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DYNAVOIE : a reduced track model allowing long 3D simulation of train/track interaction.

Etienne Balmès, SDTools, Arts et Métiers ParisTech Patricia Ferreira, IST, Tecnico U. Lisboa Sofia Costa D'Aguiar, Emmanuel Laurans, SNCF RTSE Ballast : Issues & Challenges, Paris Dec 5-6, 2013

Why DynaVoie ?

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Objective 1 : non-linear time domain train/track interaction model

– Time integration necessary

– Wheel/rail contact model, non-linear pads, non-linear ballast difficult

– Boundary elements and infinite space approaches do not live with NL transients

– Full 3D is too large for design work

Why DynaVoie ?

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• Determination of properties – Initially : ballast as spring/dashpot but

identification of properties is difficult

– Retained : 3D model with elastic properties

• Size challenge – 1 slice 60 cm, quadratic = 25e3 DOF

– 200 m : 8 million DOF

– Storing : 20e3 steps ≈ 1 TB

• Proposed strategy – Cut track in sections

– Reduce slices based on periodic assumptions

– Compute transients using reduced slice model

– Output sampling and post-expansion

velocidadevelocidadevelocidadespeed

SDTools & Structural Dynamics Toolbox

NASTRAN

ABAQUS

ANSYS

UFF / IDEAS

SAMCEF

PERMAS

Simulink

IDEAS Test

Adams Tests MATLAB

OpenFEM FEMlink

SDT, Visco, Rotor, …

Simulation

Runtime SDT

FEM

Meshing

CAD

Key competences • Model reduction & periodic/cyclic problems • Transients with contact & friction • Damping (viscoelastic & friction) • Experimental modal analysis, system

modeling

Base meshing capabilities

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• Rail : beam/volume

• Pad : beam/volume

• Sleeper volume + beam

• Track : multilayer conform mesh – half, full, half double track, …

– Coarse to meshed

– Utilities to obtain quality meshes

Periodic solutions

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• Periodic solutions – Periodic geometry {u(nDx)} allows Fourier

transform

– Complex periodic solution on base cell

– with continuity constraints

Classical approach in cyclic symmetry Used for tracks by Chebli/Clouteau/Modaressi 2004

• Target solutions for DynaVoie – Static response to load on rail : wavelength

inf, 8 , 4, 8/3, 2 cells

– Dynamic vectors for propagating waves 5 and 50 cells

Reduction using periodic solutions

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• Reduction steps – Build a collection of periodic solutions

– Build orthogonal subspace basis T by solving

– Decompose mesh in main and interface superelements

– Use Rayleigh-Ritz reduction : T for main superelements T left/right for interface superelements

Validation/verification of static

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Track box section (ballasted track)

Maximum Rail vertical displacements

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 25 50 75 100 125 150 175 200

dz r

ail (

mm

)

Q/axle (kN)

Rail displacements

Measures Track Box Static 1

Measures Track Box Satic 2

ANSYS

Dynavoie

Verification of reduction

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Verification : are equations solved correctly

• Statics : Fourier recomposition

• Dynamics : dispersion curves

Compression

Compression Shear

Shear

Sensors

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• Translation

• Resultants

• Stresses/strains

• Selected places (test analysis correlation) or all sections (settling sensors, …)

• Dynamic observation limits memory

{y} = [cT] {qR}

• Work on interactivity important focus for usability

Handling non-linearities

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• Simple penalized rail/wheel contact

• Vehicle as superelement with possible non-linearities

• Non-linear pads

Secondary supension

Primary suspension

Axle

Train direction

Kb11 Cb11

Kc Cc

Vehicle (Mc)

Kb21 Cb21

Bogie (Mb)

Me1 Me2

x

z

q

y

𝜎𝑔 = Λ ε𝑔 +

0 0 00 0 00 0 𝜎𝑁𝐿𝑔(ε𝑧𝑧 )

0

0 0

Isolated stiffer pad

Localized non-linear pad

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• Chauconin, TGV Bogie, 1 stiffer pad

• Impact of localized NL quite clear in zlin-zNL

Vertical displacement, filtered

zlin-zNL in SubLayer

Sample performance

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• Chauconin section mesh – Linear : 2300 nds, 1700 elt, 5000 DOF

– Quad : 8500 nds, 1700 elt, 20 000 DOF

• Reduction – < 100 Hz : main ≈ 100 shapes, interface ≈ 200

– Linear in 21 s (5000 free DOF)

– Quad : 78s (20 000 free DOF)

• Transient – 200 slices = 120m

20335 reduced DOFs, full ≈4e6 DOF

– Implicit : 55e3 steps, dt=2.4e-5 s ≈ 30 mn

– At fs=500 Hz, def= 100 MB

0 1000 2000 3000 4000

0

1000

2000

3000

4000

[10333 x 10333, nnz = 2184574, nz = 2184574]

Model validation : IST objectives

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• Building up of current ballasted track (VB) track case

• Geometric mesh elements

• Physical and mechanical proprieties of track elements

• Validation of dynamic calculations of ballasted track

• Analysis of database of field measurements

• Statistical post processing of database

• Comparisons of calculated results with measured results

• Critical analysis of other type of track results

• Contributions to software evolution

• Assure accurate results

• Request of new features in software

• Work toward need of practical tool for daily railway engineering applications

CASE STUDY OF CHAUCONIN TRACK SITE

Case study : Chauconin track site

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• Current Ballast Track

• Transition Zone

• Slab Track

Field Measurements : under commercial train circulation

Site Characterisation

Accelerometers Displacements

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Available measurements CASE STUDY OF CHAUCONIN TRACK SITE

•Analysis of database of field measurements

•Statistical post processing of database

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Model properties CASE STUDY OF CHAUCONIN TRACK SITE

Building up of VB track case model in Dynavoie

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Sample modes CASE STUDY OF CHAUCONIN TRACK SITE

Current ballasted track section (VB)

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Rail vertical displacements in time

Dynamic results : rail, pad CASE STUDY OF CHAUCONIN, BALLASTED TRACK

Railpad vertical displacements and force

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Sleepers, ballast, … displacement

• Expected decrease in space (bottom of sleeper, ballast, sub-layer, two levels in soil)

CASE STUDY OF CHAUCONIN TRACK SITE

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Sleeper acceleration (test/FEM) BALLASTED TRACK AT CHAUCONIN

Sleeper vertical accelerations Time signals @ 100 Hz

Comparison of numerical / measured values

Earlier validations : PhD IST 2010, Patricia Ferreira : Modelling and prediction of the dynamic behaviour of railway infrastructures at very high speeds

Train passage i1 Train passage i2

Work in progress

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• Work on verification – Model convergence (refinement, slice size, …)

– Effect of inaccuracy on dispersion curves

– Strategies on damping modeling

– Reflections -> PML

• Extend/optimize software – Reactivate settling analysis (handled through

offset on zrail) with stress/deflection sensors

– Deal with parametric studies (effects of properties)

– Optimize performance and restitution

ddN

d

Work in progress

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• Ballastless track – configuration, mechanical properties and

target simulations

• Longitudinal stiffness variation – Multiple slices built into a track

– Ballast / Slab track transition zones