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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 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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)