計測自動制御学会東北支部第176回研究集会（1998．7．24）
資料番号176−7

Stability and Nonlinear Behavior

of Poppet Valve Circuits
SatoruHayashi＊andW白iminⅥねng＊窄
＊InstituteofFluidScience，TohokuUniverslty＊＊GraduateSchoolofTbhokuUniverslty
Keywords：Hydraulics，Poppetl血1veCircuitLocalSt如ility，Nonlinea∫Behavior，HardSemxcitation，Chaos

Addre5S：InstiLuteofFluidScience，TbhohlUmiversity，2−1−1KatahhAoba−ku，Sen血，9BO一日577
SatoruHayashl，Ttl：〔022）217−5252，Fax：（O22）217−5252，E−mail：hayashis＠ifitoh8ku・aCljp

1．Introduction

2．Histori仁aIbackground

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Appendix
Governlngequationsd〔汀ilr仁d．
新宮＿㌔

Tlle gOVemlllg eqtulions fbr山e circuits showJlillモ（∫）′′＝：＋ユー♪以グ∫＋鴎Figureヰ町ed血vedas血1101l・S：

モ（∫） c∫（；t）I）i10ttyTl叩OPPCtVa［vc亡jrcuit

TheeqLlatioI10fmotioJ10fthepoppetis

椚＋謹＋項叫）＝F

1（14）（Jcv∫＋l〕

一t■〔∫） 亡rCJ（∫ユ＋ヱFェ〟上∫＋甜三〕

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す；5：l

1Vhere心拍弼＋硝（壁／昆瑚㌔一ノ川，

瑚卜若sinヰ（7〕4＝如両・屯刊腐十駈仲q，

TllereLationb亡tWCCn t］leYC10CiLi亡Sbefbreandaftcra
CロIlisio）10f111∈POPPet昭ainsttlleValveseatis

Jl「（「〕＝一己叩￣〕，

1ノち＝巧十房十〔和中晦咄．

〔16）

4＝年上叫＋屯町（8）

WhereeisLllCCOemCientofrestittltionfbrtllepOPpettO

域＝揖〝ち 蚕＝（叫由仰tlleVall′eSeataLld［￣aJ．dt＋arctiIneSJuStbeforeallda血：r

屯苗＝叫，屯q＝ら／亡十村りCロ1Iision，reSPeClivelY．
睡掴瑚＝q′砿＋㌔）

Tll巳COIltinulqIequalionofthevalvechamberis

FDrL＝0，□rl＝O，th巳PよrinEq．（lヰ〕isreducedto
廿日r・

桝

苫（J）＝

打

．で（∫） n＋1

Tlle equation of motio110f tllefluid cDJuInn jn Lhe
PIPelinebYalu−nPedparameterapproximaLiollis

Wll巳reK＝Cx／（C．，＋ち）＝aPJaXl。and7tC／（Cv＋㌔）．

Nomenclature／一丁・（J〔）。
＝ギ9−P

l」⊥：CrOSS−SeCtional訂eaOrpipe血e
A。：OpenulgafeaOforiLice

（10）

4一 班

Ap ＝CrOSS−SeCtio11alareaorva】veseat
C。：discZlargeCOem亡i亡IltOforiLi亡e

TllCnOWCllaraCteristicoftllePOPPeLvalveis
臼 ＝亡′打d′∫sinα

ち：山sc王1argCCOC伍cientofpoppetvalve
屯：dianleterOfpoppetvalveseat（11）

F：aXialnoⅥ・■f加C亡aC山1gOIlpOPPet／：Pert血ationロHlow氏汀C已五：鮎quencyofpipelinemode囲血gノ〕r＝0，11■11enf｝亡く0．

TlleftowcllaLaCterisljcoftheorificeis
乱＝亡。月。

亮：加q11印CyOFpopp巳lv…ltV巳mOde

た：5日血l∈SSOrpOPpetSPnng（12）

ム：l亡n昌仙orpipeline
椚：pOppetIⅥaSS（11）Dir亡亡t−11Ctir．gpo］7PCtVilhrccircujt

PLlttjngtlledischargecoemcientoft］lCOriLicec。→00
inEq・（12）and T／二＝ALLinEq・（9）．weobtaintllCgOVern−

P。：preS餌reinl唱lvccllambcr
P。：upSlrcalnpr亡SSllreOrOr摘c已
P∫：Sllpplypressu柑

iJl呂eqlIa山flSforadirect−aCtIngPOPPetValvecircuit．

Pr：Pert11fbatiorLOfch且nlberpressure
臼。：加1Vrat巳血ougllPOpPetV且1v仁Linearjzed equations and transfer
fun亡titInS
Weobtainlllefblloll■】nglincahzedeqltatiorL5fromEqs，tGト（12）at且Cella血st亡adyst封息

ユー ：ヽ・alv亡Ii丘〟】上＋揖←点上∫＝ロ′βf

印ぐ＝甘。一弘，J軋＝一戸。

Q。：nOWratetllrOu呂110rificc
曾亡：peHllrbationofl√alvcnow
q。：Perlurbalionofo［i缶cel10W
Lニ：VOlumeofv且1veplenumcll且111ber
耳β：Slaticvalvel山（13）∬：perturba山nofvalveli托

甘r三亡∫＝亡．几，甘。＝亡、．広一凸）旦 二initiallycoltlPrCSSedlcngu10fsuspensionspr】n苫

Cr＝り￠ノ∂Pr）か C．．＝（∂￠J∂（P。−Pr））。，んx報・り〃∂．m，α：llalfⅦgl亡Ofpoppet
β：bu［kInOdulusofworkingfluid（Oil）∂：Viscol射加画t唱C粥爪cicnt

打，＝（∂♪7∂i｝J8andLlleSubscrip【OtneansasLcadystate．

β 二d亡nSilyofwork主ng】1uid（OiりWhcrc C（＝［／7P）jsllle Valve cllELmber capacitaLIC亡，＝刊叫叫．）t厄pip亡1illCin畑ance，Cl．＝（∂せノ∂▲り。，

ー1仁山（17）