Lecture 2. Course Goal Survey
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- Magnus Dickerson
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1 Fluid Por Controls Lbortor (Copright Prr Li, -) Your on gol in this cours Offic hour: M-Tu :-: Txtbooks Fdbck on lbs so fr Lctur 66 Rvi momntum, continuit, lst squrs Brnoulli Eqution: > orific qution Flo control vlvs: Ndl vlv (lb ) Prssur compnstd flo control vlv (lb b) Prssur control vlvs (lb ): Dirct cting rlif vlv Pilot oprtd rlif vlv Simultion of hdrulic componnts nd circuits - Exmpl M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Cours Gol Surv 67 Wht is our gol for this cours (ht ou hop to lrn)? Fmilirit of fluid por sstms (7) Principls nd pplictions Motion control nd dnmic sstms (8) Lrn n tchnolog () M..E., Univrsit of Minnsot (updtd.)
2 Fluid Por Controls Lbortor (Copright Prr Li, -) Dt Fitting, Modl Discovr 68 Exmpl: Find Dlt P vs Q rltionship for ndl vlv Suppos ou msur Dlt P nd Q for ndl vlv Dt: (DP, Q), (DP, Q),. Procdur: plot dt us phsicl insights if possibl (.g. orific qution) Vrif vlidit of th hpothsizd function Modif hpothsis Find prmtrs from plot using lst squrs M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Lst Squrs nlsis 69 This is gnrl function fitting tchniqu Nd modl nd dt Exmpl: Fitting n orific qution nd flo mtr ith bis Q k ΔP Q Modl: Q unknon bis in flo mtr k unknon constnt of orific Dt ( n ΔP, Q ),( ΔP, Q ), ( ΔP n, Q ) Find Q nd k to bst xplin dt M..E., Univrsit of Minnsot (updtd.)
3 Fluid Por Controls Lbortor (Copright Prr Li, -) M..E., Univrsit of Minnsot (updtd.) 7 Lst Squrs Dt:,,.., x, x, tc. Formult into mtrix qution is knon,, unknon Qustion: Find, tht bst xplin,,, Bst solution tht minimizs E Fluid Por Controls Lbortor (Copright Prr Li, -) M..E., Univrsit of Minnsot (updtd.) 7 Lst Squr Solution Bst solution tht minimizs E is: It is clld th norml solution Cn b sil obtind in Mtlb! Wightd lst squrs? ( ) T T ˆ
4 Fluid Por Controls Lbortor (Copright Prr Li, -) M..E., Univrsit of Minnsot (updtd.) 7 Wightd Lst Squrs Rgulr lst squrs ssums ll dt r qull ccurt nd minimizs: If som dt points r knon to b mor ccurt, th rror du to tht rror cn b mphsizd: ( i > ) E E Fluid Por Controls Lbortor (Copright Prr Li, -) M..E., Univrsit of Minnsot (updtd.) 7 Wightd Lst Squrs Th ightd rror cn b minimizd nd put into rgulr lst squrs form: Modif th dt st ccordingl: E
5 Fluid Por Controls Lbortor (Copright Prr Li, -) Wightd Lst Squrs 7 ppl solution of rgulr lst squrs to modifid problm: ˆ T T ( ) ˆ T T ( W ) W Wht to st W i? Lrg W i hn rror is xpctd to b smll Smll W i hn rror is lrg Exmpl: W i /rror of th dt i M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Lst Squrs Exmpl 75 Modl:, b r unknon ( t) sin(t ) b Dt: (t, (t)), (t,(t)), (t, (t)),. ( t) sin(t ( t) sin(t ( t ) sin(t n n ) b Ho to formult polnomil fit - linr, qudrtic, cubic.? ) ) M..E., Univrsit of Minnsot (updtd.) 5
6 Fluid Por Controls Lbortor (Copright Prr Li, -) Th ORIFICE qution 76 Most fundmntl fluid por qution! Usd in ll mnnrs of vlvs Ndl vlv (lb ) Prssur compnstd flo control vlv (lb b) Prssur rlif vlv (lb ) This k Drivd from Brnoulli qution M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Brnoulli Eqution 77 Whn fluid is not t rst, Pscl s l is not strictl pplicbl If nrg is consrvd, s fluid spds up, prssur dcrss P ρ gh ρv P ρgh ρv P, v P, v Vlocitis rltd b continuit qution.. M..E., Univrsit of Minnsot (updtd.) 6
7 Fluid Por Controls Lbortor (Copright Prr Li, -) Ho smll dos rstriction hv to b for Brnoulli to b importnt? 78 Q lpm (litrs/min) 5x - m /sc D cm Prssur vrition.6 kp.5 psi D.cm Prssur vrition 6 MP 5 psi!! ρv 8ρ Q π D Vr snsitiv to chngs in dimtr!!! M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Orific Eqution 79 Upstrm r ssumd lrg (so tht v ) Brnoulli qution pplis to jt ρv P ρv P ( P ρ P ) v Q Q C d P o P.6 C d / Dischrg cofficint Q Cd ( P ρ P ) M..E., Univrsit of Minnsot (updtd.) 7
8 Fluid Por Controls Lbortor (Copright Prr Li, -) Ndl Vlv s Flo Control Flo qution is gnrll givn b th orific qution: 8 Q Cd turns) ( P ρ ( P ) Mtlb cod: function Q orific(dp, turn).;.;.; K *turn*turn^; Q K*sqrt(bs(DP))*sign(DP); function DPorific(Q,turn).;.;.; K *turn*turn^; DP(Q/K)^*sign(Q); ndl controls th opning of th flo chnnl (ffctiv orific r) Ndl vlv controls th rsistnc to flo, not flo dirctl Cn b chrctrizd b P-Q rltionship ithr grphicll, s n qution or s computr cod M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Which ndl vlv is bttr flo control? 8 Ps constnt cn choos.8.6. DP Q pprox Qd Work circuit Plod cn vr Options: Which is hich? Smll orific dq/dplod? Ps? Lrg orific dq/dplod? Ps?. Q DP M..E., Univrsit of Minnsot (updtd.) 8
9 Fluid Por Controls Lbortor (Copright Prr Li, -) Flo Control Vlvs: Ndl Vlv 8 Th gol of flo control vlvs is to mintin th flo rt t th spcifid stting Ndl vlv is ssntill n orific Q Cd ( P P ) If prssur diffrnc is fixd, ρ flo ill b constnt Snsitivit dpnds on dq/dp Orific r somstims You cn dtrmin from our xprimnt djustbl Ndl vlv cn lso b usd s prssur control vlv thn flo must b constnt Is ndl vlv bttr flo control vlv t lor prssurs or t highr prssur? Ho bout s prssur control vlv? M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Prssur Compnstd Flo Control Vlv (PCFC) 8 Motivtion: Ndl vlv cnnot mintin flo if prssur vris PCFC uss fdbck to nsur tht prssur cross n orific is constnt s prssur cross fixd orific vris, th djustbl orific tris to compnst - ho? Ho dos spring rt ffct ccurc in flo control? Wh must thr b minimum orking prssur? Poor nrg fficinc - hr is th nrg lost?? M..E., Univrsit of Minnsot (updtd.) 9
10 Fluid Por Controls Lbortor (Copright Prr Li, -) PCFC Continud 8 Rstrictr tp Q P Wht hppns hr? Ho dos spring constnt ffct flo control ccurc? M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Q PCFC - Oprtion Idntif ll componnts Wht is th flo pth? Wht is th P-Q rltionship hn th control spool is stuck opn? Wht r th forcs nd prssurs tht cus th control spool to mov? Ho dos spring rt ffct th shp of th P-Q curv? Commnt on fficinc Wht hppns hn prssur is too lo? 85 P M..E., Univrsit of Minnsot (updtd.)
11 Fluid Por Controls Lbortor (Copright Prr Li, -) Prssur control vlv: Dirct cting Rlif Vlv 86 Poppt is std ginst spring Usd to limit or to mintin prssur: Wh is this importnt?? s prssur in min lin incrss bov th prst spring forc, poppt is movd up Orific to drin is opnd Rlif flo occurs Crcking prssur vrsus full flo prssur? Qustions: Formul for crcking prssur??? Rliv vlvs r Non-pssing vlv M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Dirct cting Rlif Vlv 87 rlif vlv is non-pssing prssur control vlv Forc blnc on th spool? Crcking prssur vrsus spring rt, spring djustmnt scr? Ovr-rid vrsus spring rt? M..E., Univrsit of Minnsot (updtd.)
12 Fluid Por Controls Lbortor (Copright Prr Li, -) Dirct cting Rlif Vlv 88 Inlt prssur (P ) vrsus spool displcmnt (x) is rltd b spring constnt nd spool r. Ho to dr th prssur (P ) vrsus flo (Q) curv? Ho dos th spring constnt (K) ffct th shp of th (P vrsus Q) curv? Wht is n idl rlif vlv? For snsitivit: Stiffr or softr spring? If spring is too soft, thr m b stbilit problms. Crcking prssur is st b: Prlod in spring K x (long springs) Conflict btn high crcking prssur nd snsitivit Opn qustion: ho dos outlt prssur P ffct P vrsus Q curv? M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Pilot Oprtd Rlif Vlv 89 Soft spring Pilot oprtd rlif vlvs r supposd to b mor snsitiv thn dirct cting rlif vlvs M..E., Univrsit of Minnsot (updtd.)
13 Fluid Por Controls Lbortor (Copright Prr Li, -) Pilot Oprtd Rlif Vlv - Schmtic 9 Consists of min stg nd pilot stg Min stg is lightl spring lodd Pilot stg drt is std b prlodd spring M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Min spool nd Pilot 9 Pilot - high prssur, lo flo Min Spool - high flo, lo prssur M..E., Univrsit of Minnsot (updtd.)
14 Fluid Por Controls Lbortor (Copright Prr Li, -) Oprtion of Pilot Oprtd Rlif 9 Pilot stg limits prssur bov th spool (st b pilot spring) Whn pilot is closd, min spool is std b th light spring Whn pilot is opn, min spool ss mor forc from lor chmbr thn from uppr chmbr nd spring - hnc spool opns It is n vlnch ffct! M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Pilot Oprtd Rlif Vlv 9 This solvs th dilmm of dircting cting rlif vlv b sprting th rols of snsitivit nd crcking prssur stting. Crcking prssur dtrmind b pilot drt (poppt) nd spring stiff spring nd smll r cn b usd for high crcking prssur s pilot crcks, prssur bov min spool is rpidl rlsd. n vlnch rsults, s th min spool is hld b light spring. Snsitivit is controlld b th soft spring in th min spool M..E., Univrsit of Minnsot (updtd.)
15 Fluid Por Controls Lbortor (Copright Prr Li, -) Rmot Oprtd Pilot 9 M..E., Univrsit of Minnsot (updtd.) Fluid Por Controls Lbortor (Copright Prr Li, -) Idl P-Q curv for rlif vlvs 95 Pilot oprtd Q Which on is bttr?? Dirct cting Ho do spring rts ffct this curv For dirct cting, or Pilot oprtd rlif vlv? Crcking prssur P M..E., Univrsit of Minnsot (updtd.) 5
Lecture 1. ME4232 Course Overview
Fluid Por Controls Laborator (Copright Prr Li, -) Lctur Introductions Cours ovrvi / Sllabus Fluid Por Introduction Fluid Por Fundamntals Last Squars Fitting Cours goals Fluid Por Controls Laborator (Copright
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Contct Detils efore using the product, plese check the guide pges t the front of this ctlog. http://www.dikinpmc.com/en/ For ltest informtion, PDF ctlogs nd opertion mnuls Solenoid Pilot Operted Directionl
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Contct Detils efore using the product, plese check the http://www.dikinpmc.com/en/ For ltest informtion, DF ctlogs nd opertion mnuls Solenoid ilot Operted Directionl Control Vlve Fetures hese models relize
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