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 Articles of JSV http://goo.gl/MwI1b 

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

 

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