力學(xué)大會(huì)2015集卷筒式伸桿收展過程半徑變化規(guī)律

吳江*，+，尹立新+，+，*（工程物理系，+（西北核技術(shù)，陜西西安710024）（航天航空學(xué)院，柱形的收納筒中。收攏過程中金屬帶發(fā)生彈性變形，大量彈性應(yīng)變能。航天器入軌后，卷筒式伸和簡化的基礎(chǔ)上，給出了卷筒式伸桿金屬帶在收攏和展開過程性應(yīng)變能的理論計(jì)算。結(jié)果顯動(dòng)的工況，根據(jù)最小勢能原理推導(dǎo)了給定螺旋角時(shí)金屬帶半徑的理論計(jì)算；理論結(jié)果與仿真結(jié)果 1(a)1(b)桿，使其收攏到一個(gè)圓柱形的收納筒，如圖1(c)所示。收攏過程中金屬帶發(fā)生彈性變形，大量自展開，如圖1(d)所示。Ullrich等[1]和Coffey等[4]分別通過試驗(yàn)研究了STEREO/IMPACT工程和TEPCE[5]工程中卷筒式通過理論分析給出了卷筒式伸桿展開過程平均推力的理論計(jì)算；其中理論計(jì)算結(jié)果和仿真結(jié)果1卷筒式伸桿及相關(guān)機(jī)構(gòu)2卷筒式展開過程數(shù)值仿真與試驗(yàn)了卷筒式伸桿彈性應(yīng)變能的理論計(jì)算。隨后，根據(jù)最小勢能原理，得到了端部可以自由轉(zhuǎn)動(dòng)的卷筒式伸桿在收攏狀態(tài)和準(zhǔn)靜態(tài)展開過程中金屬帶半徑的理論計(jì)算，并通過對比理論結(jié)果和柔UU 伸桿小端和大端在平衡狀態(tài)的直徑，如圖1(b)所示?？傻?，U/U<0.8%，因此U可以忽略。R1eq0.05時(shí)，U/U1%U可以忽略。

UUU1wl

UU [D

eq)2

20

i,

其中，l為卷筒式伸桿金屬帶的長度，w為金屬帶的寬度，DDDEh3/12(12) 衡狀態(tài)卷筒式伸桿的參數(shù)；ij表示卷筒式伸桿金屬帶中面的曲率，其中曲率定義為[7]， 11

2P

P

n eqcos2eq/eqsin2eq/ eqeqsin2eq/ reqReq(ReqReq)

≈st1/st steq

ustust(rst)

D(steq)22D(steq)(steq

i,

st st eq{[1(1)cos(2)]rr(r)(r)

24(21)(rstreq

rst*

sin2eqcos21用于驗(yàn)證式(9變 單 0 1R 1RR5平衡螺旋角為616了式(9)的有效性。注意到，rst*req；eqrst*/req越大。直觀的描述是收攏后卷筒式伸桿在軸向變短、在徑向變粗；eq越大，則收攏過程變形越大，相應(yīng)地收攏后會(huì)越粗。r，則曲率為11cos2/22sin2/1221sin2/

uu(,r)

D(eq)22D(eq)(eqi,j

Eh3[rreqr2(req)2rreq(1)rreqcos(22eq24(21)r2(req顯然，給定ur的函數(shù)。根據(jù)最小勢能原理，當(dāng)卷筒式伸桿準(zhǔn)靜態(tài)展開且端部可以自由旋轉(zhuǎn)時(shí)，金屬帶處于自身彈性應(yīng)變能最小的狀態(tài)，其半徑記做r*。r*使u取最小值，即滿足

u

rr*sin2(eq)cos2(eq 注意到，式(13)是式(9)的拓展形式，將0代入式(13)即可得到式(9)。根據(jù)式(13)可知，展開過程中r*/req是的函數(shù)，如圖7所示。7金屬帶半徑的相對變化受eq影響：eq越大，則r的相對變化越大。單 12E 0 h 0w D1 D1D2 D2 綜上所述，式(13)的理論結(jié)果與柔性多體系統(tǒng)動(dòng)力學(xué)的仿真結(jié)果吻合良好，從而驗(yàn)證了式(13) PankowDavid,BesunerRobert,WilkesRobert,etal.Deploymentmechanismsonthefastsalite:Magnetometer,radialwire,andaxialbooms.SpaceScienceReviews,2001,98(1):93-111.radialwire,andaxialbooms.SpaceScienceReviews,2008,141(1):185-211.2013-.htt ChenYi,HuangRui,RenXianlin,etal.Historyofthetetherconceptandtethermissions:Areview.ISRNAstronomyandAstrophysics,2013,2013(1-7.WuJiang,ZhaoZhihua,RenGexue.Multibodyysisoftheindeployingbooms.Journalofguidance,control,anddynamics,2013,36(6):1881-6.DmitrochenkoO.N.,PogorelovD.Y.Generalizationoftefiniteelementsforabsolutenodalcoordinateformulation.MultibodySystemDynamics,2003,10(1):17-43.RADIUSOFSTACERDURINGSTOWINGANDWU YIN YANG ZHAO(1DepartmentofEngineeringPhysics,TsinghuaUniversity,Beijing100084,)(2NorthwestInsituteofNuclearTechnology,Xi’an710024,)(3SchoolofAerospace,TsinghuaUniversity,Beijing100084,Thespiraltubeandactuatorforcontrolledextensionandretraction(STACER)isthecirculartubehelicallyrolledfromthethinmetalstripwiththeconstantpithchingangle.TheSTACERiswidelyusedasdeployablestructuresinaerospace.Beforelaunch,theSTACERisaxiallycompressedtocompleystowinacylindricalcanister,whenthelengthequalsthestripwidth.Thementalstripiselasticallydeformedduringstowingandthereforestoresmuchelasticstrainenergy.Afterentryingtheorbit,theSTACERdeploysspontaneouslywithoutanyexternaldrivebyreleasingtheelasticstrainenergy.ThispaperpresentsthemultibodydynamicsmodelandtheexperimentalsystemoftheSTACERandtherelevantmechanism.SimulationsandexperimentsshowthattheSTACERstripradiuschangessignificantlyduringstowinganddeploying,whichisimportanttothedesignofthespacedeployablemechanism.Inquasi-staticstowinganddeploying,theelasticstrainenergyandtheelastic arethedominantinfluencingfactorforthestripdeformation.Thispaperpresentsthe yticalformulaofthestripelasticstrainenergybasedonapproximationsandsimplifications.Theresultsshowthattheelasticstrainenergyoftheunitareastripdependsonthelocalradiusandhelicalangle.ForthecasethattheSTACERtiprotates ly,thispaperpresentstheformulaofthestripradiusforthegivenhelicalanglebasedontheprincipleofminimumpotentialenergy;the yticalresultwellcoincideswiththenumericalresult.ThestudyshowsthattheSTACERstripradiusincreasesduringstowinganddecreasesduringdeploying;thatis,theSTACEResthinnerwhenaxiallystretchesand esthickwhenaxiallycompressed.Theradiuschangeisalsoaffect