INFLUENCE OF THE PROFILED ROTOR DESIGN ON THE PERFORMANCE OF ROTATING MACHINES

Transcription

1 INFLUENCE OF THE PROFILED ROTOR DESIGN ON THE PERFORMANCE OF ROTATING MACHINES Ph.D. Stdent Antonios DETZORTZIS, Ph.D., Pofesso, Eng. Nicolae BĂRAN, Ph.D. Stdent Malik HAWAS POLITEHNICA UNIERSITY OF BUCHAREST Abstact. The aim of this pape is to expose the elation between the constctive fom of the pofiled oto and the following paametes: the flow ate of the tanspoted flid, the diving powe of the machine, the volmetic efficiency. Thee constctive soltions of pofiled otos ae pesented. The flow ate of the flid and the diving powe of the machine ae calclated fo each one of them. The advantages and disadvantages of evey constctive soltion ae otlined. Keywods: otating machines with pofiled otos. 1. INTRODUCTION The tem otating machine efes to the fact that the otating machine pesented in this pape can be sed as: ventilato fo the tanspot of gas and steam, pe o with sspensions; pmp fo the tanspot of the liqids, esidal wates o evey high viscosity flid; low pesse compesso (blowe), the gas having a dischage pesse of ba. This type of otating machine ovetakes in pefomance the classical machines that have pistons with altenative ectilinea movement, becase ding a whole otation the moto toqe eceived fom the shaft is almost integally ceded to the tanspoted flid [1, ] (fig.1): M = F b sinα [N m] whee: F foce that pesses on the otating piston; b the foce am, namely the adis that taveses the ax of the piston; α angle between am and foce, always eqal to 90 o. Dynamically eqilibated constctive soltions of otating machines wee achieved by eliminating the slide-cank mechanism. Inetia and fiction foces ae lowe than in the case of machines with pistons. Thee constctive soltions ae analyzed in the following: I st vesion: Pofiled oto with two bladeshaped pistons (.1); I nd vesion: Pofiled oto with two pistons of tiangla shape (.); III d vesion: Pofiled oto with two pistons of cvilinea shape (.).. ROTATING MACHINE FOR THE FLUID TRANSPORT.1. Rotating machine with pofiled otos in the shape of ectangla blades The otating machine is composed by a mobile sbassembly (otos, shafts) and a fixed sbassembly (casings, intake and dischage banch pipes) (Fig. 1). The otos () and (5) otate with the same speed inside the two casings (1) and (4); thei synchonos otation is insed by the se of a geaing consisting of two sp geas with the same pitch diamete, monted on the shafts 7 and 9, otside the machine. The aspiated gas (fig.1.a) is tanspoted towads dischage and afte a 90 otation of both otos, positions fom fige 1.b and sbseqently, 1.c ae eached. We do not conside the volme of the gas fom the cavity, becase it is boght back at intake when the contact between the piston and the ppe oto takes place. Afte a 180 otation, the flid fom the sefl volme (fig 1.c), namely the space encompassed by the pistons, the lowe casing (1) and the lowe oto (), will be sent to the dischage chambe. Afte a complete otation of the shaft (9) two sch volmes will be tanspoted fom intake towads dischage [] : πr c πr l m /ot (1) The adis of the casing (R c ) is the sm between the adis of the oto (R ) and the height of the piston (z): R c =R + z [m] () 18 TERMOTEHNICA /01

2 INFLUENCE OF THE PROFILED ROTOR DESIGN ON THE PERFORMANCE OF ROTATING MACHINES Fig. 1. Rotos with blade-shaped otating pistons: 1 lowe casing; lowe oto; intake chambe; 4 ppe casing; 5 ppe oto; 6 blade shaped otating piston; 7 diven shaft; 8 dischage chambe; 9 diving shaft; 10 cavity whee the ppe oto piston entes. It eslts : lz(z R ) [m /ot] () The volmetic flow ate dischaged by a sole oto of length l [m] and otation speed n [pm] will be : n lz z R [m /s] (4) 60 Becase the machine has two identical otos the flow ate tanspoted by the machine will be: m. n lz [m /s] (5) z R 0 Fo the given vales: l=0.05 m; z=0.0 m; R =0.05 m; n = 00 pm. It eslts : m (6) 0 00 m m / s.04 m / h (7) Obviosly, it is difficlt to attach the blade to the oto fo the I st vesion; the case of a theoetical compesso was analyzed. Relations fo compting the flow ate of the gas tanspoted by the machine wee established, in the hypothesis that the blade thickness was neglectable. Fo the vesions II and III, the flow ate tanspoted by the machine will be smalle becase the volme occpied by the body of the tiangla, espectively cvilinea piston is sbtacted fom [4]... Compessos with pofiled otos having otating pistons of tiangla shape The fnctioning of this new compesso type is simila with the one pesented in paagaph.1 (Fig. ). In this case, the blade is eplaced by a tiangle dimensioned obseving mateials stength constaints. The basis of the tiangle was dimensioned, namely the section of the piston close to the oto. It is consideed that a nifomly distibted chage p = ba = 10 5 N/m acts on the piston. A potion of the piston of length b = 1 cm and of height z = cm is chosen; the vale of h mst be calclated (Fig. ). The concentated foce will be: P = p A = = 90 N (8) The bending moment: z MP Nm (9) Elastic section modls: W max nec (10) aî The otos ae made fom cast alminm, fo which σ aî is of 5 7 N/mm [16]. M 1.5 W nec Fo a ectangla section: 6 m (11) bh 6 Wnec m (1) 6 Becase b = m, it eslts the vale of h: 4 h m m 1.6 cm (1) Choosing the safety facto c = 1.85, it eslts h = cm. TERMOTEHNICA /01 19

3 Antonios DETZORTZIS, Nicolae BĂRAN, Malik HAWAS Fig.. Rotating volmetic compesso with tiangla otating pistons: 1 lowe casing; lowe oto; intake chambe; 4 ppe casing; 5 ppe oto; 6 otating piston of tiangla shape; 7 diven shaft; 8 dischage chambe; 9 diving shaft; 10 cavity whee the ppe oto piston entes. Fig.. Calcls notations. This constctive soltion gaantees a good stength of the piston and in the same time it ceates two sealing zones: between the top of the piston and the inside of the casing and between the top of the piston and the cavity. As we can emak in Fige 4, the sefl volme is edced with the volmes of the pisms ABC and A B C ; these ae eqal and togethe they fom the volme of a piston of tiangla section, namely a pism with the following dimensions: height: z = 0 mm; basis: b = 0 mm; length: l = 50 mm; The aea of the section between the basis of the pism and the oto is neglected. The volme of this pism will be: 1 1 p, II Abazei l bzl [m /ot] (14) Compaed with the theoetical flow ate tanspoted by the machine in the vesion I: n m,i lz( z R ) [m /s] (15) 0 the theoetical flow ate of the machine in this vesion II will be edced with pii. Fig..6. Section thogh the otating woking machine: 1 ppe casing; lowe casing; ppe oto; 4 lowe oto; 5, 6 shafts; 7 tiangla piston; 8 cavity. The gas flow ate tanspoted by a oto: lz z R [m /ot] (16) R p, II The machine has two identical otos, so that the flow ate tanspoted will be: m,ii lz( z R 1 n ) bzl 60 [m /s] (17) 10 TERMOTEHNICA /01

4 INFLUENCE OF THE PROFILED ROTOR DESIGN ON THE PERFORMANCE OF ROTATING MACHINES Fo the same data as in vesion I and adding b = 0.0 m, we obtain a flow ate of: m,ii (18) mii, m /s.08m /h (19) Thee is a flow ate diffeence between the vesions I and II: mi, mii, m /h (0) Fig 5. Tansvesal section thogh a otating machine 1-lowe casing; -lowe oto; -intake chambe; 4-ppe casing; 5-ppe oto; 6-otating piston of cvilinea shape; 7-diven shaft; 8-dischage chambe; 9-diving shaft; 10-cavity whee the ppe oto piston entes... Compesso with pofiled otos with cvilinea otating pistons In this constctive soltion (vaiant III) the otating pistons have a cvilinea shape (Fig. 5). This vesion was constcted in the laboatoies of the POLITEHNICA Univesity of Bchaest on the basis of eslts deliveed by a compting softwae [5]. The woking pinciple is the same as of vesions I and II. It can be emaked fom Fige 6 that the sefl volme will be edced with a volme eqal to the aeas (ABC+A B C ) mltiplied with the length of the piston (l), dimension pependicla on the plane of the fige. The aeas ABC and A B C ae eqal, hence the volme of a cvilinea piston ( p,iii ) mst be sbtacted fom. This volme eqals the piston aea (S p ) mltiplied by its length (l). p,iii Sp l SABCl [m ] (1) Hence the theoetical machine flow ate will be edced with piii leading to: lzz R p,iii [m /ot] () The flow ate tanspoted by a oto: lz p, III z R [m /s] n 60 () Fig. 6. Tansvesal section thogh the otating woking machine: 1 ppe casing; lowe casing; ppe oto; 4 lowe oto; 5,6 shafts; 7 cvilinea piston; 8 cavity. Becase the machine has two identical otos, the volmetic flow ate of the machine will be: m,iii n 0 lzz R S l [m /s] ABC (4) The aea of the sface S ABC fom Fige 6 is appoximated with the aea A ANM fom Fige 7, encompassed between the tangent to the oto in TERMOTEHNICA /01 11

5 Antonios DETZORTZIS, Nicolae BĂRAN, Malik HAWAS the point N, namely the line MN, and the pofile of a ½ of the piston, namely the cve AM. Fig. 7. Section thogh a oto with a cvilinea piston: 1 ppe casing; ppe oto; shaft. The aea of the piston section will be: S p = S ABC = S ANM [m ] (5) The coodinates of the points AN and M ae [x i ;y i ]: A(0;0.008); N(0;0.05) and M(0.0199; ) [5]. We divide the inteval NM 0.0 m in ten eqal intevals of length 0.00 m. Hence the coodinates x i of the points on OX ae: 0.00; 0.004; 0.006; 0.008; 0.010; 0.01; 0.014; 0.016; 0.018; 0.00 m. Coesponding to these vales (x i ), the closest vales x i ae chosen fom the table containing the coodinates of the points. The vales y i ae coespondingly taken fom the table. The adis of the oto (R = 0.05 m) is sbtacted fom vales y i. ales y i * that decease fom y i * = 0.0 m (point A) till y i * = (point M) ae obtained. Table 1. Coodinates of the points sitated on the ac AM No. x [m] Eqivalent * x point no. i [m] y i [m] yi yi 0,05 [m] 0 A Nmeical integation, popely the tapeze fomla, was sed fo the calcls of the aea of the cvilinea piston pofile [6]. The fist sface is eqal to the basis (h) mltiplied by the medim height of the tapeze, namely: f ( xo) f ( xo h) KL (6) Fig. 8. Calcls notations. The sface nde the fnction gaphics will be: b N1 x i0 i1 I f ( x)dx f ( x)dx (7) a h I1 yo y1 y... yn1 yn (8) Using the vales of table 1 we obtain: 0.00 I 1 ( ) m (9).97 cm Hence: S ABC = S ANM = m (0) Replacing in fomla (4), it eslts: m, III [ (1) ] 0 m,iii m / s 0.61 m / h () In conclsion, the flow ate tanspoted by the thee vesions of machines will be: M, I M, II M, III x i ().04 >.08 > 0.61 [m /h] (4) o: > > [m /s] (5) It is obvios that the volmetic efficiency (η v ) of the machine deceases when the flow ate tanspoted by the machine deceases: η v,i > η v,ii > η v,iii [7]. 1 TERMOTEHNICA /01

6 INFLUENCE OF THE PROFILED ROTOR DESIGN ON THE PERFORMANCE OF ROTATING MACHINES The diving powe of the otating machine will be: P p W (6) whee p is the pesse incease between intake and dischage; obviosly: P m,i m,ii P P (7) m,iii In the I st vesion, the machine tanspots a flow ate geate than in vesions II and III bt it needs also a geate diving powe. The design of the otos povides special sealing conditions, espectively. The cvilinea shape of the piston povides a bette contact between the otating piston and the cavity of the adjacent oto (Fig. 9). Fom the fige 9 we emak the following: If the piston has a tiangla shape, thee is a sole contact line (zone A) of length l (pependicla dimension on the plane of the fige) between the piston and the cavity of the adjacent oto. If the piston has a cvilinea shape, fom Fige 9 we emak that thee ae thee contact lines: B, A and C; heepon the flid losses between intake and dischage will be edced, diminishing the evese flow, hence the volmetic efficiency will incease when the machine woks as a pmp. Conseqently the effective efficiency of the machine will incease. B Fig. 9. Tansvesal section thogh the otating machine. A C. CONCLUSIONS The otos design inflences the flow ate, the powe and the efficiency of the machine. Fo the oto with the blade shaped (I), tiangla (II) o cvilinea (III) piston, the flow ate deceases in the following ode: I, II, III. The diving powe of the machine will decease in the same ode: I, II, III. The volmetic efficiency will incease in the ode I, II, III. In the I st vesion, between dischage and intake thee is only one sealing zone (line) (A) on all the length of the oto; accodingly, this soltion is ecommended fo the constction of the pmps. In the III d vesion, thee ae thee contact zones B,A,C, on all the length of the oto, poviding a bette sealing between dischage and intake; this soltion is ecommended fo the constction of the high pesse ventilatos and of low pesse compessos. BIBLIOGRAPHY [1] Nicolae Băan, Pete Rădcan et al., Technical themodynamics, (in Romanian), Politehnica Pess Pblishing Hose, Bchaest, 011. [] Nicolae Băan, Rotating themic machines, woking machines, foce machines (in Romanian), Matix Rom Pblishing Hose, Bchaest, 011. [] Alin Motoga, Inflence of constctive and fnctional paametes on the pefomances of otating machines with pofiled otos, Ph. D. Thesis, Politehnica Univesity of Bchaest, Bchaest 011. [4] Nicolae Băan, I.M.Călşa, A. Detzotzis, Reseach Regading the Testing of a New Type of Rotating Machine with Pofiled Rotos, Jonal of Mateials Science and Engineeing A () (01), pp [5] Nicolae Băan, D. Besnea, T. Sima, A. Detzotzis, C. Căna, Manfacting Technology fo a New Type of Pofiled Roto, Advanced Mateials Reseach ol (01) pp. 5-40, Tans Tech Pblications, Switzeland, www. scientific. net/amr [6] Macel Roşcleţ, Mathematical Analysis (in Romanian), Didactic and Pedagogic Pblishing Hose, Bchaest [7] Nicolae Băan, A. Detzotzis, A, Băăsc, The inflence of fnctional and constctive paametes on the efficiency of a new type otating machine, Poceedings of the Confeence COFRET 01, pp. 18-, ISBN , 11-1 Jne 01, Sozopol, Blgaia. TERMOTEHNICA /01 1