大型刚体惯性参数识别的三线扭摆系统实验方法改进研究

247Vol.24No.720077July2007ENGINEERINGMECHANICS592005-12-032006-08-02*(1978)CAE(E-mail:[e-mail])(1961)CAE(E-mail:[e-mail]).1000-4750(2007)07-0059-07*(100084)6~9(1)(2)()(3)(4)U463;U467.3;O313.3AIMPROVEMENTOFEXPERIMENTALIDENTIFICATIONMETHODWITHTRIFILARTORSIONALPENDULUMFORINERTIAPROPERTIESOFLARGE-SCALERIGID-BODY*SUCheng-qian,LUZhen-hua(StateKeyLaboratoryofAutomotiveSafetyandEnergy,DepartmentofAutomotiveEngineering,TsinghuaUniversity,Beijing100084,China)Abstract:Itisoneoftheimportantrequisitesintheenginemountingsystemdesigntoaccuratelydeterminetheinertiapropertiesofapowertrainrigidbody.Observingthattrifilartorsionalpendulumcanpreciselymeasuremassmomentofinertiaofcomplexrigidbody,anexperimentalmethodologyforinertiaparameteridentificationisproposed,inwhichtherigidbodyispositionedat6~9differentorientationsrepresentedwiththree-pointsontherigidbody.Thekeypointsinclude:(1)theorientationoftherigidbodyisindirectlydeterminedwiththreepointsontherigidbody,andamovablecoordinatesystemisdefinedwiththenormalvectorofplaneformedbythethreeon-bodypoints;(2)distancesbetweenthethreeon-bodypointsandreferencepointsonthependulumplate(definingaglobalcoordinatesystem)aremeasuredforeachtest,andglobalcoordinatesofthethreeon-bodypointsandthecoordinatetransformationbetweenthetwocoordinateframesaredetermined(3)therotationaxisorientationoftherigidbodyandthemomentofinertiaforeachtestunderthemovablecoordinatesarecalculated;and(4)utilizingleastsquareprinciple,theoptimalintersection“point”oftherotationaxisofeachtestis60determinedtobethecenterofgravity,andthenasetoflinearequationsderivedfromthetransformationformulaofrigid-bodymomentofinertiaaboutdifferentaxisrotationissolvedtoidentifyinertiatensoroftherigidbody.Somefactorsthatmayproduceerrorsstillexistintheproposedidentificationprocedure,buttheycanbeestimatedandeffectivelyreducedateverystepwithleastsquaremethod.Thepracticabilityandreliabilityoftheprocedureisillustratedbyerroranalysis,validationofcuboidmassblockandmanytestsofrealpowertrains.Keywords:inertiaproperties;lage-scalerigid-body;trifilartorsionalpendulum;parameteridentificationprocedure;leastsquareprinciple[1]CAD[2]CAD[3][4][5~7][8,9][10]1%()()1XZY3(1,2,3)iPi=CAD()±5mm1%6122.11(O)0Φ(5o)OZ1.2.3.4.1234OZLR1Fig.1Testprincipleoftrifilartorsionalpendulummeasurementforrigid-bodymassmomentofinertia20OZMgRJLφφ+=(1)JOZOZMφLROL/R(5)(1)T2224πOZJLTMgR=(2)TJOZ2224πOZMgRTJL=(3)JPOZJOZPJJJ=−(4)2.2JCxxxyxzyxyyyzzxzyzzJJJJJJJJJ⎡⎤−−⎢⎥=−−⎢⎥⎢⎥−−⎣⎦CJlcJlcTlcJ=⋅⋅CaJa(5)T[cos,cos,cos]αβγ=alcN(5)JC⋅lccJ=HJ(6)H222111111111222222222222222222222222NNNNNNNNNlmnlmmnnllmnlmmnnllmnlmmnnl⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎣⎦H######()=cos,=cos,=cos1,2,...,iiiiiilmniNαβγ=T12[,,,]lclclcNJJJ=lcJT[,,,,,]xxyyzzxyyzzxJJJJJJ=−−−CJJC66N≥(6)HcJT-1T()=⋅=⋅+clclcJHJHHHJ(7)69N≤JCJ0U01023JJJ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦J0102030010203010203010203[]llluuummmnnn⎡⎤⎢⎥==⎢⎥⎢⎥⎣⎦U2.3NNdGli62(i=1,2,…,N)(xCG,yCG,zCG)dGli(lci,mci,nci)111GliciciciCGcpiCGcpiCGcpiijkdlmnxxyyzz=−−−GGGSD21NDGliiSd==∑(8)SD2.4OXYZO1X1Y1Z1Bj(j=1,2,…,m)BjPi(i=1,2,3)O1X1Y1Z12Piq(4q≥)Bkdik({k1,k2,k3,k4}[1,q])Pi(xpi,ypi,zpi)DiOP1P2P3X1Z1Y1Bk1XYZBk2Bk4Bk32Fig.2Three-pointsorientatingmethod22221(()()())qipiBkpiBkpiBkikkDxxyyzzd==−+−+−−∑(9)DiPiO1X1Y1Z12.5(1)Pi()(2)O(3)(2)6(4)(6)HJlc33.13.2(3)(3)6322JMRTLJMRTL∆∆∆∆∆≤+++(10)0.4%,0.3%,0.1%,0.1%MRTLMRTL∆∆∆∆====/0.9%JJ∆≤3.3(9)ijd∆PiBk()||||/||||XijiijSeDXd=∆∆(11)Pizpixpiypiijd∆1.5mm()2ijSeD3.4(6)HHH22()||||||||condN+=⋅HHH()936(4)(4)44.1(3)200mm×300mm×600mm256kg1693Fig.3TestposturesofCuboidinthreemainaxesofinertia11Table1Cuboidmassmomentofinertiainthreemainaxes/(kg·m2)/%19.65679.60000.5968.53038.53330.0492.79442.77330.764.22~N(0)28(5mm)8645mm2Table2IdentificationresultsofcenterofgravityofapowertrainN/mm282.5,-56.7,-213.9/mm/mm/mm∆X∆Y∆Z13.92.62.90.223.73.31.6-0.833.5-3.01.4-1.142.1-1.7-0.5-1.151.21.1-0.0-0.564.11.70.53.874.5-2.7-1.0-3.588.60.1-6.75.493.3-1.41.7-2.44.3943XYZ1234567894Fig.4Testingrotationaxiesofapowertrain3Table3OrientationanglesoftestingaxesinthemovingcoordinatesystemOX/(°)OY/(°)OZ/(°)191.3991.421.98293.44129.9140.12383.9936.7053.95486.687.7583.01572.4989.8317.516126.3188.8636.3473.2392.8488.46874.3520.28102.589107.4328.17111.40(7)JCJ0U0(4)(6)(5)4Table4Resultsofinertiapropertiesofapowertrain6.9160.0198-0.9330.019811.935-0.782JC/(kg·m2)-0.933-0.78210.159J0/(kg·m2)6.66010.09512.254-0.9640.258-0.069-0.036-0.380-0.924U0-0.265-0.8880.37615.51104.9786.0487.9667.6522.45/(°)74.6327.37112.065Table5RelativeerroranalysisofidentifiedresultsJlci/(kg·m2)Jlci/(kg·m2)/%110.24210.309-0.66211.73211.7300.02310.41610.472-0.54411.69211.6080.7359.3269.2540.7869.8879.8500.3876.8816.895-0.21811.92411.955-0.25911.53611.563-0.2351%(6)6N6N(6)61273486N(N=9)N6(1)(H)(4)656Table6Relativeerroranalysisofidentificationresultswithseveraldifferentsetsoftestingaxes12341234589135678912345689356789Ncond(H)34.52.69.52.3N/%Jxx24.14-0.08-4.680.18Jyy-0.440.450.130.59Jzz0.70-0.090.33-0.75Jx015.89-0.15-5.040.04Jy06.920.220.49-0.15Jz0-0.560.220.100.15/%10.23-0.75-0.30-1.422-0.24-0.050.22-0.503-0.39-0.04-0.4