influence of locomotive tractive effort on the forces between wheel and rail · ·...
TRANSCRIPT
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Influence of Locomotive Tractive Efforton the Forces between Wheel and RailInfluence of Locomotive Tractive Efforton the Forces between Wheel and Rail
Oldrich POLACH
AdtranzDaimlerChrysler Rail Systems (Switzerland) Ltd
Winterthur, Switzerland
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Contents
� Calculation of wheel-rail forces in railway vehicle dynamics
� Differences in the calculation of wheel-rail forces in vehicledynamics and in drive dynamics
� Model of wheel-rail forces suitable for computer simulation ofvehicle and drive dynamics interaction
� Influence of tractive effort on the wheel-rail forces during curving
� Co-simulation of vehicle dynamics and traction control
� Conclusions
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� Wheel-rail forces are functions of at least four independentvariables (multi-dimensional problem):
Fx, Fy = f (sx, sy, �, a/b, Q, f)
� Wheel-rail forces are functions of at least four independentvariables (multi-dimensional problem):
Fx, Fy = f (sx, sy, �, a/b, Q, f)form of the
contact areacreepages
Calculation of Forces Between Wheel and Railin Vehicle Dynamics
� The calculation is repeated many times for each wheel in eachintegration step
� the calculation time is very important
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A Time Saving Methodof Wheel-Rail Forces Calculation
� Compromise between calculation time andnecessary accuracy
� Spin taken into account
� Calculation time comparable withsaturation functions or look-up tables
� Pre-calculation superfluous
� Accuracy comparable with FASTSIM orlook-up tables
� Principle and computer code published atthe 16th IAVSD Symposium, Pretoria 1999
normalstress �
tangentialstress �
area ofadhesion
area ofslip
x
�, �
x
y
a
b
directionof motion
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Comparison of Simulation and MeasurementADAMS/Rail Model of Locomotive SBB 460
� 51 rigid bodies� 84 bushings� 4 bump-stops� 24 dampers
Vehicle Model:
Coupling shaft
Wheelset
Axle box
Linkage
Mechanismof Wheelset Coupling:
Mechanismof Wheelset Coupling:
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-20
0
20
40
60
Wheelset
Y rig
ht
[kN
]
-60
-40
-20
0
20
Wheelset
Y le
ft
[kN
]
FASTSIMproposedmeasurement
1 2 43
alat = 1.1 m/s²
-20
0
20
40
60
Wheelset
Y rig
ht
[kN
]
-60
-40
-20
0
20
Wheelset
Y le
ft
[kN
]
FASTSIMproposedmeasurement
1 2 43
Lateral wheel-rail forcealat = - 0.3 m/s² R = 300 m
Comparison of Simulation and MeasurementResults
-0.6
-0.4
-0.2
0
0.2
Wheelset
Y/Q
left
[
- ]
FASTSIMproposedmeasurement
1 2 43
-0.2
0
0.2
0.4
0.6
Wheelset
Y/Q
right
[
- ]
-0.6
-0.4
-0.2
0
0.2
Wheelset
Y/Q
left
[
- ]
FASTSIMproposedmeasurement
1 2 43
-0.2
0
0.2
0.4
0.6
Wheelset
Y/Q
right
[
- ]
Derailment quotientalat = 1.1 m/s²alat = - 0.3 m/s²
prop
osed
FAST
SIM
Calculationtime
prop
osed
FAST
SIM
Calculationtime
prop
osed
FAST
SIM
Calculationtime
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Differences of Creep-Force Functionsin Vehicle Dynamics and Drive Dynamics
� Possible for use in vehicledynamics (small creep)
� Used for longitudinal and lateraldirections
� Function of creep
� Necessary for drive dynamics (largecreep - slip)
� Usually used only for longitudinaldirection
� Function of slip velocity
Slip velocity
Cre
ep fo
rce
dry
wet
Drive Dynamics
Creep
Cre
ep fo
rce
dry
wet
Vehicle Dynamics
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Creep
Adh
esio
n co
effic
ient
Slip velocity
Fric
tion
coef
ficie
nt
� Friction coefficientdecreasing with slip velocity
Wheel-Rail Model for Computer Simulationof Vehicle and Drive Dynamics
� Reduction of Kalker‘s factor
+Creep
Adh
esio
n co
effic
ient
Kalker'sfactor = 1
Kalker'sfactor < 1
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0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
sx [%]
�x
Calculation
water+sand
water
soap solution
Wheel-Rail Model for Computer Simulationof Vehicle and Drive Dynamics
� Modelling of measured creep-force functions(Measurement on locomotive SBB 460)
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25 30 35 40Creep [%]
Adh
esio
n co
effic
ient
Calculation
V = 40 km/h, wetAverage curve of 7 measurements
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
sx [%]
�x
Measurement
water+sand
water
soap solution
V = 20 km/h
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Wheel-Rail Model for Computer Simulationof Vehicle and Drive Dynamics
� Influence of vehicle speed
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25Creep [%]
Adh
esio
n co
effic
ient
V = 10 km/h
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25Creep [%]
Adh
esio
n co
effic
ient
V = 40 km/h
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25Creep [%]
Adh
esio
n co
effic
ient
V = 70 km/h
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25Creep [%]
Adh
esio
n co
effic
ient
V = 90 km/h0 3 6
9 1215
1040
70
100
00.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
�x [-]
sx [%]
v [km/h]
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Simulation of Vehicle and Drive DynamicsModel of Loco SBB 460 Including Drive System
Vehicle Model:
294 Degrees of Freedom
Drive System:Drive System:
Motor
Pinion
Idler
Wheelset
Hollowshaft
Large gearwheel
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Influence of Locomotive Tractive Efforton the Wheel-Rail Forces in a Curve
0 2 4 6 8��� [mrad]
Steering angle
�
R = 300 m, alat = 1 m/s²wet condition, friction coefficient
function of slip velocity
Forces between wheel and rail
-10
0
10
20
30
40
Y 2r
[
kN]
-10
0
10
20
30
40Y
1r
[kN
]
-20 -10 0 10 20 30
X 1r [kN]
-20 -10 0 10 20 30
X 1l [kN]
-50
-40
-30
-20
-10
0
Y 1l
[
kN]
-50
-40
-30
-20
-10
0
Y 2l
[
kN] -20 -10 0 10 20 30
X 2l [kN]
-20 -10 0 10 20 30
X 2r [kN]
Z = 0 kN
Z = 100 kN
Z = 200 kN
Tractive force:
-10
0
10
20
30
40
Y 2r
[
kN]
-10
0
10
20
30
40Y
1r
[kN
]
-20 -10 0 10 20 30
X 1r [kN]
-20 -10 0 10 20 30
X 1l [kN]
-50
-40
-30
-20
-10
0
Y 1l
[
kN]
-50
-40
-30
-20
-10
0
Y 2l
[
kN] -20 -10 0 10 20 30
X 2l [kN]
-20 -10 0 10 20 30
X 2r [kN]
-10
0
10
20
30
40
Y 2r
[
kN]
-10
0
10
20
30
40Y
1r
[kN
]
-20 -10 0 10 20 30
X 1r [kN]
-20 -10 0 10 20 30
X 1l [kN]
-50
-40
-30
-20
-10
0
Y 1l
[
kN]
-50
-40
-30
-20
-10
0
Y 2l
[
kN] -20 -10 0 10 20 30
X 2l [kN]
-20 -10 0 10 20 30
X 2r [kN]
0 2 4 6 8��� [mrad]
0 2 4 6 8��� [mrad]
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Adhesion Tests with Locomotive SBB 460
� Test composition
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Lateral displacement of wheelset relative to track
-4
-20
24
6
0 5 10 15 20
time [s]
y [
mm
]
Wheelset 1
Wheelset 2
Steering angle between the wheelsets
-1
0
1
2
3
0 5 10 15 20
time [s]
�
[mra
d]
Longitudinal force in steering linkages
-20
0
20
40
60
0 5 10 15 20
time [s]
Fx
[kN
] Wheelset 1
Wheelset 2
Rotor traction torque
-5
0
5
10
15
0 5 10 15 20
time [s]
M
[kN
m] Rotor 1
Rotor 2
Longitudinal force of wheelset 1
-10
0
10
20
30
0 5 10 15 20
time [s]
X 1 [k
N]
Ws 1 left
Ws 1 right
Longitudinal force of wheelset 2
-10
0
10
20
30
0 5 10 15 20
time [s]
X 2 [k
N] Ws 2 left
Ws 2 right
Curve: R = 400 mCurve: R = 400 m Rail conditions: wetRail conditions: wetVehicle speed: V = 70 km/hVehicle speed: V = 70 km/h
Simulation of the Adhesion Test
� Time plots of the values on the leading bogie
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Co-Simulation of Vehicle Dynamicsand Traction Control
� Mechanics(ADAMS/Rail)
� Adhesion Controller(MATLAB-SIMULINK)
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� Mechanics(ADAMS/Rail)
� Adhesion Controller(MATLAB-SIMULINK)
nRs2
nRs1
Msoll
MR1
MR2
Co-Simulation of Vehicle Dynamicsand Traction Control
TractionMotorControl
TractionMotor
Speed FilterGradient
Computation
GradientController
SpeedController
SpeedSensor
Fz1
Fz2
nref
nw, opt
nx
nx,f
gw
gx nT
=3~
DSC
3~
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Co-Simulation Results of the Interactionof Vehicle Dynamics and Traction Control
Vehicle speed
0
10
20
30
0 50 100 150 200 250 300
Distance along the track [m]
V [
m/s
]
Rotor torque
0
3
6
9
12
0 50 100 150 200 250 300
Distance along the track [m]
M1,
2
[kN
m]
Rotor 1Rotor 2
Longitudinal force of wheelset 1
0
10
20
30
40
0 50 100 150 200 250 300
Distance along the track [m]
X 1 [k
N]
Ws 1 left
Ws 1 right
Traction rod force
0
10
20
30
40
0 50 100 150 200 250 300
Distance along the track [m]
F [
kN]
Lateral force of wheelset 1
-30
-15
0
15
30
0 50 100 150 200 250 300
Distance along the track [m]
Y 1 [k
N]
Ws 1 left
Ws 1 right
Steering angle between the wheelsets
-5
0
5
10
0 50 100 150 200 250 300
Distance along the track [m]
�
[mra
d]Bogie 1Bogie 2
Rail conditions: wetRail conditions: wetTrack design: straight, curve R = 300 m, straight, curve R = 385 mTrack design: straight, curve R = 300 m, straight, curve R = 385 m
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Conclusions
� The method of wheel-rail forces calculation developed by theauthor is suitable for computation of full non-linear wheel-railforces; it takes spin into account and saves calculation time
� The presented extension of the proposed method allows aparallel simulation of vehicle and drive dynamics
� The proposed method was verified by measurements and issuitable for investigations of interaction of traction dynamics,traction control and vehicle behaviour