Correlation analysis of FEA and EMA modal models of an [629061]

Correlation analysis of FEA and EMA modal models of an
electric locomotive bogie
I Manea1, I Gîrniță1, I Sebeșan2, M Matache3, S Arsene2 and R Zglimbea1
1SC Softronic SRL, Craiova, Str. Calea Severinului, No.40, Romania
2University Politehnica of Buchares t, Department of Railway Rolling Stock, Splaiul
Independenței Street No. 313, Romania,
3INMA Bucharest, Sector 1, Str. Ion Ionescu de la Brad, No. 6, Romania

E-mail: [anonimizat]

Abstract. Experimental modal analysis (EMA) can be successfully used for validation of a
structure analytical model made by finite element analysis (FEA), both models being
characterized by the same modal parameters: modal frequencies and modal shapes. Usually,
validation of analytical model through experimental model is done through correlation analysis
of the two modal models. A good analytical model, validated through experimental data, can
be successfully used to assess the stresses response and lifetime of the mechanical structure at
hypothetical or realistic opera ting loads. In article is presented an application for validation of
FEA modal model through correlation analysis with EMA modal model of a three -axle
locomotive bogie frames. Validation of analytical model was performed for the preliminary
analytical asse ssment of the structural response of the bogie frame, before being send to
laboratory tests at static and fatigue loads. Article presents the theoretical background of EMA
and FEA analysis and the modal parameters and modal shapes of the bogie frame determ ined
through EMA and FEA analysis.
1. Introduction
Bogies are complex equipment that plays an essential role in the operation of railway vehicles. They
have the main role of supporting the bodywork of the railway vehicles, but also of enabling the
transmissio n of the traction and braking forces from the equipment mounted inside or over the carriage.
Given the importance of the bogie in the locomotive security and long lifetime of more than 18 years,
plus the fact that the new regulations require the structural force of a bogie frame to be certified to the
various static and dynamic loads that may appear during the operation time of this equipment.
Structural requirements of bogie frames are regulated by standard EN 13749/20011, according to
which the certificat ion program shall include: analysis, static tests, fatigue tests and track tests.
In the construction and realization of a new bogie frame, all research stages are used, and in terms of
fatigue analysis, other tests can be used to determine the lifetime of the equipment. This reason is based
on the fact that fatigue tests are done in complex laboratories and tests are very expensive and time
consuming. Sending to laboratory a bogie frame with bad design or execution, represents an important
financial loss a nd a great loss of time. To the tests must be sent only products rigorous verified.
Currently, before sending to the tests, is performed a rigorous finite element analysis (FEA) of the
bogie frame with commercial finite elements programs, as Ansys. To be t rust, the FEA model must be
validated through experimental data collected from the structure in the natural scale.

The experimental modal analysis (EMA) provides a very good tool for validation of the FEA modal
model through EMA modal model, both of which being characterized by the same modal parameters:
modal frequencies and modal shapes. Experimental modal analysis provides additional information about
the system modal damping. Currently, validation of FEA modal model through EMA modal model is done
by co rrelation analysis of the two modal models. The assessment of the lifetime of the bogie frame is made
using both the analytical model and the experimental model. In both situations, the bogie is analysed for the
static requests and fatigue, using realistic operating loads or synthesis loads simulated in laboratory.
The article presents an application realized on a three -axle bogie frame designed to equip the
LEMA 6000 kW electric locomotive manufactured at Softronic Craiova – Romania.
Using Ansys, it was pe rformed the finite element analysis of the bogie frame, determining the modal
parameters. On the same bogie frame, it was carried out an EMA test determining the same parameters.
Using a correlation analysis software, it was validated the FEA model of bog ie frame.
2. Theoretical basis of the EMA and FEA analysis
By the definition of experimental modal analysis (EMA), this allows the construction of a
mathematical model based on a series of experimental data resulting from measurements performed on
a structure brought into a controlled vibrational state. The controlled vibrational system is excited
under well -defined conditions so that the laws of evolution of vibration response and excitation can be
determined. These laws then identify the modal model, which i s determined by modal parameters:
modal frequencies, modal damping and modal modalities.
The mathematical model used specifically for EMA, which presents the dynamics of a system with
N degrees of freedom (DOF), is described by a system of differential equ ations that can be written
both in the time domain, relation (1), but also in the frequency domain, the relation (2).

()()()()tF txKtxCtxM =++   (1)

()()()()    Q XK XC i XM =++−2 (2)
where:
M ,
C and
K – the mass, damping and rigidity matrix;
()tx ,
()tx and
()tx – the acceleration,
velocity and displacement column vectors;
()X – the Fourier Transform of displacement column vector ;
()tF
– the excitation forces column vector;
()Q – the generalized forces column vector;
 – the angular frequency.
Mass, rigidity and damping are the unknown elements to be estimated in the fir st phase using
experimental data, based on the measurements in the two work domains (time and frequency). Once the
matrices elements are determined, the modal parameters will be found as a solution of an eigenvectors
and eigenvalues problem. Based on equat ions (1) and (2), the mathematical models most often used to
describe the dynamics of a system can be arranged in the form of a frequency response function,
()pqH
or a response function in the case of unit pulses
()thpq as can be seen in relations (3) and (4).

()t
pqrN
rt
pqr pqr r e A e A th**
1 +  == (3)

()**
1
rpqr N
r
rpqr
pqiA
iA
H

−+ −== (4)
where: p – measured DOF of response; q – measured DOF of input; r – modal number vector; N –
number of modal frequencies;
pqrA – residue for th e r mode;
r – system pole for the r mode.
Unit impulse response functions,
()thpq are never directly measured, but they can be calculated
from associated frequency response functions,
()pqH via inverse Fast Fourier Transform (FFT).
In terms of finite element analysis (FEA), where the structure can be divided into several finite
elements, among which there are mathematical equivalence connections with the situations of physical

connections that occur bet ween the adjacent elements and the environment. In the case of a physical
model corresponding to a mathematical FEA model, it can be written by a similar pattern determined
by the mathematical model given by the EMA. The difference between the two ways of writing
mathematical models is that the FEA model does not consider system damping, the relationship (5).

()()()tF txK txM =+ (5)
The analytical determination of modal shapes and modal frequencies is achieved by solving the
differential equations syste m. These sizes must be similar to those determined by experimental modal analysis
because we refer to the same system. For finite element analysis, it uses an approximate mathematical model,
since geometric and of material characteristics approximations ma y be larger or smaller. If the mathematical
model determined by the relation (5) would be perfect, it will provide another approximate modal model,
because it is well known that in modelling the material characteristics do not usually coincide with the act ual
material characteristics. It should also be borne in mind that any geometric modelling may introduce more or
less rough execution errors of the model, errors that cannot be translated into the geometric model.
From the above it can be said that a good and reliable FEA analysis model can be obtained only by
validation with the data provided by the real system by experimental EMA tests.
3. Correlation analysis of a three -axle locomotive bogie frame
3.1. Technical characteristics of the three -axle LE -MA 6000 kW bogie
– Wheel diameter: 1.25 m (new state)/1.21 m (semi -used state); – Axle load: 210.13 kN±2%; –
Distance between axles 1 and 2: 2.25 m / Distance between axles 2 and 3: 2.10 m; – Bogie maximum
length: 8384 mm; – Maximum speed: 160 km/h; – Bogie total weight with traction motors: 28668 kg; –
Bogie total weight without traction motors: 19533 kg;
Material used in the bogie frame is steel type S355 NL, with the main characteristics: – Yield strength, Re:
345 Mpa; Ultimate strength, Rm: min 470Mpa; – Young modulus, E: 210 Gpa; Poisson coefficient, m: 0.29.
3.2. Finite Element Analysis
It was performed the finite element analysis of the bogie frame. For geometrical modelling it was used
SolidWorks, and for modal and structural analysis were used Modal and Str uctural modules of Ansys.
Analysis was made in linear elastic regime, the bogie being modelled as follows: – the frame model
consists of volumes described by Solid 92 tetrahedral elements; – the primary suspension is modeled
using spring elastic elemets ty pe Combin 14; – axles are modeled using rigid bar elements type Beam;
The bogie frame structure was modelled using 806471 tetrahedral elements and 1490919 nodes.
To validate the FEA model from a dynamic behaviour point of view, it was run the Modal module of
Ansys. It was determined the vibration eigenmodes in the frequency range of 10 to 100 Hz. The FEA
modal shapes are presented in correlation analysis section in connection with the EMA modal shapes.
3.3 Experimental modal analysis
Based on relations 1 to 4, the commercial experimental modal analysis programs have implemented
several algorithms to identify modal parameters based on measured data in frequency or time domain.
The actually available methods help us to calculate modal parameters from data that , in the most
cases, are presented as frequency response functions (FRF), but can also be presented as sequences in
time domain. The most common methods in worldwide for identification of modal parameters are
Rational Fraction Polynomial -Z and Polyreferenc e Time, both being advanced multi degree of freedom
methods where the iterations are based upon increasing order of the underlying polynomial equation.
For the EMA model, a three -axle bogie frame was used to equip LE -MA 6000 kW electric locomotives,
produ ced by Softronic Craiova – Romania, where the tests were carried out. For these tests (EMA tests),
four helical springs were used, each having an elastic constant of k = 519 N / mm. On these springs is
placed the bogie frame so that it can be considered as a free system, without any DOF restrictions.

To excite of the bogie, frame the impact method was used by means of a 25 kN hammer, which
was hit in a single point. In the frequency range 10 to 100 Hz, in which the modal analysis was
performed, a mediation of more than five pulses was made to eliminate noise in measurements but at
the same time, and to obtain high precision and FRF.
Given that in normal operation conditions the bogie frame is predominantly subjected to the loads
from the track, that occur in the vertical and transverse directions, during the EMA tests the dynamic
response in acceleration was measured only on these directions. The acceleration response was
measured in a number of 45 points, for each measuring point the response being measured on vertical
and transverse directions, resulting a number of 90 DOF measured. The choice of measuring points is
made in such a way that a suggestive animation of the bogie frame is allowed in vibration modes.
For EMA tests was used the following excitation and measuring equipment and software:
– Piezoelectric accelerometers type 355B03, 15pcs., 10.19 mV/(m/s²), ± 490 m/s²; – Impact
Hammer type 086D201, pcs., 0.23 mV/N, ±22.240 kN pk; – LAN -XI type 3053B120, 1 pcs., 12 input
channels, 25.6 kHz; – LAN -XI typ e 3160A042, 1 pcs., 4 input channels, 2 output channels, 51.2 kHz; –
Structural Dynamics Test Consultants, a dedicated software, working under PulseLabshop, to provide
measurement environment for structural dynamic measurements; – Pulse Reflex Modal Analys is, a
post-processing module for classical modal analysis, using shaker or hammer excitation. Works with
FRF measured data and express the eigenmodes by modal parameters: damped frequency, damping,
and residues; – Pulse Reflex Correlation Analysis, provide s a good tool to verify and validate the FEA
modal model by true EMA modal model. The correlation analysis is accomplished by graphical
comparisons, shape animations and numerical Modal Assurance Criterion (MAC).
Rational Fraction Polynomial -Z method was u sed to determine the modal parameters using a number
of 40 successive approximations. The EMA analysis was performed in frequency range of 10 to 100Hz.
3.4 Correlation analysis of the FEA and EMA modal models
Pulse Reflex Correlation module loads and expos es in the front panel the analytical geometric model together
with associated FEA modal shapes as well as the experimental geometric model together with associated
EMA modal shapes. Calculates the degree of correlation of pairs of modal shapes in MAC matri x. MAC
criterion can take values in the range of 0, for total uncorrelated modes and 1, for total correlated modes.
Figure 1 shows the front panel of Pulse Reflex Correlation module for three -axle locomotive bogie
frame of LE -MA 6000kW electric locomotive. Table 1 presents the results of correlation analysis of
analytical and experimental models, in the frequency range of 10 to 100Hz, the predominant frequency
domain of excitations that came from track. In this frequency range the bogie frame has 7 principa l
eigenfrequencies, corresponding to eigenmodes in vertical and transverse directions. For the two
modal models are presented the amortized frequencies and the evaluation error in terms of analytical
frequency determination. It is presented the MAC criteri on of modal shapes for the two models. The
first five own modes of vibration of the bogie frame are shown in figures 2 to 6.

Table 1. Results of FEA and EMA correlation analysis for three -axle LE -MA locomotive bogie frame.
Mod.
No. FEA Model FEA model Frequency error
(%) Modal Assurance
Criterion MAC Damped
frequency (Hz) Damped frequency
(Hz) Damping
(%) Complexity
1 30.73 30.19 0.28 0.0128 -1.7925 0.975
2 37.43 37.95 0.32 0.2374 0.0138 0.910
3 48.10 49.08 0.17 0.0015 0.01992 0.968
4 60.64 61.86 0.14 0.0014 0.01982 0.788
5 66.66 65.66 0.13 0.0031 -0.0152 0.970
6 81.68 85.30 0.10 0.0048 0.04246 0.900
7 88.18 89.92 0.10 0.0013 0.01935 0.902

Figure 1. Pulse Reflex Correlation front panel for three -axle LE -MA locomotive bogie frame .

Figur e 2. The 1st eigenmodes, vertical direction, left FEA 30.73 Hz, right EMA 30.19 Hz.

Figure 3. The 2nd eigenmodes, vertical direction, left FEA 37.43 Hz, right EMA 37.95 Hz.

Figure 4. The 3rd eigenmodes, transverse direction, left FEA 48.10 Hz, ri ght EMA 49.08 Hz.

Figure 5. The 5th eigenmodes, vertical direction, left FEA 66.66 Hz, right EMA 65.66 Hz.

Figure 6. The 7th eigenmodes, transverse direction, left FEA 88.18 Hz, right EMA 89.92 Hz.
From figures 2 to 6, it can be seen that most e igenmodes are in the vertical direction except modes
3 and 7 which are in the transverse direction.
4. Conclusions
In this paper, it is presented how an analysis is made on a bogie frame. In this respect, research
methods are used, both an FEA modelling model and a real modal model for a modal analysis for
experimental validation by EMA.
Analysing the data presented in table 1 and figures 2 to 6, it can be concluded that: – The damped
frequency error estimated by FEA is less than 2% compared to EMA; – The MAC correlation criterion is
greater than 0.7; – Modal shapes calculated by FEA are very similar to modal shapes calculated by EMA.
Taking into account the validation criteria by eigenfrequencies and MAC criterion for modal
shapes, it can be concluded that the analytical finite element model is a correct model and can be used
with confidence to analyse the structural response of bogie frame to dynamic fatigue stresses and for
assessing of the bogie frame lifetime under realistic operating conditions.
5. References
[1] Ewins D J 1984 Modal Testing: Theory and Practice , John Wiley and Sons, Inc., New York ;
[2] EN 13749 2011 Railway applications – Wheelsets and bogies – Method of specifying the
structural requirements of bogie frames;
[3] Manea I, Sebesan I, Matache M, Prenta G and Firicel C 2018 Analytical evaluation of the
lifetime of a three -axle bogie frame using the analytical model validated through
experimental modal analysis , MATEC Web of Conf. vol. 211 0600 4;
[4] Manea I, Sebesan I, Ene M, Matache MG and Arsene S. 2017 System for measurement of
interaction forces between wheel and rail for railway vehicles MATEC Web of Conf. vol.
137, 01006;
[5] Manea I, Sebesan I, Ghita G, Matache MG, Arsene S and Prenta G 2017 Experimental modal
analysis of an electric locomotive body, MAT EC Web of Conf . vol. 112, 07008 ;
[6] Arsene S, Sebesan I, Popa G, and Gheti MA 2018 Considerations on studying the loads on the
motor bogie frame MATEC Web of Conf. vol. 400, 042003 ;