Analysis of piston behavior according to eccentricity ratio of disk in bent-axis type piston pump

Transcription

1 Journal of Mhanial Sin an Thnology (8) 76~733 Journal of Mhanial Sin an Thnology DOI.7/s Analysis of piston bhavior aoring to ntriity ratio of isk in bnt-axis typ piston pump Il-Hyun Bak, Ihn-Sung Cho, Ja-Youn Jung 3,* an Lu Hong 4 Prision Mhanial Enginring, Chonbuk National Univrsity, 664-4, Ga, Dukjin-Dong, Jonju, Jonbuk,56-756, Kora Division of Mhanial & Arospa Systm Enginring, Chonbuk National Univrsity, 664-4, Ga, Dukjin-Dong, Jonju, Jonbuk,56-756, Kora 3 Division of Mhanial & Arospa Systm Enginring an Rsarh Cntr of Inustrial Thnology, Chonbuk National Univrsity, 664-4, Ga, Dukjin-Dong, Jonju, Jonbuk,56-756, Kora 4 Shool of Mahanial an Eltronial Enginring, Wuhan Univrsity of Thnology 437, Luoshi Roa, Wuhan, China (Manusript Riv Otobr, 7; Rvis April 6, 8; Apt Jun 4, 8) Abstrat To improv th prforman of th bnt-axis typ axial piston pump rivn by th tapr piston, it is nssary to know th riving haratristis an mhanism of th tapr piston an th ylinr blok. Sin ah piston not only rotats on its axis an riproats in th ylinr bor but also rvolvs aroun th axis of th riving shaft, it is iffiult to analyz th riving mhanism thortially. Th thortial mhanism for th bnt-axis typ axial piston pump is stui by using th gomtrial mtho. Th riving rang of th tapr piston is trmin by thortial quations. Th rsults show that th ylinr blok is rivn by on tapr piston in a limit rang an th or paramtrs suh as th tilting angl of th piston an th aha lay angl influn prforman of th bnt-axis typ axial piston pump. Kywors: Hyrauli piston pump; Tapr piston; Swivl angl; Dlay angl; Entriity ratio Introution Th oil hyrauli systm us in larg an havy quipmnt has bn moifi onstantly baus of its limit prforman, ngativ nvironmntal influn, an nois. To solv ths problms, rsarh has bn arri out in th aras of siz rution of oil hyrauli systms, high sp an prssur, ltroni ontrol, substitut oil, nois ras, an t. Th bnt-axis typ oil hyrauli piston pump ating as th or powr sour in th oil hyrauli systm is no xption to this thniqu tnny. It is us as th main pump in havy onstrution quipmnt baus it offrs high sp an prssur, high total ffiiny an istinguish variabl livry. * Corrsponing author. Tl.: , Fax.: arss: jungjy@honbuk.a.kr KSME & Springr 8 Rlat rsarhs in this fil ar xtrmly limit. Th ylinr blok in th rotary part is rivn by a tapr piston onnt to th isk of th shaft an th gomtrial mhanism of this typ of pump is vry ompliat an iffiult to analyz. Suh sar but valuabl rsarh that has bn arri out as mntion abov fouss on th prforman of th axial piston pump [], th riving mhanism of th axial piston pump [], th frition loss of th axial piston pump [3] an so on. Th riving mhanism of th bnt-axis typ piston pump rivn by th piston ro is th fous of this stuy. Th piston ro rivs th ylinr blok, so th tapr angl of th piston ro an th swivl angl btwn th ylinr blok an th shaft ar vry important sign fators. If th abov sign fators o not satisfy th optimiz onitions, th frition loss btwn th ylinr bor an th piston ro

2 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~733 woul inras, an th pump oul vn fail to run in onitions with svr frition an war. Whn th piston ro riproats in th ylinr bor with high vloity, it rotats on its own axis an rvolvs about th ntr lin of th ylinr blok, an th riving for prou in th ontat part btwn th tapr piston ro an th innr surfa of th ylinr bor rivs th ylinr blok simultanously. Baus of all thos ompliat mos of motion, it is not asy to analyz th pump s riving mhanisms. Morovr, in th manufaturing prosss of th isk, th ylinr blok an th piston, th tolrans rlat to th sign rawing an th implmnts tak pla. Aoringly, onsiring ths tolrans, th riving mhanism boms vry ompliat an it is almost impossibl to analyz. In this stuy, th riving haratristi aoring to th hangs of th position tolran of th isk s sphrial part whih unrgos th iffiulty of th tolran managmnt in oil hyrauli makr is trmin. Thrfor, in this papr, th riving mhanism of th piston ro in th bnt-axis typ piston pump rivn by th piston ro has bn grasp; an, whn th ntr of th isk is ntri, a thortial analysis is prform of th influns of ntri paramtrs on th lay angl of th piston ro an th riving rangs of th piston. othr han, th n of th piston ro onnts with th ylinr bor, an th onsqunt latral for at on ontat part of th ylinr bor an th piston ro rivs th ylinr blok to rotat about th ntr lin of th ylinr blok. Th piston ro riproats in th ylinr bor, an at th sam tim, it rotats on its own axis an rvolvs on th ntr of th ylinr blok simultanously. Baus of th swivl angl btwn th ylinr blok an th riving shaft, as th shaft rotats, th piston movs upwars to TDC an working oil flows in from th sution port in th valv plat to th ylinr blok. Thn th piston movs ownwars to BDC an working oil flows out from th ylinr blok to th isharg port. Fig. shows th riving mhanism of th piston ro of th bnt-axis typ piston pump. From th viwpoint of th ylinr blok, th irl of th sphrial part of th isk with raius of R is sn as an llips an R is xprss by th following quation: R = R sin θ + ( os θ os α ). Unr onition without isk ntriity Fig.. Diagram of axial piston pump. () Fig. 3 shows th iagram of th phas angl an th tilting angl rlat with th bhavior of th piston ha.. Gomtrial mhanism of piston ro Fig. illustrats th funtion prinipl of th piston pump. Whn th riving shaft is rivn by a motor (an ltroni motor, an ngin, t.), th ha of th piston ro onnt to th ntr of th sphrial part in th isk rotats on th axis of th shaft. On th 77 Fig.. Driving mhanism of axial piston pump. Fig. 3. Diagram of phas angl an tilting angl.

3 78 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~733 With th shaft rotating, th aha bhavior of th ntr of th piston ha ( P ) rsults in th angl iffrns btwn th ntr of th ylinr blok ( O ) an th ntr of th ylinr bor ( O b ). Th two angls ar th so-all aha lay angl an th phas angl. Th orrsponing quations of th aha lay angl ( δ ) in four quarants ar list: θ < R sinθ δ = sin θ R θ < R sinθ δ = sin θ + R 3 θ < R sinθ δ = sin θ + R 3 θ R sinθ δ = sin θ + R an thn, th phas angl is givn as follows: () (3) (4) (5) Fig. 4. Diagram of lay angl. Fig. 5. Entri istan an angl on isk of shaft. ϕ = sin R sinδ ( R R osδ ) + ( R sinδ ) (6) Th tilting angl β is th angl iffrn btwn th ntr lin of piston ( P P ) an th ntr lin of piston bor ( OP ) b β R + R R R osδ L = sin (7) Fig. 4 shows th lay angl gnrat btwn th piston ro an th ylinr blok. Whn th rotating angl of th shaft is θ, from th viwpoint of th ylinr blok, th angl btwn PO an P O is th lay angl ( δ ). x ( sinξ ) R + R L δx = os δ (8) RR. Unr onition with isk ntriity Fig. 5 shows a plan skth of th piston ro whn th isk is ntri with a rtain gr φ an istan. Hr, th ntri istan is th prout of th ntriity ratio an th raius of th isk s sphrial part. Unr this onition, from th viwpoint of th isk, th istan ( R ) btwn s P an O is givn as follows: ( φ θ) ( φ θ) Rs = R os + R sin (9) Hr, R is quivalnt with R, whih is xprss abov in Eq. (). It hangs aoring to th ntri angl φ an ntri istan, an th quation is shown as follows: ( ) R Rs sin θ osαosθ = + ()

4 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~ Thn, th quivalnt aha lay angl ( δ ) varis with th rotating angl, an th quations in th iffrnt quarants ar: θ < R os ( ) sin( ) φ θ R R φ θ + sinθ () δ = sin θ R θ < R os ( ) sin( ) φ θ R R φ θ + sinθ δ = sin θ+ R () 3 θ < R os ( ) sin( ) φ θ R R φ θ + sinθ δ = sin θ+ R (3) 3 θ R os ( ) sin( ) φ θ R R φ θ + sinθ δ = sin θ+ R (4) Th quivalnt phas angl ( ϕ ), th quivalnt tilting angl ( β ), an th quivalnt aha lay angl δ ) ar also work out on by on: ( ϕ = sin R sinδ ( R sinδ ) + ( R R osδ ) (5) R + R RRosδ β = sin (6) L ( ξ ) R + R Lsin δe = os δ (7) RR Th main paramtrs n in th analysis of th rotary part in th bnt-axis typ piston pump rivn by th piston ro ar arrang in Tabl. Tabl. Gomtri ata of rotary part. Raius, R (g) ~E-4 - α 5~3 [g] L 6 [mm] R 73.5 [mm] R 69.5 [mm] ξ.9 [g] Fig. 6. Raius Aha Dlay Angl, δ ο (g) Rotating Angl, θ (g) R to swivl angl. α=5 α=5 α=5 α=7 α=3 α=5 α=5 α=5 α=7 α= Rotating Angl, θ (g) Fig. 7. Aha lay angl to swivl angl. 3. Thortial rsults 3. Unr onition without isk ntriity Fig. 6 shows th influn on R whn th swivl angl is 5, 5, 5, 7, an 3g, rsptivly. Whn th swivl angl inrass, th piston strok boms largr; onsquntly, th iffrn btwn th maximum an minimum of R inrass. Fig. 7 shows th influn of th inras of th swivl angl on th aha lay angl. Baus th bnt-axis typ piston pump is rivn by th tapr

5 73 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~733 Dlay Angl, δ x (g) Dlay Angl, δ x (g) α=5 α=5 α=5 α=7 α= null α=5 α= α=5 α= α=5 α=7 α=3 Rotating Angl, θ (g) (a) Total lay angl Rotating Angl, θ (g) (b) Driving rang in lay angl Fig. 8. Dlay angl to swivl angl. piston ro an th aha lay angl xists, it is impossibl to riv th piston ro an th ylinr blok simultanously. That is, whn th riving shaft rotats, th ha of th piston ro onnt with th ntr of th sphrial part in th isk rvolvs on th axis of th shaft, th n of th piston ro onnts with th ylinr bor, an th onsqunt latral for at on th ontat part of th innr surfa of th ylinr bor an th piston ro rivs th ylinr blok to rotat about th ntr lin of th ylinr blok. By th abov prinipl, as th swivl angl is th largr, th rat of inras of th aha lay angl is also gratr. Fig. 8 shows th influn of th lay angl with th hang of th swivl angl. In th bnt-axis typ piston pump rivn by th piston ro, baus th lay angl an istinguish th possibility of normal riving, it is gnrally us as a ritrion for th optimum sign of th swivl angl an th tapr angl. A singl piston ro prforms th riving ation on th ylinr blok twi at on rvolution of th shaft []. Bas on th assumption that th piston has svn piston ros, th riving rang of on piston ro with th minimum lay angl is about 5.7 g, an thr ar two riving rangs for on rotation of th piston ro. Fig. 8 shows that th riving rangs whr piston ro maks th ylinr bor rotat mainly xist in th first an th thir quarants. Whn th rotating angl passs by 45 g an 5 g, th istan btwn th ha of th piston an th ntr of th ylinr bor boms shortr an th aha lay angl rass, so th riving rangs with th minimum lay angl ar gnrat In aition, th minimum lay angl graually approahs zro with th inras of th swivl angl, an whn th swivl angl is abov 7 g, th minimum lay angl boms lss than zro, so it is impossibl to riv normally. 3. Unr onition with isk ntriity Consiring Fig. 8, it is noti that th lay angl hangs gratly vn for a slight hang of th swivl angl. So in th ral sign pross, th gomtrial tolrans will onsquntly triorat th prforman baus of th hang of th lay angl. Baus th lay angl is th fous in this papr, th influn of th isk ntriity from th ntr of th shaft whih is th main fator trmining gomtrial tolrans on th lay angl has to b unrstoo. Figs. 9 to 3 show th hang of th quivalnt lay angl aoring to th ntriity ratio of th isk from th ntr of th shaft (whr α = 5, 5, 5, 7, 3 g). Fig. 9 shows th hang of th lay angl aoring to th hang of th ntriity ratio for α = 5 g. Th minimum lay angl approahs zro whn th ntriity ratio inrass. Assuming that thr ar svn piston ros, th riving rang of on piston ro with th minimum lay angl is about 5.7 g, an it an b onfirm that thr ar two riving rangs at on rotation of th piston ro. Whn th ntriity ratio is E-4, th minimum lay angl rass blow zro, an th piston ro annot riv th ylinr blok normally. Fig. an Fig. show th hangs of th lay

6 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~ Fig. 9. Dlay angl to ntri ratio (α =5g). Fig.. Dlay angl to ntri ratio (α =7g). Fig.. Dlay angl to ntri ratio (α =5g). Fig.. Dlay angl to ntri ratio (α =5g).. angl aoring to th hang of th ntriity ratio whn th swivl angl is 5 an 5g, rsptivly. Th minimum lay angl approahs zro with th inras of th ntriity ratio of th isk, an it xhibits th sam tnny as that in Fig. 9. Fig. 3. Dlay angl to ntri ratio (α =3g). Fig. shows th hang of th lay angl aoring to th hang of th ntriity ratio whn th swivl angl is 7g. Aoring to th hangs in th ntriity ratio of th isk, th ritial valu of th lay angl, whos minimum lay angl is narst to zro, is isplay. Fig. 3 shows th tnny that, if th swivl angl is abov 7g, th minimum lay angl is always lss than zro rgarlss of th ntriity ratio. Whn th minimum lay angl boms lss than zro, th piston ro hangs th riving irtion from along th irtion of shaft rotation to th opposit irtion, so it annot riv th ylinr blok normally. Fig. 4 shows th hang of th lay angl aoring to th hang of th swivl angl whn th ntriity ratio is 5E-4. Whn th swivl angl is lss than 7 g, th valus of th lay in th riving rangs ar gratr than zro, so normal riving is possibl.

7 73 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~733 givn, th following onlusions an b obtain : Fig. 4. Dlay angl to ntri ratio ( =5E-4). () In th bnt-axis typ oil hyrauli piston pump rivn by piston ro, whn th minimum valu of th lay angl is gratr than zro, thr xist normal riving rangs that tak th point of th minimum lay angl as ntrs in th first quarant an th thir quarant. () In th sam onition, th maximum swivl angl of th bnt-axis typ oil hyrauli piston pump rivn by th piston ro an b trmin by thortial analysis. An thn, whn th swivl angl is gratr than th alulat maximum valu, th lay angl boms lss than zro, rgarlss of th ntriity ratio, so th normal riving by th piston ro is impossibl. (3) If th ntriity ratio of th isk ntr is lss than 5E-4 an th swivl angl is blow th alulat maximum valu, th minimum lay angl is always largr than zro, so normal riving is possibl. Howvr, if th ntriity ratio is gratr than 5E-4, th minimum lay angl is always lss than zro irrsptiv of th swivl angl, so normal riving is impossibl. Fig. 5. Dlay angl to ntri ratio ( =E-4). Fig. 5 shows that whn th ntriity ratio is E-4, thr xists a valu whih is lss than zro in th riving rang of th lay angl, rgarlss of th hang of th swivl angls, an it is impossibl to riv normally. Thrfor, whn th tapr angl ξ, th raius of th isk s sphrial part R, th raius of th ylinr bor R, an th lngth of th piston ro L ar hosn bforhan, th maximum swivl angl an b trmin an th maximum ntriity ratio an b sign. 4. Conlusions Bas on th abov thortial analyss about th riving mhanism of th bnt-axis typ oil hyrauli piston pump rivn by a piston ro, if th sign paramtrs suh as th tapr angl ξ, th raius of th isk s sphrial part R, th raius of th ylinr bor R, an th lngth of th piston ro L ar Nomnlatur : Entri istan btwn O an : Entriity ratio btwn an R O L : Lngth btwn P an P in tapr piston O : Cntr of riving shaft O : Cntr of isk on riving shaft O : Cntr of ylinr blok O : Cntr of ylinr bor b P : Cntr of piston ha P : Aha ntr of piston ha P : Cntr of piston n P : Bhin ntr of piston n R : Raius btwn O an O b R : Raius btwn O an P R : Distan btwn O b an projt P on ylinr blok R : Equivalnt istan btwn O an b projt P on ylinr blok R : Distan btwn s O an P θ : Rotational angl of riving shaft α : Swivl angl btwn ylinr blok an riving shaft

8 I.-H. Bak t al. / Journal of Mhanial Sin an Thnology (8) 76~ β : Tilting angl ( P PO ) b β : Equivalnt tilting angl ( P PO ) b δ : Aha lay angl ( POO ) b δ : Equivalnt aha lay angl ( POO ) b δ : Dlay angl ( x POP) δ : Equivalnt lay angl ( E POP) φ : Entri angl φ : Entri angl ratio φ an /7 ϕ : Phas angl ( POO) b ϕ : Equivalnt phas angl ( POO) b ξ : Tapr angl of piston Rfrns [] Mansour A. Karkoub, Osama E. Ga an Mahmou G. Rabi, Priting axial piston pump prforman using nural ntworks, Mhanism an Mahin Thory, 34 (8) (999) -6. [] J. K. Kim an J. Y. Jung, Driving Mhanism of Tapr Pistons in Bnt-Axis Dsign Axial Piston Pumps, KSME Intrnational Journal, 7 () (3) [3] Y. S. Hong an Y. H. Doh, Analysis on th Frition Losss of a Bnt-Axis Typ Hyrauli Piston Pump, KSME Intrnational Journal, 8 (9) (4) [4] P. Casoli an A. Vaa, Grmano Franzoni an Gian Luigi Brta, Moling of flui proprtis in hyrauli positiv isplamnt mahins, Simulation Moling Prati an Thory, 4 (8) (6) [5] M. K. Bahr, J. Svoboa an R. B. Bhat, Vibration Analysis of Constant Powr Rgulat Swash Plat Axial Piston Pumps, Journal of Soun an Vibration, 59 (5) (3) [6] P. Kaliaftis an Th. Costopoulos, Moling an simulation of an axial piston variabl isplamnt pump with prssur ontrol, Mhanism an Mahin Thory, 3 (4) (995)