Railway
dynamics
There are many different
engineering problems associated with railway dynamics that affect vibration and
noise radiation, safety, maintenance costs, etc.,...
and all of them are worthy of studying. Below there are some articles that could
help you to understand a few of these problems.
The animation shows a
vibrating railway wheelset that is running on a corrugated track. This result
is obtained from simulation of a track-vehicle model where the wheelset
rotation effect is taken into account (gyroscopic and moving load effect).
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Journal
papers
Train-track
dynamics
José
Martínez-Casas, Juan Giner-Navarro, Luis Baeza, Francisco D. Denia
Improved railway wheelset–track interaction model in the high-frequency domain
Journal of Computational and Applied Mathematics, Volume 309, 1 January 2017,
Pages 642–653.
http://dx.doi.org/10.1016/j.cam.2016.04.034
Abstract: As it is well known, there are various phenomena
related to railway train–track interaction, some of them caused by the high
frequency dynamics of the system, such as rolling noise when the vehicle runs
over the track, as well as squeal noise and short-pitch rail corrugation for
curved tracks. Due to these phenomena and some others unsolved so far, a large
effort has been made over the last 40 years in order to define suitable models
to study the train–track interaction. The introduction of flexibility in
wheelset and rail models was required to have a more realistic representation
of the wheel–rail interaction effects at high frequencies. In recently
published train–track interaction models, the rails are modelled by means of Timoshenko
beam elements, valid up to 1.5 kHz for lateral rail vibration and up to 2 kHz
for vertical vibration. This confines the frequency range of validity for the
complete train–track model to 1.5 kHz. With the purpose of extending the range
of validity above 1.5 kHz, a 3D track model based on the Moving Element Method
(MEM) is developed in this paper to replace the Timoshenko beam considered in
earlier studies, adopting cyclic boundary conditions and Eulerian coordinates.
The MEM approach considers a mobile Finite Element (FE) mesh which moves with
the vehicle, so the mass of the rail ‘flows’ with the vehicle speed but in the
opposite direction through the mesh. Therefore, the MEM permits to fix the
contact area in the middle of a finitely long track and to refine the mesh only
around the contact area, where the forces and displacements will be more
significant. Additionally, a modal approach is adopted in order to reduce the
number of degrees of freedom of the rail model. Both strategies lower
substantially the computational cost. Simulation results are presented and
discussed for different excitation sources including random rail roughness and
singularities such as wheel flats. All the simulation cases are carried out for
a Timoshenko beam and a 3D MEM track model in order to point out the
differences in the contact forces above the range of validity of the Timoshenko
beam.
L. Baeza,
H. Ouyang
A railway track dynamics model based on modal substructuring
and a cyclic boundary condition
Journal of Sound and Vibration 330 (2011) 75–86.
http://dx.doi.org/10.1016/j.jsv.2010.07.023
This paper is in the Top 25 Hottest
Articles of JSV http://cort.as/1bbz
Abstract: This article presents a technique for modelling the
coupled dynamics of a railway vehicle and the track. The method is especially
useful for simulating the dynamics of high speed trains running on non-linear
tracks. The main hypothesis is a cyclic system: an infinite track on which
there is an infinite set of identical vehicles spaced at a regular interval of
distance. Thus the main problems of the finite length track models (e.g. the
waves that reflect at the end of the track and interact with the vehicle; and
the time interval of integration must be shorter than the track length divided
by the velocity) are avoided. The flexibility of the method can be observed
from the case studies presented in the present work: a vehicle passing over a
hanging sleeper, and the vehicle-track dynamics for different ballast
compaction cases. The results show the influence of the hanging sleeper gap on
the wheel-rail contact forces, and the bending moment at the sleeper for
different ballast compaction cases.
L. Baeza,
A. Roda, J.C.O. Nielsen
Railway vehicle/track interaction analysis using a modal substructuring
approach
Journal of Sound and Vibration 293 (2006) 112-124.
http://dx.doi.org/10.1016/j.jsv.2005.09.006
This paper is in the Top 25 Hottest
Articles of JSV http://cort.as/6Ymu
Abstract: A method for simulation of the dynamic interaction
between vehicle and railway track is proposed. The model has been designed to
take into account the complexity of wheel-rail contact, railpad
and ballast, with low computational requirements. A modal description of the
rails and the sleepers is presented, imposing the coupling between these
elements and the vehicle by means of the associated interaction forces. This
provides a model with a reduced number of coordinates and therefore a low
computational cost is achieved. It is shown that this model also enables to
incorporate the associated non-linear characteristics between the different
elements by means of a simple formulation.
L. Baeza, A. Roda, J. Carballeira, E. Giner
Railway Train-Track Dynamics for Wheelflats with
Improved Contact Models
Nonlinear Dynamics 45 (2006) 385 – 397.
http://dx.doi.org/10.1007/s11071-005-9014-8
Abstract: A variety of
methods have been proposed to calculate the dynamic response caused by a
railway vehicle affected by a wheelflat. Most of the
sophisticated procedures evaluate the elastic properties of the wheel–rail
contact by means of the Hertz model. However, the hypotheses that must be
satisfied in order to apply the Hertzian contact
model are not fulfilled when the wheel-rail contact occurs in the area of wheel
affected by the flat. This gives rise to deviations in the results of the
dynamic model compared to the real situation. With the objective of analysing
the influence of the elastic wheel-rail contact model, a procedure was
developed to determine the dynamic response caused by a geometric irregularity
(in rail or wheel) by means of Hertzian and non-Hertzian contact models. Results of the wheelflat
impact simulations given by both types of contact model have been compared in
this work.
Corrugation
in rails
Paloma Vila, Luis Baeza, José Martínez-Casas, Javier Carballeira
Rail corrugation growth accounting for the flexibility and rotation of the
wheelset and the non-Hertzian and non-steady state
effects at contact patch.
Vehicle System Dynamics 52 (Supplement 1) (2014) 92-108.
http://dx.doi.org/10.1080/00423114.2014.881513
Abstract: In this work, it
is developed a simulation tool to analyse the growth of rail corrugation consisting
of several models connected in a feedback loop in order to account both for the
short-term dynamic vehicle-track interaction, and for the long-term damage. The
time-domain vehicle-track interaction model comprises a flexible rotating
wheelset model, a cyclic track model based on a substructuring
technique and a non-Hertzian and non-steady state
three-dimensional wheel-rail contact model, based on the variational
theory by Kalker. Wear calculation is performed with
the Archard’s wear model by using the contact
parameters obtained with the non-Hertzian and
non-steady three-dimensional contact model. The aim of this paper is to analyse
the influence of the excitation of two coinciding resonances of the flexible
rotating wheelset on the rail corrugation growth in the frequency range from 20
Hz to 1500 Hz, when contact conditions similar to those arising while a
wheelset is negotiating a gentle curve are simulated. Numerical results show
that rail corrugation grows only on the low rail for two cases in which two
different modes of the rotating wheelset coincide in frequency. In the first
case, identified by using the Campbell diagram, the excitation of both the
backward wheel mode and the forward third bending mode of the wheelset model
(B-F modes) promotes the growth of rail corrugation with a wavelength of 110 mm
for a vehicle velocity of 142 km/h. In the second case, the excitation of both
the backward wheel mode and the backward third bending mode (B-B modes) gives
rise to rail corrugation growth at a wavelength of 156 mm when the vehicle
velocity is 198 km/h.
L. Baeza, P. Vila, G. Xie, S.D. Iwnicki
Prediction of rail corrugation using a rotating flexible wheelset coupled with
a flexible track model and a non-Hertzian/non-steady
contact model
Journal of Sound and Vibration, 330 (2011) 4493-4507.
http://dx.doi.org/10.1016/j.jsv.2011.03.032
Abstract:
This
paper presents a model for simulating vehicle-track interaction at high frequencies
for investigations of rail roughness growth. The dynamic interaction model
developed employs a substructuring technique and the
whole system consists of a number of substructures that can be modelled
independently. The systems are coupled through the forces at the wheel-rail
contact and the railpad. A coupled, rotating flexible
wheelset, a flexible track model and a non-Hertzian/non-steady
contact model have been implemented and results are presented here for a free
wheelset on a symmetrical track system with initial random and sinusoidal
roughness. Both rigid and flexible wheelsets are considered.
.
Paloma Vila, Juan Fayos and Luis Baeza
Simulation of the evolution of rail corrugation using a rotating flexible
wheelset model
Vehicle System Dynamics 49 (2011) 1749–1769.
http://dx.doi.org/10.1080/00423114.2011.552619
Abstract: This paper presents a simulation tool designed for
predicting the wear pattern on the running surface of the rails, and for
studying the evolution of rail corrugation after thousands of wheelset
passages. This simulation tool implements a cyclic track model, a rotating
flexible wheelset model, a wheel-rail contact model and a wear model. The
vehicle-track system is modelled by using a substructuring
technique, by which the vehicle, the rails, the sleepers are treated
independently of each other and are coupled by the forces transmitted through
the wheel-rail contact and the railpad. The vehicle
model takes only account of the wheelset since the sprung masses of the vehicle
are not relevant in the frequency range analysed. The wheelset model considers
the flexibility of the wheelset and the effects associated with rotation. By
using the Campbell diagram, two cases have been identified in which the
combined effect of two different modes may give rise to higher wheel-rail
contact forces and wear.
Paloma Vila, Andrés Rovira, Juan Fayos and
Luis Baeza
Dynamic model of a railway wheelset for corrugation problem analysis
Noise & Vibration Worldwide, Volume 40, Number 11, December 2009 , pp.
10-17(8)
http://dx.doi.org/10.1260/095745609790251579
Abstract: In the present work a model of flexible shafts is
adapted for modelling the railway wheelset. The dynamic properties of the solid
are obtained from a solid finite element model of a real wheelset. The model
adopts an Eulerian coordinate set for numerical
efficiency. Results of the crossed-receptance and
mobility functions are presented, where the excitation is the vertical
wheel-rail contact force and the displacement (or velocity) is measured in the
wheel-rail contact plane. These results let us know that the gyroscopic effect
may contribute to define the wavelength-fixing mechanism in some corrugation
problems, even if the train speed is low.
Luis Baeza, Paloma Vila, Alejandro Roda and
Juan Fayos
Prediction of corrugation in rails using a non-stationary wheel-rail contact
model
Wear 265 (2008) 1156–1162.
http://dx.doi.org/10.1016/j.wear.2008.01.024
Abstract:
Most
of the models used for simulating the conditions existing in the wheel-rail
contact are based on stationary theories. In such theories, the parameters
associated with the wheel-rail contact are independent on the conditions
applied on it previously. This supposition is a simplification of the real phenomenon, whose validity lies in the rapid convergence of
the contact parameters to their stationary values. However, the conditions
simulated by means of non-stationary theories may differ from those obtained by
using stationary theories when external conditions vary rapidly. Certain types
of rail corrugation may be related to high-frequency normal or tangential
forces transmitted through the contact, which may determine the effect of the
temporal history on the contact parameters, and consequently on the rail wear.
In order to investigate the influence of the contact process on the results of
models of corrugation calculation, a methodology for estimating the rail wear
depth due to a wheel running on a stretch of rail is developed. The method
implements an improved contact model where non-stationary hypotheses and an
exact elastic model are taken into account. The results show the influence of
the more realistic hypotheses adopted in the proposed method.
Wheel-rail
contact mechanics
A. Alonso, A. Guiral, L. Baeza, S. Iwnicki
Wheel–rail contact: experimental study of the creep forces–creepage
relationships
Vehicle System Dynamics 52 (Supplement 1) (2014) 469-487.
http://dx.doi.org/10.1080/00423114.2014.907923
Abstract: The wheel–rail
contact problem plays an important role in the simulation methods used to solve
railway dynamics problems. As a consequence, many different mathematical models
have been developed to calculate wheel–rail contact forces. However, most of
them tackle this problem purely from a theoretical point of view and need to be
experimentally validated. Such validation could also reveal the influence of
certain parameters not taken into account in the mathematical developments.
This paper presents the steps followed in building a scaled test-bench to
experimentally characterise the wheel–rail contact problem. The results of the
longitudinal contact force as a function of the longitudinal creepage are obtained and the divergences with respect to Kalker's simplified theory are analysed. The influence of
lateral creepage, angular velocity and certain
contaminants such as cutting fluid or high positive friction modifier is also
discussed.
A. Guiral, A. Alonso, L. Baeza, J.G. Giménez
Non-steady state modeling of wheel-rail contact
problem
Vehicle System Dynamics, 51 (2013) 91-108.
http://dx.doi.org/10.1080/00423114.2012.713499
Abstract: Among all the
algorithms to solve wheel-rail contact problem, Kalker's
FastSim has become the most useful computation tool
since it combines a low computational cost and enough precision for most of the
typical railway dynamics problems. However some types
of dynamic problems require the use of a non-steady state analysis. Alonso and Giménez developed a non-stationary method based on FastSim, which provides both, sufficiently accurate results
and a low computational cost. However, it presents some limitations; the method
is developed for one time-dependent creepage and its
accuracy for varying normal forces has not been checked. This paper presents
the required changes in order to deal with both problems and compares its
results with those given by Kalker's Variational Method for rolling contact.
L. Baeza, F. J. Fuenmayor, J. Carballeira and A. Roda
Influence of the wheel-rail contact instationary
process on contact parameters
Journal of Strain Analysis 42 (2007) 377 – 387.
http://dx.doi.org/10.1243/03093247JSA247
Abstract:
The
rapid convergence of the tangential rolling contact parameters to their
stationary values combined with the high computational cost associated with
calculations using instationary models have meant that
stationary models are usually employed in railway dynamics. However, the
validity of stationary models when the applied contact conditions are subjected
to rapid changes has not been sufficiently investigated. With the objective of
deducing the effects of the evolution of the instationary
process on the contact parameters, the tangential contact problem is solved for
a set of reference conditions. For this purpose a
calculation model is adapted, from which it is possible to analyse the
evolution of the contact parameters when the forces exerted between rail and
wheel are subjected to rapid changes. From the calculations done, situations
impossible to simulate by means of stationary theories are obtained according
to the frequency of variation of the forces, such as slip zones in the leading
edge of the contact area and reverse contact (locally, the traction field is
opposite to the direction of the external force transmitted to the contact).
TALGO trains and vehicle
dynamics
Ramy Shaltout, Cristian Ulianov, Luis Baeza
Development of a simulation tool for the dynamic analysis of railway
vehicle-track interaction
Transport Problems 10 (2015) 47-58.
http://transportproblems.polsl.pl/pl/Archiwum/2015/zaszytSE/2015t10zSE_00.pdf
Abstract:
The
importance of modelling and simulation in the field of railway systems has
greatly increased in the last decades. Various commercial simulation packages
have been developed and are used to analyse the dynamic performance of railway
systems. However, although sometimes the user needs to analyse various
non-standard solutions, the possibility to integrate further modifications into
the structure of such software is quite limited. Therefore, in some cases, in
particular for specific modelling and analysis tasks, a feasible option is to
develop flexible and robust simulation tools capable of using different
configurations by modifying the models performing the dynamic analysis. The
paper presents the mathematical modelling background and the conceptual design
of a new of a new computational tool for the dynamic simulation of railway
vehicle systems. The formulations employed in the proposed mathematical model
are based on the multibody techniques. The developed model uses a combined
frame of references that allows the use of independent coordinates without the
possibility to have singularity configurations depending on the rotation
sequence. The simulation tool is designed in a flexible form that enables the
study of different configurations of the railway vehicles, as well as various
track combinations.
J. Carballeira, L. Baeza, A. Rovira, E.García
Technical characteristics and dynamic modeling of Talgo trains
Vehicle System Dynamics 46 Supplement 1 (2008) 301-316.
http://dx.doi.org/10.1080/00423110801939170
Abstract:
One
main characteristic of Talgo trains from the very
beginning in 1942 is the use of single-axle running gears with independently
rotating wheels and non-active steering systems. This feature has allowed the
use of other technical solutions that are usually more difficult to implement
in conventional rolling stock, such as the lower coach floor, the automatic
variable gauge system or the natural tilting technology. The present paper
deals with the singularities in the modelling of the dynamic behaviour of Talgo trains, due to their particular characteristics.
L. Baeza, J. Carballeira, A. Roda and J.E.
Tarancón
A method for obtaining the modal properties of articulated trains equipped with
independently rotating wheels
Vehicle System Dynamics 44 (2006) 841 - 854.
http://dx.doi.org/10.1080/00423110600643700
Abstract:
Independently
rotating wheels in railway vehicles could represent an alternative to standard
technology as a solution to dynamic problems such as hunting instability or
steering forces in curves. Among the proposed design solutions, the train with
independently rotating wheels and with the most practical applications is that
developed by Talgo. The Talgo
technology is based on the use of a passive steering technique of the wheelset
through a mechanism. The absence of automatic control systems means that a
careful selection of the mechanical parameters of the vehicle is required to
improve its dynamic characteristics. Aspects such as dynamic stability or the
effect of vibration on passenger comfort could be analysed by extracting the
modal properties of the train from mathematical models. In this article, a
methodology for determining the low-frequency modal properties of articulated
trains equipped with independently rotating wheels and passive steering system (Talgo-type) is proposed. The singularity of this
application based on the use of non-conventional wheelsets necessarily involves
the development of a specific methodology.
Railway
wheelset dynamics
Astrid Pieringer, Luis Baeza, Wolfgang Kropp
Modelling of Railway Curve Squeal Including Effects of Wheel Rotation
Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 126 (2014)
417-424
http://link.springer.com/chapter/10.1007/978-3-662-44832-8_50
Abstrat: Railway vehicles negotiating tight curves may emit an
intense high-pitch noise. The underlying mechanisms of this squeal noise are
still a subject of research. Simulation models are complex since they have to
consider the non-linear, transient and high-frequency interaction between wheel
and rail. Often simplified models are used for wheel and rail to reduce
computational effort, which involves the risk of over-simplifications. This
paper focuses on the importance to include a rotating wheel instead of a
stationary wheel in the simulation models. Two formulations for a rotating
wheel are implemented in a previously published wheel/rail interaction model: a
realistic model based on an Eulerian modal coordinate approach
and a simplified model based on a rotating load and moving Green’s functions.
The simulation results for different friction coefficients and values of
lateral creepage are compared with results obtained
for the stationary wheel. Both approaches for the rotating wheel give almost
identical results for the rolling speed considered. Furthermore, it can be
concluded that a model of a stationary flexible wheel is sufficient for both
capturing the tendency to squeal and predicting the resulting wheel/rail
contact forces.
José Martínez-Casas1, Egidio Di Gialleonardo, Stefano Bruni, Luis Baeza
A comprehensive model of the railway wheelset-track interaction in curves
Journal of Sound and Vibration 333 (2014) 4152-4169
http://dx.doi.org/10.1016/j.jsv.2014.03.032
Abstrat: Train-track interaction has been extensively studied
in the last 40 years at least, leading to modelling approaches that can deal
satisfactorily with many dynamic problems arising at the wheel/rail interface.
However, the available models are usually not considering specifically the
running dynamics of the vehicle in a curve, whereas a number of train-track
interaction phenomena are specific to curve negotiation. The aim of this paper
is to define a model for a flexible wheelset running on a flexible curved
track. The main novelty of this work is to combine a trajectory coordinate set
with Eulerian modal coordinates; the former permits to consider curved tracks,
and the latter models the small relative displacements between the trajectory
frame and the solid. In order to reduce the computational complexity of the
problem, one single flexible wheelset is considered instead of one complete
bogie, and suitable forces are prescribed at the primary suspension seats so
that the mean values of the creepages and contact
forces are consistent with the low frequency curving dynamics of the complete
vehicle. The wheelset model is coupled to a cyclic track model having constant
curvature by means of a wheel/rail contact model which accounts for the actual
geometry of the contacting profiles and for the non-linear relationship between
creepages and creep forces. The proposed model can be
used to analyse a variety of dynamic problems for railway vehicles, including
rail corrugation and wheel polygonalisation, squeal
noise, numerical estimation of the wheelset service loads. In this paper,
simulation results are presented for some selected running conditions to
exemplify the application of the model to the study of realistic train-track
interaction cases and to point out the importance of curve negotiation effects
specifically addressed in the work.
José Martínez-Casas, Laura Mazzola, Luis Baeza, Stefano Bruni
Numerical Estimation of Stresses in Railway Axles Using a Train-Track
Interaction Model
International Journal of Fatigue, 47 (2013) 18–30.
http://dx.doi.org/10.1016/J.IJFATIGUE.2012.07.006
This paper is in the Top 25 Hottest
Articles of JoF http://cort.as/4LgV
Abstrat: The fatigue design of railway axles requires that the
stresses arising in the axle in real service are accurately quantified. This paper
describes a method to compute the dynamic stresses arising in railway axles as
the effect of train-track interaction, based on the numerical simulation of the
dynamic interaction between a flexible wheelset and a flexible track. The
wheelset is modelled as a flexible rotating body using an
Eulerian approach, whereas track is regarded as an infinite periodic system
with the rail modelled as a Timoshenko beam resting on discrete elastic
supports, considering the inertia associated with the sleepers. The paper
presents an application of the proposed procedure to the calculation of the
dynamic stresses caused in the axle by different types of geometric
imperfection occurring on the wheel and rail surfaces, considering the cases of
a single harmonic rail corrugation, random rail roughness and a wheelflat.
P. T. Torstensson, J. C. O. Nielsen and L. Baeza
High-frequency vertical wheel-rail contact forces at high vehicle speeds -the
influence of wheel rotation
Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 118
(2012) Pages 43-50
http://dx.doi.org/10.1007/978-4-431-53927-8_6
Abstrat: Dynamic vehicle–track interaction at high vehicle
speeds is investigated in a frequency range from about 20 Hz to 3 kHz. The
inclusion of wheel rotation in the vehicle model is investigated by
implementing a structural dynamics model of a rotating wheelset in an existing
simulation environment. Calculated wheel–rail contact forces using this
comprehensive flexible wheelset model are compared with contact forces based on
less detailed, non-rotating wheelset models. Load cases including broad-band
wheel–rail excitation due to vertical rail irregularities (rail corrugation)
and impact excitation caused by a local deviation from the nominal wheel radius
(wheel flat) are considered. Viewed from the excitation point, each wheelset
resonance peak of multiplicity two splits into two peaks; the separation of the
two peaks increases with increasing rotational speed. If the wheelset model is
excited at a frequency where two different mode shapes, due to the wheel
rotation, have coinciding resonance frequencies, the contact force calculated
for the rotating wheelset model differs significantly from those of the
non-rotating models. Further, the use of a flexible rotating wheelset model is
recommended for load cases leading to large magnitude contact force components
in the high-frequency range (above 1.5 kHz). In particular, the influence of
the radial wheel eigenmodes with two or three nodal
diameters is significant.
P.T. Torstensson, J.C.O. Nielsen, L. Baeza
Dynamic train-track interaction at high vehicle speeds - considering the
inertial effects due to rotation
Journal of Sound and Vibration 330 (2011) 5309–5321.
http://dx.doi.org/10.1016/j.jsv.2011.05.030
This paper is in the Top 25 Hottest
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Abstract: Vertical dynamic train–track interaction at high
vehicle speeds is investigated in a frequency range from about 20 Hz to 3 kHz.
The inertial effects due to wheel rotation are accounted for in the vehicle
model by implementing a structural dynamics model of a rotating wheelset.
Calculated wheel–rail contact forces using the flexible, rotating wheelset
model are compared with contact forces based on rigid, non-rotating models. For
a validation of the train–track interaction model, calculated contact forces
are compared with contact forces measured with an instrumented wheelset. When
the system is excited at a frequency where two different wheelset mode shapes,
due to the wheel rotation, have coinciding resonance frequencies, significant
differences are found in the contact forces calculated with the rotating and
non-rotating wheelset models. Further, the use of a flexible, rotating wheelset
model is recommended for load cases leading to large magnitude contact force
components in the high-frequency range (above 1.5 kHz). In particular, the
influence of the radial wheel eigenmodes with two or
three nodal diameters is significant.
L. Baeza, J. Fayos, A. Roda and R. Insa
High frequency railway vehicle-track dynamics through flexible rotating
wheelsets
Vehicle System Dynamics 46 (2008) 647 – 659.
http://dx.doi.org/10.1080/00423110701656148
Abstract:
Some
railway problems such as the corrugation of rails or the impact caused by a wheelflat are associated with a vehicle-track coupled
dynamic phenomenon. Models for the analysis of these problems must account for
the structural vibrations of the track components (rails and sleepers), but the
most adequate approach for the wheelset has not been sufficiently investigated
until present. The wheelset can be considered as an undeformable
solid, as an elastic structure where the rotation effects are neglected, or as
a rotating flexible solid. In order to fill this gap, this article presents a
methodology to use the structural vibrations of a rotating wheelset in high
frequency railway dynamics analyses. The model makes use of Eulerian modal
coordinates, a formulation that provides very low computational cost. The
method is applied in this article to a wheelflat
impact calculation and a vehicle running on a corrugated track. The results
show the importance of the more realistic model in the simulations, mainly in
certain frequencies.
Vibration
and acoustics
F. D. Denia, E. M. Sánchez-Orgaz, L. Baeza, R.
Kirby
Point collocation scheme in silencers with temperature gradient and mean
flow
To be published in Journal of Computational and Applied Mathematics
Abstract:
This
work presents a mathematical approach based on the point collocation technique
to compute the transmission loss of perforated dissipative silencers with
transversal temperature gradients and mean flow. Three-dimensional wave
propagation is considered in silencer geometries with arbitrary, but axially
uniform, cross section. To reduce the computational requirements of a full
multidimensional finite element calculation, a method is developed combining
axial and transversal solutions of the wave equation. First, the finite element
method is employed in a two-dimensional problem to extract the eigenvalues and
associated eigenvectors for the silencer cross section. Mean flow as well as
transversal temperature gradients and the corresponding thermal-induced
material heterogeneities are included in the model. In addition, an axially
uniform temperature field is taken into account, its value being the
inlet/outlet average. A point collocation technique is then used to match the
acoustic fields (pressure and axial acoustic velocity) at the geometric
discontinuities between the silencer chamber and the inlet and outlet pipes.
Transmission loss predictions are compared favorably
with a general three-dimensional finite element approach, offering a reduction
in the computational effort.
E. M. Sánchez-Orgaz,
F. D. Denia, J. Martínez-Casas, L. Baeza
3D Acoustic Modelling of Dissipative Silencers with Nonhomogeneous
Properties and Mean Flow
Advances in Mechanical Engineering Volume 2014 (2014), Article ID
537935, 10 pages
http://dx.doi.org/10.1155/2014/537935
Abstract:
A
finite element approach is proposed for the acoustic analysis of automotive
silencers including a perforated duct with uniform axial mean flow and an outer
chamber with heterogeneous absorbent material. This material can be characterized
by means of its equivalent acoustic properties, considered coordinate-dependent
via the introduction of a heterogeneous bulk density, and the corresponding
material airflow resistivity variations. An approach has been implemented to
solve the pressure wave equation for a nonmoving
heterogeneous medium, associated with the problem of sound propagation in the
outer chamber. On the other hand, the governing equation in the central duct
has been solved in terms of the acoustic velocity potential considering the
presence of a moving medium. The coupling between both regions and the
corresponding acoustic fields has been carried out by means of a perforated
duct and its acoustic impedance, adapted here to include absorbent material
heterogeneities and mean flow effects simultaneously. It has been found that
bulk density heterogeneities have a considerable influence on the silencer
transmission loss.
Francisco D. Denia, José
Martínez-Casas, Luis Baeza, F. Javier Fuenmayor
Acoustic modelling of exhaust devices with nonconforming finite element
meshes and transfer matrices
Applied Acoustics 73 (2012) 713–722
http://dx.doi.org/10.1016/j.apacoust.2012.02.003
Abstract:
Transfer
matrices are commonly considered in the numerical modelling of the acoustic
behaviour associated with the exhaust devices in the breathing system of
internal combustion engines, such as catalytic converters, particulate filters,
perforated mufflers and charge air coolers. In the frame of a multidimensional
finite element approach, a transfer matrix provides a relationship between the
acoustic fields of the nodes located at both sides of a particular region. This
matrizant approach is particularly useful and
accurate when one-dimensional propagation dominates the acoustic phenomena
taking place within the region substituted by the transfer matrix. As shown in
recent investigations, the sound attenuation of catalytic converters can be
properly predicted if the monolith is replaced by a plane wave four-pole
matrix, while retaining the finite element discretization for the
multidimensional acoustic fields within the inlet/outlet and tapered ducts. In
this case, only plane waves are present within the capillary ducts, while
three-dimensional propagation is allowed in the rest of the catalyst
subcomponents. Also, in the acoustic calculation of perforated mufflers by
means of the finite element method, the central passage can be replaced by a
transfer matrix whose (1,2) offdiagonal term is the
acoustic impedance relating the pressure difference between both sides of the
perforated surface with the acoustic velocity through the perforations. In the
reported works associated with the previous problems, the finite element meshes
considered are conforming at the connecting interfaces, therefore leading to a
straightforward evaluation of the coupling integrals. From a practical point of
view, however, and to gain flexibility for the mesh generation process, it is
worth developing a more general procedure valid for the connection of acoustic
subdomains by transfer matrices when the discretizations
are nonconforming at the connecting interfaces. In this work, an integration
algorithm, similar to those considered in the framework of the mortar finite
element method, is then implemented for nonmatching grids in combination with
acoustic transfer matrices. A number of numerical test problems related to some
relevant exhaust devices are then presented to assess the accuracy and convergence
performance of the proposed procedure.
José Martínez-Casas, Juan Fayos, Francisco D. Denia and Luis Baeza
Dynamics of damped rotating solids of revolution through an Eulerian modal
approach
Journal of Sound and Vibration 331 (2012) 868–882.
http://dx.doi.org/10.1016/j.jsv.2011.10.003
Abstract: This article presents a technique for modelling the
dynamic response of rotating flexible solids with internal modal damping. The
method is applicable to solids with geometry of revolution that rotate around
their main axis at constant spinning velocity. The model makes use of an Eulerian modal coordinate system which adopts the
vibration modes in a non-rotating frame as basis
functions. Due to the coordinate system, the technique is particularly suitable
for studying the dynamic interaction between rotating solids and non-rotating
structures and permits to obtain Frequency Response Functions. The approach has
been adopted to study the dynamics of a simply-supported cylinder in order to
obtain the receptance function and the modal
properties of the rotating solid.
Luis Baeza, Huajiang Ouyang
Modal approach for forced vibration of beams with a breathing crack
Key Engineering Materials 413 (2009) 39-46.
http://dx.doi.org/10.4028/www.scientific.net/KEM.413-414.39
Abstract:
This
paper presents a method for the vibration of a beam with a breathing crack
under harmonic excitation. The infinitely thin crack is characterised by a
parameter ac that takes into account the
shape and the depth of the crack. The closed- and the open-crack states are
both modelled through a modal approach: two sets of equations of motion cast in
the modal coordinates of their own individual mode shapes. The state change
(from closed-crack to open or vice versa) involves the calculation of the
coordinates associated with the new state from the coordinates of the previous
state. By imposing beam displacement and velocity continuity, the matrix that
transforms the modal coordinates from one state to the other is determined and
proved to be the Modal Scale Factor matrix. This analytical approach takes
advantage of exact nature and mathematical convenience of beam modes and is
time-efficient. Forced vibration at various values of crack parameter ac is
determined. It is found that as ac decreases
(crack length increases), vibration response becomes increasingly erratic and
finally chaotic.
Huajiang
Ouyang, Luis Baeza, Shaolin Hu
A receptance-based method for predicting latent roots
and critical points in a type of asymmetric systems.
Journal of Sound and Vibration 321 (2009) 1058–1068
http://dx.doi.org/10.1016/j.jsv.2008.10.020
Abstract:
This
paper studies the latent roots and critical points of friction-induced
vibration problems in which the stiffness matrix is asymmetric. The asymmetric
terms are represented by a parameter or parameters related to the friction
coefficient. As the parameter value increases, some latent roots of the
asymmetric system change, and even become complex with positive real parts at a
critical point, indicating flutter instability. A method is put forward for
computing the latent roots and predicting the critical value of this parameter
at the flutter instability boundary of the asymmetric system based on the receptance of the symmetric system.When measured receptances
of the symmetric system (at those locations where friction forces would be
acting in the corresponding asymmetric system)are available, the simulated
numerical example shows that this method is efficient.
Luis Baeza; Huajiang Ouyang
Vibration of a truss structure excited a by moving oscillator
Journal of Sound and Vibration 321 (2009) 721–734.
http://dx.doi.org/10.1016/j.jsv.2008.09.049
Abstract:
This
paper studies the vibration of a truss structure comprised of a number of
rigidly connected Timoshenko beams. The excitation is provided by a moving
oscillator of an unsprung mass that supports another
mass through a spring (oscillator) and slides on top of the truss structure.
Each component beam of the structure is meshed with an adaptable number of
Timoshenko beam elements to allow efficient modelling of the vibration of the
structure for a wide range of travelling speeds of the moving oscillator.
Numerical modes are first obtained and then replaced with analytical modes
using the elemental shape functions. Due to the axial motion and the rotation
of each component beam, the relative location of the moving oscillator differs
slightly from its horizontal journey. This small difference is also included in
the dynamic model of the whole system. Vibration of the structure and vibration
of the oscillator are studied through simulated examples.
Luis Baeza; Huajiang Ouyang
Dynamics of an elastic beam and a oscillator moving in the longitudinal
direction of the beam
Structural Engineering and Mechanics 30 (2008) 369-382.
http://goo.gl/QJW0J
Abstract:
An
oscillator of two lumped masses linked through a vertical spring moves forward
in the horizontal direction initially at a certain height over a horizontal Euler
beam and descends on it due to its own weight. Vibration of the beam and the
oscillator is excited at the onset of the ensuing impact. The impact produced
by the descending oscillator is assumed to be either perfectly elastic or
perfectly plastic. If the impact is perfectly elastic, the oscillator bounces
off and hits the beam a number of times as it moves forward in the longitudinal
direction of the beam, exchanging its dynamics with that of the beam. If the
impact is perfectly plastic, the oscillator sticks to the beam after its first
impact and then may separate and reattach to the beam as it moves along the
beam. This interesting and seemingly simple dynamic problem actually displays
rather complicated dynamic behaviour and has never been studied in the past. It
is found through simulated numerical examples that multiple bounces and impacts
can take place for both perfectly elastic impact and perfectly plastic impact
(though more of the former) and the dynamic response of the oscillator and the
beam looks noisy when there is an impact. For the perfectly plastic impact, the
oscillator can experience multiple events of consecutive separation from and
reattachment to the beam.
Luis Baeza; Huajiang Ouyang
Dynamics of a Truss Structure and its Moving-Oscillator Exciter with Separation
and Impact-Reattachment
Proceedings of the Royal Society A - Mathematical Physical And Engineering
Sciences 464 (2008) 2517–2533.
http://dx.doi.org/10.1098/rspa.2008.0057
Abstract:
The
dynamic response of a stationary structure excited by a moving structure is
studied in this paper. The stationary structure is in the form of a truss made
of a number of rigidly connected Timoshenko beams while the moving structure
consists of two masses linked by a spring and a dashpot (oscillator). To
facilitate the mathematical model of the moving-load dynamics of the whole
system, the frequencies and modes of the stationary structure are first
obtained by the finite element method and then they are cast in an analytical
form within each element through the element shape functions. This is a
distinct advantage of this paper. Each component beam of the stationary
structure is meshed with an adaptable number of Timoshenko beam elements to
allow efficient modelling of the vibration of the structure for a wide range of
travelling speeds of the moving oscillator. During the horizontal travel and
vertical vibration of the oscillator, it may separate from the vibrating
stationary structure and subsequently may reattach to the stationary structure
with impact. These two phenomena have been studied in only a few papers for
simple moving-load problems in the past and have never been studied for the
present problem. It is found through simulated examples that the dynamic
response at high speeds can be several times higher than the relevant static
response, and separation and reattachment with impact produce a noticeable
difference in the dynamic response. Multiple separation and impact events are possible
at high speeds.
J. Fayos, L. Baeza, J. E. Tarancón and F. D. Denia
An Eulerian coordinate-based method for analysing the structural vibrations of
a solid of revolution rotating about its main axis
Journal of Sound and Vibration 306 (2007) 618–635.
http://dx.doi.org/10.1016/j.jsv.2007.05.051
Abstract:
This
article presents a technique for modelling the dynamic response of spinning
solids of revolution. The method is especially adequate for considering those
cases where the interesting displacements and the external forces are
associated with points at which the Eulerian coordinates are constant. The
method is based on the modal properties of solids of revolution: any deformed
shape of the solid after rotation can be calculated as a linear combination of
the non-rotating modes. The obtained formulation takes account of the
flexibility of the solid and the inertial and gyroscopic effects due to the
rotation. In this paper the method is applied to a cylinder (considering an
analytical and a numerical approach), and to a railway wheelset.
FEM
M. Tur, E. García, L. Baeza, F.J. Fuenmayor
A 3D absolute nodal coordinate finite element model to compute the initial
configuration of a railway catenary
Engineering Structures Volume 71 (2014) 234–243.
http://dx.doi.org/10.1016/j.engstruct.2014.04.015
Abstract:
In
this paper we propose a method of finding the initial equilibrium configuration
of cable structures discretized by finite elements applied to the shape-finding
of the railway overhead system. Absolute nodal coordinate formulation finite
elements, which allow for axial and bending deformation, are used for the
contact and messenger wires. The other parts of the overhead system are
discretized with non-linear bars or equivalent springs. The proposed method
considers the constraints introduced during the assembly of the catenary, such
as the position of droppers, cable tension, and height of the contact wire. The
formulation is general and can be applied to different catenary configurations
or transitions both in 2D and 3D with straight or curved track paths. A
comparison of the results obtained for reference catenaries in the bibliography
is also included.
M. Tur, L. Baeza, F.J. Fuenmayor, E. García,
PACDIN statement of methods
To be published in Vehicle System Dynamics.
http://dx.doi.org/10.1080/00423114.2014.963126
Abstract:
PAntograph–Catenary Dynamic Interaction
(PACDIN) is a code developed by the vehicle technology research centre (CITV)
of the Universitat Politècnica
de València in collaboration with the railway company
Talgo S.L. The model of the catenary is a finite
element model using absolute nodal coordinates. It is based on a general
formulation that can be applied for analysing a wide range of catenary
configurations, including stitch wire, transitions or non-straight path tracks.
The formulation is fully non-linear and includes large deformations, dropper
slackening and contact interaction. The model is linearised
when deformations are small, as in the case of the benchmark dynamic analysis.
The results of the PACDIN code show a good agreement with the average results
of other benchmark codes.
E. Giner, F. J. Fuenmayor, L. Baeza, J. E. Tarancón
Error estimation for the finite element evaluation of GI and GII
in mixed-mode linear elastic fracture mechanics
Finite Elements in Analysis and Design 41 (2005) 1079-1104.
http://dx.doi.org/10.1016/j.finel.2004.11.004
Abstract:
A
discretization error estimator for the finite element evaluation of the strain
energy release rates (SERRs) GI, GII is presented for
mixed-mode bidimensional problems of the linear
elastic fracture mechanics (LEFM). The estimator is related to one of the most
efficient energetic methods: the equivalent domain integral method (EDI). A
continuum approach of the shape design sensitivity analysis (SDSA) is applied
to the fracture mechanics problem in combination with the field decomposition
technique to obtain separate estimates of the discretization error for each
mode. The error estimator enables an a posteriori
improvement of GI, GII for a given finite element mesh.
The improvement is achieved by adding the estimated errors to the previously
calculated values of GI, GII by means of the discrete
analytical stiffness derivative method (DASD). This is verified through
numerical examples based on theWestergaard’s problem
and a finite domain problem.
J.E. Tarancón, F.J. Fuenmayor, L. Baeza
An a posteriori error estimator for the p- and hp-versions
of the finite element method
International Journal for Numerical Methods in Engineering 62 (2005) 1-18.
http://dx.doi.org/10.1002/nme.1162
Abstract:
An a posteriori error estimator is proposed in this
paper for the p- and hp-versions of the
finite element method in two-dimensional linear elastostatic
problems. The local error estimator consists in an enhancement of an error
indicator proposed by Bertóti and Szabó
(Int. J. Numer. Meth. Engn.
1998; 42:561–587), which is based on the minimum complementary energy
principle. In order to obtain the local error estimate, this error indicator is
corrected by a factor which depends only on the polynomial degree of the
element. The proposed error estimator shows a good effectivity index in meshes
with uniform and non-uniform polynomial distributions, especially when the
global error is estimated. Furthermore, the local error estimator is reliable
enough to guide p- and hp-adaptive
refinement strategies.
F.J. Fuenmayor, J.L. Restrepo, J.E. Tarancón,
L. Baeza
Error estimation and h-adaptive refinement in the analysis of natural
frequencies
Finite Elements in Analysis and Design 38 (2001) 137-153.
http://dx.doi.org/10.1016/S0168-874X(01)00055-5
Abstract:
This
paper deals with the estimation of the discretization error and the definition
of an optimum h-adaptive process in the finite element analysis of natural
frequencies and modes. Consistent and lumped mass matrices are considered. In
the first case, the discretization error essentially proceeds from the
stiffness modelization, so it is possible to apply
the same error estimators than those considered in static problems. On the
other hand, the error associated with the modelization
of the inertial properties must be taken into account if lumped mass matrices
are used. As far as h-adaptivity is concerned,
it is usually interesting to obtain meshes with a specified error for each
mode. However, traditional criteria for static problems consider only one load
case. Defining the optimum mesh as the one that gets the desired error with the
minimum number of elements, a method is proposed for the h-adaptive
process taking into account a set of natural modes simultaneously. The proposed
methods have been validated by applying them to bi-dimensional test problems.
Measurement
techniques
Ricardo Insa, Javier Inarejos, Pablo Salvador
and Luis Baeza
On the filtering effects of the chord offset method for monitoring track
geometry
Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail
and Rapid Transit, 226 (2012) 409-420.
http://dx.doi.org/10.1177/0954409712447481
Abstract:
A
recently published paper in the literature used a particular method to
establish the correspondence between the vertical accelerations registered in
the axlebox of a wheel and the rail vertical profile
which caused them as a way of monitoring the track conditions. However, that
work did not consider the filtering effects due to the asymmetric chord
approach that underpinned the process. As a result of this, it is suggested
that such method may produce some errors in the measurements at certain
frequencies. The present work shows how the technique can be amended in order
to maintain its quality.
Select
group of Projects
Active
suspension http://www.talgo.com/index.php/en/activa.php
Low frequency
dynamics http://www.talgo.com/index.php/en/analisis.php
Instrumented wheelsets for
measuring wheel-rail contact force http://www.talgo.com/index.php/en/eje.php
Instrumented pantograph
/ Pantograph-catenary dynamics
http://www.talgo.com/index.php/en/interaccion.php