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TURNINGCHARACTERISTICSOFMULTIAXLEVEHICLESABSTRACTTHISPAPERPRESENTSAMATHEMATICALMODELFORMULTIAXLEVEHICLESOPERATINGONLEVELGROUNDCONSIDERINGPOSSIBLEFACTORSRELATEDTOTURNINGMOTIONSUCHASVEHICLECONFIGURATIONANDTIRESLIPVELOCITIES,EQUATIONSOFMOTIONWERECONSTRUCTEDTOPREDICTSTEERABILITYANDDRIVINGDECENCYOFSUCHVEHICLESTURNINGRADIUS,SLIPANGLEATTHEMASSCENTER,ANDEACHWHEELVELOCITYWEREOBTAINEDBYNUMERICALLYSOLVINGTHEEQUATIONSWITHSTEERINGANGLESANDAVERAGEWHEELVELOCITYASNUMERICALINPUTSTOELUCIDATETHETURNINGCHARACTERISTICSFAULTYAXLEVEHICLES,THEEJECTOFFUNDAMENTALPARAMETERSSUCHASVEHICLESPEED,STEERINGANGLESANDTYPEOFDRIVINGSYSTEMWEREEXAMINEDFORASAMPLEOFMULTIAXLEVEHICLESADDITIONALLY,FIELDTESTSUSINGFULLSCALEVEHICLESWERECARRIEDOUTTOEVALUATETHEBASICTURNINGCHARATARACTICSONLEVELGROUNDKEYWORDSMULTIAXLEVEHICLESTURNINGMANEUVERABILITYMATHEMATICALMODEL1INTRODUCTIONTRACKLAYINGRUNNINGGEARHASBEENMAINLYUSEDINTHEFIELDSOFMILITARYANDCONSTRUCTIONFORHEAVYVEHICLEAPPLICATIONSRECENTLY,RUNNINGGEARWITHPNEUMATICTIRESHASBEENEXPANDINGTOHEAVYVEHICLESINSUCHFIELDS,SINCETIREEQUIPPEDVEHICLESEXCELINSPEED,SILENCEANDENERGYECOGENCYSEVERALPAPERSHAVEBEENPUBLISHEDONTHESUBJECTOFTRACTABILITYANDMANEUVERABILITYOFMULTIAXLEVEHICLES1,2ATHEORETICALSTUDYTOEVALUATETHETURNINGMOTIONOFSKIDSTEERINGVEHICLESWASALSODEVELOPEDBYRENOIRANDCRAVAT3MORERECENTARMYVEHICLES,SUCHASTHEMODIX,AREDESIGNEDTOBEEQUIPPEDWITHINDEPENDENTWHEELDRIVEANDSTEERING,ANDLOADCONTROLSUSPENSIONS4THEMODIXCANTURNBYNORMALSTEERING,SKIDSTEERING,ORAMIXTUREOFBOTHADDITIONALLY,THECONVERSIONFROMMECHANICALDRIVETOANELECTRICDRIVEUNITCONTROLLEDBYEACHINHUBMOTORHASBEENEXAMINED57AHYBRIDWHEELSTEERSYSTEMISBEINGDEVELOPEDTOCOMPLEMENTTHEINDEPENDENTDRIVECAPABILITYOFTHEINHUBWHEELMOTORSHOWEVER,THEREHASNOTBEENAPAPERORTECHNICALPUBLICATIONDEALINGWITHTHESUBJECTCOMPREHENSIVELYANDINALOGICALSEQUENCEBECAUSETHEPHENOMENONOFDYNAMICMOTIONSOFTHEMULTIAXLEVEHICLEISCOMPLEXTHISPAPERDESCRIBESACOMPUTERSIMULATIONMODELTOPREDICTTURNINGCHARACTERISTICSOFMULTIAXLEVEHICLESTHEEQUATIONSOFMOTIONFORTHEVEHICLESARECONSTRUCTEDFORLEVELGROUNDTRACTATEANDSIDEFORCESACTINGUNDERPNEUMATICTIRESDUETOINTERACTIONWITHTHEGROUNDAREOFFUNDAMENTALIMPORTANCETOPREDICTTHEMOTIONOFVEHICLESINTHENUMERICALSIMULATION,THEBRUSHMODELBASEDONAPHYSICALAPPROACHWASADOPTEDFORTHETIREMODEL8THEBRUSHMODELISANIDEALIZEDREPRESENTATIONOFTIRESINTHEREGIONOFCONTACTINORDERTODETERMINETHETURNINGMOTIONOFMULTIAXLEVEHICLES,THEEJECTSOFFUNDAMENTALPARAMETERSSUCHASVEHICLESPEED,STEERINGANGLESANDTYPEOFDRIVINGSYSTEMAREEXAMINEDBYUSINGSPECIFICATIONOFANEXAMPLEVEHICLEFIELDTESTSONMULTIAXLEVEHICLESWEREALSOCONDUCTEDANDCOMPAREDTOTHEPREDICTEDRESULTSWITHTHEDATANUMERICALLYOBTAINEDBYTHEMODELTHERESULTSDEMONSTRATEDTHATTHEPROPOSEDMATHEMATICALMODELCOULDACCURATELYASSESSTHETURNINGCHARACTERISTICSOFMULTIAXLEVEHICLES2MATHEMATICALMODELOFMULTIAXLEVEHICLES21COORDINATESYSTEMANDKINEMATICSOFTHEVEHICLEFIG1SHOWSCOORDINATESYSTEMSUSEDTODESCRIBEAMULTIAXLEVEHICLEWITHVELOCITYVECTORVANDYAWANGULARVELOCITYHATTHEMASSCENTERTHECOORDINATESYSTEMX1,X2ISFIXEDONTHELEVELGROUNDWITHUNITBASEVECTORSE1,E2AMOVINGCOORDINATESYSTEMX1,X2ISATTACHEDTOTHEVEHICLE,WHOSEORIGINISLOCATEDATTHEMASSCENTER,WITHUNITBASEVECTORSE1,E222EQUATIONSOFMOTIONNEWTONSSECONDLAWAPPLIEDTOTHEVEHICLEYIELDSWHEREMANDIARETHEMASSANDTHEMOMENTOFINERTIAFORTHEVEHICLE,RESPECTIVELYTHEFRICTIONALFORCEQISDEFINEDUNDERTHEITCHWHEEL,ANDXIDENOTESTHEPOSITIONVECTOROFTHEITCHWHEELINASTEADYSTATETURN,THEEQUILIBRIUMEQUATIONSFORTHEVEHICLEAREOBTAINEDBYSETTINGVANDZERO23TIRESLIPANDFRICTIONALFORCESMODELINGOFSHEARFORCEGENERATIONFORPNEUMATICTIRESHASBEENREVIEWEDBYPACIFICAANDSHARP8WHOCOVERSPHYSICALANDEMPIRICALMODELSTHEBRUSHMODEL,ANANALYTICALMODELPHYSICALLYDERIVED,HASBEENWIDELYUSEDFORVEHICLEDYNAMICSSTUDIESTHERELATIONBETWEENDEFORMATIONSOFTIRETREADSANDSHEARFORCES,IE,SIDEFORCEANDTRACTATEFORCE,ISSIMPLIFIEDANDTHEMODELIDEALIZESTHEREPRESENTATIONOFTIRESINTHEREGIONOFCONTACTTHEHORIZONTALSHEARFORCESACTINGUNDERTHETIREDUETOINTERACTIONWITHTHEGROUNDAREASSUMEDTOBELINEARLYDEPENDENTONTHETREADDISPLACEMENTFROMTHETREADBASEINTHISPAPER,THEBRUSHMODELHASBEENADOPTEDTOTHEVEHICLEMODELASCHEMATICSLIPMOTIONOFATIREWITHSLIPANGLEISSHOWNINFIG2THESLIPVELOCITYVECTORVISISDEFINEDBYTHERELATIVEVELOCITYOFTREADSURFACEANDTHEGROUNDASFOLLOWSWHEREVIANDVIRDENOTETHETRAVELINGVELOCITYVECTORANDTHEPERIPHERALSPEEDVECTOR,RESPECTIVELY,OFTHEITCHWHEELANONDIMENSIONALSLIPRATIOSISDEFINEDBYTHERATIOOFTHENORMOFSLIPVELOCITYWITHTHEMAGNITUDEOFTHEPERIPHERALVELOCITYFRICTIONALFORCEYIELDSATTHELIMITOFTHEADHESIONANDTHECOINCIDENTOFYIELDINGFRICTIONISEXPRESSEDASAFUNCTIONOFSLIPRATIOASFOLLOWSWHEREKISAPOSITIVECONSTANTDEPENDENTONTHESTAIDNESSOFTHETIRE,ANDL0ISTHEMAXIMUMCOINCIDENTOFFRICTIONTHELIMITOFSLIPRATIOSMREPRESENTSTHEFULLSLIDINGSTATEOFTHETIRETHROUGHOUTTHETREAD,EXPRESSEDBYSM1/KFIG4SHOWSTHELATERALFORCEVERSUSTHELONGITUDINALFORCEBRAKINGORTRACTIONFORCEPLOTTEDATGIVENVALUESOFSLIPANGLESRODFORATIREWITHTHEPROPERTYOFK50ASTHEDRIVINGPOWERFROMTHEENGINEISTRANSMITTEDTOTHEWHEELTHROUGHTHEDEFERENTIAL,THEDRIVINGFORCEANDTHEROTATIONALSPEEDOFEACHWHEELAREINFLUENCEDBYPOWERTRAINTYPESTHEGENERALTYPEOFDRIVINGSYSTEMFORMULTIVALVEVEHICLESISILLUSTRATEDINFIG5DEFERENTIALAREMOUNTEDINEACHAXLETODISTRIBUTEEQUALTRACTATEFORCETOBOTHSIDEWHEELSANDTHEROTATIONALSPEEDSOFTHEWHEELSDEPENDONTHEPATHLENGTHOFTHETIRESTHEPROPERTYOFDIFFERENTIALISMATHEMATICALLYEXPRESSEDASCONSTRAINTEQUATIONSWHEREQLIISTHETRACTATEFORCEORTHELONGITUDINALSHEARFORCEONTHEITHTIRE,ANDVR0ISTHEAVERAGEPERIPHERALVELOCITYOFTHETIRES3EXPERIMENTALEVALUATIONFIELDTESTSWERECONDUCTEDBYUSINGTWOFULLSCALEVEHICLESTHELOWSPEEDTURNINGPERFORMANCEOFTHEVEHICLESWASEVALUATEDONACONCRETETESTGROUNDANDONSANDYGROUNDONEVEHICLEWASANEIGHTWHEELVEHICLEWITHFRONTFOURWHEELSTEERING,WHICHISIDENTIFIEDBYVEHICLEATHEOTHERWASATADANOALLTERRAINVEHICLEORVEHICLEB,WHICHISANEIGHTWHEELVEHICLEWITHALLWHEELSTEERINGSHOWNINFIG6THEMAXIMUMCOINCIDENTOFFRICTIONL0DEPENDSONTHEGROUNDCONDITIONTHECOERCIONSWEREMEASUREDINTHEFIELDANDL006WASOBTAINEDWITHVEHICLEBONTHECONCRETEGROUNDANDL008WITHVEHICLEAONTHESANDYGROUNDINTHEFIELDTESTS,TWOSTEERINGTYPESWEREEXAMINEDONEWASSTEERINGBYTHEFRONTFOURWHEELS,ANDTHEOTHERBYALLTHEWHEELSFIG7SHOWSTHEEXPERIMENTALANDPREDICTEDRESULTSOFTHETURNINGRADIUSVERSUSSTEERINGANGLESTHEPARAMETERINDICATESTHEAVERAGESTEERINGANGLEOFTHEFRONTWHEELSAND,FORALLWHEELSTEERINGTHEANGLESOFTHEREARFOURWHEELSAREFIXEDATAMAXIMUMINITSSTEERINGCAPABILITYITISCLEARTHATTHETURNINGRADIIOFTHEVEHICLESAANDBDECREASEASTHESTEERINGANGLESINCREASETHELOWERLINEFORVEHICLEBINDICATESTHERESULTSOFALLWHEELSTEERINGWITHREARSTEERINGANGLES,3137,230,143,250FROMFIG7ITCANBESEENTHATTHETURNING478RADIUSHASBEENSUBSTANTIALLYDECREASEDBYMAKINGUSEOFALLTHEWHEELSFORSTEERING4NUMERICALSIMULATIONANDRESULTS41VEHICLERESPONSEINFOURWHEELSTEERINGINORDERTOEVALUATETHETURNINGCHARACTERISTICSOFMULTIVALVEVEHICLES,THENUMERICALSIMULATIONWASCARRIEDOUTUSINGTHESPECIFICATIONSOFAFULLSCALEVEHICLETHEMASSISM24,500KGANDTHEMASSCENTERISLOCATEDATTHEGEOMETRICCENTERTHEDETERMINATIONOFSTEERINGANGLEOFEACHWHEELISSHOWNINFIG8FORTHECASEOFTHEFIRSTANDSECONDAXLEWHEELSBEINGSTEERED4WSFOURWHEELSTEERINGEACHWHEELSTEERINGANGLEDCANBEOBTAINEDGEOMETRICALLYSUCHTHATALLWHEELSHAVEASTEERINGCENTERCONTHEMIDDLELINEBETWEENTHETHIRDANDTHEFOURTHAXLES,INASIMILARWAYTOTHEACKERMANANGLEDETERMINATIONINTHISSIMULATION,ITISASSUMEDTHATTHEREISANIMAGINARYWHEELINTHEMIDDLEOFTHETWOWHEELSONTHEFIRSTAXLEANDTHEANGLEOFTHEIMAGINARYWHEELDISUSEDTOREPRESENTTHEAVERAGEANGLEOFTHEFRONTWHEELSFIG9SHOWSTHESTEERINGANGLESVERSUSTIMEUSEDINTHESIMULATIONSTHEVEHICLEMODELSTARTSATTHEORIGINANDACCELERATESINTWOSECONDSUPTOWHEELVELOCITYVR014M/S,INFIGS9AND10THETIMEAXISBEGINSATTHISPOINTTHENAFTER05SOFSTRAIGHTMOTION,THEVEHICLEBEGINSSTEERINGUPTOTHEMAXIMUMSTEERINGANGLE10ADDITIONALLY,THELATERALFORCEONTHETHIRDAXLEISMUCHLARGERTHANTHEFORCESONTHEFIRSTANDSECONDAXLESITWASFOUNDFROMTHENUMERICALRESULTSTHATTHESIDESLIPANGLEOFTHETHIRDAXLETIRESISLARGEANDOPPOSITEINDIRECTIONCOMPAREDTOTHEOTHERTIRES42EFFECTOFREARWHEELSTEERINGONTURNINGCHARACTERISTICSTHETURNINGRADIUSOFVEHICLESATLOWSPEEDISEXPECTEDTODECREASEIFTHEREARWHEELSARESTEEREDWITHOPPOSITEANGLESTOTHEFRONTWHEELSFIG13SHOWSTHESTEERINGRADIUSWHENTHETIRESONTHETHIRDANDFOURTHAXLESAREINVERSELYSTEEREDTOTHEFRONTWHEELSTHEAVERAGESTEERINGANGLEOFTHEREARWHEELSISDEFINEDASTHEANGLEOFANIMAGINARYWHEELINTHEMIDDLEOFTHEWHEELSONRTHEFOURTHAXLEASSHOWNINFIG13THECHANGEINTURNINGRADIUSVERSUSREARSTEERINGANGLESATL10MISILLUSTRATEDINFIG14RFORTHEFRONTSTEERINGANGLES,D10,20AND30ITISCLEARTHATTHETURNINGRADIUSDECREASESCONSIDERABLYASTHEREARSTEERINGANGLEINCREASESINTHEDESIGNOFMULTIAXLEVEHICLESTHESTEERCENTERSOFTHEFRONTWHEELSDONOTGENERALLYCOINCIDEWITHTHECENTEROFTHEREARWHEELS,ASSEENPREVIOUSLY作者KWATANABE,JYAMAKAWA,MTANAKA,TSASAKI国籍AMERICAN出处THENATIONALDEFENSEACADEMY,11020HASHIRIMIZU,YOKOSUKA2398686,JAPANAVAILABLEONLINE29MARCH2006多轴车辆的转向特性摘要本文为平地上操作多轴车辆的数学模型,考虑有关的可能因素构建转向车辆配置和轮胎滑移速度,如运动预测的可操作性和这些车辆的驾驶效率。车轮中心转弯半径,滑移角被包含其中,通过车轮角的方程式解决,说明了转折点特征多轴车辆,效果的基本参数,如车速,转向角度和行驶系统类型,多轴车辆的样本。此外,实地测试,使用大型车辆进行了评估水平地面上的基本转折点特征关键词多轴车辆,可操作性,数学模型1引言主要运用于军事履带运行车辆和建筑领域的重型车辆,由于轮胎车辆配备擅长在速度,低噪音和高能源效率。最近运行与充气轮胎的齿轮的规模不断扩大至重型车辆的这些领域。已有多份发表的文件关于多轴车辆的通过性和可操作性,RENOU和CHAVAN还进行了一个关于防滑方向盘汽车的评估,更近的军队车辆,如MODIX,被设计为具有独立配备四轮驱动和转向和负荷控制悬浮,MODIX能够由正常的车轮,滑移车轮或是两者的混合转动,此外,转换从机械传动电动驱动装置控制每个轮毂电机已审查。混合四轮转向系统正在开发,以补充独立的毂轮马达驱动器的能力。然而,有没有得到全面处理这个问题的论文或技术出版物,并在日志逻辑顺序,因为动态运动的多轴车辆是复杂的现象。本文介绍了一种计算机模拟模型来预测多轴车辆的转向特点,汽车运动的微方程构造为平地,牵引力和侧力的作用下充气轮胎由于与地面交互的基本精神的重要性,来预测车辆的议案,在数值模拟,基于物理的方法刷模型通过轮胎模型,在接触区域里刷模型是理想化的代表轮胎。为了确定多轴转动车辆的运动,如基本参数的影响车辆行驶速度,转向角度和驾驶系统类型检查的一个例子,多轴车辆的实地测试也进行与数字数据的预测结果相比得到的模型。结果表明,提出了数学模型,可以准确地评估多轴车辆的转向特性2多轴车辆的数学模型21坐标系统和车辆的运动学图1所示的坐标系统,用来形容多轴车辆的速度矢量V和偏航角速度重心Q。坐标系统(X1,X2)的水平地面上的固定单位基向量E1,E2,连接到一个移动的坐标系统(X1,X2)的车辆,其原产地是在质量中心位于单位基向量E1,E2,车辆N个轮子一方独立悬挂弹簧和具有相同属性的支持车身。22运动方程式牛顿第二定律应用于汽车产量NIIQMV21()NIIIXEI213213E其中M和I分别是车辆的质量和惯性矩,摩擦力Q是指车轮受到的力,以及表示车轮的位置坐标,在稳定的转向中,汽车运动方程式中包含有V和IQ。23轮胎滑行和摩擦力充气轮胎产生剪切力的建模已由PACIFICA和SHARP报道过其中包含有物理和实证模型。刷模型是分析模型物理派
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