be that the car body structure is

large and complex, and its durability and dynamic

stress/strain field tests are too expensive. If only a

constant amplitude load spectra and static load test

results are used to evaluate the fatigue strength of the car

body structure, it can result in some serious problems. This is because of in-service fatigue failures caused by

the stochastic dynamic loads. Much of the research in

modern locomotive vehicle industry is aimed to produce

safe, reliable and lightweight car body structure to tackle

the increased speeds of railway vehicles.

Extending our earlier works [8-10], in this paper, an

integrated fatigue life and durability evaluation method

based on multibody dynamics simulation (MBS) and

finite element analysis for a locomotive car body is

presented. A multi-disciplinary optimization algorithm is

developed to handle the conflicting requirements of lightweight and good fatigue resistant car body structure

designs.

2. Multi-disciplinary durability analysis

method and MDO

2.1. Multi-disciplinary Durability Analysis Process

Excessive structural dynamic stress is the basic reason

for car body structure fatigue damage. In order to solve

the problem of occurred fatigue damage, the following

three aspects need to be understood:

• The dynamic characteristics of full vehicle

structure and stress/strain loading data - stress/

strain time histories.

• Obtaining structure material S-N curve and the welded joint fatigue characteristics data through

the material specimen fatigue test.

• Parameters for the car body structure durability

analysis method.

Railway car body fatigue life prediction is based on

hybrid models consist of flexible car body and some

other rigid bodies. The proposed multi-disciplinary

durability analysis method for evaluating fatigue life of

railway car body structure is shown in Fig. 1. Fatigue

life prediction process includes the following steps:

1. Multibody dynamics modelling of one full

locomotive and obtaining the load time histories

using rigid-flexible dynamics simulations. 2. Establishing a detailed finite element model of

the structure, performing a modal analysis to

determine the structure natural frequency and

mode shape, and a substructure analysis to reduce

the finite element model degrees of freedom.

3. Obtaining the structure material S-N curve or

weld joints S-N curve.

4. Selecting a suitable structure fatigue life

prediction method, and the calculation of stress/

strain time histories using quasi-static stress

analysis method in the time domain followed by a

rainflow count and average stress modifications using MATLAB WAFO procedure.

5. Identifying critical areas using the standard time

domain approach that involves stress or strain

cycle counting, damage prediction and finally

fatigue life estimation.

6. Applying a multi-disciplinary optimization

algorithm that considers the fatigue life as an

objective function for modifying the structure.

2.2. Rigid and Flexible Multibody Dynamics

Simulation

The locomotive car body dynamic model simulation

includes vehicle model, wheel/rail interaction contact

model and track model. Equations of dynamic motion

for considering car body flexible displacements are

generated with the help of finite element method in a

local coordinate system. Fig. 2 shows the Locomotive

MBS model (flexible car body), which was created in

multibody software SIMPACK (version 8.514). The rail

coordinate system (Z direction down, X direction

forward, and Y direction sideway) is adopted to describe the railway vehicle MBS model, such as XYZ directions

relative to the motion of the car body, can also been seen

in the Fig. 2 [7].

Modal synthesis method is used to reduce the large

scale FE model into a lesser degrees of freedom FE

model for increasing the efficiency of simulation. The

main idea of the modal synthesis approach is a

substitution of a full set of modal coordinates with a set

of required modal coordinates. It significantly reduces

the number of coordinates of car body MBS model. The

reduced model can also decreases the computational costs during the simulation of hybrid systems whilst the

stress/strain of flexible car body can be obtained with an

acceptable calculation precision. The railway vehicle

dynamic equation of motions is given by:

VVVV fKxxCxM =++ &&& (1)

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

87

Carbody structure

FEM

Carbody structure

design

CAD

Imposing on

quaisi-static load

Finite element

Analysis

FEA

Multibody

Dynamic

Analysis

Typical

Load

cases

load time histories

(such as force,

accerlerate,etc.)

Stress Influence

Coefficient

superpose

loaction

Calculating

stress/strain histories

Peak-valley

value editing

Dynamic

stress test

Rainflow

cycles count

Principle life

prediction

Detailed life

prediction

WAFO

Critical

location

Carbody

DurabilityAnalysis

START

Full vehicle

dynamics parameter MBS

multi-disciplinary

Optimization

Rigid Carbody

Interface between MBS

and FE

FEMBS

SID

Substructure analysis/

Mode analysis

Flexible

carbody

END

Local

stress/strain

Matrial performance

S-N curve

Applying structure

optimization

algorithm

Good fatigue

performance

NO

YES

Aerodynamical

analysis

Fig. 1: Car body multi-disciplinary durability analysis process

Fig. 2: Locomotive MBS model (flexible car body)

According to the modal analysis approach, the

flexible car body displacements are calculated by a

summation of static displacement and eigen mode

product using:

∑Φ=i

iiqu (2)

The starting point for car body fatigue analysis is the

prediction of dynamic response of the car body structure,

which is usually expressed as a stress or strain time

history. A quasi-static stress analysis method is one of

standard time domain approaches used to obtain the dynamic stress for fatigue life assessment [4]. It is a

linear elastic analysis that is associated with external

load variations. The main idea behinds this method is

that the external load history acting on the structure can

be replaced by a static unit load acting on the same

location in the same direction as the load history. The

quasi-static stress analysis is then performed for each

individual unit loads.

Dynamic stresses calculated for each individual load

history can be evaluated by multiplying the load history

by the static stress influence coefficients that result from

the corresponding unit load. The stress influence coefficient is defined as the stress due to unit load

applied to the car body at an identical location and in the

same direction as these applied load histories. The load

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

88

histories can be measured or evaluated by applying the

multibody system analysis techniques [2, 4]. The

mathematical form of this method at a specific finite

element mode for plane stress conditions is given by:

( )

( )

( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( )

( )

( )

=

tF

tF

tF

ttt

ttt

ttt

t

t

t

nxynxyxy

ynyy

xnxx

xyi

yi

xi

M

2

1

21

21

21

...

...

...

τττ

σσσ

σσσ

τ

σ

σ

(3)

2.3. Car Body Fatigue Load Cases

All sources of cyclic loading which can causes the car

body structure fatigue damage shall be identified.

Realistic load histories that reflect the car body safe

service environment are required prior to the application of the FEM. The actual load histories can be

experimentally measured if a physical prototype is

available. At the early stages of product design, accurate

load histories can be evaluated by applying the

multibody system analysis techniques [1-7].

In this paper, car body’s load histories are obtained

by creating a full vehicle multibody dynamics model and

a three-dimensional finite element (FE) model. The car

body fatigue damage assessment is carried out based on

the nature of analysis, the form of load cases and a way

in which they are combined shall be agreed between designer and operator. The track induced loads resulting

from the vertical, lateral and twist irregularities of the

track may be determined from:

• Full vehicle multibody system dynamics

modelling (from the data relating to the track

geometry and roughness);

• Measured data over the intended or similar route

or represented by empirical data (accelerations,

displacement etc.).

• Significant aerodynamic load may arise in train

passing at high speeds, tunnel operations, and exposure to high cross winds. Hence, the

aerodynamic effects of the car body should be

considered when the train speed is higher than

200 km/h.

• Typical car body structure load cases and load

histories including running on straight track,

passing curves and etc. are considered. The load

cycles due to traction and braking should also be

determined from the performance data supplied

by the operator.

Fatigue life is computed according to the uni-axial fatigue assessment method. The car body structure

failure consists of a crack initiation phase and a crack

propagation phase. The crack propagation requires the

calculation of stress intensity factors and re-meshing of

the cracked region; this becomes computationally

intensive and takes longer solver time. Hence, the car

body fatigue life is defined as the time to initiate a crack.

The standard time domain approach involves the counting of stress/strain cycle, damage prediction and

finally the car body fatigue life estimation. Firstly, the

stress/strain at the critical region of car body structure

are estimated, and the rainflow cycle counting method is

then used to reduce the load time histories based on the

peak-valley values [4-7]. The next step is to use the FEM

to convert the reduced load time histories into a

stress/strain time history and also calculate stress/strain

in the highly stressed areas. Finally, the crack initiation

methods are used to evaluate the flexible car body

fatigue life by Palmgren Miner damage rules.

2.4. Strategies for Multi-Disciplinary Optimization

Car body structure optimization process based on fatigue

life of dynamically loaded structures is shown in Fig. 3.

This optimization has been performed to obtain the

lightweight structure meeting the required structure

fatigue performance. These conflicting objective

functions and constraints limit the solution and

optimization strategies. In addition to some discrete

searches, robust optimization algorithms are required to

solve the multi-objective optimization problem with

optimality criteria methods [11, 12].

Creating

FE-model

FEA

(Finite element analysis)ANSYS

Est imiat ing Structure damage

fat igue life

FE-FATIGUE

Requirement

is satified?

Predicting load histories

Multibody dynamics

Simulation

SIMPACK

Calculating stress/strain histories

New designOptimizedCarbody

modeFRONTIER

Applying an multi-object optimization algorithm that

considers life as base for modifying the carbody

structure.

YESNO

Fig. 3: Car body multi-disciplinary optimization process

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

89

Fully stressed design technique is adopted in car

body structure optimization based on the predicted

fatigue life. The car body design is iteratively modified

to lightweight structure, until the properties of the

structure meet the optimization design object. The car

body structure multi-disciplinary optimization was

fulfilled using modeFRONTIER (version 3.2) software

using a parametric FE model, the objective functions and

constraints as given in Table 1.

Table 1: MDO objective functions and constraints [11]

Minimization Maximization

Lightweight (weight, mode) First Eigen frequency Stress Stiffness Strain Fatigue life

3. Numerical Simulations

A typical main line locomotive car body (see Fig. 3)

running on Kunming-Weishe track in China is used to

illustrate the proposed multi-disciplinary durability analysis and MDO method. This locomotive car body

has two crack initiations near the traction seat location of

car body. In order to predict the car body fatigue life and

damage distribution correctly, the car body is assumed to

be rigid in one case and flexible in another.

Fig. 3: Photo of locomotive used in dynamic stress test

The load histories of car body are obtained by

creating an accurate full locomotive MBS model using

multibody system code SIMPACK, and running this

model over a virtual track. When dynamic behaviour of

locomotive system is analyzed with MBS, it is very

important how to transform the track spatial spectra to a

time domain track excited signal with correct excited

spectra characteristics such as frequency, phase and

amplitude. The track excitation spectrum is calculated

using a frequency-time transformation technique [7].

The problem of track spectral distribution characteristics

is solved successfully and corresponds to the real track

line which is a benefit of the multibody system dynamic

simulation.

The typical load cases in the locomotive operating conditions, including straight track running, curve

passing and traction/braking etc, have been established

to perform the multibody system dynamic simulation.

For the typical load case in full vehicle multibody

dynamics simulation, 35 load histories which include

forces, velocities, acceleration and angular velocities etc,

have been calculated. In addition to the flexibility of the

primary and secondary suspensions in full vehicle

dynamics model, the car body structure flexibility and its

coupling with the bogie dynamics can have a significant

effect on the full vehicle structure fatigue performance.

When the car body structure flexibility is modelled in the flexible multibody algorithms using

experimentally identified modal characteristics, standard

modal analysis techniques can be used to determine the

car body modal parameters such as the natural

frequencies, mode shapes, and modal damping

coefficients. To generate standard input data (SIC) of

flexible bodies MBS simulation, the interface program

FEMBS as shown in Fig. 4 is used between the FEA

codes - ANSYS and SIMPACK.

A detailed car body structure is idealised using the

FEA software ANSYS (Version 9.0) and the FE model is shown in Fig. 5. Finer meshes are used to prevent any

possible stress concentration effects. The FE model has

376073 nodes and 101273 elements, such as shell63,

mass21, and combin14 elements. The stress/strain

histories at the critical areas of the car body structure can

be calculated using Eqn. (3). The modal characteristics

of the structure can also be obtained using modal

analysis techniques. Modal analysis of the car body

structure is helpful to predict the natural frequencies,

mode shapes, and to identify the critical locations of the

car body structure. To consider the influence of car body flexibility in FEMBS, the FE model size is reduced by

exploiting sub-structuring analysis techniques.

Carbody Finite

Element model

Substructure

AnalysisResults Files

FEMBSSIMPACK

SID files

Marker connected to bogie

Eigenvalues mode

Frquency reponse modes

Structure dampe definition

ANSYS FEM Preprocessor

MBS Preprocessor

SIMPACK/FEMBS

Super element;

Substructure files;

Eigenvalues calculation

Master Nodes

Definition

Fig. 4: Obtaining standard input data (SIC) with FEMBS

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

90

Fig. 5: Car body finite element model (shown inverted for clarity)

The fatigue life of the car body structure is

calculated using Wave Analysis for Fatigue and

Oceanography (WAFO, Version 2.0.02) [13] toolbox in

MATLAB (Version 7.0). With rainflow matrix and

Markov chain theory, the material S-N curve, structure dynamic stress, and Palmgren-Miner damage summary

theory, the car body structure fatigue life can be

evaluated using WAFO toolbox. Safety factor analysis

based on the stress can also be performed using fatigue

analysis software - nSoft’s FE-Fatigue (Version 6.0) to

obtain the damage distribution with stress safety factors

for the car body structure.

4. Results and Discussions

Table 2 shows the car body structure’s modal analysis

results. The first vertical bending mode shape with

relative displacement of the locomotive car body is

shown in Fig. 6.

Table 2: Modal analysis results of car body structure

No. Frequency (Hz)

Mode Shape Relative disp-lacement (m)

1 6.120 1st torsion 0.01751 2 10.699 1st Vertical bending 0.02607

3 11.340 1st Lateral bending 0.03490 4 16.211 Breathing 0.17478 5 16.421 Breathing 0.17445 6 17.054 2nd Lateral bending 0.04523

Fig. 6: First vertical mode shape (10.699 Hz) and relative

displacement of locomotive car body

In order to determine the accuracy of the proposed

simulation method, the dynamic stress results from the

FEMBS simulation are also compared with the results

from the dynamic stress test of the locomotive car body

on the Kunming-Weishe track in China. The dynamic

stress field distribution of car body from the tests is

shown in Fig. 7. The statistics results of the

experimental and simulated stress for the rigid and

flexible body models can be found in Table 3. The results obtained from the proposed hybrid simulation

method to evaluate the car body structure life and

damage distribution are in good agreement with the

experimental test data.

Fig. 7: Photo of field dynamic stress test point distribution

Table 3: Stress results comparison at traction seat location

Stress (MPa)

Test point

Rigid Node

Flexible Node

Mean -0.383 -0.121 -0.114

Max. 35.205 35.114 40.3

Min. -29.421 -27.959 -29.384

Range 64.626 63.073 69.684

The WAFO toolbox [13] is used to extract the

rainflow cycles from the measured load sequences, and

to predict the rigid and flexible node’s load histories.

The experimental point’s rainflow count load

distribution is shown in Fig. 8. The rainflow count load

distribution for the corresponding node at the test point’s

is shown in Fig. 9 and 10 for the case of rigid and

flexible car body respectively.

Fig. 8: Test point experimental rainflow count load distribution

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

91

Fig. 9: FEMBS node rainflow count load distribution (rigid car

body case)

Fig. 10: FEMBS node rainflow count load distribution (flexible car

body case)

The danger nodes’ stress Power Spectral Density

(PSD) is shown in Fig. 11. The stress PSD of node

90594 is shown in Fig. 12.

0 5 10 15 20 25 30 35 40 45 500

2000

4000

6000

8000

10000

1.95313

2.197277.22656

9.47266

10.2051

10.8398

Von

Mis

es P

SD

(M

Pa

2/H

z)

Frequency(Hz)

Node91851

Node91860

Node93562

Node93552

Node92522

Node92535

Node93074

Node93088

Node93652

Node93642

Fig. 11: Stress power spectral density for danger nodes

100

101

102

10-2

10-1

100

101

102

103

Frequency (Hz)

Str

ess

PS

D (

MP

a2/H

z)

Node 90594 stress PSD

Fig. 12: Stress power spectral density for node 90594

The car body fatigue damage and safety factors

based on the stress from the simulation results are shown

in Figs. 13 (rigid car body) and 14 (flexible car body).

Table 4 compares the predicted fatigue life from tests

and the ones obtained from FEMBS simulation results at

the critical regions of the car body structure. The fatigue

life predictions from FEMBS simulation are closely

matches with experimental results with an exception of

node 95707 (location 5-1 as in Fig. 7). The mean fatigue life prediction error is approximately 30.7%.

Fig. 13: Car body safety factor and damage distribution (rigid car

body case)

Fig. 14: Car body safety factor and damage distribution (flexible

car body case)

Table 4: Car body fatigue life evaluation results comparison

No. Elm. ID

Node ID

Test life (hrs.)

Predicted life (hrs.)

Err. %

3-5 95152 90594 2.2887E6 3.1876E6 39.28 5-1 95707 91033 2.6374E6 4.4958E6 70.46 5-8 95660 91016 2.6265E5 3.0538E5 16.27

5-5 95735 91079 8.6351E5 7.3477E5 14.91 5-2 83609 81316 2.0567E6 2.3662E6 15.05 4-2 83543 81195 7.3546E6 5.2581E6 28.51

5. Conclusions

A multi-disciplinary analysis method for railway car

body structure fatigue life and durability evaluation has

been proposed in detail. The proposed approach is

illustrated using a locomotive car body test results and

simulations results. A multi-disciplinary optimization is

adopted to handle the conflicting objective functions for

B. Miao et al. 2009. Int. J. Vehicle Structures & Systems, 1(4), 85-92

92

lightweight and better fatigue performance requirements.

The following conclusions can be drawn:

• The major of the fatigue damage to the car body

mainly takes place at or below 15Hz and the

dynamic behaviour of the locomotive plays a

significant role in occurrence of car body

structure fatigue failure.

• The full vehicle dynamic property at critical

regions of the locomotive car body is relatively weak as the car body structure fatigue crack

initiation damage has occurred two times.

• Alternative to expensive field dynamic tests, the

proposed FEMBS hybrid method proved

successful in evaluating the fatigue life

characteristics of the large complex locomotive

car body structure. The FEMBS simulation

results – stress and fatigue life (in hrs) predictions

are in good agreement with the results obtained

from field dynamic stress tests.

• The conflict requirements between car body fatigue property and structure lightweight can be

solved well with the proposed multi-disciplinary

optimization algorithm. This multi-disciplinary

analysis method, when used in early stages of

railway car body fatigue design, may reduce the

cost of product development and potential time

savings.

ACKNOWLEDGEMENTS:

This research work was supported by the National Basic

Research Program of China (2007CB714705) and the China Postdoctoral Science Foundation (20080431266).

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