Modeling of Road Traffic Events

309 Pages·2022·12.264 MB·English

by  Jerzy Kisilowski, Jarosław Zalewski

Jerzy Kisilowski
Jarosław Zalewski
Modeling
of Road
Traffic Events
Modeling of Road Traffic Events
·
Jerzy Kisilowski Jarosław Zalewski
Modeling of Road Traffic
Events
JerzyKisilowski JarosławZalewski
KazimierzPułaskiUniversity WarsawUniversityofTechnology
ofTechnologyandHumanitiesinRadom Warsaw,Poland
Radom,Mazowieckie,Poland
ISBN978-3-030-91397-7 ISBN978-3-030-91398-4 (eBook)
https://doi.org/10.1007/978-3-030-91398-4
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Contents
1 Introduction ................................................... 1
References ..................................................... 3
2 SelectedTechnicalAspectsofaMotorVehicleMotion ............. 5
2.1 SelectedElementsofMechanicsofVehicleMotion ............. 5
2.2 TheProblemofVehicleCrashMechanicsinaModelApproach ... 10
2.3 SelectedAspectsofVehicleCrashSimulation .................. 17
2.4 TheProblemofVehicleStabilityinTheoreticalApproach ........ 18
2.5 Possibilities of Stability Analysis of Motor Vehicles
inPracticalTerms .......................................... 22
2.6 AnalysisRelatedtoSpeedingandBrakingtheMotorVehicle ..... 23
References ..................................................... 27
3 VehicleCollisions—TheSelectedIssues ........................... 41
3.1 MechanicsofVehicleCollisioninGeneral ..................... 42
3.2 VehicleCollisionwiththeResultantMotion .................... 46
3.3 MechanicsofVehicleCollisionsinCaseoftheSideImpact ...... 57
3.4 SelectedAspectsoftheUseofRestitutionCoefficients .......... 74
3.5 CollisionSimulations—SelectedAspects ...................... 78
References ..................................................... 87
4 SelectedAspectsofMotorVehicleResearchBackgrounds .......... 91
References ..................................................... 100
5 TheRoleofDisturbancesoftheSelectedVehicleParameters
intheStabilityExaminationResearch ............................ 103
5.1 DisturbancesoftheMass–InertiaParameters ................... 104
5.2 DisturbancesofMotionResultingfromtheStructuralChanges .... 112
5.3 DisturbancesResultingfromtheRoadIrregularities ............. 119
5.4 TheProblemofChangingtheParametersofaVehicleBody
asaResultoftheImpact ..................................... 125
v
vi Contents
5.5 PossibilityofPracticalApplications ........................... 133
References ..................................................... 141
6 ReviewoftheSelectedDefinitionsofStability ..................... 145
6.1 StabilityintheSenseofLyapunov ............................ 147
6.1.1 AsymptoticStabilityintheSenseofLyapunov ........... 148
6.1.2 Stability in the Sense of Lyapunov in the Case
oftheConstantlyActingDisturbances .................. 148
6.2 StabilityintheSenseofLagrange ............................. 149
6.3 OrbitalStability ............................................ 150
6.4 StabilityinthePoissonSense ................................ 151
6.5 TechnicalStability .......................................... 152
6.6 TheStochasticTechnicalStability ............................ 153
6.6.1 Assumptions ........................................ 153
6.6.2 DefinitionoftheStochasticTechnicalStability ........... 154
6.7 StabilityofaMotorVehicleasaRealObjectAccording
toISO8855 ............................................... 155
6.8 The Initial Conclusions on the Possible Comparisons
oftheStabilityinaMathematicalSensewiththeStability
oftheRealObjects ......................................... 156
References ..................................................... 158
7 Selected Aspects of the Stochastic Technical Stability
Examination ................................................... 161
7.1 StochasticTechnicalStabilityTestsfortheSelectedType
ofVehicle’sModel ......................................... 161
7.2 Comparison of Simulation Results with Stability
inAccordancewithISO8855:1991 ........................... 203
7.3 PossibleApplicationsandProblemRelatedtothePractical
DefinitionsofStochasticTechnicalStability .................... 207
References ..................................................... 212
8 SelectedProblemsinMotorVehicleBrakingandAcceleration ...... 215
8.1 SelectedAspectsofaMotorVehicle’sBraking ................. 215
8.2 SelectedAspectsofWheel–RoadCooperationintheVehicle
AccelerationProcess ........................................ 232
8.3 AdditionalFactorsInfluencingontheSelectedMaintenance
FeaturesofaMotorVehicle .................................. 237
References ..................................................... 239
9 OtherProblemsofMotionoftheMotorVehicles .................. 241
9.1 InfluenceoftheRandomlyUnevenRoadsontheResponse
ofaMotorVehicle .......................................... 241
9.2 TheLateralMotionofaMotorVehicle ........................ 251
9.3 TheSteeringWheelRelease ................................. 261
Contents vii
9.4 ThePoweroffStraightLineMotion ........................... 270
9.5 TurningAroundManeuver ................................... 284
References ..................................................... 302
Summary ......................................................... 305
Important Symbols
A ThefrontSurfaceofthevehicle(m2)
C The coefficient determining the road surface conditions
accordingtotheISO8608standard(m3/rad)
corr Thecoefficientdeterminingthesimilarityoftheroadprofiles
lp
fortheleftandtherightwheelsofamotorvehicle
c Thecoefficientoftheairresistance
x
I The moment of inertia in relation to the vertical axis that
passesthroughthecenterofmassofagivenvehicle(kgm2)
I ,I Themomentsofinertiaofthecollidingvehiclesinrelationto
A B
theverticalaxespassingthroughtheircenterofmass(kgm2)
I ,I ,I Themomentsofinertiaofamotorvehicleinrelationtothe
X0 Y0 Z0
axespassingthroughaso-calledorigopoint(kgm2)
I ,I ,I The moments of deviation of a motor vehicle in relation to
XY0 XZ0 YZ0
theaxespassingthroughaso-calledorigopoint(kgm2)
I ,I ,I Themomentsofinertiainrelationtotheaxespassingthrough
X1 Y1 Z1
thecenterofmassofanunladenvehicle(kgm2)
I ,I ,I The moments of deviation in relation to the axes passing
XY1 XZ1 YZ1
throughthecenterofmassofanunladenvehicle(kgm2)
L Thewheelbase(m)
m Themassofavehicle(kg)
m ,m Themassofadriver(kg)
1 k
m ,m Themassofapassenger(kg)
2 p
m ,m The mass of the vehicle A and B, respectively, which is
A B
involvedinacollision(kg)
m Themassofabaggage(kg)
B
m Themassofthevehicle’sunladenbody(kg)
N
m Themassofthevehicle’sladenbody(kg)
NO
m The total mass of the vehicle without a driver, a passenger
P
andabaggage(kg)
m The total mass of the vehicle weight after loading with a
PO
driver,apassengerandabaggage(kg)
ix
x ImportantSymbols
m Themassofthepassengersittingbehindthedriver(kg)
t1
m Themassofthepassengersittingintherearontheright(kg)
t2
n ,t ,n ,t ,b ,b Thecoordinatesofthecentersofmassofthevehiclesinvolved
A A B B A B
incollisionrelativetothegeometriccenterofcollisioninthe
normal,tangentialandbinormaldirection(m)
N Thenumberofeventsinthejthclassoftheareaofacceptable
Kj
(cid:2) solutions
N Thesumofalleventsinallclassesoftheacceptablesolutions
Kj
P The indicator enabling a quantitative assessment of the
stochastictechnicalstabilityofamathematicalmodelofthe
motorvehicle,basedonthenumberε
r Thecoordinatespecifyingthepositionofthecenterofmass
in a vehicle involved in collision relative to the point of
applicationoftheimpulseoftheresultantimpactforce(m)
R,R The restitution coefficients for the tangential and normal
t n
velocities, respectively, in relations to the plane of impact
(theplaneofcontactbetweenthevehicles)
S Impulseoftheresultantimpactforce(Ns)
S ,S ,S The components of the impact force impulse in the normal
n t b
(n),tangential(t)andbinormal(b)directionstothecollision
plane(Ns)
S ,S ,S The normal, tangential and binormal components of the
wn wt wb
inertiaforceimpulseresultingfromtherelativeaccelerations
intheresultantmotion(Ns)
S ,S ,S The normal, tangential and binormal components of the
un ut ub
transportationforceimpulseincomplexmotion(Ns)
S ,S ,S The normal, tangential and binormal components of the
cn ct cb
impulseofcoriolisforceintheresultantmotion(Ns)
v Vehicle’svelocity(m/s)
v ,v Thecomponentsofthelongitudinalvelocitiesofbothvehi-
At Bt
clestangentialtothecollisionplane(m/s)
v ,v Thecomponentsofthelongitudinalvelocitiesofbothvehi-
An Bn
clesnormaltothecollisionplane(m/s)
v ,v Thecomponentsofthelongitudinalvelocitiesofbothvehi-
Ab Bb
clesbinormaltothecollisionplane(m/s)
v ,v The relative velocities of the vehicles along the tangential
Zt Zn
andnormalaxesofthelocalcoordinatesystemlocatedinthe
geometriccenterofcollision(m/s)
w Therelativetangentialvelocityinthecollisionmodelbased
t
ontheRouthmethod(m/s)
w Therelativenormalvelocityinthecollisionmodelbasedon
n
theRouthmethod(m/s)
W(K ) Thefrequencyofsolutionsremaininginj-class
j
X(t) The stochastic process defined for the definition of the
stochastictechnicalstability
ImportantSymbols xi
x ,y ,z Thecoordinatesofthecenterofmassrelativetothe‘origo’
C C C
point(m)
z (s),z (s) The realizations of signals used to determine the randomly
1 2
uneven road profile for the left and the right wheels of the
vehicle
α Theanglebetweenthenormal(n)andthevelocityvectorof
thevehicleinvolved(º)
α (cid:2) VehiclepositionangleAaftercollisionwithrespecttonormal
A
totheplaneofimpact(º)
α (cid:2) VehiclepositionangleBaftercollisionwithrespecttonormal
B
tothecollisionplane(º)
α ,α ,α The indicators used to determine the impulses of collision
tt nt nn
forcesintheRouthmethod(1/kg)
β Thedampingcoefficient
δ Theindicatoroftheso-calledroadwavinessthatdetermines
whetherthespectrumhaslongorshortwavelengths
ε Thepositivenumberusedasanindicatorofdeterminingthe
probabilityofasolutionremainingintheareaofacceptable
solutions (Ω) according to the definition of the stochastic
technicalstability
η(t) TheabsoluteintegrablestochasticprocessusedintheLips-
chitzcriterion
λ Thewavelengthofroadunevenness(m)
μ Thecoefficientofadhesionbetweenthewheelsandtheroad
ξ(t) The stochastic process describing the randomly occurring
disturbancesofmotion
ω The limited and open area of the initial conditions in the
definitionofthestochastictechnicalstability
ω Theangularvelocityofthevehiclearoundtheverticalaxes
passingthroughthecenterofmass(rad/s)
ω ,ω Theangularvelocitiesofthevehiclesinvolvedinthecollision
A B
inplanarmotion(rad/s)
Ω The limited and closed area of acceptable solutions in the
definitionofthestochastictechnicalstability
Ω Thecircularfrequencyoftheroadirregularities(rad/m)
Ω The so-calledreference circular frequency, usually equal to
0
1(rad/m)