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BOGIE 07 Conference September 3rd – 6th, 2007
Budapest – HUNGARY
Numerical simulation for improving the design of running gear – Part 1: improvement of vehicle dynamic behaviour
Paolo BELFORTE, S. BRUNI (Politecnico di Milano - Department of Mechanical Engineering)
Michael JÖCKEL (Fraunhofer Institute for Structural Durability and System Reliability - LBF)
Paolo Belforte (Politecnico di Milano - Italy)
MODTRAIN Project
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“ “ Innovative modular vehicle concepts for an integrated Innovative modular vehicle concepts for an integrated European railway system “European railway system “
6th FRAMEWORK PROGRAMME PRIORITY 6.3 – Transport6th FRAMEWORK PROGRAMME PRIORITY 6.3 – Transport
4 Years Project – Started January 20044 Years Project – Started January 2004
MODTRAIN projectMODTRAIN project
Modular approach to train designModular approach to train design
Interoperability: new generation rolling stockInteroperability: new generation rolling stock
Harmonised European criteria for rolling stock Harmonised European criteria for rolling stock homologationhomologation
Paolo Belforte (Politecnico di Milano - Italy)
MODTRAIN Project
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It consist of five different sub-projects:It consist of five different sub-projects:
MODBOGIEMODBOGIE
MODCONTROLMODCONTROL
MODPOWERMODPOWER
MODLINKMODLINK
MODUSERMODUSER
Paolo Belforte (Politecnico di Milano - Italy)
INTRODUCTION: NUMERICAL SIMULATIONS TOWARDS “VIRTUAL HOMOLOGATION”
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• In last years, the improved calculation technologies allowed the development of more detailed and accurate numerical models of rail vehicle dynamics, which can be used as a very useful tool for the design and development of a railway stock.
• With the development of new generations of HS trains, numerical simulations can give an important contribution in order to raise service speed and satisfy operators requirements which claims always for improved performance in terms of comfort and safety
• This work targets the capabilities of multi body simulation models in the design and verification phase of the railway running gear.
Paolo Belforte (Politecnico di Milano - Italy) 6
INDEX
Paolo Belforte (Politecnico di Milano - Italy) 7
Vehicle model: HS concentrated power locomotive
Carbody with two motor bogies
Two motors bogie-suspended by means of dedicated motor hangers per each bogie
VEHICLE SCHEMATISATIONVEHICLE SCHEMATISATION
41,,,, ....;;;;; T
w
T
w
Tenr
Tbr
Tenf
Tbf
Tc
TV qqxxxxxx
The equation of motion The equation of motion Lagrange equations Lagrange equations
txxQxQvxxQQxKxRxM VVCVnlVVmVVVVVVV ,,,,
REFERENCE SYSTEMSREFERENCE SYSTEMS
W/R contact forces
Vehicle inertia
Fixed reference
Moving reference with constant speed V
Moving reference on body c.o.g .
XG
ZG
YG
Xo
Zo
Yo
ZGi
YGi
V
i
i
i
Loco of a concentrated power train
Only rigid modes also for the wheelsets problem confined to low frequency
Paolo Belforte (Politecnico di Milano - Italy) 8
rail and wheel profilescontact geometrical
parametersgeometrical analysis
elastic deformation in normal direction
(penetration)
tangential & longitudinal creepages
generalized contact forcestangential & longitudinal
forces(Shen-Hedrick-Elkins
theory)
normal forces(multi-hertzian model)
Wheel rail contact forces model
Paolo Belforte (Politecnico di Milano - Italy)
COMPARISON A.D.Tre.S. – SIMPACKEigenvalues and time histories comparison
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Natural frequencies comparison
Z
X z
x
z
x
V
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Nat
ura
l F
req
ue
nc
y [H
z]
Vertical Lateral Yaw Pitch Roll
ADtres
Simpack
Carbody natural frequencies
Straight track with concentrated track defect:
• 5 mm lateral and 14 mrad roll;• 20 m wavelength;• speed 72 km/h.
Leading Wheelset of Bogie 1: Vertical Force at Right Wheel
60000
64000
68000
72000
76000
80000
84000
88000
92000
96000
100000
2 3 4 5 6 7
Time [s]
Force
[N]
SimpackADTreS
Leading Wheelset of Bogie 1: Lateral Force at Right Wheel
-6000
-4000
-2000
0
2000
4000
6000
2 3 4 5 6 7
Time [s]
Force
[N]
SimpackADTreS
Paolo Belforte (Politecnico di Milano - Italy) 10
INDEX
Paolo Belforte (Politecnico di Milano - Italy) 11
Tuning procedure by sensitivity analysis
TYPE OF ANALYSIS : parametric analysis on primary suspension parameters and bogie wheel-base:
straight track running behaviourstraight track running behaviour -> critical speed
curve negotiationcurve negotiation -> steady state Q (vertical force values)
steady state Y (lateral force values)
steady state ‘wear index’
Paolo Belforte (Politecnico di Milano - Italy) 12
Tuning procedure by sensitivity analysis: effect of wheel-base
Vehicle configurations
Wheelbase[m]
Cz[kN/mm]
Cy[kN/mm]
AD 3 10 18V1 2.7 10 18V2 2.5 10 18
Reducing the wheelbase the critical Reducing the wheelbase the critical speed decreasesspeed decreases
Reducing the wheelbase the vehicle has a Reducing the wheelbase the vehicle has a better steering behaviourbetter steering behaviour
Paolo Belforte (Politecnico di Milano - Italy)
Tuning procedure by sensitivity analysis: effect of wheel-base
Vehicle configurations
Wheelbase[m]
Cz[kN/mm]
Cy[kN/mm]
AD 3 10 18V1 2.7 10 18V2 2.5 10 18
Reducing the wheelbase the track shift Reducing the wheelbase the track shift force is lightly increasedforce is lightly increased
Wear index is lower in case of reduced wheelbase
Radius curve [m]
Paolo Belforte (Politecnico di Milano - Italy) 14
INDEX
Paolo Belforte (Politecnico di Milano - Italy) 15
Analysis of technological options: ‘virtual dynamic homologation’ simulation acc. to EN14363
Vehicle configurations taken into account for EN14363 full Vehicle configurations taken into account for EN14363 full analysisanalysis
Vehicle configurations
Bogie Wheelbase
[m]
Longitudinal axlebox stiffness[kN/mm]
Lateral axlebox stiffness [kN/mm]
Reference 3 10 18
V1 3 30 15
V2 2.5 30 15
Three curve ranges are considered:• Small radius curve (250 – 400 m);• Medium-small radius curve (400 – 600 m);• Large radius curve (600 – 2500 m) .
Paolo Belforte (Politecnico di Milano - Italy) 17
‘Virtual dynamic homologation’ procedure: main curving indexes
TRACK SHIFT FORCEEN14363 limit
EN14363 limit
Y/Q
VERTICAL FORCE
EN14363 limit
Main parameters are obtained for all vehicle configurations
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‘Virtual dynamic homologation’ procedure: critical speed and wear index.
WEAR INDEX CRITICAL SPEED
Additional information is the wear index which can be used for the evaluation of the aggressiveness of the vehicle.
Paolo Belforte (Politecnico di Milano - Italy)
Sensitivity analysis and scatter prediction
Numerical simulation can be used even for the evaluation of the impact of the scatter variation of vehicle’s parameters on running
behaviour.
Paolo Belforte (Politecnico di Milano - Italy)
Sensitivity analysis and scatter prediction: effect of damper parameters
Exemplary Simulation Results (12 Parameters Varied Simultaneously): example of the correlation of the damper parameters with vertical wheel/rail contact forces.
0 2 4 6 8 10 12
x 104
9.6
9.65
9.7
9.75
9.8x 104
outp
ut
D11
0.5 1 1.5 2 2.5 3
x 104
9.6
9.65
9.7
9.75
9.8x 104
outp
ut
Max
. nor
mal
forc
e F
ma
x [N
]
Damper coefficient D1 [Ns/m] Damper coefficient D2 [Ns/m]
Strong correlation No correlation
Scatter
of
output
Secondary suspension:
vertical damper (“left”)
Primary suspension:
vertical damper (“left
front”)
Each point: Output for one sample-set (simulation)
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INDEX
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Full factorial approach:• Dynamic performances analysis in straight track: vehicle stability• Dynamic performances analysis in curved track: curving performance
Nine configuration are taken as reference, according to the full
factorial approach
NUMERICAL SIMULATIONS
CURVING PERFORMANCE
OPTIMIZATION
STRAIGHT TRACK
Methodology for the assessment of technological options:FULL FACTORIAL APPROACH
Paolo Belforte (Politecnico di Milano - Italy)
Methodology for the assessment of technological options:FULL FACTORIAL APPROACH
Definition of factor and factor levels: bogie wheelbase: 3 m - 2.75m - 2.5 m; lateral axlebox stiffness:10-25-40 kN/mm; longitudinal axlebox stiffness: 10-30-50
kN/mm.
ANOVA method : distinction random and systematic variation polinomial equation of full factorial plan where coefficients are determined applying the least square analysis
2128
2217
226
215
21423121ˆ
xxxxxx
xxxxy
polynomial equation that describes the full factorial plan
Reduced number of configurations
Evaluate the influence of a simultaneous variation of parameters
Paolo Belforte (Politecnico di Milano - Italy)
RESULTS IN STRAIGHT TRACK: critical speed as a function of bogie wheelbase and axle boxes stiffness
Higher axlebox stiffness, leads to an increase of the critical speed
Higher bogie wheelbase stabilises the vehicle running dynamics
BW = 2.5 m
BW = 2.75 m
BW = 2.5 m
BW = 3 m
265 km/h245 km/h
230 km/h
24%
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Reducing bogie wheelbase -> lower wear rate
Increasing axlebox stiffness -> higher wear rate
Leading outer wheel frictional work: small radius curve
20%
18 kJ
14 kJ
BW = 3 m
BW = 2.5 m
RESULTS IN CURVEDTRACK: wear rate as a function of bogie wheelbase and axle boxes stiffness
Paolo Belforte (Politecnico di Milano - Italy)
Wear index based optimisationWear index based optimisation
Reference vs. Opt.1:Reference vs. Opt.1: reduced wear 2%
increased critical speed 5%
SolutionSolution Bogie Bogie wheelbase wheelbase
[m][m]
CzCz
[kN/mm][kN/mm]
CyCy
[kN/mm][kN/mm]
Wear Wear
[kJ][kJ]
Critical Critical speed [km/h]speed [km/h]
Reference 33 1010 1818 1230012300 210210
Opt. 1 2.752.75 1010 21.521.5 1206912069 221221
Two different optimisation functions were used.
Combined optimisation:Combined optimisation:
Reference vs. Opt. 2:Reference vs. Opt. 2: increased critical speed of 16 %
increased wear of 4%
SolutionSolution Bogie Bogie wheelbase wheelbase
[m][m]
CzCz
[kN/mm][kN/mm]
CyCy
[kN/mm][kN/mm]
Wear Wear
[kJ][kJ]
Critical Critical speed [km/h]speed [km/h]
Reference 33 1010 1818 1230012300 210210
Opt. 2 33 1010 37.237.2 1257812578 256256
OPTIMIZATION: results with different optimization functions
)max(),,_( _ WIspeedcryz CCkkbasewf
Paolo Belforte (Politecnico di Milano - Italy)
CONCLUSIONS
• Numerical simulation can be used in order to complement physical testing for homologation;
•Montecarlo approach coupled with multi-body simulations can account for the effect of scatter in component performances on ride safety;
• Numerical simulations can also be used for optimising vehicle performances still meeting the constraints imposed by ride safety.
Paolo Belforte (Politecnico di Milano - Italy) 29
Thanks for your attention
Paolo BELFORTE Paolo BELFORTE paolo.belforte@polimi.itpaolo.belforte@polimi.it
Stefano BRUNI Stefano BRUNI stefano.bruni@polimi.itstefano.bruni@polimi.it
BOGIE ’07 Conference September 3rd - 6th, 2007
Budapest – HUNGARY
Michael Michael JÖCKEL michael.joeckel@lbf.fraunhofer.demichael.joeckel@lbf.fraunhofer.de
Paolo Belforte (Politecnico di Milano - Italy)
33Methodology for the assessment of technological options:SIMULATIONS PARAMETERS
STRAIGHT TRACKSTRAIGHT TRACK •Per each configurationPer each configuration:
MB simulations increasing speed (steps 5 km/h) Evaluation of rms values Evaluation of prescribed limits & identification of critical speed
•Simulation parameters:Simulation parameters: W/R profile: theo. Rail / worn wheel cant 1:40 Track irreg: ERRI LOW
The overall assessment of one vehicle configuration requires at least 50 simulations
RMS calculation:
• Fourier trasform of the last 10 s of the simulation
• Frequency f0 corrisponding to the maximum spectrum value identified
• Time history filtered with a band-pass filter f0±2 Hz
220 225 230 235 240 245 2500
1
2
3
4
5
6
7Leading bogie - Critical speed - RMS Lateral acc. criterion
limit lateral acceleration EN 14363: 4.83m/s2 Vlim 240km/h
rms(
y )
[m/s
2 ]
V [km/h]
Lead. axle
Trail. axle
Paolo Belforte (Politecnico di Milano - Italy)
34
CURVED TRACK CURVED TRACK Simulation parametersSimulation parameters
Steady state condition for different radius curve (300 – 2500 m) – random combination of Track irregularityW/R profileCant deficiency
Methodology for the assessment of technological options:SIMULATIONS PARAMETERS
Three tests zone: Three tests zone:
small radius curves [250 -400 m];
small radius curves [400 – 600m];
radius curves [600 – 2500m];
For each zone -> 30 sections -> data collected with simulations
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
2
2.5
3
[sample number]
[Sf ij]
Paolo Belforte (Politecnico di Milano - Italy)
35Methodology for the assessment of technological options:OPTIMISATION PROCEDURE
)max(),,_( wwCSyz CCCCwbbogief
Best vehicle w.r.t stability and wear optimisation function
Ccs & Cww critical speed and minimum frictional work
& weighting coefficient
All the indexes prescribed in the standard were considered as constrains
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Results -- CURVED TRACK:Guiding force as function of bogie wheelbase and axle boxes stiffness
Low bogie wheelbase has positive effects on the vehicle curving behaviour
Longitudinal stiffness reduces the bogie steering capability
BW = 2.5mBW = 2.5mBW = 3mBW = 3m
Leading outer wheel guiding force: small radius curve Leading outer wheel guiding force: small radius curve
Paolo Belforte (Politecnico di Milano - Italy)
37Results -- OPTIMISATION
Best vehicle parameters : optimisation procedure resultBest vehicle parameters : optimisation procedure result
high lateral stiffness and high boogie wheelbase
Ref vs Opt.1:Ref vs Opt.1: Increased critical speed of 16 %
Increased wear of 4%
Ref vs Opt.2:Ref vs Opt.2: Increased critical speed of 16 %
decreased wear of 2%
SolutionSolution Bogie Bogie wheelbase wheelbase
[m][m]
CzCz
[kN/mm][kN/mm]
CyCy
[kN/mm][kN/mm]
Wear Wear
[kJ][kJ]
Critical Critical speed [km/h]speed [km/h]
Reference 33 1010 1818 1230012300 210210
Opt.1 33 1010 37.237.2 1257812578 256256
Opt.2 2.752.75 1010 21.521.5 1206912069 221221
Paolo Belforte (Politecnico di Milano - Italy) 38
INDEX
)max(),,_( _ WIspeedcryz CCkkbasewf