system dynamics of radial and lateralelastic railway wheels
DESCRIPTION
lateralTRANSCRIPT
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Concluding Colloquium of DFG–Priority–Program, Stuttgart, 13–15 March 2002
System Dynamics of Radial– andLateralelastic Railway Wheels
H. Claus, W. Schiehlen
Contents: � Motivation
� Vertical Motion
� Lateral Motion and Stability Analysis
� Parameter Studies
� Conclusion
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� Rigid wheelsets result at high speeds in droning noiseand polygonalization by inhomogeneous wear.
� Radialelastic wheelsets reduce the generation andtransmission of noise as well as the dynamic loads towheelrim and rail.
� First design for German ICE train was not reliable.
� However, the fundametal principle is still valid.
Radialelastic versus Rigid Wheelsets for High–Speed Trains
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Design Variation for Radialelastic Wheels
Rubber suspendedsteel ring on wheel disc
Elastically suspended reinforcedsteel ring on double wheel disc
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estimated mass and inertia
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mass and inertia of the wheelset inreference configuration correspond
with the rigid wheelset
How to choose stiffness and damping???
Proposed Design Features of Radial and Lateral Elasticity
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radial– andlateralelastic
wheel
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carbody
bogie frame
trackexcitations
vertical eigenmodes starting with
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flexible bogie frame
FE Modeling
Modal Reduction
Multibody Formalism
radialelastic wheelset
Model of a quarter passenger coach witha half bogie frame and one wheelset
Modeling
joint ofbogie pin
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Soundpowerlevel
Evaluation of Droning Noise and Wheel/Rail Forces
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Noisetransmission
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mean square value,restricted in frequency range
mean square valueof wheel/rail forces
carbody
bogie frame
track ���+�
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Spectral Density of Vertical Acceleration
10–12
10–8
10–4
10 0
Spe
ctra
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sity
2/s
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10 10020 30 40 60 80 200
Model shows the positive effect of radialelastic wheels for droning noise reduction
Acceleration amplitudes decrease considerably between 70 and 100 Hz
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Reference: Claus, On Dynamics of Radialelastic Railway Wheelsets, VSDIA’2000
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Design variables
Applied algorithms
Design vektor
Limits for design variables
— Evolutionary strategy
— MCDM (NEWOPT/AIMS, PVM)
— NEWSIM (Simulation)
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Static deflection 5mm :
other parameters may vary between0.1 and 10 of the initial value of rubbersuspended wheel
carbody
bogie frame
track
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Optimization of carbody accelerationand wheel/rail force
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Reduction of droning noise and wheel/rail force
by optimization of the radial elasticity of the wheels
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Wheelset suspension of ICE
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3D–Modeling
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carbody
bogie frame
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Track parameterTrack stiffness (for contact force)
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Primary stiffness coefficients:
Primary damping coefficients:
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Modeling of Suspension and Damping
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Springs/Dampers fixed atcoordinate systems:
–> not rotating–> general damping
Springs/Dampers fixedat material points:
–> rotating–> specific damping
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Bogie frame with 2 rolling rigid wheelsets,i=1,2
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10 root locus plots over velocity
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Degrees of freedom
Bogie frame: 2
Wheelset: 2x4
Im(�i)
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10001200carbody
bogie frame
Im(�i)
Re(�i)
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20
40
60
Eigenvaluesof the
hunting motion
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Re(�i)–400 –300 –200 –100 0
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60
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Root locus plot over velocity
Bogie frame with 2 rolling elastic wheelsets i=1,2
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Degrees of freedomBogie frame: 2 Wheelset: 2x4
carbody
bogie frame
Wheel rim: 4x5
Stiffness and damping coefficents
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Verification of model
Results correspond to the rigid model–> rigid and elastic model are consistent
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Parameter of radial suspension:
Large stiffness required to guarantee stability.
105
106
107
108
109
103
104
105
106
1070
100
200
300
400
]m/N[ y,ERc tiekgifietS
Kritische Geschwindigkeit
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v krit [
km/s
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pmaD
linear critical speed
damping coeff. dRE,y [Ns�m] stiffness coeff. cRE,y [N�m]
vIgLin � 285, 5 km�h
Springs/Dampers fixedat coordinate systems:
Variation of Lateral Stiffness and Damping (cRE,y, dRE,y)
/h]
[km
vIIgLin � 284, 8 km�h
according to optimizationresults of vertical dynamics
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Parameter of lateral, yaw androll suspension:
Optimal parameters of radial stiffness result in robust behavior
105
106
107
108
109
103
104
105
106
1070
100
200
300
400
]m/N[ z,ERc tiekgifietS
Kritische Geschwindigkeit
]m/sN[ z,ERd gnuf
v krit [
km/s
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pmaD
linear critical speed
damping coeff. dRE,z [Ns�m] stiffness coeff. cRE,z [N�m]
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Variation of Radial Stiffness and Damping (cRE,z, dRE,z)
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Springs/Dampers fixedat coordinate systems:
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Linear systems with periodic coefficients
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Floquet’s Theory:
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Transition matrix �(T) through integration of
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Computation time for �(T)
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Floquet (Multiplication,Friedman 1977)
Floquet (Integration)
Time integration of eqn.of motion (5 Maxima)
0.06 s
0.14 s
2.00 s
Wheelset (8 dof, no primary suspension):
Floquet (Multiplication)
Time integration (withsuitable initial conditions)
3 days
15 min
Stability tests by time integration–> better computation efficiency
System is asymptotically stabil for
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Comparison with general damping:At lower stiffness values increased critical speed
Variation of Lateral Stiffness and Damping (cRE,y, dRE,y)Springs/Dampers fixedat material points:
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Parameter of radial suspension:
according to optimizationresults of vertical dynamics
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106
107
108
103
104
105
106
1070
100
200
300
400
linear critical speed
damping coeff. dLE,y [Ns/m] stiffness coeff. cLE,y [N/m]
vcr
it [
km/h
]
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High critical speed even for low damping coefficients,instability for low stiffness coefficients
Variation of Radial Stiffness and Damping (cRE,z, dRE,z)Springs/Dampers fixedat material points:
–> rotating
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Parameter of lateral, yaw androll suspension:
106
107
108
103
104
105
106
1070
100
200
300
400
linear critical speed
damping coeff. dRE,z [Ns/m] stiffness coeff. cRE,z [N/m]
vcr
it [
km/h
]
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Comments on Design Parameter for Elastic Wheels
Damping coefficients turn out to be less critical
Stability behavior very robust for�+1�� � � ? ��,-@��
For comparison, stiffness in vertical direction
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The lateral stiffness has to be considerably higherthan the radial stiffness
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Variation of lateral and radialsuspension coefficients ofthe wheels (general andspecific damping)
Outlook: Nonlinear criticalspeed for radial– und laterale-lastic wheels
Reduction of droning noiseand wheel/rail force
Damping coefficients less critical
Verification of the results ofthe linear model
Optimization of the verticalmodel (with radialelasticwheels)
Korr–Opt.MCDS
Optimal parameters of radialstiffness –> robust behavior
Small stiffness coefficients notsuitable