driving dynamics modelling with modelica€¦ · multi-links struts. johan andreasson, division of...
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![Page 1: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/1.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving Dynamics
Driving Dynamics Driving Dynamics ModellingModellingwith with ModelicaModelica
Johan Andreasson, Division of Vehicle DynamicsJohan Andreasson, Division of Vehicle DynamicsRoyal Royal InstituteInstitute of Technology, Swedenof Technology, Sweden
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
OutlineOutline
• Aim with the Car.mo library• From the top to the bottom!• Library contents• Examples• Related libraries• Future improvments
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
AimAim with the with the Car.moCar.mo librarylibrary
• Driving Dynamics evaluation– Critical maneouvres– Lateral performance – Longitudinal performance– Comfort– Etc.
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving Dynamics
From the From the toptop to the to the bottombottom!!
Focus on chassisFocus on chassis
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
A A carcar modelmodel
driver
power train
chassis trailer
environment
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Chassis interfaceChassis interface
steeringflange
bodyframe
drive shafts
Tyre-roadinteraction as a field
![Page 7: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/7.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Chassis Chassis modelmodel
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
front suspension
rear suspension
body
wheels
![Page 8: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/8.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Suspension InterfaceSuspension Interface
nameleft
MacPherson connectionto body
(steeringflange)
wheelconnectors
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Suspension Suspension modelmodel (MacPherson)(MacPherson)
frame_U
_1
fram
e_U
_2
frame_C
L
R
flange_SW
L
f_s=f(s)f_d=f(der(s))
forceTable_1f_s=f(s)
f_d=f(der(s))
forceTableA
f_s=f(s)f_d=f(der(s))
forceTable_2
datasuspensionparameters
anti-roll linkage
MacPherson linkages
steering
![Page 10: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/10.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
frame_U
_1
fram
e_U
_2
frame_C
A
AL
f_s=f(s)f _d=f (der(s))
forceTable_1
f _s=f (s)f _d=f (der(s))
forceTable_2
f _s=f (s)f _d=f (der(s))
f orceTableA
data
Suspension Suspension modelmodel (MultiLink4)(MultiLink4)
suspensionparameters
anti-roll linkage
multi-links
struts
![Page 11: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/11.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
LinkageLinkage modelmodel (MacPherson)(MacPherson)
frame_C frame_U
frame_L12
f_s=f(s)f_d=f(der(s))
forceTable
r=rCL1_scaled
lower
wish-bone(A-arm)
MacPherson strut
![Page 12: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/12.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ComponentComponent modelmodel (MacPherson strut)(MacPherson strut)
frame_L1L2
frame_C
r=rUS - rUL1L2
lowerFrameTranslation
fram
e_W
prismatic=rCS - rUSlowerShape
cylinder
upperShape
cylinder
body
Shap
e
box
a b
C
Spherical1
r=rU
W -
rUL1
L2
oute
rFra
meT
rans
latio
n
f_s=f(s)f_d=f(der(s))
forceTable
r=rCS
upperFrameTranslation
![Page 13: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/13.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
L
Vehicle model
HierarchyHierarchy
![Page 14: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/14.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
L
Vehicle model
HierarchyHierarchy
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
Chassis model
![Page 15: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/15.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
L
Vehicle model
HierarchyHierarchy
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
Chassis modelSuspension model
frame_U
_1
fram
e_U
_2
frame_C
L
R
flange_SW
L
f_s=f(s)f_d=f(der(s))
forceTable_1f_s=f(s)
f_d=f(der(s))
forceTableA
f_s=f(s)f_d=f(der(s))
forceTable_2
data
![Page 16: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/16.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
L
Vehicle model
HierarchyHierarchy
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
Chassis modelSuspension model
frame_U
_1
fram
e_U
_2
frame_C
L
R
flange_SW
L
f_s=f(s)f_d=f(der(s))
forceTable_1f_s=f(s)
f_d=f(der(s))
forceTableA
f_s=f(s)f_d=f(der(s))
forceTable_2
data
Linkage modelframe_C frame_U
frame_L12
f_s=f(s)f_d=f(der(s))
forceTable
r=rCL1_scaled
lower
![Page 17: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/17.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
L
Vehicle model
HierarchyHierarchy
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
Chassis modelSuspension model
frame_U
_1
fram
e_U
_2
frame_C
L
R
flange_SW
L
f_s=f(s)f_d=f(der(s))
forceTable_1f_s=f(s)
f_d=f(der(s))
forceTableA
f_s=f(s)f_d=f(der(s))
forceTable_2
data
Linkage modelframe_C frame_U
frame_L12
f_s=f(s)f_d=f(der(s))
forceTable
r=rCL1_scaled
lower
frame_L1L2
frame_C
r=rUS - rUL1L2
lowerFrameTranslation
fram
e_W
prismatic=rCS - rUSlowerShape
cylinder
upperShape
cylinder
body
Shap
e
box
a b
C
Spherical1
r=rU
W -
rUL1
L2
oute
rFra
meT
rans
latio
n
f_s=f(s)f_d=f(der(s))
forceTable
r=rCS
upperFrameTranslationComponent model
![Page 18: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/18.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving Dynamics
LibraryLibrary contentscontents
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
LibraryLibrary contentscontents
Vehicle models
Chassis models
Suspension models
Linkage models
Component models
Car.Examples
Car.Chassis
Car.Chassis.Suspensions
Car.Chassis.Components
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving Dynamics
UsageUsage
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
UsageUsage –– ExsistingExsisting examplesexamples
Library
Chassis
Library
Wheels
Library
Drivers
Library
Examples
Library
Utilities
Library
Environments
![Page 22: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/22.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Example
MyCar
Model
UsageUsage –– OwnOwn modelsmodels
Library
Chassis
Library
Wheels
Library
Drivers
Library
Examples
Library
Utilities
Library
Environments
![Page 23: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/23.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Example
MyCar
Model
UsageUsage –– With With otherother librarieslibraries
Library
Chassis
Library
Wheels
Library
Drivers
Library
Examples
Library
Utilities
Library
Environments
Library
PowerTrain
Library
PowerTrainHevLib
Library
PowerTrain?
![Page 24: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/24.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ResultsResults??
UsageUsage –– VisualisedVisualised performanceperformance
![Page 25: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/25.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
UsageUsage -- Suspension Suspension mappingmapping
![Page 26: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/26.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
UsageUsage -- Comfort Comfort issuesissues
![Page 27: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/27.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving Dynamics
RelatedRelated librarieslibraries
![Page 28: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/28.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
PlanarMultiBody.moPlanarMultiBody.mo
flange_SW
BGR
flange_2 flange_4
flange_1 flange_3
y
x
y
x
Wheel_1
y
x
y
x
Whe
el_2
y
x
y
x
Wheel_3
y
x
y
x
Whe
el_4
freeMotion
frontSuspension
left
XYSuspension
rearSuspension
left
XYSuspension
twoD
2Thr
eeD
ground
xy
bodyFi
xed1
=0
![Page 29: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/29.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
Forces.moForces.mo
Library
Utilities
a b a b
a b a b a b
ElastoGap
Library
Examples
a b
ElastoGap3D
![Page 30: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/30.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
SummarySummary
– Chassis modelling– Driving dynamics simulation– Interfacing other Modelica libraries
![Page 31: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/31.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving Dynamics
FutureFuture ImprovementsImprovements
![Page 32: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/32.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
EvaluationEvaluation aidsaids
• Related models– Drivers- Automatic test rigs- ...
• Motion constraints– Constant speed maneouvres– Constant radius turns– ...
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ExtendedExtended flexibilityflexibility
• With/without bushings• Linear/nonlinear spring-dampers• Swapping tyre models• 1D-2D-3D geometries and combinations
![Page 34: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/34.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ExtendedExtended flexibilityflexibility
• Different models share same interface.– Model focus/viewpoint can be changed easilly!
![Page 35: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/35.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
Different Different modelsmodels shareshare same interfacesame interface
![Page 36: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/36.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
flange_SW
BGR
flange_1 flange_3
ground
xy
whe
el_2
wheel_1
wheel_3
whe
el_4
freeMotion
frontSuspension
left
MacPherson
rearSuspension
left
TwistBeam
flange_SW
BGR
flange_2 flange_4
flange_1 flange_3
y
x
y
x
Wheel_1
y
x
y
x
Whe
el_2
y
x
y
x
Wheel_3
y
x
y
x
Whe
el_4
freeMotion
frontSuspension
left
XYSuspension
rearSuspension
left
XYSuspension
twoD
2Thr
eeD
ground
xy
body
Fixe
d1=0
Different Different modelsmodels shareshare same interfacesame interface
planar
![Page 37: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/37.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ExtendedExtended flexibilityflexibility
• Different models share same interface.– Model focus/viewpoint can be changed easilly!– Higher requirements on interfaces!
![Page 38: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/38.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
SuitableSuitable interfaces?interfaces?
four wheelsteering?
Activesuspension?
![Page 39: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/39.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ExtendedExtended flexibilityflexibility
• Different models share same interface.– Model focus/viewpoint can be changed easilly!– Higher requirements on interfaces!– Over-all model structure that is suitable!
![Page 40: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/40.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
SuitableSuitable structurestructure
L?
X-by wire? Fuel cell technology?
Vehicle dynamicscontrol systems?
Energy management?
![Page 41: Driving Dynamics Modelling with Modelica€¦ · multi-links struts. Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics Linkage model (MacPherson)](https://reader035.vdocuments.us/reader035/viewer/2022063016/5fd6da6d501a473b70589465/html5/thumbnails/41.jpg)
Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ExtendedExtended flexibilityflexibility
• Different models share same interface.– Model focus/viewpoint can be changed easilly!– Higher requirements on interfaces!– Over-all model structure that is suitable!– Sub-models must know their limitations!
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ModelModel limitiationslimitiations!!
-15 -10 -5 0 5 10 15
4
2
0
-2
-4
kN
o
αv
α
y
Magic FormulaLinear model
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
AcknowledgementsAcknowledgements
• Dynasim AB• DLR
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Johan Andreasson, Division of Vehicle Dynamics, KTH Driving DynamicsDriving Dynamics
ContactContact