Advances in Engineering Software 33 (2002) 541–552 www.elsevier.com/locate/advengsoft
Structural dynamics and ride comfort of a rail vehicle system A. Striberskya,*, F. Mosera, W. Rulkab b
a Siemens SGP Verkehrstechnik GmbH, Brehmstraße 16, A-1110 Vienna, Austria DLR, Institute of Aeroelasticity, Vehicle System Dynamics, P.O. Box 1116, D-82230 Weßling, Germany
Received 16 November 2000; accepted 1 July 2002
Abstract The paper describes the development of a virtual vehicle system using virtual prototyping computer tools. The virtual vehicle is used for the prediction of the structural dynamics. Since the modelling process for complete rail vehicle systems becomes increasingly more complex, time and cost can be saved by the use of a database concept and an automated assembling process for the vehicle of interest. Supported by a modular design concept, vehicle components for a metro train have been modelled and stored as substructures in a specific vehicle component database. Using this database, train configurations up to a three-car train can be assembled very quickly to perform structural dynamics analyses and to predict the ride comfort. Experimental results have been compared with simulation results of the rail vehicle to improve the modelling technique and the accuracy of the developed virtual vehicle system. The mathematical modelling of the rail vehicle system featuring elastic components, the structure of the database as well as numerical and experimental results are presented in this paper. q 2002 Civil-Comp. Ltd and Elsevier Science Ltd. All rights reserved. Keywords: Virtual prototyping; Structural dynamics analyses; Ride comfort; Rail vehicle system; Product development; Lightweight structure; Computer tool; Database concept
1. Introduction Since cities are growing and people are becoming busier, urban transport systems have to improve. Vehicle manufacturers are investing to raise the travelling speed, to increase the passenger capacity of the vehicles, as well as to provide better passenger comfort [6]. With the use of advanced lightweight structures for the vehicle design, structural dynamics in connection with vehicle running dynamics is increasingly important. In the field of vehicle development, objectives that are driven by the competition, like to shorten the time to market, to create innovative designs, and to lower the vehicle costs, are forcing the vehicle engineers to use new development methods. Virtual prototyping computer tools have made considerable progress in recent years. They are widely used for modelling and simulating the dynamic motion of complex vehicle systems [7]. Working with virtual proto* Corresponding author. Tel.: þ 43-51707-41686; fax: þ 43-5170751586. E-mail address:
[email protected] (A. Stribersky).
typing technology has shown potential to improve the product development process. The paper describes work done by Siemens using virtual prototyping computer tools. New rail vehicle designs have been modelled and the dynamic motion of complex moving structures has been simulated. The virtual vehicle developed is used for the optimisation of the ride comfort of future metro trains by numerical simulation. As an example for the use of the developed software tool, the virtual system of a metro train will be discussed. The following issues will be addressed: † † † †
the modelling done for the structural dynamics analyses; the structure of the newly developed database; the automated generation of the virtual metro; numerical results predicting the structural dynamics and the ride comfort of the newly developed vehicle system.
The work described has been done using the computer tools I-deas, Abaqus and Simpack [2]. The numerical results have been compared to the results of experimental modal analyses and measurements of the ride comfort using a real prototype vehicle (Fig. 1).
0965-9978/02/$ - see front matter q 2002 Civil-Comp. Ltd and Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 5 - 9 9 7 8 ( 0 2 ) 0 0 0 7 2 - 8
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Fig. 1. New metro train for Vienna.
2. The virtual vehicle system In recent years the rail industry has strengthened their competitiveness through the development of product platforms for rail vehicles. Know-how gathered from former projects has been used to define the concepts for modular vehicle families, to select the manufacturing technologies and to engineer basic component modules as well as predesigned options, which are ready for implementation. Supported by a modular design concept for the newly developed metro train by Siemens, which leaves the customers with a choice of system configurations, a database for a virtual vehicle has been developed. Using substructure techniques, pre-designed vehicle components from the database can be used to automatically build up the virtual vehicle model of interest, ready to perform structural dynamics analyses. 2.1. The Simpack database concept Within the multibody software Simpack models for assemblies can be stored as substructures and later be used within complete vehicle simulations. Changes made to the assembly model in the substructure automatically transfer to the main vehicle model. The wide range of the Simpack database concept allows that almost every modelling element can be added to the database. This concept allows it to build a specific vehicle component database for a complete vehicle family. Simpack offers the user a database, which is organised in five different levels (Fig. 2). Level 1 contains the main vehicle model. Level 2 contains the substructures of the multibody system. Level 3 contains single elements of the
multibody system like bodies or force elements as well as input parameter sets. Level 4 contains tables and data files used by the elements of the levels 1– 3: for example the three dimensional CAD geometry, the wheel/rail contact tables or the standard input data (SID) file to integrate the flexible body data obtained from finite element analyses. Most of these data files are the results of Simpack preprocessor programs, like the SID file for a flexible body, which has been derived using the Simpack-FEM preprocessor Fembs. The bottom level 5 contains unfiltered data, like measured wheel and rail profiles, which are input to the preprocessors. The element and structure databases of levels 2 and 3 have a prime importance. The parameters of all elements stored in these databases are non-modifiable, except for the parameters which depend on the build-in into the full vehicle model. For example does the nominal pre-stress force of a spring-damper element depend on the vehicle loads and masses, while all other parameters like the stiffness are fixed. With this feature it is possible to group many of the vehicle system parameters and to give these groups genus names. These names can be defined according to the linguistic usage of each user or company. The gain of this feature is based on the long term judging of the development process. The grouping technique allows an interpretation of the full vehicle model without the necessity to have special knowledge about the sometimes over 10,000 system parameters. So it addresses mainly the maintenance of the virtual vehicle models than the model set-up process. For example is the ensemble ‘PrimarySuspension’ of a supplier sufficiently described with the genus ‘PrimarySuspension_Supplier_XX_SeriesId_123’ and does not need
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Fig. 2. The Simpack database levels.
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Fig. 3. The virtual intermediate car of a metro train.
the detailed knowledge about the mathematical modelling and about the parameter values of the stiffness, damping and friction coefficients. Content of force-element database entry:
tures with the identical physical content a compromise between unambiguousness and handling is provided. So it is possible to define additional elements like markers on substructure bodies which are necessary to import and to
While the database level 3 combines the mathematical modelling and parameters of single elements, are these single elements composed to the so-called substructures in the database level 2. Again all the parameters are nonemodifiable, which describe the inner structure of element interconnections. But with regard to avoid many substruc-
interconnect the substructure with the full vehicle model. Simpack also provides the well-known parameterizing technique of the model parameters for the database given elements, substructures and full vehicle components. In contrast to the database feature that serves for the grouping purpose and the hiding of detail-knowledge, the
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Fig. 4. Interior design.
parameterizing technique enables the separation of significant design parameters from the vehicle or component models. The parameterizing technique can be used especially for setting up product families. 2.2. The database for the virtual vehicle For the Siemens metro a database has been created and the vehicle components have been modelled and stored in that database. Using that database all the possible train configurations up to a three-car train can be assembled very quickly using a product specific and user customisable graphical interface to communicate with the database manager. The database manager allows the automated assembling of the vehicle configuration of interest. After the selection of components a configuration file is written, which defines the automated loading of the chosen components from the database. With the use of the customised graphical database interface the following vehicle configurations can be assembled: † single car, † two-car unit, † three-car train. The different cars are divided into separate modules. Every module is a separate unit, which can be integrated into the complete vehicle by predefined interfaces. The following vehicle modules have been modelled as substructures:
† Car body A for the end wagon modelled as rigid body. † Car body B for the intermediate cars modelled as elastic structure. On the car body B a traction container, two cooling containers and two roof mounted air conditioning units are mounted as elastically supported rigid bodies. † Car body B for the intermediate cars modelled as rigid body. † Automatic coupler. † Semi-permanent coupler. † Driving bogie with two traction units. † Trailing bogie. Each substructure has been tested separately before it has been added to the database and used for the vehicle simulation. Fig. 3 shows an assembled single vehicle made of the car body B as an elastic structure, the traction and cooling containers, the roof mounted air conditioning units and two driving bogies. Since the car body structure has been modelled elastically for structural dynamic analyses, the interfaces between the car body and the bogies regarding the secondary air suspension, the vertical dampers, the antiyaw dampers and the traction rods are defined separately. The attachment points of the force elements have been modelled at the actual position on the flexible structure.
3. Mathematical modelling The overall system has been modelled as a multibody system, taking into account the flexibility of the lightweight
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Fig. 5. Finite element model.
structures. The representation of the finite element structures in the multibody system uses a modal approach. 3.1. Vehicle modelling To predict the vehicle dynamic behaviour the methods developed for multibody systems have been used. The equations formulated by the software allow the simulation of non-linear kinematics having large angular displacements. The overall system has been modelled with the aid of modelling elements like rigid bodies, joints and force elements, which can be chosen from a library provided by the multibody software Simpack (Fig. 3). The non-linear lateral suspension modelling includes a linear spring, a bump stop with a progressive stiffness characteristic for the rubber element of the bump stop, as
well as a viscous damper. To determine the wheel-rail geometric constraint relations, numerical analysis is used. The motion of a wheelset is constrained by the geometry of the wheel and rail profiles. The profiles are represented by cubic spline functions. The contact geometry and the constraint functions are precomputed and stored in tabular form. The modelling of the wheel –rail interaction is one of the main features of the multibody program Simpack. In a library a general wheel – rail contact element is provided for the user. The calculation of the creep forces is based on equivalent Hertzian contact properties and uses the Fastsim algorithm, which applies Kalker’s simplified non-linear theory of rolling contact [4]. As a total the vehicle model for the intermediate car of the metro train includes 54 bodies, 120 joint states, with 16
Fig. 6. Multibody system software within an integrated design process. CFD (computational fluid dynamics); CACE (computer aided control engineering); CAD (computer aided design); FEM (finite element method); MBS (multibody system).
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of these being restricted by constraints, and 108 force elements.
full vehicle analysis offers interfaces to the CAE-environment on three levels:
3.2. The flexibility of the lightweight structures
† the co-simulation, specially to control system design software and finite element analyses (FEA) tools; † the import and export of mathematical models as program code; † the import of subsystem-parameters, where the mathematical modelling of the subsystem is part of the Simpack library elements. This import/export is supported by Simpack pre/post-processors, where a lot of expert know-how is implemented to enable a widely automatic process. Examples are the CAD (computer aided design) and FEM interfaces, which have been used in the metro project.
For ride comfort evaluations the elastic modes of the car body structure together with the interior equipment have been included in the simulation model using finite element software. The actual interior design of the vehicle is shown in Fig. 4. The car body shell is a self-supporting structure, made out of large aluminium extrusions, which are welded together. The lightweight structures of the aluminium car body as well as the interior equipment have been modelled in detail using shell elements, elastic and rigid beam elements, point masses and spring elements. Using the software I-deas additionally to the car body structure the following components have been modelled elastically: windows, the ceiling frame, the floor structure, seats and handrails. The rigid mounted part of the underfloor equipment has been modelled using rigid beams and point masses. In Fig. 5 the finite element model of the interior equipment can be seen. As a total the finite element model for the intermediate car body of the metro train consists of approximately 88,000 finite elements, 62,000 nodes and 369,000 degrees of freedom. The elastic body properties have been calculated using the finite element software Abaqus. The classical Guyan reduction method has been applied to reduce the elastic problem to a set of matrices. The quality of the approximation depends on an appropriate selection of master degrees of freedom. For the reduction process 391 master nodes and 1326 master degrees of freedom have been selected. The master nodes are shown as small cubes in Fig. 3. Using this approach the mass and the stiffness matrices have been reduced to the master degrees of freedom before the natural frequencies and mode shapes have been calculated. 3.3. Multibody system algorithm for the full vehicle simulation As master simulation tool for the metro full vehicle analysis the multibody system (MBS) tool Simpack is taken. It primarily supports the non-linear motion of mechanical subsystems and the metro full train bodies in extreme manoeuvres as well as the modelling of the track and wheel/rail contact elements. It also provides large libraries with mathematical models for the vehicle sub-components like dampers, air springs, friction, sensors, actuators, and controllers. Many interfaces are offered to import experimental field data. The elastic body behaviour is taken into account by Simpack’s equations of motion through the import of pre-reduced finite element method (FEM) models. Generally the vehicle design process is multidisciplinary and uses different CAE (computer aided engineering) programs, as shown in Fig. 6. Simpack as a tool for the
The Simpack multibody system algorithm [5] is based on relative coordinates, that means the non-linear body motions are mathematically described relative to each other. The relative coordinates enable most flexible and most comfortable modelling techniques. They include as a subset the socalled absolute coordinate modelling. The mathematical description of bodies by relative motions leads automatically to a minimum coordinate representation for the equations of motion of all bodies in the kinematic tree. The provided equations for the non-linear motions of the full system are the most general over-determined differential algebraic equation system (DAE): 0 1 p€ B C B q€ C 2 gðp; _ p; z; q; _ q; l; j; d; tÞ ¼ 0 ð1aÞ @ A z_ cp ðp; q; z; j; d; tÞ ¼ 0 _ p; q; _ q; z; j; d; tÞ ¼ cv ðp;
ð1bÞ
›c p y_ þ c v ðp; q; z; j; d; tÞ ¼ 0 ð1cÞ ›y
€ p; _ p; q; € q; _ q; z; j; d; tÞ ca ðp; ¼
›c p _ p; q; _ q; z; j; d; tÞ ¼ 0 y€ þ c a ðp; ›y
€ p; _ p; q; € q; _ q; z_ ; z; l; j; d; tÞ ¼ 0 cj ðp;
ð1dÞ ð1eÞ
Here Eq. (1a) represents the differential equations of motion with Np equations defining the rigid body positions, Nq equations for the elastic body deformations and Nz differential equations of first order, provided by force eigendynamics. The states used for describing the motions are: p q z l
position states of the rigid body motions modal states of deformations of elastic bodies modelled as FE structures states of differential equations describing dynamic force elements algebraic states, representing the constrained forces of kinematic closed loops
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Fig. 7. The diagonal distortion. The elastic deformation of the car body structure is shown exaggerated.
j
d y
algebraic states of additional non-linear index 1 equations, like positions of contact points on general 3D surfaces or states for algebraic loops in control laws with acceleration feedback values of discrete controllers vector y combines the mechanical position states: yT ¼ ðpT ; qT Þ Eqs. (1b) – (1e) are non-linear algebraic equations:
cp
cv
ca
cj
the Nl algebraic equations on position level describing the kinematic closing loop conditions of constraints the Nl algebraic equations describing the kinematic closing loop conditions on the level of velocities. They may be obtained as derivative of cp and therefore they are linear in the mechanical velocity states y_ T ¼ ðp_ T ; q_ T Þ the Nl algebraic equations describing the kinematic closing loop conditions on the level of accelerations the Nj algebraic equations defining the states j
€ q; € z_ in Eq. (1d) by Eq. (1a) gives ca as nonSubstituting p; linear equations _ p; q; _ q; z; l; j; d; tÞ ¼ 0 ca ðp;
ð2Þ
for the evaluation of the Nl constraint forces l at given body positions and velocities. The time integration by standard solvers for states p; q; z; l; j which uses the differential equations (1a) and constraints ca, cj causes drift-off problems. For ensuring precise and robust time integration Simpack solvers are enhanced for solving the over-determined DAE-system. Here the so-called index 2 constraints cv on velocity level defining l and the kinematic constraints cp on position level for stabilising the time integration [3] are used. The
robustness of the numerical solution methods is the main premise for any automatic parameter field study. cj are algebraic index 1 constraints and need no special numeric stabilising. The Simpack time domain analysis methods are enhanced to efficient solutions of stiff differential equations of MBS-models, which include discrete elements, like controllers, and support state dependent discontinuities like bumps or slip-stick effects. While the relative co-ordinates achieve pre-reduced differential equations of motion, the knowledge about the kinematic tree structure is used by a specially established O(N )-algorithm for the automatic generation of these equations. O(N ) means that the amount for the equation generation increases only linearly with the number of bodies. When Gear-methods are addressed for time simulations the knowledge about their equation structure is taken into account, resulting for example into the support of an O(N )-residues algorithm, which halves the amount of equation generation again, compared to the explicit O(N )algorithm. Additional structure information about bodies, which are connected by applied forces, is passed to the solution methods resulting not only in robust, but also in fast simulations. For linear system analysis Eqs. (1a)– (1e) are reduced to the standard linear equations D_x ¼ A·Dx þ B·uðtÞ
ð3Þ
with the system matrices A, B, the state vector xT ¼ ðp_ T ; p T ; q_ T ; q T ; zT Þ and the excitation vector uðtÞ: p and q are the independent mechanical position states or the so-called minimum states. The linear equations (3) are the base to the computational methods like eigenvalue, frequency response, linear system response, spectral- and covariance-analysis calculation. For automated parameter studies and optimisation
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procedures all these analysis methods can be combined with pre-calculations, like static equilibrium. 3.4. Modelling the hybrid multibody system In the metro project the elastic body deformation is considered by modelling the flexibility as part of the multibody equations. The goal is to approximate the large FEM-equations with about 300,000 degrees of freedom by a reduced equation set (less than 100 degrees of freedom) including only these car body vibration modes, which are significant for stability and comfort. Simpack derives the equations of motion starting out from the non-linear kinematics of a mass point dm (Fig. 7). The absolute position of this mass point can be calculated as rI;dm ¼ rIR ðtÞ þ rel ðs; uel ðs; tÞÞ
ð4Þ
where rIR ðtÞ describes the position of the body fixed reference frame and rel ðs; uel ðs; tÞÞ describes the relative position of the mass point dm on the elastic deformed body. Here s indicates the relative position of the mass point in the undeformed state and uel are the elastic coordinates. The linearization with respect to elastic co-ordinates instead of the use of small cartesian elastic deformations leads to equations of motion which include all coupling terms between large rigid body movements and elastic deformations, as well as captures the full influence of the nominal preload. In the multibody system code the elastic displacements are represented by a Ritz approach. The displacements uel ðs; tÞ are expressed by linear combinations of mode shapes fj ðsÞ; which are weighted with the time dependent modal coordinates qj ðtÞ uel ¼
n X
wj ðsÞ·qj ðtÞ
ð5Þ
j¼1
Using the Ritz approach the infinite number of degrees of freedom of the elastic bodies has been reduced to the number of modes. To import the elastic body properties into the multibody system, the preprocessor Fembs to the multibody software Simpack has been used as interface. In order to achieve short simulation times as well as good approximation of the flexible deformations, all calculated mode shapes up to the frequency of 30 Hz have been selected. The Abaqus FEM model and therefore the eigenmodes represent a car body not coupled to its environment. In the full vehicle the car body deformation is influenced by its elastically underfloor or roof mounted equipment and by its interactions to the bogies. To improve the accuracy particular modes, which describe local deflections, have to be considered. The preprocessor Fembs supports the generation of frequency response modes [1] of the FEM model obtained by harmonic
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excitations at the attachment points. The computation procedure automatically selects only such frequency response modes, which are significant for the coupled movement and the frequency range of interest. Compared to a static mode approach no time consuming modification of the FEM model and constraint modelling is needed to obtain adequate modes, which needs a lot of expert know-how and will not be possible for many coupling conditions. Another important feature concerns the fact, that often nodes, where the coupling elements to the bogies and equipment are attached, are not part of the FEM model. Here Simpack interpolates the movement from nodes lying in the neighbourhood of the desired attachment points. The multidisciplinary expert know-how implemented in the Fembs preprocessor supports a widely automatic import of FEM models to the multibody system and minimises the effort of the experts from the different departments involved in the vehicle design process. In the hybrid model of the equipped car, all elastically mounted equipment attached to the flexible structure has been modelled in the multibody system and not in the FEM model. This kind of modelling has allowed us to vary the stiffness and damping of the container mounts without doing the Guyan reduction process, performing the eigenvalue extraction and importing the elastic properties into the multibody system several times. Frequency response modes have been calculated for all the attachment points. In total a reduced modal representation with a combination of 12 eigenmodes and 27 frequency response modes has been used to simulate the ride comfort of the single intermediate car for the metro train.
4. Simulation results 4.1. Car body shell For the car body shell of the intermediate car the following eigenmodes have been calculated using the software Abaqus: Mode no.
Frequency (Hz)
1 2 3 4 5 6 7
15.3 18.1 19.7 19.9 22.9 27.2 29.8
Diagonal distortion Body shell breathing Vertical bending Torsion Body shell breathing 2 Diagonal distortion 2 Vertical bending 2
Up to a frequency of 20 Hz four different elastic mode shapes exist. The mode shape with the lowest frequency shows a diagonal distortion of the car body structure. At this
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Fig. 8. Simulated transfer functions. Vertical acceleration on the floor at the car centre close to the side wall and above the bogie close to the side wall. (Abaqus: full FEM model, Simpack: reduced FEM model).
mode shape the side walls of the car body are vibrating against each other. At higher frequencies breathing, a vertical bending and a torsion of the car body exist. For frequencies from 20 up to 30 Hz three mode shapes of higher order have been calculated. 4.2. The fully assembled intermediate car To validate the modelling used in the multibody system, the eigenmodes for the fully assembled intermediate car body together with the elastically mounted underfloor containers and the roof mounted air conditioning units have also been calculated using Abaqus. This finite element model now includes the elastically mounted equipment. With an upper frequency limit of 30 Hz the calculation has shown 41 different modes of the unsupported structure. Up to a frequency of 20 Hz the model indicates seven different mode shapes with dominant elastic deformations of the car body structure:
Mode no.
Frequency (Hz)
1 2 3 4 5 6 7
10.3 10.9 12.4 14.5 15.3 16.6 18.2
Diagonal distortion Vertical bending, A Vertical bending, B Torsion Torsion Vertical bending 2 Diagonal distortion 2
Both, the diagonal distortion and the vertical bending are above the desired lower frequency limit of 10 Hz. In comparison to the car body shell, due to the elastically mounted containers additional mode shapes exist. For the vertical bending mode A, the elastically mounted traction container oscillates in phase with the vertical bending of the car body structure. For the vertical bending mode B, the traction container and the car body are oscillating against each other. The given values for the eigenfrequencies are for
Fig. 9. Simulated transfer functions showing the influence of the frequency response (f.r.) modes.
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Fig. 10. Simulated frequency spectrums of the vertical acceleration on the floor at the car centre close to the side wall and above the bogie close to the side wall.
the full finite element model. In Fig. 7 the mode shape for the diagonal distortion is shown. To import the elastic body properties into the multibody system the Guyan reduction method has been applied to the FEM model of the car body without the elastically mounted equipment. For the reduced model the obtained eigenfrequencies up to 20 Hz differ not more than 0.5% compared to the full model. For frequencies above 20 Hz higher differences than 0.5 % have been accepted. In the multibody model all mode shapes up to 30 Hz have been taken into consideration. To compare the different kinds of modelling and to show the influence of the eigenmodes, transfer functions for the equipped car body structure have been calculated. For these calculations the car body has been excited with a force, F acting vertically on the car body above one air suspension of one bogie. In Fig. 8 the vertical acceleration on the floor at the car centre close to the side wall can be seen. The numerical results from calculations using the full finite element model and the software Abaqus are in good agreement with the results using the multibody software Simpack and the
hybrid model. At the car centre the vertical bending as well as the diagonal distortion have a major influence on the transfer function. In Fig. 8 also results for the simulated transfer function on the floor above the bogie close to the side wall are shown. On the floor above the bogie the torsion of the car body has a significant influence in addition to the vertical bending. Using Simpack the frequency response modes have been used for the calculation. In Fig. 9 the influence of the frequency response modes on the transfer function can be seen. Shown are the results with and without using frequency response modes. The use of the frequency response modes leads to a frequency shift and improves the accuracy for the model, if attachments are involved. To predict the ride comfort of the intermediate car, simulations of the vehicle running on a track with irregularities have been performed. For different travelling speeds the accelerations on the floor of the car body have been calculated. As a result, frequency weighted rms values can be seen in Fig. 11. For a travelling speed of 80 km/h frequency spectrums of the vertical accelerations have been calculated for different
Fig. 11. Simulated and measured vertical and lateral accelerations (rms) on the floor at the car centre close to the side wall.
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floor positions. In Fig. 10 the simulated frequency spectrum of the vertical acceleration on the floor at the car centre close to the side wall is shown. Also the simulated frequency spectrum of the vertical acceleration on the floor above the bogie close to the side wall is shown in Fig. 10. In addition to the rigid body eigenfrequencies of the bogies the eigenfrequencies of the elastic car body structure are clearly visible.
vehicle shown in Fig. 1 have been performed. In Fig. 11 the frequency weighted vertical and lateral accelerations on the floor at the car centre close to the side wall measured at different forward velocities of the train are shown as rms values. In Fig. 11 also results from the simulation of the virtual vehicle system are drawn. Both, simulated vertical and lateral accelerations are in good agreement with the measured data.
5. Experimental results
6. Conclusions
5.1. Car body shell
Working with the model database saves time and cost during the virtual development process. Complex structural dynamics calculations for predicting the ride comfort of the vehicle system have been automated. Since the numerical results of the virtual intermediate car are in good agreement with the measured data from the hardware, the virtual system can now be used for a further optimisation of the ride comfort for the real metro train. Well verified additional components will be modelled and know-how will be gathered and stored in the company specific database of the virtual metro train. Also other vehicle concepts will be built virtually using the developed database concept. With the use of the automated assembling process vehicles and train combinations can be assembled very fast to be ready for predicting the structural dynamics and the ride comfort.
To improve the modelling technique an experimental modal analysis has been performed using a real prototype car body structure. For the car body shell of the intermediate car the following eigenmodes have been measured, which are in good agreement with the calculated results: Mode no.
Frequency (Hz)
1 2 3 4 5 6 7
16.0 17.4 19.8 21.8 22.4 29.7 29.2
Diagonal distortion Body shell breathing Vertical bending Torsion Body shell breathing 2 Diagonal distortion 2 Vertical bending 2
5.2. The fully assembled intermediate car As a next step, an experimental modal analysis for the fully assembled intermediate car body structure has been done. The following eigenmodes have been measured: Mode no.
Frequency (Hz)
1 2 3 4 5
10.3 11.6 12.8 16.5 17.5
Vertical bending, A Diagonal distortion Vertical bending, B Torsion Torsion
In addition to the eigenfrequencies the damping values for the different eigenmodes have been measured. It has been found, that the diagonal distortion mode is less damped than the vertical bending mode. For the torsion mode the damping is higher than for the bending mode. To evaluate the virtual vehicle system also hardware measurements of the ride comfort using the prototype
References [1] Dietz S. Vibration and fatigue analysis of vehicle systems using component modes. Fortschritt-Berichte VDI, Reihe 12 Nr. 401; 1999. [2] Intec GmbH. SIMPACK Users Manuals. Homepage http://www. simpack.de. [3] Fuehrer C, Leimkuhler BJ. Numerical solution of differential-algebraic equations for constrained mechanical motion. Numerische Mathematik 1991;59:55–69. [4] Kalker JJ. A simplified theory for non-Hertzian contact. Proceedings of the Eighth IAVSD-Symposium, Cambridge, USA, Amsterdam: Swets & Zeitlinger; 1983. [5] Rulka W. Effiziente Simulation der Dynamik mechatronischer Systeme fu¨r industrielle Anwendungen. Doctoral Dissertation. Vienna University of Technology; 1998. [6] Stribersky A, Steidl S, Mu¨ller H, Rath B. In: Segel L, editor. On dynamic analyses of rail vehicles with electronically controlled suspensions. Proceedings of the 14th IAVSD-Symposium, Ann Arbor, Amsterdam: Swets & Zeitlinger; 1995. p. 614– 28. [7] Stribersky A, Rulka W, Netter H, Haigermoser A. Modeling and simulation of advanced rail vehicles. In: Papageorgiou M, Pouliezos A, editors. Preprints of the Eighth IFAC/IFIP/IFORS Symposium on Transportation Systems, Chania, Greece, vol. 12; 1997. p. 476–81.
