Rail Vehicles 2011

8/10/2019 Rail Vehicles 2011

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GraSMech Multibody 1

GraSMech course 2010-2011

Railway vehicle dynamics

Paul Fisette([email protected])


Contents

Part I : Wheel-rail contact in railway dynamics

Contact geometry

Contact forces

Wheelset dynamic behavior

Part II : Railway dynamics - multibody approach

Multibody representation

Wheel/rail contact independent wheel model

Flange contact model

Validations - Applications

Other topics


Contact geometry

Wheelset with conical wheel on knife-edge rails

Rolling radii :

Equivalent conicity :

Rolling radii difference (left-right) :

Roll angle :

( In practice : 0 ~ 1/20e 1/40e )

= r / 2y =>

Data : r0, l

0, 0


2/19


Contact geometry

Wheelset kinematic motion (~ first order kinematics)

Hypothesis : pure rolling motion (no slip)

Kinematic relations (first order)

Constraints (in yand ) :

Lateral (y) :

Yaw () :

Motion of a wheelset initiallycenteredo n the track

Combinedlateral-yawm otion of a wheelset

Given : V, (= V / r0 )


Contact geometry

2 d.o.f. kinematic equations(= constraintsat velocitylevel)

Periodic Solution :

frequency :

Wheelsetkinematicyaw (underpure rollingassumption)

Wheelset kinematic motion (next)

Wavelength:

(Klingelformula, 1883 !)

=> demo !


Contact geometry

Wavelength:

Bogie : yaw kinematic motion (similar reasoning)

l : halfwheelsetbase

l0

: half wheelset length

Wheel/rail with circular profiles (as a matter of interest)

More complex kinematics

Roll angle :

vertical disp.:

equiv. conicity :4 bar-mechanism


3/19


Contact geometry

=> Longitudinal shift of the contact point ( shift angle ) due to wheelsetyaw + wheelconicity

Wheel/rail contact : yaw angle influence on contact geometry

Insignificant for the tread contact point (angle ~ 0.05 rad)

Fundamental for the flange contact point (angle > 1 rad) : see latter on


Contact geometry

Real wheel profiles : numerical somution

Profile definition (analytical form or numerical measurements)

ex. UIC 60 rail (piecewise circular), S1002 wheel (piecewise polynomials)

Numerical determinationof the contact(s) point(s) = f (y, )

Pre-computation (look-up tables => f (y, ) )

In-line computation (Newton-Raphson, dichotomic method, see Part II)

Computation of the left/right rolling radii rand contact angles :

y y

r


Contact geometry

Double (flange) contact point

Tramway clear double contact (tread + flange)

Train the contact point moves fromtread to flange (with possible jump!!)

Alwayspresent

intermittent


4/19


Contact geometry

Double (flange) contact point

Tramway clear double contact (tread + flange)

Train the contact point moves fromtread to flange (with possible jump!!)

Alwayspresent


Contact geometry

Contact point jump

Exists on theoretical new profiles (ex. S1002 wheelset on UIC60 rail)

on produces:

Exists also on worn profile (but their location change with wear !)

New rail :

Slightly worn rail :

ROBOTRAN results

(IAVSD benchmark #1, 1991)


Contents


Contact geometry

Contact forces







Other topics


5/19


Contact forces

Coulombs law : No slip =>

Slip =>

Creepage ( between slip and pure rolling )

Longitudinal creepage :

Lateralcreepage :

Spin creepage :

with : Point of contact assumption !!!!!Vwheel


Contact forces

Creepage computation (not MBS approach !)


Lateralcreepage :

Spin creepage :


Contact forces

Contact surface

Non uniform pressure distribution

Contact ellipse (a, b)Hertz (but + creepage)

A, B, m, n depend on

contact curvature radii


6/19


Contact forces

Kalkers theory

Lineartheory

*

*

with :

Heuristic modelingof saturation :

Non linear theories : Duvorol, Fastsim (Kalker), Contact (Kalker), full FEM (2009 )


Contents


Contact geometry

Contact forces







Other topics



Linear model

Hypotheses :

suspended wheelset

Linearized equations of motion :

Solution :

=> Linear Critical speed VLim:

Hunting eigenmode

Eigenvalue versus speed :

Real ()

Im ()

or.:Jashinski thesis(Delft)

=> demo !


7/19



Linear model : example

ROBOTRAN/MBsysLab model :http://www.prm.ucl.ac.be/FDP/Tutorial/Medium/Bogie/Introduction.html

=> Comparison between linearnon linear model




y

=> Behavior at low and high velocity





=> Evolution of the hunting mode versus velocity

(via successive modal analyses)


stable

unstable Top view (Robotran)

Rear view(Robotran)


8/19


9/19


Demonstration in the Lab


Contents


Contact geometry

Contact forces

Wheelsetdynamicbehavior


Multibodyr epresentation

Wheel/rail contact independentwheel model


Validations -Applications

Other topics


The BAS2000 bogie : a general case

Six 3D kinematicloopsThe tram2000

Four independent wheel/rail contacts

=> No more wheelset, even artificial (left-right)


10/19


MBS : wheel or wheeset - doesnt matter!

In relative coordinates, a wheel is a leaf body to which forces apply

Independent w heels W heelset = (axle + 2 locked indep. wheels)


The BAS2000 bogie : a general case

A wheel = a leaf body which is constrained on a rail (inertial body)

TheBAS2000 cannotbe modeled as a bogie

but as a mechanism with wheels! => relative coordinates approachsuitable


Contents


Contact geometry

Contact forces

Wheelsetdynamicbehavior


Multibodyr epresentation

Wheel/rail contact independentwheel model


Validations -Applications

Other topics


11/19


=> 5 dof + 1 normal constraint

The wheel/rail joint


Recall : coordiante partitioning reduction

Coordinate partitioning :

ODE !


A Single Wheel on a Rail : 5 d.o.f.

Q

i

h

k

G

xj

_

w

( ( ( (w)

...

jj

3-D Contact Constraints :

1. Point Q belongs to Rail Surface

2. Wheel/ Rail Surfaces Tangent at Point Q

=> Lagrange Multipliers Technique

2 Auxiliary variables :

w: lateral position

: Shift angle

w

(w)


12/19


Robust solution of contact constraints

A dichotomic method embeded into the Newton-Raphson algorithm

Wheel on rail: Constraints solution

rail profile

2 = 0 !!

3 = 0 !!


Wheel on rail: Constraints solution

requires

= 0 when the constraints are satisfied


Wheel on rail: Constraints derivative

{R}

I12I

3I

O

Q

{X}{S}

{Y}

P

P

G

x

u

w

{T}

cos = + /2_

h(q) satisfied

1 = FN


13/19


Wheel on rail: Constraints 2d derivative

R

I12I

3I

O

Q

{X}{S}

Y

P

P

G

x

u

w

{T}


Wheel on curved rail


Wheel on curved rail


14/19


Creepages : a real MBS computation

Lateral creepage :


Spin creepage :{R}

I1

2I

3I

O

Q

{X}{S}

{Y}

P

P

G

x

u

w

{T}


Wheel on rail: Kalkers model

R

I1

2I

3I

O

Q

{X}{ S}

{Y}

P

P

G

x

u

w

{T}

Kalker (linear) :


Wheel on rail: flange forces (tramways)


15/19


Wheel on rail: flange forces

Influence of the shift angle

No wheel yaw With wheel yaw

For the flange contact force, in terms of tangent slip,

the tread contact ( creepage ) can be seen as a pure rolling motion (~ICR)


Contents


Contact geometry

Contact forces







Other topics : towards multiphysics


Geometrical validation

UCL

Delft


16/19


Wheelset limit cycle

UCL Delft

x x


Bogie : non linear critical speed

Cycle limiteDeraillement stable

ROBOTRAN results

(IAVSD benchmark #2, 1991)


The BAS 2000 articulated bogie


17/19


Ping-pong effect on a straigth track

Yaw deformation

time

BAS 2000 : straight track behavior


The Tram 2000 tramway

The "Tram 2000"

Model:

Complete TRAM 2000 in Entry Curving :

- 4 Sub-Systems

- 74 Variables

- 32 Constraints

- 42 Degrees of Freedom

Carbody A

Front BAS 2000Bogie

Carb ody C Ca rbod yB

Conventionnal Bogie Back BAS 2000 BogieV

Velocity : 25 km/h

Initial Conditions : Tramway Centered on the Straight Track


Result:

Wheel/Rail Alignment ina Low Radius Curve (R = 50 m)

V

wheel

rightrail

Wheel / Rail Angle of Attack

Tram 2000 tramway - results

Carbody A

Front BAS2000 Bogie

Ca rb od yC C ar bo dy B

C onven tionn al B ogie B ack B A S 2000B ogieV


18/19


Comparison of bogie behaviors

BW : Rigidbogie with wheeslets

BI : Rigid bogie with independent wheels

BA : BA2000 articulated bogie

Bogies :

Situation : entry curving

BW

BI

BA


Comparison of bogie behaviors

Steady state equilibrium : tread and flange lateral forces

- Crab-wise behavior

- Crab-wise behavior

BW

BI

BA

- Low longitudinal

tread forces

- Distorted, no crab-wise- Dissipated powerminimized


Contents


Contact geometry

Contact forces







Other topics : towards multiphysics


19/19


Railway bogies actuated by three

phase induction motors

Problem:

Torque oscillations lead to

fatigue stress in the chassis

Fz

Fz

Cm

Cm

Fz in the-motortochassis-joint

electromechanicaltorque Cm

Multibody and railway electro dynamics

=> Next lecture


Multibody and railway pneumatic suspension

=> Next lecture

Multibody system

Pneumatic system

Hybrid system

Rail Vehicles 2011

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