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:1004-132Ò(2002)08-0714-05:,Weierstrass-Mandelbrot(W-M)Majumdar-Bhushan(M-B)2,,2:;;;:TH161.14:A:20000822:(50176003);,,,,,[1]Mandelbort1982,,,[27][2],[3],[4][3][4][5][6][7][5]RöS[8]W-M,6,Hasegawa[5];[7],RöSHurst1951,,[8]2,[9]Fourier,[10,11],,DaubechiesW-MM-B,7,,,11{7k,n(x)}L2(R)(),7k,n(x)=2kö27(2kx-n)(1)k,nZ(),7k,n(x)[9]2Wk{7k,n(x)}L2(R)L2(R)Wk(©),Vk=©Wk-2©Wk-1(2){k,n(x)}Vkfk+1Vk+1,fk(x)Vk41713820024gk(x)Wk,fk+1(x)=gk(x)+fk(x)(3)fk(x)gk(x)fk(x)=6n=-ck,nk,n(2kx-n)gk(x)=6n=-dk,n7k,n(2kx-n)(4)ck,n=(fk,Uuk,n)dk,n=(gk,7k,n)(5){ck+1,n}{ck,n}{dk,n};{ck,n}{dk,n}{ck+1,n};{ck,n}{dk,n}f(x)k,f(x),{fN[n2N]},N,n,1n2NDaubechies[9]1988,,Mallat,{fN[n2N]}ck,nö2=6nm=-M+nam-nck+1,mdk,nö2=6nm=-M+nbm-nck+1,m(6)ck+1,n=6n+Mm=n[an-mck,nö2+bn-mdk,nö2](7)(6)(7)k=N-1,N-2,,11n2kbm=(-1)m+1a-m+M,0mM,M=2r,r=2,3,,10,{cN,n},{fN[n2N]}:cN,n=62Ni=1fN[i2N]fiv(i-n)(8)fiv(i-n)=-H(t)N,n(t+i-n)dt(9),H(t)=sinPtPt(9)Romberg[9]f(x)L2(R),f(x)CA{cN,n}dk,n[9]ûdk,nûE2-k(A+1ö2)(10),E,0A1f(x)D=2-A(11)EminE,dk,n,(10)62kn=1ûdk,nû2k=Emin2-k(A+1ö2)(12)d3k=62kn=1ûdk,nû2k(13)(12),log2d3k=log2Emin-k(A+1ö2)(14)(14)EminA[9]d3k{dk,n},,[9],,[12]2W-M,f(x)=6+-(1-cosCnx)C(2-D)n(15),MajumdarBhushan[2](15)f(x)=G(D-1)6n=nlcos(2PCnx)C(2-D)n(16),D;C(16)M-BC=1.5Fourier,f(x)nl,,rnl=1öL,L,GL=4,G=9.810-11,W-MM-B1,Dth,Dc3W-MB-M,RöS712,2517(a)W-M(b)M-B1W-MM-B(a)W-M(b)M-B2W-MM-BDcDth1W-M1.21.51.8(%)(%)(%)1.14204.83331.35539.64671.575012.50001.11007.50001.664110.94001.168135.10601.21851.54171.51961.30671.84062.25561.15583.68331.46502.33331.79730.1500RöS1.16952.54171.38547.64001.64698.50561.15593.67501.42594.94001.65937.81671.527627.30001.54983.32001.63719.05001.17971.69171.50410.27331.78980.56672M-B1.21.51.8(%)(%)(%)1.329810.81671.48441.04001.64768.46671.19960.03331.673411.56001.413521.47221.460321.69171.61557.70001.87364.08891.341311.77501.57985.32001.84012.2278RöS1.28376.97501.51130.75331.72923.93331.29858.20831.49860.09331.70865.07781.338611.55001.43454.36671.81871.03891.19160.70001.49170.55331.81230.6833:(1),10%,,(2),,,,,[5,7](3)W-M(5%),M-B,,(),,(4)RöSW-M5%,M-B,,(5),,5%,M-B,(6),1.5,10%Fourier61713820024,(7)W-M,,,,(d31),,M-B2,22,7,2%,4,[2,4],SRAT-1,,2Lm,01001Lm,()1125Lm52mm304H62,,5[12]35,1.25Lm,8mm3304H62,4304,53304H62,W-MM-B,43045304,?212=4096,Daubechies,2,6(a)(b)6,,,[9]717::[1]SaylesRS,ThomasTR.SurfaceTopographyasaNon-StationaryRandomProcess.Nature,1978,271(2):431434[2]MajumdarA,BhushanB.RoleofFractalGeometryinRoughnessCharacterizationandContactMechanicsofSurfaces.ASMEJ.ofTribology,1990,112(1):205216[3]GagnepainJJ,Roques-carmesC.FractalApproachtoTwo-DimensionalandThree-DimensionalSurfaceRoughness.Wear,1986(109):119126[4]ZHOUGY,LeuMC.FractalGeometryModelforWearPrediction.Wear,1993(170):114[5]HasegawaM,LiuJC,OkudaKetal.Calculationofthefractaldimensionsofmachinedsurfaceprofiles.Wear,1996(192):4045[6]MajumdarA,TienCL.FractalCharacterizationandSimulationofRoughSurfaces.Wear,1990(136):313327[7],..,1997,17(4):354362[8]KaramavrucAI,ClarkNN.AFractalApproachforInterpretationofLocalInstantaneousTemperatureSignalsAroundaHorizontalHeatTransferTubeinaBubblingFluidizedBed.PowderTechnology,1997,90(3):235244[9]..:,1999:207208[10],..,1998,19(4):254257[11],..,1999,23(4):343346[12],..,2001,37(8):6569():,,1974(100083),,196520022002InternationalIndustryPartsFairInternationalBearing,StandardParts&LubricatorEquipmentFair200281215:::021-6334176663341738:021-63341551E2mail:Jasonexpo@sh163.net:81713820024Reasoning)andRBR(Rule-BasedReasoning)features,theapplicationdomainofC&R_BRispresented.RelationofC&RBDandgeneralexperiencedesignisanalysized.Web-basedTrawlWinchesIntegrationC&RBRsolutionmodelisstudied,anditsmainkeyproblemsareanalyseddeeply.CasefeatureandindexmodelconsideringcontextvariablesandTrawlWinchesRBRanewdesignareputforward.Keywords:trawlwinchesC&RBRcontextvariablessimilitudecasesAlgorithmofComplexLayoutDesignProblemsQIANZhiqin(DalianUniversityofTechnology,Dalian,China)TENGHongfeip6962699Abstract:Alotofcomplexlayoutdesignproblems(CLDP)belongtopackingproblemswithbehavioralconstraints(inertia,balance,stability,vibration,electromagneticfield,temperaturefieldetc.),NPCandschemedesignproblems.Theseproblemsareconcernedmoreandmoreinrecentyears.ThispaperintroducesthesolutionmethodsforCLDPandtheirapplications.Theexistingproblemsandtrendofdevelopmentarealsodiscussed.Keywords:complexlayoutschemedesignalgorithmANovelMethodandSystemfor3DProfileMeasurementBasedonProjectionMoirewithChangingLightsforPhaseShiftingLIGenqian(NorthwesternPolytechnicalUniversity,Xian,China)LUOZijianWANGXueliTANYushanp6992701Abstract:Anovelmethodandsystemfor3DprofilemeasurementweredevelopedbasedonprojectionMoirewithchanginglightsforphaseshiftingthroughrealtimecomputercontrol.andthemeasuringspeedhasbeenraisedsignificantly.BecausethestructureofverticalprojectionandtwoCCDsinclineimagingwereemployed,thereflectionandshadowwereeliminated,thelightfieldgetsmoreuniform,themeasuringareareaches350mm350mm,andthemeasuringerroriswithin40Lm.Experimentalresultsindicatethattheproposedmethodandsystemaresuitableforbigarea3Dprofilemeasurementwithhighsp
本文标题:机械加工表面形貌分形特征的计算方法
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