a multibody methodology for railway dynamics applications · joão carlos pombo...

João Carlos [email protected]

Desenvolvimento de uma Ferramenta Computacional para a Análise

Dinâmica de Veículos Ferroviários

28 de Maio de 2007

10º Ciclo de Palestras em Engenharia Civil/UNIC 2007Faculdade de Ciências e Tecnologia – Universidade Nova de LisboaUNIC - Centro de Investigação em Estruturas e Construção da UNL

A Multibody Methodology for Railway Dynamics Applications

Motivation1999 – 2000: PEDIP ProjectResearch project in Dynamics of Railway Vehicles promoted by ADtranz/Portugal with the following partners:

Divisão SOREFAME

PORTUGAL

REFER EP

Rede Ferroviária Nacional

ADtranz/Portugal - Portuguese Rolling Stock ManufacturerIDMEC/Instituto Superior TécnicoMetropolitano de Lisboa - Lisbon Subway CompanyCP - Portuguese Railway CompanyREFER - National Railroad Company

Motivation

Development of methodologies to build computational models of railway vehicles using a commercial program

Perform experimental tests in order to validate the computational results

Some objectives of the PEDIP Project

Commercial Program ADAMS/Rail

MotivationLimitations found in the commercial program

Its application is basically limited to horizontal tracks

Does not allow to study the lead and lag contact

Development of a formulation for the accurate description of fully 3D track geometries

Investigate the railway vehicle performance by implementing a methodology that includes:

Motivation for the present work:

• Parameterization of the wheel and rail surfaces• Accurate location of the wheel-rail contact points• Study the problem of two points of contact (flange

contact), including the lead and lag contact configuration


Parameterisation of each rail as a separate body to account for their relative motion due to track irregularities

Implementation of a methodology for the accurate description of the wheel and rail surfaces

Development of a formulation to obtain the location of the wheel-rail contact points

Calculation of the normal and tangential (creep) forces that develop in the wheel-rail interface

Objectives (1/2)

Build a computational model of the trailer vehicle of the ML95 trainset, which is used by Lisbon subway company for transportation of passengers

Demonstration of the methodologies through application to the dynamic analysis of the ML95 vehicle in different operation scenarios

Discussion of the dynamic analyses results by comparison with those obtained with:

Conclusions and future developments

• Commercial program ADAMS/Rail• Experimental testing

Objectives (2/2)






Objectives (1/2)

Description of 3D Track GeometriesParameterization of the Track Centerline

…..…..…..…..…..…..…..…..

Cant Anglezyx

User Input Data to Parameterize the Track Centerline

Track Centerline Parameterization as a Function of the Track Length

Parameterisation with Cubic Splines

Parameterisation Shape Preserving Splines

Parameterisation with Akima Splines

A parametric cubic curve is defined as:

P4 P5

P3

P2

P1

P6

y

z

x

3 23x 2x 1x 0x

3 23y 2y 1y 0y

3 23z 2z 1z 0z

( ) = a + a + a + a( ) = a + a + a + a( ) = a + a + a + a

x u u u uy u u u uz u u u u

⎧⎪⎨⎪⎩

3 23 2 1 0( ) = + + + u u u ug a a a a

Description of 3D Track GeometriesTrack Parameterization with Cubic Splines

The algebraic coefficients a i can be written in terms of the segments boundary conditions. In this sense, each spline segment is given by:

( )( )( )

( )( )

1 00

2 01

3 12

n-1 n-3n-2

n-1 n-2n-1

3 - '2 13 - '1 4 13 - '1 4 1

=

3 - '1 4 13 - '1 2

⎧ ⎫⎧ ⎫⎡ ⎤⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥ ⎪ ⎪ ⎪ ⎪

⎨ ⎬ ⎨ ⎬⎢ ⎥⎪ ⎪ ⎪ ⎪⎢ ⎥⎪ ⎪ ⎪ ⎪⎢ ⎥⎪ ⎪ ⎪ ⎪⎢ ⎥

⎢ ⎥ ⎪ ⎪ ⎪ ⎪⎣ ⎦ ⎩ ⎭ ⎩ ⎭

g ggg ggg gg

g ggg gg

MMO

{ }3 2

2 -2 1 1 (0)-3 3 -2 -1 (1)

( ) = 10 0 1 0 '(0)1 0 0 0 '(1)

u u u u

⎡ ⎤ ⎧ ⎫⎢ ⎥ ⎪ ⎪⎪ ⎪⎢ ⎥ ⎨ ⎬⎢ ⎥ ⎪ ⎪⎢ ⎥ ⎪ ⎪⎣ ⎦ ⎩ ⎭

gg

ggg

The spline derivatives are calculated to ensure C 2 continuity between segments. For natural cubic splines they are obtained as:

• DISADVANTAGE: Algorithm introduces undesired oscillations in track model

Description of 3D Track GeometriesTrack Parameterization with Cubic Splines

The pre-processor uses the routine DCSAKM, from IMSL Fortran 90 math library, to compute the Akima splines that interpolate the sets of points (ui, xi), (ui, yi) and (ui, zi). The parametric curve obtained consists of three piecewise cubic polynomials defined as:

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

2 33 41 2

2 3 13 41 2

2 33 41 2

+ + + 2 6

( ) = = + + + ;

2 6

+ + + 2 6

x xx x i ii i i i i

y yi iy y i i

i i i i i

z zz z i ii i i i i

c cc c u u u u u ux( u )

u u uc cu y( u ) c c u u u u u ui = 1,

z( u )c cc c u u u u u u

+

⎧ ⎫− − −⎪ ⎪

⎪ ⎪⎧ ⎫≤ <⎪ ⎪⎪ ⎪ − − −⎨ ⎬ ⎨ ⎬

⎪ ⎪ ⎪ ⎪⎩ ⎭ ⎪ ⎪

− − −⎪ ⎪⎩ ⎭

g ... , N 1−

• ADVANTAGE:No unwanted oscillations, from the original track geometry, are introduced by the Interpolation algorithm.

• DISADVANTAGE:Only ensures C1 continuity between spline segments and the continuity of the centerline curvature is not ensured.

Description of 3D Track GeometriesTrack Parameterization with Akima Splines

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

2 33 41 2

2 33 41 2

2 33 41 2

+ + + 2 6

( ) = = + + + 2 6

+ + + 2 6

x xx x x x xi ii i i i i

y yj jy y y y y

j j j j j

z zz z z z zk kk k k k k

c cc c u u u u u ux( u )

c cu y( u ) c c u u u u u u

z( u )c cc c u u u u u u

⎧ ⎫− − −⎪ ⎪

⎪ ⎪⎧ ⎫⎪ ⎪⎪ ⎪ ⎪ ⎪− − −⎨ ⎬ ⎨ ⎬

⎪ ⎪ ⎪ ⎪⎩ ⎭ ⎪ ⎪

− − −⎪ ⎪⎪ ⎪⎩ ⎭

g 1

1

1

; ; ;

x xi i xy yj j yz z

k k z

u u u i = 1, ... , N 1u u u j = 1, ... , N 1u u u k = 1, ... , N 1

+

+

+

⎧ ≤ < −⎪ ≤ < −⎨⎪ ≤ < −⎩

The pre-processor uses the routine DCSCON, from IMSL Fortran 90 library, to compute the shape preserving splines that interpolate the sets of data points (ui, xi), (ui, yi) and (ui, zi). The parametric curve obtained consists of three piecewise cubic polynomials as:

• ADVANTAGES:– Is consistent with the concavity of the data, preserving convex and

concave regions imposed by the control points.– Guarantees C2 continuity between spline segments, ensuring that the

parameterized curve has a continuous curvature.

Description of 3D Track GeometriesTrack Parameterization Shape Preserving Splines

• Coordinates of a point in a parametric curve

( )( ) ( )

( )

x uu y u

z u

⎧ ⎫⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

≡ =g g

u

u=

gtg

uu uuu u

2u

.

= − =

g g kk g g ; nk g

= ×b t n

Rectifying plane

Osculating plane

Normal plane

nr

br

tr

Description of 3D Track GeometriesProperties of Parametric Curves – Frenet Frames

• Principal unit normal vector

• Unit tangent vector

• Binormal vector

Description of 3D Track GeometriesTrack Centerline Geometric Information

Once the track centerline is parameterized, it is possible to obtain the following information as a function of the track length, L:

( )( ) ( )

( )

x LL y L

z L

⎧ ⎫⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

=g

• Coordinates of a point in the parametric curve

• Frenet frames associated to the parametric curve

( ) L=t t

( ) L=b b

( ) L=n n

Unit tangent vector

Unit normal vector

Unit binormal vector

Track Centerline

y

z

x

L

br

nr

tr( )Lg

Description of 3D Track GeometriesCant Angle ContributionThe pre-processor automatically accounts the contribution of the track cant for the calculation of the curve geometry.The cant angle is defined as the angle between vector n and the osculating plane, measured in the normal plane :

The new components of the Frenet frame (tc, nc, bc), after the rotation:

( ) ( )( ) ( )

= = cos sin

= sin + cos

c

c

c

⎧⎪ −⎨⎪⎩

t tn n bb n b

ϕ ϕϕ ϕ

y

z

x

L br

nrcbur

ct t≡r ur

cnuur

ϕ

Track Centerline

( )Lg

x

yz

• Track Geometry:

Description of 3D Track GeometriesApplication Example – Roller Coaster Model

Development of a general rail track kinematic joint to prescribe the spatial displacement and orientation of the vehicles wheelsets over the track

• Implementation Needs:

General Rail Track JointConstraint the Wheelset wrt Track Centerline

A certain point, of a rigid body, has to follow a reference path

The spatial orientation of body remains unchanged wrt to the moving Frenet frame (t, n, b) associated to the reference curve

• Prescribed Motion Constraint

• Local Frames Alignment Constraint

g(L)

y

z

x

L

P

η i

ζ i

ξ iirr

Pisr

Pirr

g(L)L

η iζ i

ξ i

tr

br

nr

uξ

uuruζ

uur

uη

uur

P

Table that stores all parameters necessary to define the geometric characteristics of the track and the rail track joint

The parameters are organized in 37 columns and as a function of the track length, L

…..…..…..…..…..…..…..…..…..…..…..…..…..

…..…..…..…..…..…..…..…..…..…..…..…..…..

…..…..…..…..…..…..…..…..…..…..…..…..0.10

…..…..…..…..…..…..…..…..…..…..…..…..0.05

…..…..…..…..…..…..…..…..…..…..…..…..0.00

…..txzyxL2

z2

d bdL

x2

2ddL

y2

2ddL

z2

2ddL

zddL

yddL

xddL

Roller Coaster ModelConstruction of the Track Centerline Database

• z Cartesian coordinates of the roller coaster model:

Cubic splines parameterization leads to oscillations in the transition between the straight segment and the circular segment

79,988

79,990

79,992

79,994

79,996

79,998

80,000

80,002

28 29 30 31 32 33 34 35

L (m)

z (m

)

Cubic Splines

A kima Splines

Shape Preserv ing

Roller Coaster ModelTrack Model

• Conclusion:

1067.6 m4.9×10-22m 42s2 ms51 seg.Cubic Splines

1067.5 m4.9×10-22m 28s2 m/s51 seg.Shape Preserving

1065.5 m3.3×10-12m 38s2 m/s51 seg.Akima Splines

Travelled Distance

Constraint Violations

CPU Time

Initial Velocity

Analysis TimeTrack Model

Akima splines parameterization produces maximum constraint violations almost 10 times higher than the other interpolation schemes.

• Comparative parameters of dynamic analysis performed in the track model with control points increment of 1 m:

Roller Coaster ModelDynamic Analysis

The results obtained using Akima splines for track parameterization are not satisfactory

• Conclusion:

• Rear wheelset acceleration in z direction:

Roller Coaster ModelDynamic Analysis

-30

-20

-10

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45 50

Time (s)

Acc

eler

atio

n in

Z D

irect

ion

(m/s

2 ) Cubic SplinesShape Preserving

Good agreement between the results obtained for the track modelsparameterized with cubic and shape preserving splines

• Conclusion:

x

yz

Roller Coaster ModelAnimations from Dynamic Analysis






Objectives (1/2)

Description of 3D Track GeometriesParameterization of Track Irregularities

…..…..…..

Gauge variation

…..…..…..

LL R

…..…..…..

LL L

…..…..…..

AL R

…..…..…..

AL L

…..…..…..1.0…..0.0

Cant variationL

User Input Data to Parameterize the Track Irregularities

Track Irregularities Parameterization as a Function of the Track Length

Interpolation with Cubic Splines

• Track Alignment

AL L

AL R


• Longitudinal Level


LLL

LLR

• Gauge G and Cant Angle ϕ

G

D

W

h

ϕHorizontal plane

Outer rail

Inner rail


Once the track irregularities are parameterized, it is possible to obtain the irregularities parameters as a function of the track length, L

( ) R RAL AL L=Alignment left rail ( ) L LAL AL L=

( ) R RLL LL L=

( ) Lϕ ϕΔ = Δ

( ) L LLL LL L=

( ) G G LΔ = Δ

Alignment right rail

Long. level left rail Long. level right rail

Gauge variation Cant angle variation

y

z

x

L

Track Centerline

Notice that the cant angle variation is added to the nominal track cant before the calculation of the cant angle contribution for the track model.

Description of 3D Track GeometriesTrack Irregularities Information

Description of 3D Track GeometriesParameterization of each Rail Space Curve

Nodal Points that Define the Space Curves for the Left and Right Rails

Left and Right Rails Space Curves Parameterized as Function of their

Respective Arc Lengths

Parameterisation with Cubic Splines

Parameterisation Shape Preserving Splines

Parameterisation with Akima Splines

RIGHT RAIL DATABASELEFT RAIL DATABASE

Description of 3D Track GeometriesNodal Points for Left and Right Rail Space Curves

The control points that characterize the geometry of the space curves for the left and right rails are given by:

cnr

ctrcb

r

L

Prr

QP

Qrr rr

PsrQsr

z

yx

'Q Q= +r r A s

'P P= +r r A s

( ) ( ) ( ) c c cL L L⎡ ⎤⎣ ⎦= t n bA

Left rail

Right rail

where:

( )L=r g

0

2 2'P R

R

D GAL

LL

⎧ ⎫⎪ ⎪Δ⎪ ⎪− + −⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

=s

0

2 2'Q L

L

D GAL

LL

⎧ ⎫⎪ ⎪Δ⎪ ⎪+ +⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

=s

Once the left and right rail space curves are parameterised, it is possible to obtain the necessary geometric information for both rails as function of the length of each rail:

( )L L LL=g g

• Coordinates of a point in the parametric curves

• Frenet frames associated to the parametric curves

Rnr

Rtr

Rbr

LL RL

z

yx

Lnr Ltr Lb

r

LgRg

( )R R RL=g g

( )L L LL=t t ( )R R RL=t t

( )L L LL=n n ( )R R RL=n n

( )L L LL=b b ( )R R RL=b b

Description of 3D Track GeometriesLeft and Right Rails Geometric Information

• The direct use of the equations obtained from the parametric descriptions of the rails space curves is neither practical nor computationally efficient

• A pre-processor is developed in order to make all necessary calculations that are required to define the left and right rails geometric parameters

• The information is stored in two databases, as function of the length of each rail, and is used by the multibody code

…..…..…..…..…..…..…..…..…..…..…..…..…..

…..…..…..…..…..…..…..…..…..…..…..…..0.2

…..…..…..…..…..…..…..…..…..…..…..…..0.1

…..…..…..…..…..…..…..…..…..…..…..…..0.0

bzbybxnznynxtztytxzyxL

Description of 3D Track GeometriesDatabases for the Left and Right Rails

User

Input Data to Parameterize the Track Centerline

Cubic Splines

Akima Splines

Cubic Splines

Shape Preserving Splines

Input Data to Parameterize the Track Irregularities

Track Centerline Parameterized as a Function of the Track Length

Track Irregularities Parameterized as a Function of the Track Length

Obtain the Nodal Points that Define the Space Curves for the Left and Right Rails

Cubic Splines Shape Preserving Splines Akima Splines

Left and Right Rails Space Curves Parameterized as Function of their Respective Arc Lengths

LEFT RAIL DATABASE RIGHT RAIL DATABASE

Description of 3D Track Geometries






Objectives (1/2)

Description of the Rail SurfaceRail Profile Parameterization

Notice that this formulation allows using rail profiles with arbitrary geometries that can be obtained from direct measurements

Nodal Points

rζ

rη

ru

( )r rf u

User Coordinates of Nodal Points

Interpolation with Akima Splines



RAIL PROFILE PARAMETERIZATION

( )r rf u

'P PRr Rr Rr= +r r A s

( ) ( ) ( ) R R RRr Rr Rr Rrs s s

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

= t n bA

where:

Coordinates of a point on the rail surface:

( )RRr Rrs=r g

( ){ } 0 ' TPRr Rr r Rru f u=s

Rrsz

yx

Rnr

Rtr

Rbr

RrrrPrr

P

The rail surface is obtained by translating the two dimensional curve that defines the rail profile

Description of the Rail SurfaceArbitrary Rail Surface

P

Rbr

Rnr

PRrsr

Rru

( )r Rrf u

Description of the Wheel SurfaceWheel Profile Parameterization

Notice that this formulation allows using wheel profiles with arbitrary geometries that can be obtained from direct measurements

Nodal Points

wζ

wη

( )w wf u

wu

User Coordinates of Nodal Points

Interpolation with Akima Splines



WHEEL PROFILE PARAMETERIZATION

( )w wf u

The wheel surface is a surface of revolution obtained by a complete rotation, about the wheel axis, of the two dimensional curve that defines the wheel profile.

( ) ' 'P P Pws ws ws ws ws Rw Rw Rw= + = + +r r A s r A h A s

( ) ( )

( ) ( )

cos 0 sin 0 1 0

sin 0 cos

Rw Rw

Rw

Rw Rw

s s

s s

⎡ ⎤− −⎢ ⎥−⎢ ⎥⎢ ⎥−⎣ ⎦

=A

Coordinates of a point on wheel surface:

( ){ } 0 ' TPRw Rw w Rwu f u=s

, ws wsAr - Obtained Multibody Formulation

0 0 2

T

RwH⎧ ⎫−⎨ ⎬

⎩ ⎭=h

z

y

x

Rwζ

Rwη

PRwsr

P

Rwξ

( )w Rwuf

wsrr

Prr

wsζ

wsηwsξ

Rws

Rwu

Rwhr

Description of the Wheel SurfaceArbitrary Wheel Surface






Objectives (1/2)

Wheel-Rail Contact PointsLocation of the Wheel-Rail Contact Points

Formulation to search for the possible contact points between two parametric surfaces p(u,w) and q(s,t)

= 0 =

= 0

T uj i

j i T wj i

⎧⎪× ⇒ ⎨⎪⎩

n t0

tn n

n

Geometric equations for the possible contact points:

= 0 =

= 0

T ui

i T wi

⎧× ⇒ ⎨

⎩

d t0

d td n

Obtain the 4 surface parameters u, w, s, t

(4 equations)z

yx

( ),p u wr

( ),q s tr

inr

jnr

dr

uitr

witr

tjtr

sjtr

( )i

( )j

• The formulation to obtain the location of the wheel-rail contact points requires convex parametric surfaces

• The wheel profile is represented by two independent functions for the wheel tread and wheel flange

• The concave region in the wheel surface is neglected

Wheel-Rail Contact PointsRestriction to Convex Surfaces

Concave Region

wζwη

( ) tw wf u

wu

( ) fw wf u

vr Flange Contact

Tread Contact

vr

rω

Lead Contact

Flange Contact

Tread Contact

vr

vr

rω

Radial Position

Flange Contact

Tread Contact

vr

vr

rω

Lag Contact

Wheel-Rail Contact PointsThe Two Points of Contact Scenario

• The methodology allows the detection of two points of contact

• Takes advantage of the fact that the wheel profile is represented by two different functions






Objectives (1/2)

Wheel-Rail Contact ForcesNormal Contact Force

The normal contact force model includes:• Hertzian component that is a function of the indentation• Hysteresis damping component proportional to the

velocity of indentation

( )2n

( )

3 1= 1+

4e

N K δ δδ −

⎛ ⎞−⎜ ⎟⎜ ⎟⎝ ⎠

&

&

N

δ

Loading

Unloading

Energy LossN

, Mφφ

ζη ξvr

ξυFξ

ηυ

Fη

Contact Area

Three different formulations are implemented in order to calculate the creep (tangential) forces that develop in the wheel rail interface.

Wheel-Rail Contact ForcesTangential (Creep) Force Models

Kalker Linear Theory

11

22 23

23 33

0 0

G 0

0

cFF ab c ab cM ab c ab c

⎡ ⎤⎧ ⎫ ⎧ ⎫⎢ ⎥⎪ ⎪ ⎪ ⎪= −⎨ ⎬ ⎨ ⎬⎢ ⎥

⎪ ⎪ ⎪ ⎪⎢ ⎥− ⎩ ⎭⎩ ⎭ ⎣ ⎦

ξ ξ

η η

φ

υυφ

Heuristic Nonlinear

Model

2 31 1 ; 33 27

; 3

F F FN F NF N N N

N F N

⎧ ⎡ ⎤′ ′ ′⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ′⎪ − + ≤⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟= ⎨ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦⎪

′ >⎩

υ υ υυ

υ

υ

μ μμ μ μ

μ μ

Polach Formulation

; c c c

F F F F F= = +ξ ηξ η ηφ

υ υ φυ υ υ






Objectives (2/2)

MotorTrailerMotor MotorTrailerMotor MotorTrailerMotor

Trailer Vehicle of ML95 TrainsetTrainset

Vehicle used by Lisbon Subway

Company

Carbody(Rigid body)

Front Wheelset(Rigid body)

Revolute joints

Front Axle-boxes(Rigid body)

Primary Suspension

Rear Wheelset(Rigid body)

Revolute joints

Rear Axle-boxes(Rigid body)

Primary Suspension

Front Bogie Frame(Rigid body)

Secondary Suspension

Track

Front Wheelset(Rigid body)

Revolute joints

Front Axle-boxes(Rigid body)

Primary Suspension

Rear Wheelset(Rigid body)

Revolute joints

Rear Axle-boxes(Rigid body)

Primary Suspension

Rear Bogie Frame(Rigid body)

Secondary SuspensionRear Bogie Front Bogie

Trailer Vehicle of ML95 TrainsetSchematic Representation

Bogie Frame

Chevron Springs

Axle-box

Liftstop

Bumpstop

Wheelset

Trailer Vehicle of ML95 TrainsetPrimary Suspension

Bogie elements:• 1 Bogie frame• 2 Wheelsets• 4 Axle-boxes

• 8 Chevron springs• 4 Bumpstops• 4 Liftstops

Trailer Vehicle of ML95 TrainsetPrimary Suspension Multibody Model

Bogie Model: • 5 Rigid bodies• 2 Revolute joints

• 8 Horizontal spring-damper elements• 4 Lateral spring-damper elements• 4 Vertical spring damper elements

xK

xC

xK

xC

yKyC

zK zC

Vertical Damper

BumpstopBogie Frame

Carbody

Liftstop Airspring

Trailer Vehicle of ML95 TrainsetSecondary Suspension

• 1 Carbody• 2 Bogies• 4 Airsprings

• 4 Vertical dampers• 4 Bumpstops• 4 Liftstops

Elements:

Trailer Vehicle of ML95 TrainsetSecondary Suspension Multibody Model

Model:• 1 Carbody• 2 Bogie frames• 4 Vertical dampers

• 4 Horizontal airspring models• 4 Lateral airspring models• 4 Vertical airspring models

Carbody

Bogie Frame

zC

zK zC

xK

xCyK

yC

Traction Rod

Center Plate

Carbody Pivot

Bogie Frame

Lateral Damper

Lateral Bumpstop

Trailer Vehicle of ML95 TrainsetBogie-Carbody Connection

Elements:• 2 Carbody pivots• 2 Center plates• 4 Traction rods

• 4 Lateral dampers• 4 Lateral bumpstops

Trailer Vehicle of ML95 TrainsetMultibody Model of Bogie-Carbody Connection

Model• 4 Long. springs• 4 Lat. dampers

Bogie Frame

Longitudinal Springs

Center Plate

Carbody

Lateral Damper

Vertical Damper






Objectives (2/2)

Dynamic Analysis of the WheelsetStraight Track

According to stability theory of railway vehicles, an unsuspended wheelset is always unstable due to hunting

Initial forward speed of 54 Km/h

NoYes19 sec.PolachNoYes19 sec.HeuristicYesYes19 sec.Kalker

DerailmentFlange Contact

Analysis Time

• Initial forward velocity of 54 Km/h• Creep forces by the Kalker Linear Theory• Flange contact and derailment during dynamic analysis

Dynamic Analysis of the WheelsetStraight Track

Dynamic Analysis of the WheelsetSmall Radius Curved Track

Flange contactFlange contact

Flange contact / DerailmentV = 54 Km/h

Flange contactPolachFlange contactHeuristic

Flange contact / DerailmentKalkerV = 36 Km/h

Heuristic / PolachKalker Linear Theory

Dynamic Analysis of the Single BogieStraight Track

NoNoNo

V = 72 Km/h

YesNoPolachYesNoHeuristicYesNoKalker

V = 180 Km/hV = 36 Km/h

Flange contact for velocities of 36, 72 and 180 Km/h

-0.009

-0.006

-0.003

0.000

0.003

0.006

0.009

0 40 80 120 160 200 240 280

Traveled Distance [m]

Late

ral D

ispl

acem

ent [

m]

V = 10 m/s (36 Km/h) V = 20 m/s (72 Km/h) V = 50 m/s (180 Km/h)

Dynamic Analysis of the Single BogieStraight Track – Stability Critical Speed

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0 40 80 120 160 200 240 280


Late

ral D

ispl

acem

ent [

m]

V = 30 m/s (108 Km/h) V = 38 m/s (137 Km/h)

V = 39 m/s (140 Km/h) V = 40 m/s (144 Km/h)

• 108, 137 Km/h: Wheelset decaying oscillation leading to center of track• 144 Km/h: Initial amplitude increases leading to unstable running• 140 Km/h: Hunting motion with zero decay rate – CRITICAL SPEED

Dynamic Analysis of the Single BogieSmall Radius Curved Track

Flange contactFlange contact

Flange contact / DerailmentV = 72 Km/h

Flange contactPolachFlange contactHeuristic

Flange contact / DerailmentKalkerV = 36 Km/h

Heuristic / PolachKalker Linear Theory

Dynamic Analysis of the Single BogieSmall Radius Curved Track

Lateral flange forces on both wheels of the leading wheelset for velocity of 36 Km/h, using the Polach creep force model

-1000

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 3 6 9 12 15 18 21 24 27 30

Time [s]

Late

ral F

lang

e Fo

rce

[N]

Left Wheel (Polach)

Right Wheel (Polach)

Dynamic Analysis of ML95 VehicleStraight Track

NoNoNo

V = 180 Km/h

YesNoPolachYesNoHeuristicYesNoKalker

V = 252 Km/hV = 108 Km/h

-0.009

-0.006

-0.003

0.000

0.003

0.006

0.009

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280


Late

ral D

ispl

acem

ent [

m]


Flange contact for velocities of 108, 180 and 252 Km/h

Dynamic Analysis of ML95 VehicleStraight Track – Stability Critical Speed

• 216 Km/h: Wheelset decaying oscillation leading to center of track• 223 Km/h: Initial amplitude increases leading to unstable running• 220 Km/h: Hunting motion with zero decay rate – CRITICAL SPEED

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300


Late

ral D

ispl

acem

ent [

m]


Dynamic Analysis of ML95 VehicleSmall Radius Curved Track

Simulation:• V0 = 36 Km/h• Curve: R = 200 m• Flange contact

during curve negotiation






Objectives (2/2)

Dynamic Analysis of ML95 VehicleComparison Commercial Software ADAMS/Rail

-4000

-3000

-2000

-1000

0

1000

2000

3000

0 5 10 15 20 25 30

Time [s]

Late

ral W

heel

For

ce [N

]

Left Wheel - ADAMS/Rail

Left Wheel - DAP-3D

• Straight track with measured track irregularities• Lateral contact forces on left wheel of leading wheelset


17000

19000

21000

23000

25000

27000

29000

31000

0 5 10 15 20 25 30

Time [s]

Ver

tical

Whe

el F

orce

[N]

Left Wheel - ADAMS/RailLeft Wheel - DAP-3D

• Straight track with measured track irregularities• Vertical contact forces on left wheel of leading wheelset


-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25 30

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

ADAMS/RailDAP-3D

• Straight track with measured track irregularities• Lateral accelerations on carbody of ML95 trailer vehicle


-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 5 10 15 20 25 30

Time [s]

Ver

tical

Acc

eler

atio

n [m

/s2 ]

ADAMS/RailDAP-3D

• Straight track with measured track irregularities• Vertical accelerations on carbody of ML95 trailer vehicle






Objectives (2/2)

Dynamic Analysis of ML95 VehicleComparison with Experimental Data

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 5 10 15 20 25 30

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

ExperimentalDAP-3D

• Straight track with measured track irregularities• Lateral accelerations on carbody of ML95 trailer vehicle


• Straight track with measured track irregularities• Spectra of the lateral accelerations on carbody

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Frequency [Hz]

Am

plitu

de

ExperimentalDAP-3D

Most meaningful frequencies of 0.9 Hz and 1.1 Hz


-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15 20 25 30

Time [s]

Ver

tical

Acc

eler

atio

n [m

/s2 ]

ExperimentalDAP-3D

• Straight track with measured track irregularities• Vertical accelerations on carbody of ML95 trailer vehicle


• Straight track with measured track irregularities• Spectra of the vertical accelerations on carbody

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Frequency [Hz]

Ampl

itude

ExperimentalDAP-3D

Most meaningful frequencies of 1.2 Hz and 1.7 Hz






Objectives (2/2)

• An appropriate procedure is developed for the general representation of realistic three-dimensional tracks suitable for the multibody simulation of railway vehicles

• The major drawback of the cubic splines formulation is that it leads to undesired oscillations in the track model

• Akima splines lead to high constraint violations in the transitions between parts of the track with different geometric characteristics

• The use of shape preserving splines leads to the best representation of spatial track geometries

• The methodology used to describe the wheel and rail surfaces is general, representing any spatial configuration and any wheel and rail profiles

Conclusions

• The formulation used to predict the location of the contact points allows to study the problem of two points of contact, including lead and lag contact

• The normal contact forces in the wheel-rail interface are calculated using an elastic force model

• The tangential contact forces are calculated using three distinct creep force models

• The application examples demonstrate that the methodology proposed here allows determining the maximum stability speed of a railway vehicle

• When running on a straight track, close to the critical speed, or on a small radius curved track flange contact is likely to occur

Conclusions

• When flange contact occurs, there are significant differences among the results obtained with the Kalker linear theory and the others force models

• The comparison of the results with experimental data and with the results from ADAMS/Rail, allows to conclude that the developed models and methodologies are qualitatively and quantitatively correct for straight tracks

• The formulation integrates, in an efficient way, the main requirements associated to the dynamic analysis of railway vehicles

Conclusions

Future Developments

• Inclusion of nonlinear springs and bumpstops, with user defined stiffness characteristics and clearances, when modeling the primary and secondary suspensions

• Definition and implementation of a detailed mathematical model to represent the airspring elements

• Description of the couplers that are usually used to interconnect the cars that compose a trainset

• Inclusion of the track flexibility effect in the track model

Future Developments

• Investigate how vehicle performance is sensitive to the different types of track irregularities

• Investigate the vehicle dynamic behavior in presence of worn wheel-rail profiles

• Improve the wheel-rail contact model in order to consider the concave region of the wheel surface for the identification of the contact points

• Development of a new contact forces algorithm that is able to deal with non-elliptical wheel-rail contact

• Build the multibody model of the UQE railway vehicle and perform its dynamic analysis on a curved track. Compare the results with those available from ADAMS/Rail and from experimental data

Present Research/Work

Present Research/Work•Post-doc researcher at IDMEC/IST in the project

EUROPAC – FP6/012440, “European Optimized Pantograph Catenary Interface”.

Present Research/WorkStudy of the Pantograph-Catenary Interaction

Tests in France

ALSTOM

2007/04/12

V = 570 km/h

World Record

Acknowledgements

The support of the Fundação para a Ciência e Tecnologia (FCT) through the PRAXIS XXI nº BD/18180/98, on “Métodos Avançados para Aplicação à Dinâmica Ferroviária” is gratefully acknowledged.

The support of the Fundação para a Ciência e Tecnologia(FCT) through the grant with the reference BPD/19066/2004 made this work possible and it is also gratefully acknowledged.

João Carlos [email protected]

Desenvolvimento de uma Ferramenta Computacional para a Análise

Dinâmica de Veículos Ferroviários

28 de Maio de 2007

10º Ciclo de Palestras em Engenharia Civil/UNIC 2007Faculdade de Ciências e Tecnologia – Universidade Nova de LisboaUNIC - Centro de Investigação em Estruturas e Construção da UNL

A Multibody Methodology for Railway Dynamics Applications

Thank you – Obrigado

a multibody methodology for railway dynamics applications · joão carlos pombo...

Documents