粉体堆积密度的理论计算

15Vol.15No.5Oct.2009155200910CHINAPOWDERSCIENCEANDTECHNOLOGYdoi:10.3969/j.issn.1008-5548.2009.05.00191，2，3（1.，100084；2.，510640；3.，510800）：，，、。，，，，，；；、。：；；：TU411.2：A：1008-5548（2009）05-0076-06TheoreticalCalculationforPackingDensityofPowderWuChengbao1，HuXiaofang2，DuanBaitao3（1.DepartmentofMaterialsScienceandTechnology，TsinghuaUniversity，Beijing100084；2.SchoolofMechanicalandAutomobileEngineering，SouthChinaUniversityofTechnology，Guangzhou510640；3.HeidelbergYuexiuCementCo.Ltd，Guangzhou510070，China）Abstract：Therelationshipbetweenthenumberofsizefractionandthetheoreticalvalueofpackingdensityofmixedpowderswithmultipleparti-clesizeideadsphericalparticles，thecharacterofitssizedistribution，andtherelationshipbetweenthetheoreticalvalueofpackingdensityandvoidageofpowderwithsingleparticlesize，particleinterferencewidthwereinvestigated.Theresultsshowedthatthelargertheprimarypackingdensitywas，thefewerthenumberofsizefractionswaswhenthemixedpowderwithmultipleparticlesizeideadsphericalparticlesreachedthesamepackingdensity.Thevolumecontentofeachsizefractiondecreasedexponentiallywiththeincreasingnumberofsizefraction，thelargertheprimarypackingdensity，thefasterthedescendingspeedwas，andthesizedistributionofthemixedpowderwaslognormaldistribution.Theresultsalsoindicatedthattherelationshipbetweenthetheoreticalvalueofpackingdensityandvoidageofpowderwithsingleparticlesize，particleinterefer-encewidthobeyedbinaryquadraticnonlinearequation.Keywords：powder；packingdensity；theoreticalcalculation。，，。，、、。、、[1-2]。，，SuzukiM.[3]，[4-5]。LiuJ.X.[6]，。StovallT.[7]。ThorstenReschke[8-9]，[10]。，，；、。1、、。，、，。1[11]。，，：D＝1－ε100，（1），D；ε，％。，（1），：2008-08-14，：2008-10-15。：，：29706005。：（1978-），，，。：15257253438，E-mail：[e-mail]。：（1957-），，，，。E-mail：[e-mail]。··56812810120.52360.60460.74050.60460.69810.7405/%47.6439.5425.9539.5430.1925.951Tab.1Packingparametersofmono-dispersesphericalparticles，1。，，；，，。2，。，，，1。，[10]：D（n）＝1－ε010000n=1-（1－D0）n，（2），D（n）n；D0；ε0，％；n。1，（2）。1，2。，，，，。，，，0.7405，，11；，0.5236，，20；，，0.6046，，16；，0.7405，，11。[9]、[10]，，XiSi，opt：Si,opt＝（1-D0）i-1D0D（n），（3）ni=1ΣSi,opt＝1。（4）3~4n＝8。1Fig.1Relationshipbetweenpackingdensityandsizefractionofmulti-gradesphericalparticlesforsquaresystem2Fig.2Relationshipbetweenpackingdensityandsizefractionofmulti-gradesphericalparticlesforobliquesystem3Fig.3Volumefractionofeachsizegradeparticlesofmulti-gradeparticlesforsquaresystem，：··77··15，；，。。，？，，，2，y，x。2，。3，、RRSB，，，。，，，，，。SchwandaF.[8]，，ReschkeT.[9]Schwanda，。，，KW。3.1KK。[9-10]：K＝εD，（5），ε；D。（5）（1），，3。，0.625，0.375，0.60，3。3.2W，。。[9-10]：W＝lgXsXw，（6），W；Xs；Xw，，。3.3h[9]，h：hs=K0-ni=1Σas，iSi，（7），hs；K0；as，ii；Sii；n。，3，，，，as，i＝Kc＋1，（7）：hs=Kc-ni=1Σ（Kc＋1）Si，（8），Kc；（7）。，“”，2Tab.2Fittingcurvesforlogarithmicnormaldistributiony＝0.3536x-0.7774y＝0.4265x-1.3703y＝0.5988x-2.7656y＝0.4265x-1.3703y＝0.5360x-2.2595y＝0.5988x-2.7656R＝0.9978R＝0.9989R＝0.9998R＝0.9989R＝0.9996R＝0.99983Tab.3Volumefractionofidealmono-dispersesphericalparticlesK0.910.650.350.650.430.350.604Fig.4Volumefractionofeachsize-gradeparticlesofmulti-gradeparticlesforobliquesystem··78··5，，as，i＝Kf，（7）：hs=Kf-ni=1ΣKfSi，（9），Kf；（7）。，，。：as，i=lgXiXs00·K0+1-W000，（XiX）；as，i=0，（Xi＝X）；as，i=lgXiXs00·K0W000（Xi＝X）00000000000000000。（10），Xii；Xss；W0；。（10）（7），（7）：hs=K0-s-1i=1ΣlgXiXs00·K0+1-W000·Si-ni=s+1ΣlgXiXs00·K0W000·Si，（11）。3.43，0.35、0.43、0.60、0.65、0.91；0.70、0.75、0.80、0.85、0.90、0.95；18，1、2、4、8、16、32、60、70。0.0159、0.0773、0.0939、0.1671、0.2239、0.2884、0.1322、0.0013，，as，iSi，4。4（hs，max），4hs，0.08，：D＝11＋hs，max，（12）11＋0.08=0.9259。，K，W，Dz，5。5，，，；，，，。，，4（K0＝0.35，W0=0.9）Tab.4Calculatingmodelforthevoidage（K0＝0.35，W0=0.9）12345678/μm124816326070Si0.01590.07730.09390.16710.22390.28840.13220.00131.001a1，iSi0.0000.0090.0220.0590.1050.1660.0910.0010.452-0.1022a2，iSi0.0070.0000.0110.0390.0790.1320.0760.0010.3440.0063a3，iSi0.0140.0350.0000.0200.0520.0980.0600.0010.2800.074a4，iSi0.0220.0700.0420.0000.0260.0640.0450.0000.2700.085a5，iSi0.0290.1050.0850.0750.0000.0310.0300.0000.354-0.0046a6，iSi0.0350.1360.1230.1440.0920.0000.0150.0020.546-0.1967a7，iSi0.0420.1710.1660.2190.1930.1300.0000.0000.922-0.5728a8，iSi0.0440.1790.1750.2360.2150.1590.0130.0001.022-0.672Σhs=K0-Σas，iSi5Fig.5Packingdensityofmixedpowdersatthesameparticleinterferencewidthandvolumefractionofmono-disperseparticles，：··79··15，，6~7。，，，，。，，，5～6，，5，6。5，，；，、。a，b，：D＝aW+b。（13），，a=-0.4675W+0.1653，b=0.8275W+0.2835。a、b（13），：D=-0.4675K·W+0.8275W+0.1653+0.2853。（14）6，，；，、。c，d，：D=cK+d。（15），，，c＝－0.1624K-0.2833，d=-0.1790K+1.2950。c、d（15）：D＝－0.1624W·K-0.2833K-0.1970W+1.2950。（16）（14）、（16）、。，，（14）（16）。，7。7，（14）1.33%~18.96%，（16）6Fig.6Relationshipbetweentheoreticalpackingdensityandvoidageofmono-disperseparticles7Fig.7Relationshipbetweenparticleinterferencewidthandtheoreticalpackingdensity5Tab.5Relationshipbetweentheoreticalpackingdensityandvoidageofmono-disperseparticlesbyleastsquaremethodW0.700.750.800.850.900.95D=-0.3515K+1.0305D=-0.3397K+1.0368D=-0.3372K+1.0529D=-0.3314K+1.0664D=-0.3207K+1.0820D=-0.3062K+1.0999R＝-0.9970R＝-0.9955R＝-0.9974R＝-0.9976R＝-0.9979R＝-0.99826Tab.6Relationshipbetweentheoreticalpackingdensityandpartic