a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
Influence of Locomotive Tractive Effort
on the Forces between Wheel and Rail
Oldrich POLACH
Adtranz
DaimlerChrysler Rail Systems (Switzerland) Ltd
Winterthur, Switzerland
OP / BWED
22 Aug., 2000 - Seite -1VortrICTAM-2.ppt
Contents
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Calculation of wheel-rail forces in railway vehicle dynamics
l Differences in the calculation of wheel-rail forces in vehicle
dynamics and in drive dynamics
l Model of wheel-rail forces suitable for computer simulation of
vehicle and drive dynamics interaction
l Influence of tractive effort on the wheel-rail forces during curving
l Co-simulation of vehicle dynamics and traction control
l Conclusions
OP / BWED
22 Aug., 2000 - Seite -2VortrICTAM-2.ppt
Calculation of Forces Between Wheel and Rail
in Vehicle Dynamics
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Wheel-rail forces are functions of at least four independent
variables (multi-dimensional problem):
Fx, Fy = f (sx, sy, w, a/b, Q, f)
creepages
form of the
contact area
l The calculation is repeated many times for each wheel in each
integration step
è the calculation time is very important
OP / BWED
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A Time Saving Method
of Wheel-Rail Forces Calculation
Compromise between calculation time and
necessary accuracy
l
Spin taken into account
l
Calculation time comparable with
saturation functions or look-up tables
l
Pre-calculation superfluous
l
Accuracy comparable with FASTSIM or
look-up tables
l
Principle and computer code published at
the 16th IAVSD Symposium, Pretoria 1999
OP / BWED
22 Aug., 2000 - Seite -4VortrICTAM-2.ppt
normal
stress s
direction
of motion
s, t
tangential
stress t
x
y
b
l
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
area of
slip
area of
adhesion
a
x
Comparison of Simulation and Measurement
ADAMS/Rail Model of Locomotive SBB 460
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
Mechanism
Mechanism
of
ofWheelset
WheelsetCoupling:
Coupling:
Wheelset
Linkage
Vehicle Model:
l
l
l
l
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22 Aug., 2000 - Seite -5VortrICTAM-2.ppt
51 rigid bodies
84 bushings
4 bump-stops
24 dampers
Coupling shaft
Axle box
Comparison of Simulation and Measurement
Results
00
2
3
2
3
4
[-]
left
YY/Q
[kN]
left
0.2
20
-0.2
-20
11
33
22
44
0 0
-20-0.2
-0.4
-40
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Wheelset
Wheelset
200.2
0
0
-0.6
-60
Calculation
time
00
4
Y left [kN]
Y/Q left [ - ]
1
20
0.2
-20
-0.2
Wheelset
Wheelset
1
40
0.4
Wheelset
Wheelset
FASTSIM
FASTSIM
proposed
proposed
measurement
measurement
-40-0.4
-60-0.6
Wheelset
Wheelset
FASTSIM
FASTSIM
proposed
proposed
measurement
measurement
proposed
Y right [kN]
Y/Q right [ - ]
20
0.2
R = 300 m
lat
60
0.6
40
0.4
-0.2
-20
alat
a = =1.1
1.1m/s²
m/s²
FASTSIM
= -- 0.3
0.3 m/s²
m/s²
lat=
aalat
60
0.6
Y/Q
[-]
right
Y right
[kN]
Lateral
wheel-rail
force
Derailment
quotient
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
Differences of Creep-Force Functions
in Vehicle Dynamics and Drive Dynamics
Vehicle Dynamics
Drive Dynamics
dry
Creep force
dry
Creep force
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
wet
Creep
wet
Slip velocity
l
Possible for use in vehicle
dynamics (small creep)
l
Necessary for drive dynamics (large
creep - slip)
l
Used for longitudinal and lateral
directions
l
Usually used only for longitudinal
direction
l
Function of creep
l
Function of slip velocity
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Wheel-Rail Model for Computer Simulation
of Vehicle and Drive Dynamics
Friction coefficient
decreasing with slip velocity
l
Kalker's
factor = 1
+
Slip velocity
Kalker's
factor < 1
Creep
Adhesion coefficient
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Reduction of Kalker‘s factor
Adhesion coefficient
Friction coefficient
l
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
Creep
Wheel-Rail Model for Computer Simulation
of Vehicle and Drive Dynamics
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Modelling of measured creep-force functions
(Measurement on locomotive SBB 460)
V = 20 km/h
V = 40 km/h, wet
Average curve of 7 measurements
Measurement
0.4
Adhesion coefficient
0.4
water+sand
0.3
mx
0.3
Calculation
0.4
water+sand
0.3
water
mx
water
0.2
0.2
0.2
0.1
0.1
Calculation
0
0.1
soap
solution
0
0
0
5
10
15
20
Creep
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25
[%]
30
35
40
soap
solution
0
10
20
sx
30
[%]
40
50
0
10
20
sx
30
[%]
40
50
Wheel-Rail Model for Computer Simulation
of Vehicle and Drive Dynamics
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Influence of vehicle speed
0.4
0.36
0.32
0.28
0.3
0.2
V = 10 km/h
0.1
0
0.2
0.3
0.2
V = 40 km/h
0.1
0
0
0.24
5
10
Creep
15
20
0
25
5
10
Creep
[%]
15
20
25
20
25
[%]
0.16
0.4
0.08
10
0.04
40
0
0
3
6
sx [%]
70 v [km/h]
9
12
100
15
Adhesion coefficient
0.12
0.4
0.3
0.2
V = 70 km/h
0.1
0
0.3
0.2
V = 90 km/h
0.1
0
0
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Adhesion coefficient
m x [-]
Adhesion coefficient
Adhesion coefficient
0.4
5
10
15
Creep
[%]
20
25
0
5
10
Creep
15
[%]
Simulation of Vehicle and Drive Dynamics
Model of Loco SBB 460 Including Drive System
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
Drive
DriveSystem:
System:
Wheelset
Motor
Hollow
shaft
Large gear
wheel
OP / BWED
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Pinion
Idler
Vehicle Model:
294 Degrees of Freedom
Influence of Locomotive Tractive Effort
on the Wheel-Rail Forces in a Curve
Forces between wheel and rail
30
30
[kN]
[kN]
30
30
10
10
Y
Y 2r
2r
Z = 200 kN
40
40
[kN]
[kN]
Z = 100 kN
40
40
Y
Y 1r
1r
Tractive force:
Z = 0 kN
10
10
20
20
00
-10
-10
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
R = 300 m, alat = 1 m/s²
wet condition, friction coefficient
function of slip velocity
20
20
00
Steering angle
-10
-10
-20
-10
10
20 30
30
-20 -10
-10 00
0 10
10 20
20
30
-20
[kN]
X 1r
X
[kN]
[kN]
X
1r
1r
-20
-10
10
20
30
-20-10
-10 000 10
10 20
20 30
30
-20
[kN]
XX2r2r [kN]
[kN]
X
2r
0
-40
-40
-50
-50
OP / BWED
22 Aug., 2000 - Seite -12VortrICTAM-2.ppt
[kN]
[kN]
[kN]
-30
-30
-20
-20
Y
YY2l2l2l
[kN]
[kN]
[kN]
X 1l1l
X
-10
-10
Y 1l
1l
00
-20 -10
10 20
20 30
-10 00 10
30
-20
0
00
-10
-10
-10
-20
-20
-20
-30
-30
-30
-40
-40
-40
-50
-50
-50
-20
-10 00
10
20 30
30
-20 -10
-10
0 10
10 20
20
30
-20
[kN]
X
X 2l2l
[kN]
2l
[kN]
X
2
4
6
b [mrad]
b
8
Adhesion Tests with Locomotive SBB 460
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Test composition
OP / BWED
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Simulation of the Adhesion Test
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l
Time plots of the values on the leading bogie
Curve:
Curve: R
R == 400
400 m
m
Longitudinal force in steering linkages
Rotor traction torque
60
10
Rotor 1
5
Rotor 2
0
0
5
10
tim e
15
20
0
-20
y [mm]
X1 [kN]
0
-10
tim e
15
20
b [mrad]
X2 [kN]
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10
tim e
15
[s]
10
15
20
[s]
Steering angle between the wheelsets
0
-10
5
3
Ws 2 right
5
0
-2 0
tim e
Ws 2 left
0
[s]
Wheelset 2
2
[s]
Longitudinal force of wheelset 2
10
20
-4
30
20
15
Wheelset 1
4
10
10
Lateral displacement of wheelset relative to track
6
Ws 1 right
5
5
tim e
Ws 1 left
0
0
[s]
30
10
Wheelset 2
20
Longitudinal force of wheelset 1
20
Wheelset 1
40
Fx [kN]
M [kNm]
15
-5
Rail
Rail conditions:
conditions: wet
wet
Vehicle
Vehicle speed:
speed: VV == 70
70 km/h
km/h
20
2
1
0
-1
0
5
10
tim e
15
[s]
20
Co-Simulation of Vehicle Dynamics
and Traction Control
l Adhesion Controller
(MATLAB-SIMULINK)
OP / BWED
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a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Mechanics
(ADAMS/Rail)
Co-Simulation of Vehicle Dynamics
and Traction Control
l Adhesion Controller
(MATLAB-SIMULINK)
nRs1
nref
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l Mechanics
Fz1
(ADAMS/Rail)
nw, opt
gw
MR1
Fz2
nRs2
Gradient
Controller
nx,f
Speed
Controller
DSC
=
Msoll
Gradient
Computation
gx
Speed Filter
nT
nx
OP / BWED
22 Aug., 2000 - Seite -16VortrICTAM-2.ppt
3~
3~
Speed
Sensor
Traction
Motor
Control
Traction
Motor
MR2
Co-Simulation Results of the Interaction
of Vehicle Dynamics and Traction Control
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
Track
Track design:
design: straight,
straight, curve
curve R
R == 300
300 m,
m, straight,
straight, curve
curve R
R == 385
385 m
m
Rail
Rail conditions:
conditions: wet
wet
Longitudinal force of wheelset 1
Vehicle speed
40
X1 [kN]
V [m/s]
30
20
10
0
30
20
Ws 1 left
10
Ws 1 right
0
0
50
100
150
200
250
300
0
50
100
Distance along the track [m ]
300
250
300
250
300
Lateral force of wheelset 1
9
6
Y1 [kN]
M 1, 2 [kNm]
250
30
Rotor 1
Rotor 2
3
0
0
50
100
150
200
250
15
0
-15 0
-30
300
50
Ws 1 right
Traction rod force
40
b [mrad]
30
20
10
0
50
100
150
200
Distance along the track [m ]
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150
200
Distance along the track [m ]
Steering angle between the wheelsets
10
0
100
Ws 1 left
Distance along the track [m ]
F [kN]
200
Distance along the track [m ]
Rotor torque
12
150
250
300
Bogie 1
Bogie 2
5
0
0
50
100
150
200
-5
Distance along the track [m ]
Conclusions
a~áãäÉê`ÜêóëäÉê=o~áä=póëíÉãë
l The method of wheel-rail forces calculation developed by the
author is suitable for computation of full non-linear wheel-rail
forces; it takes spin into account and saves calculation time
l The presented extension of the proposed method allows a
parallel simulation of vehicle and drive dynamics
l The proposed method was verified by measurements and is
suitable for investigations of interaction of traction dynamics,
traction control and vehicle behaviour
OP / BWED
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