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
Development of a formulation for the accurate description of fully 3D track geometries
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)
Development of a formulation for the accurate description of fully 3D track geometries
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)
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
Development of a formulation for the accurate description of fully 3D track geometries
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)
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
Description of 3D Track GeometriesParameterization of Track Irregularities
• Longitudinal Level
Description of 3D Track GeometriesParameterization of Track Irregularities
LLL
LLR
• Gauge G and Cant Angle ϕ
G
D
W
h
ϕHorizontal plane
Outer rail
Inner rail
Description of 3D Track GeometriesParameterization of Track Irregularities
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
Development of a formulation for the accurate description of fully 3D track geometries
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)
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
Interpolation with Cubic Splines
Shape Preserving 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
Interpolation with Cubic Splines
Shape Preserving 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
Development of a formulation for the accurate description of fully 3D track geometries
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)
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
Development of a formulation for the accurate description of fully 3D track geometries
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)
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
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)
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
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)
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
Traveled Distance [m]
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
Traveled Distance [m]
Late
ral D
ispl
acem
ent [
m]
V = 30 m/s (108 Km/h) V = 50 m/s (180 Km/h) V = 70 m/s (252 Km/h)
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
Traveled Distance [m]
Late
ral D
ispl
acem
ent [
m]
V = 60 m/s (216 Km/h) V = 61 m/s (220 Km/h) V = 62 m/s (223 Km/h)
Dynamic Analysis of ML95 VehicleSmall Radius Curved Track
Simulation:• V0 = 36 Km/h• Curve: R = 200 m• Flange contact
during curve negotiation
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)
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
Dynamic Analysis of ML95 VehicleComparison Commercial Software ADAMS/Rail
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
Dynamic Analysis of ML95 VehicleComparison Commercial Software ADAMS/Rail
-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
Dynamic Analysis of ML95 VehicleComparison Commercial Software ADAMS/Rail
-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
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)
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
Dynamic Analysis of ML95 VehicleComparison with Experimental Data
• 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
Dynamic Analysis of ML95 VehicleComparison with Experimental Data
-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
Dynamic Analysis of ML95 VehicleComparison with Experimental Data
• 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
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)
• 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
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