Mdeling f Hydaulic Wind Pwe Tansfes Sina Hamzehluia and Mshin zadian Seni Membe Abstact- The enegy f wind can be tansfeed t the geneats by using a geabx thugh an intemediate medium such as hydaulic fluids. n this methd a high-pessue hydaulic system is utilized t tansfe the enegy pduced fm a wind tubine t a cental geneat. n this pape a gealess hydaulic wind enegy tansfe system is intduced and the dynamic mdel f the system is btained. A pessue lss mdel is intduced t addess tansmissin efficiency. The dynamic mdel is veified with a detailed mdel ceated by using the SimHydaulics tlbx f MATLAB. The cmpaisn f the simulatin esults mathematical mdel. demnstated successful validatin f the. NTRODUTON TH tilizatin f eewable enegies as an altenative f fssl fuels S emegmg fast due t the exhaustin f fuels and an inceasingly envinmental cncens f hydcabns [] [2]. While pspective suces f enewable enegy available aund the wld can ptentially fulfill the entie enegy and eliminate the negative effects f fssil fuels [3] advanced efficient technlgies ae demanded t ecnmically substantiate the enegy havesting pcesses. Recent advancements in wind tubine manufactuing have educed pductin csts such that wind tubines can nw becme a maj suce f pwe f the wld's demands [4] expeiencing an expansin f 3% in ecent yeas [] [ 6]. ntegated in a nacelle typical hizntal axis wind tubines (HA WT) huse a divetain cnsisting f a geabx and an electic geneat. The divetain cmpnents and the geabx specifically ae expensive bulky and equie egula maintenance which makes the wind enegy pductin expensive. Futheme pwe electnic cnvetes ae equied t pvide eactive pwe f the geneat and t pvide A pwe f the gid. Opeatin f such system is cstly and equies sphisticated cntl systems. Meve placement f the geabx and geneat at tp f the twe equies expensive maintenance and eplacements. While the expected lifetime f a utility wind tubine is 2 yeas geabxes typically fail within -7 yeas f peatin and this eplacement cst accunts f appximately pecent f the tubine installatin expenses [7]. nvesely gealess hydaulic wind enegy havesting systems pvide seveal advantages ve thei geaed cuntepats. The fcal advantage is the eplacement f Manuscipt eceived Nvembe 3 2. This wk was suppted by UPU RSFG Funds and a gant fm the Slutin ente and was cnducted at zadian's Lab Pudue Schl f ngineeing and Technlgy UPU. S. Hamzeluia and A. zadian ae with the Pudue Schl f ngineeing and Technlgy UPU ndianaplis N. 4622. mail: izadian@ieee.g. geabx with the cupling f wind tubine with a hydaulic tansmissin system. Unlike taditinal wind pwe geneatin this system ffes lwe peating and maintenance csts and allws f integatin f multiple wind tubines t ne cental geneatin unit. The new wind enegy havesting technique incpates all the disseminated pwe geneatin equipment n individual wind twes in a lage cental pwe geneatin unit. With the intductin f this new appach the wind twe nly accmmdates a hydaulic pump which passes the hydaulic fluid thugh high-pessue pipes attached t the hydaulic mt cupled t a geneat. Meve the geabx is eliminated and the geneat can be lcated at the gund level. This will esult in enhanced eliability inceased life span and educed maintenance cst f the wind tubine twes. Othe benefits f this technique include high-enegy tansfe ate achievement and eductin f the size f the pwe electnics. alie eseach has shwn the pssibility f using this type f pwe tansfe technlgy in a wind pwe plant even thugh it is nt pemitted in its electical cuntepat [ 9-]. This pape intduces a mathematical mdel f a hydaulic wind pwe tansmissin system and demnstates the pefmance f the mdel within a ange f speed atis. The mdel was develped accding t the gvening equatins f hydaulic cicuit cmpnents namely wind-diven pumps geneat-cupled hydaulic mts hydaulic safety cmpnents and pptinal flw cntl elements. The dynamic peatin and step espnse f the system t a speed change wee mdeled and veified with the esults being btained by a MATLAB/Simulink SimHydaulics simulatin package. This pape is ganized as fllws: sectin explains the veall hydaulic pwe tansfe system and its system cmpnents. Sectin pesents the dynamic mdel f the hydaulic tansmissin system. A pessue lss calculatin mdel is intduced in sectin V. Finally sectin V includes the mathematical mdel veificatin with cmpute simulatins.. HYDRAUL WND NRGY TRANSFR SYSTM The hydaulic wind pwe tansfe system cnsists f a fixed displacement pump diven by the pime mve (Wind tubine) and ne me fixed displacement hydaulic mts. The hydaulic tansmissin uses the hydaulic pump t cnvet the mechanical input enegy int pessuized fluid. Hydaulic hses and steel pipes ae used t tansfe the havested enegy t the hydaulic mts [8]. A schematic diagam f a wind enegy hydaulic tansmissin system is illustated in Figue. As the figue 978--477-683-6/2/$26. 22
2 demnstates a fixed displacement pump is mechanically cupled with the wind tubine and supplies pessuized hydaulic fluid t tw fixed displacement hydaulic mts. The hydaulic mts ae cupled with electic geneats t pduce electic pwe in a cental pwe geneatin unit. Since the wind tubine geneates a lage amunt f tque at a elatively lw angula velcity a high displacement hydaulic pump is equied t flw high-pessue hydaulics t tansfe the pwe t the geneats. The pump might als be equipped with a fixed intenal speed-up mechanism. Flexible highpessue pipes/hses cnnect the pump t the piping twad the cental geneatin unit. Fig.. Schematic f the high-pessue hydaulic pwe tansfe system. The hydaulic pump is in a distance fm the cental geneatin unit. The hydaulic cicuit uses check valves t insue the unidiectinal flw f the hydaulic flws. A pessue elief valve ptects the system cmpnents fm the destuctive impact f lcalized high-pessue fluids. The hydaulic cicuit cntains a specific vlume f hydaulic fluid which is distibuted between hydaulic mts using a pptinal valve. n the next sectin the gvening equatins f the hydaulic cicuit ae btained.. MATHMATAL MODL The dynamic mdel f the hydaulic system is btained by using gvening equatins f the hydaulic cmpnents in an integated cnfiguatin. The gvening equatins f hydaulic mts and pumps t calculate flw and tque values [9-4] ae utilized t expess the clsed lp hydaulic system behavi. A. Fixed Displacement Pump Hydaulic pumps delive a cnstant flw detemined by Qp =D/p -klp' () whee Q is the pump flw delivey D is the pump p p displacement klp is the pump leakage cefficient and Pp is the diffeential pessue acss the pump defined as Pp = P - (2) whee p and P ae gauge pessues at the pump teminals. q The pump leakage cefficient is a numeical expessin f the hydaulic cmpnent pbability t leak and is expessed as fllws klp = KHPp/ pv (3) whee p is the hydaulic fluid density and v is the fluid kinematic viscsity. K HPp cefficient and is defined as _ DpOJllmp(-7l'lp)vllmP K p- PlOmp is the pump Hagen-Piseuille whee (() nmp is the pump's nminal angula velcity vnm is the nminal fluid kinematic viscsity p nmp is the pump's nminal pessue and 7l' l p is the pump's vlumetic efficiency. Finally tque at btained by (4) the pump-diving shaft is whee 7mechp is the pump's mechanical efficiency and is expessed as 7mechp = 7'l"p/7v 'p. B. Fixed Displacement Mt Dynamics The flw and tque equatins ae deived f the hydaulic mt using the mt gvening equatins. The hydaulic flw supplied t the hydaulic mt can be btained by whee Qm is the mt flw delivey Dm is the mt displacement k Lm is the mt leakage cefficient and P is the diffeential pessue acss the mt whee p" and ae gauge pessues at the mt teminals. The mt leakage cefficient is a numeical expessin f the hydaulic cmpnent pssibility t leak and is expessed as fllws whee p is the hydaulic fluid density and v kinematic viscsity. K HP m cefficient and is defined as K = DmOJnmm(l-7v"m) v"mp HPm P nmm () (6) (7) (8) (9) is the fluid is the mt Hagen-Piseuille () whee OJllmm is the mt's nminal angula velcity v" m S the nminal fluid kinematic viscsity P. mm is the mt nminal pessue and 7vlm is the mt's vlumetic efficiency. Finally tque at the mt diving shaft is btained by T" = DmP'7mechm ' () whee 77mechm is the mechanical efficiency f the mt and is expessed as 7mechm = 7tta"m/7v"m. (2) The ttal tque pduced in the hydaulic mt is expessed as the sum f the tques fm the mt lads and is given as (3)
3 whee Tm is ttal tque in the mt and ; T s T L epesent inetial tque damping fictin tque and lad tque espectively. This equatin can be eaanged as (4) whee m is the mt inetia wm is the mt angula velcity and Bm is the mt damping cefficient.. Hse Dynamics The fluid cmpessibility mdel f a cnstant fluid bulk mdulus is expessed in []. The cmpessibility equatin epesents the dynamics f the hydaulic hse and the hydaulic fluid. Based n the pinciples f mass cnsevatin and the defmitin f bulk mdulus the fluid cmpessibility within the system bundaies can be witten as Qc = (Vj fj)(dpjdt) () whee V is the fluid vlume subjected t pessue effect f3 is the fixed fluid bulk mdulus P is the system pessue and Qc is the flw ate f fluid cmpessibility which is expessed as Qc = Qp- Qn' (6) Hence the pessue vaiatin can be expessed as dpjdt = (Qp - Qm) {3jV. (7) D. Pessue Relief Valve Dynamics Pessue elief valves ae used f limiting the maximum pessue in hydaulic pwe tansmissin. A dynamic mdel f a pessue elief valve is pesented in [6]. A simplified mdel t detemine the flw ate passing thugh the pessue elief valve in pening and clsing states [] is btained by {kv(p-pjp = > P. Q pv (8) pp.' whee kv is the slpe cefficient f valve static chaacteistics P is system pessue and P" is valve pening pessue.. heck Valve Dynamics The pupse f the check valve is t pemit flw in ne diectin and t pevent back flws. Unsatisfacty functinality f check valves may esult in high system vibatins and high-pessue peaks [7]. F a check valve with a sping pelad [8] the flw ate passing thugh the check valve can be btained by {l ( P-l)Adisc P > P. Qcv = b ks (9) PP. whee Qcv is the flw ate thugh the check valve is the flw cefficient lb is the hydaulic peimete f the valve disc P is the system pessue P. is the valve pening pessue Adisc is the aea in which fluid acts n the valve disc and ks is the stiffness f the sping. Fig. 2. Hydaulic wind enegy havesting mdel schematic diagam. The veall hydaulic system can be cnnected as mdules t epesent the dynamic behavi. Blck diagams f the wind enegy tansfe using MA TLAB Simulink ae demnstated in Figues 2 and 3. The mdel incpates the mathematical gvening equatins f individual hydaulic cicuit cmpnents. The bulk mdulus unit geneates the pessue f the system. - -. _p = DpOJp - kl.pp Pp ::;P"+PBP = D p p /'lm«h. p V. L-..:...-...:.J T.-TL"""(dw"/{h)+B"@" n 8 PRSSUR Lss ALULA non The enegy in the hydaulic fluid is dissipated due t viscsity and fictin. Viscsity as a measue f the esistance f a fluid t flw influences system lsses as me-viscus fluids equie me enegy t flw. n additin enegy lsses ccu in pipes as a esult f the pipe fictin. The pessue lss and fictin lss can be btained by cntinuity and enegy equatins (i.e. Benulli's quatin) f individual cicuit cmpnents such as tansmissin lines pumps and mts [9]. The Reynlds numbe which detemines the type f fluid in the tansmissin line (lamina tubulent) can be used as a design pinciple f the system cmpnent sizing. The Reynlds numbe is a efeence t pedict the type f the flw in a pipe and can be btained by Re = pvl = vl (2) Ji v whee p is the density f the fluid L is the length f the pipe f-l is the dynamic viscsity f the fluid v is the kinematic viscsity and v is the aveage fluid velcity and is expessed as v= -- Q (2) Apipe n A
4 whee Q is the flw in the pipe and A. ppe is the inne aea f the pipe. The enegy equatin is an extensin f the Benulli's equatin by cnsideing fictinal lsses and the existence f pumps and mts in the system. The enegy equatin is expessed as Z Vl2 P 2 vi +-+-+H -H -H L=Z 2 +-+-' (22) p m 2g 2g whee z is the elevatin head v is the fluid velcity P is the pessue g is the acceleatin due t gavity is the specific weight H p is the pump head pessue H m is the mt head pessue and is calculated by the cmpessibility equatin and H L is the head lss. The pipe head lss is calculated by Dacy's quatin which detemines lss in pipes expeiencing lamina flws by L v2 H L = f D 2g (23) whee D is the inside pipe diamete v is the aveage fluid velcity in the pipe and f is the fictin fact and is defined f a pipe expeiencing lamina flw as f= 64. (24) Re The enegy equatin is utilized alng with Dacy's equatin and the cmpessibility equatin t calculate the pessue lss at evey pipe segment (bth hizntal and vetical) and the head f each pump in the system. V. MODL VRFATON AND DSUSSON The SimHydaulics tlbx f MAT LAB has been used as a pweful tl t mdel and implement hydaulic enegy tansfe f wind pwe tansfe [2]. The SimHydaulics tlbx was utilized t ceate a hydaulic system simila t Figue. The hydaulic pump and mt ae gvened by identical equatins cmpaed t the nes implemented in the ppsed hydaulic mdel. Meve bth systems ae assumed t cntain the same type f hydaulic fluid which tanslates int simila fluid density fluid bulk mdulus and fluid kinematic viscsity espectively dented by pp v espectively. The diffeences between the mathematical mdel and SimHydaulics ae in the details f hse dynamics and centalized cmpessibility mdel. The gemetic chaacteistics f the pipes alng with the ttal vlume f fluid subjected t pessue effect ae assumed simila in bth mdels n de t validate the ppsed hydaulic mathematical mdel with SimHydaulics and t analyze the impact f dissimilaities f the hse dynamics n dynamics f the system a specific pump angula velcity pfile was supplied t bth mdels and simulatin esults wee cmpaed unde identical peating cnditins. The fllwing assumptins wee cnsideed t develp the mdel [2]: inetia fictin sping and etc.). 3. Leakage inside the pump and mt ae assumed t be linealy pptinal t thei espective pessue diffeential [ 3]. n simulatins a fixed displacement pump with a displacement f.7 in 3 ev supplies hydaulic fluid t a pimay mt (Mt A) and an auxiliay mt (Mt B) bth with fixed displacements f.97 in 3 lev. Figue 4 depicts the angula velcity pfile which is supplied t the hydaulic pump as a step inputs fm 3pm t 4pm and fm 4pm back t 3pm. 4 [' :; 3 f----' 'u Pump Angula Velcity +---- ' ----. + 2 "--------+----.. n :; --i-----::±===±====±===±= < -- pm Step Vaiatin Time [] Fig. 4. Hydaulic pump angula velcity pfile. 2 2 3 Table Shws the simulatin paametes f bth SimHydaulics and simulatin mdels. Symbl D p DmA DmB ma mb ma mb KL p KL.mA KLmB 7llal 7' p P v TABL SMULATON PARAMTRS QUANTTY Pump Displacement.7 Pimay Mt.97 Displacement Auxiliay Mt.97 Displacement Value Pimay Mt netia. Auxiliay Mt netia. Pimay Mt Damping.26 Auxiliay mt Damping.22 Pump Leakage efficient. Pimay Mt Pump. Leakage efficient Auxiliay Mt Pump. Leakage efficient PumplMt Ttal.9 fficiency PumplMt Vlumetic.9 fficiency Fluid Bulk Mdulus 8369 Fluid Density.3 Fluid Viscsity 7.283 Unit kg.m 2 kg.m 2 N.m/(adls) N.m/(adls) psi b/in 3 The cmpaisn between the simulatin espnse f the SimHydaulics mdel and the deived mathematical mdel t the supplied hydaulic pump angula velcity pfile ae shwn in Figues (-2). cst. The hydaulic fluid is assumed incmpessible. 2. N lading is cnsideed n pump and mt shafts (i.e.
] ii u:: Fig...8.6.4 --- PumpAw l ----- Mathematical --+---+--- --- Sim Hydaulics f..2 2 2 3 mpaisn between the hydaulic pump flw f the mathematical mdel and SimHydaulics mdel. ] ii u:: Fig. 6. Pimay Mt Aw. ----- ---- --.-..4.3.2. ' f. J i.. i --- SimHydaulics fi. ----. athematical l 2. 2 3 mpaisn between the pimay hydaulic mt flw f the mathematical mdel and SimHydaulics mdel..8.6 s.4 " u::.2 Fig. 7. i l Auxiliay Mt Aw.. '" J :----. athemtical. l--- SimHydaulics 2 2 3 mpaisn between the auxiliay hydaulic mt flw f the mathematical mdel and SimHydaulics mdel. Figue illustates pump flw in espnse t the step change in the pump shaft speed. As the figue illustates the geneated pump flw in mathematical mdel matches that f the SinHydaulics tlbx. The tansients f the mathematical mdel fllw the same patten as the simulatin sftwae and each the same steady state values. This similaity is due t negligible dependency f pump flw t pessue vaiatin. Althugh pump flw is a functin f teminal pessue small pump leakage cefficient minimizes the effect f pessue vaiatin. As a esult f the step vaiatin in the pump shaft speed the flws geneated and distibuted in the hydaulic cicuit pimay and auxiliay mts ae demnstated in Figues 6 and 7. The esults shw that the simulated mt flws ae identical. [. : 'u... s :; c(. la. Pimay Mt Angula Velcity. t --- Sim Hydaulics ----- Mathematical ----:: Fig. 8. mpaisn between the pimay hydaulic mt angula velcity f the mathematical mdel and SimHydaulics mdel. 2 2 Auxiliay Mt Angula Velcity.-----. : 'u. ::: c( 3 '-" ' '" T F --- Sim Hydaulics ----- Mathematical 2 2 3 Fig. 9. mpaisn between the auxiliay hydaulic mt angula velcity f the mathematical mdel and SimHydaulics mdel. + 2 :=::7 == Pump Diffeential Pessue 3 "--'--'--T--i---- ' ".. Fig. ".l l.. 2 2 3 mpaisn between the hydaulic pump teminal pessue f the mathematical mdel and SimHydaulics mdel. Figues 8 and 9 depict the angula velcity assciated t pimay mt and auxiliay mt. The velcities geneated fm mathematical mdels esult in simila tansient and steady state values hweve due t sme details cnsideed in SinHydaulics mdel thee is a slight deviatin between mt utput angula velcities btained fm mathematical mdel and SinHydaulics mdel. Figue illustates hydaulic pump teminal pessue geneated fm mathematical mdel and fm SinHydaulics. As the figue illustates the pessues fllw simila patten and the mathematical esults shws cnsideable similaity in bth tansient and steady state espnse with the SinHydaulics mdel. The pessue in mathematical mdel has been btained fm a simple cmpessibility mdel while the pessue mdel in SinHydaulics cnsides cmplex pipe dynamics.
6 D ::::J e- -..4.3.2. L Pimay Mt Tque --.-- ' --- im Hyd:aulic -- - - -- -- - t.. -----.. ----- --- i.. ---- Time [] ----- Mathematical [ - [ 2 2 3 Fig.. mpaisn between the pimay hydaulic mt utput tque f the mathematical mdel and SimHydaulics mdel. D ::::J e- -. ----.4.3.2. L Auxiliay Mt Tque 'L - - -- im Hyd:auliS ----- Mathematical - Time []. 2 2 3 Fig. 2. mpaisn between the auxiliay hydaulic mt utput tque f the mathematical mdel and SimHydaulics mdel. Figues and 2 illustate the shaft tque f pimay mt and auxiliay mt. As the figues demnstate the calculated tque fm mathematical mdel and the ne btained fm SimHydaulics fllw the same patten and esult in a clse steady state values with accuacy f less than 2% deviatin. n summay this sectin cmpaed the simulatin espnse f the dynamic mdel t a detailed mdel built with the SimHydaulics tlbx f MATLAB. Tw distinct angula velcity pfiles wee supplied t the hydaulic pump in bth mdel and the simulatin esults wee cmpaed. The pump speed system pessue and mt speeds flws and tques btained fm mathematical mdels wee in gd ageement with the esults btained fm sftwae simulatin. Sme deviatins wee als bseved in the simulatin esults which ae due t simplified mdel f cmpessibility and dynamics f tansmissin lines. The main benefits f the mathematical mdel besides a clse dynamic simulatin is the simplicity f the gvening equatins and achievement f a high-speed simulatins cmpaed t the sftwae packages. The next sectin veifies the accuacy f the mathematical mdel and its gvening equatins in expeimental setup. V. ONLUSON This pape intduced a mathematical mdel f a gealess hydaulic wind enegy tansfe system. A mdel f the hydaulic system was ceated with MATLAB/Simulink. The dynamic mdel was veified with a detailed mdel ceated by using the SimHydaulics tlbx f MATLAB. The cmpaisn f the simulatin demnstated successful validatin f the mdel. The mathematical mdel culd be used t scale the system f an industial level wind pwe plant. AKNOWLDGMNT This wk was suppted by a gant fm the UPU Slutin ente. RFRNS [] T. Senjyu R. Sakamt N. Uasaki H. Higa K. Uezat and T. Funabashi "Output Pwe ntl f Wind Tubine Geneat by Pitch Angle ntl Using Minimum Vaiance ntl " ngineeing in Japan vl. 4 n. 2 26. lectical [2] J. G. Sitweg H. Plinde and W.. Kling "Dynamic Mdelling f a Wind Tubine with Dubly Fed nductin Geneat" Pwe ngineeing Sciety Summe Meeting 2. [3] J. G. Sitweg S. W. H. de Haan H. Plinde and W.. Klimg "Geneal Mdel f Repesenting Vaiable Speed Wind Tubine in Pwe Systen Dynamics Simulatins" Tansactin n Pwe Systems v.83 n. Febuay 23. [4] Y. Lei A. Mullane G. Lightbdy and R. Yacamini "Mdeling f Wind Tubine with a Dubly Fed nductin Geneat f Gid ntegatin Studies" vl. 2 n. Mach 26. Tansactin n negy nsevatin. [] "Wind negy by 23 - nceasing Wind negy's ntibutin t U.S. lecticity Supply" U.S. Depatment f negy May 28. DO/GO- 28-267 http://wwwl.eee.enegy.gv/windandhyd/pdfs/4869.pdf [6] http://www.awea.glpubs/factsheets/maket_ Update.pdf [7] A. Ragheb and M. Ragheb "Wind Tubine Geabx Technlgies" Pceedings f the st ntenatinal Nuclea and Renewable negy nfeence (NRO) Amman Jdan Mach 2. [8] K. Wu et a. "Mdelling and identificatin f a hydstatic tansmissin hadwae-in-the-p simulat" ntenatinal Jumal f Vehicle Design vl. 34 pp. 2-64 24. [9] S. Hanzehluia A. zadian A. Pusha and S. Anwa "ntls f Hydaulic Wind Pwe Tansfe" ON 2. [] A. Pusha A. zadian S. Hanzehluia N. Giens and S. Anwa "Mdeling f Gealess Wind Pwe Tansfe" ON 2. [] A. zadian "ental Wind Tubine Pwe Geneatin" US Patent Applicatin US2 /6 972 [2] M.V. Gbeshk. "Develpment f Mathematical Mdels f The Hydaulic Machiney f Systens ntlling the Mving mpnents." Hydtechnical nstuctin. Vlume 3 N. 2. 997 [3] http://www.mathwks.cmlhelp/tlbxlphysmdlhydlefi.fixeddispla cementpump.htnl [4] http://www.mathwks.cmlhelp/tlbxlphysmdlhyd/efi.hydaulic mt.htnl [] A. V. Akkaya "ffect f Bulk Mdulus n Pefmance f a Hydstatic Tansmissin ntl System" Sadhana vl. 3 Pat. Octbe 26 pp. 43-6. [6] G. Licsk A. hampneys and. Hs "Dynamical Analysis f a Hydaulic Pessue Relief Valve" Pceedings f the Wld ngess n ngineeing 2 vl. 2 July -3 29 Lndn U.K. [7] A. Pandula and G. Halasz "Dynamic Mdel f Simulatin f heck Valves in Pipe Systems." Peidica Plytechnica Mech. ng. Seies vl 46/2 pp. 9-22. [8] Y. Hu. Li P. He Y. Zhang and. hen "Shck Absbe Mdeling and Simulatin Based n Mdelica" Pceedings f the 8th ntenatinal Mdelica nfeence issue 63 pp. 843-846 Mach 2-22 2. [9] A. spsit Fluid Pwe with Applicatin 7'h ditin Pentice Hall 29. [2] S. M. Pabhu J. Wendlandt J. Glass and T. gel "Multi-Dmain Mdeling and Simulatin f an lect-hydaulic mplement System." SA 26 mmecial Vehicle ngineeing ngess and xhibitin 26. [2] http://www.mathwks.cmlhelp/tlbxlphysmdlhyd/efi.fixeddispla cementpump.htnl