Analysis of Dissipated Power Caused by Lubrication in Ringless Reciprocating Systems

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1 Analysis of Dissipated Powe Cased by Lbication in Ringless Recipocating Systems 1 M. Razaghi, M. Layeghi, 3 M. Bomand, 4 A. Shiazi 1&3&4 Dept. of Mechanical Engineeing, Ian Univesity of Science and Technology (IUST), Tehan, Ian Faclty of Wood and Pape Science and Technology, Univesity of Tehan, Kaaj, Ian 1 azaghimajid@gmail.com Abstact The ppose of this pape was to evalate the electomoto inpt powe loss cased by oil viscosity between piston and cylinde in ecipocating systems sch as compessos, pesses and pmps with cank and slide dive withot oil ing o ingless pistons. Using the nmeical and analytical appoaches espectively fo nonlinea and linea oil velocity pofiles assmed between piston and cylinde, dissipated powe cased by oil viscosity was calclated and eslts of these two appoaches wee compaed to validate finite diffeence eslts. Finally, the effect of vetical o hoizontal position of piston and cylinde wee compaed in the case of nonlinea oil velocity pofile fo diffeent applications. Keywods- Dissipated powe, Lbication, Linea and nonlinea oil velocity pofiles, Ringless piston, Analytical and nmeical methods. I. INTRODUCTION simlate a piston ing, Ronen et al. [11] pesented a hydodynamic comptational model in ecipocating paallel Piston and cylinde systems ae widely sed in powe sface beaings. They conclded that appopiately sized engineeing applications. Calclation of dissipated powe dimples can consideably edce fictional loss. This effect cased by lbication between piston and cylinde in ecipocating systems is essential fo installation, design was confimed in the expeimental wok of Zhao et al. [1] pocess, analysis, and optimization. The main applications and late in a wok by Ryk et al. [13]. They have shown that of these systems ae in ecipocating compessos, ecipocating pesses, ecipocating pmps, and so many pessization of tapped lbicant cased by defomation of othe systems diven by cank and slide mechanism [1]. a pocket nde load and sface oghness in bonday and In ecipocating compessos which ae sed in domestic mixed lbicated contacts decease solid contact pesse. efigeatos in which vey low fiction loss is needed, Using nmeical and expeimental appoaches, Nathan et al. ingless pistons ae being tilized to minimize the fiction [14] investigated the potential fo sface pattening and between piston and cylinde. To lessen the fictional losses feates to edce fiction at the piston ing cylinde line of the piston and cylinde systems, the cylinde boe s inteface. Meng et al. [15] analyzed the inflence of oil film length is edced. In ealy stdies, Li et al. [] and Zh et al. inetia on piston skit lbication in a high speed engine [3-4] tied to minimize the fiction loss in ecipocating sing an iteation method. The eslt has shown that the pistons of atomotive engines. Aftewads, Gommed and atio of piston skit's length to its diamete inceases the Etsion analyzed gas lbication of a ingless piston in a effect of oil film inetia on the fiction foce. Mixed seies of papes [5-7] in a low heat ejection (LHR) engine. lbication analysis fo the piston ing pack pefomed by Paata et al. [8] pefomed a dynamic analysis fo the oil Yong et al. [16] with consideations of aveage Reynolds film between piston and cylinde in small efigeating eqation and aspeity contact model. Also, to detemine the compessos. aspeity contact foces, Choi et al. [17] pesented a complete To diminish both fiction loss and efigeant gas leakage one-dimensional mixed lbication model fo the piston ing thogh the piston and cylinde cleaance in the high in which the aveage flow model is sed to calclate the efficiency compessos of domestic efigeatos, it is mean hydodynamic film pesse. In this model of the eqied to pefom a dynamic analysis of the seconday piston ing, the effects of the oghness height, pattens, and motion of the piston. Kim [9] has pesented a fomlation engine speed on the nominal minimm oil film thickness fo the piston dynamics consideing hydodynamic foces (MOFT), fictional foce, and powe losses wee and moments between piston and cylinde and the vaiation investigated. in beaing length of the piston. Jeng [10] indicated that the Theefoe, that piston ing plays the key ole in fiction pedominant soce of fiction in ecipocating engines is between piston and cylinde wall; howeve, in this pape, the piston ing assembly and estimates epesent that 40% of ingless piston which is going to be sed widely in the mechanical losses ae de to piston ing. In addition, to ecipocating systems is analyzed. In ecipocating systems, depending on the size of cleaance between piston and Intenational Jonal of Mechanical and Indstial Engineeing (IJMIE), ISSN No , Volme-1, Isse-3, 01 79

2 cylinde walls, nonlinea velocity pofiles cold be appoximated as linea velocity pofiles [18]. Ths, in pesented pape, the dissipated powe cased by the lbication between ingless piston and cylinde has been estimated sing the linea velocity pofile as veification fo finite diffeence eslts of the nonlinea velocity pofile. It has been conclded that the dissipated powe in the case of nonlinea velocity pofile is 41.1% moe than that of linea one. The most dominant facto to contol this diffeence is cleaance between piston and cylinde and this fact is physically explained in this stdy. Becase of lots of applications of ingless piston and cylinde in vetical o hoizontal positions of ecipocating systems, the effect of vetical o hoizontal position of piston and cylinde on dissipated powe has been compaed in the case of nonlinea velocity pofile. As a case in point, ecipocating pesses ae mostly vetical, while ecipocating compessos [19] ae mostly hoizontal. Hence, in the case of nonlinea velocity pofile, diffeent cases have been consideed consisting of vetical position of cylinde with downwad and pwad motions of piston and the hoizontal position of piston and cylinde. In fact, dissipated powe in hoizontal position of piston and cylinde is nealy eqal to the aveage dissipated powes of pwad and downwad motions of piston. II. GEOMETRY, PEROBLEM DEFINITION, AND GOVERNING EQUATIONS The schematics of linea and nonlinea oil velocity pofiles ae given in Fig. 1. Also, cank and slide mechanism and its notations sed in this wok ae illstated in Fig. and to compae linea and nonlinea oil pofiles, the constant paametes ae evalated in Table 1. Fige 1. (a) linea and (b) nonlinea oil velocity pofiles between piston and cylinde Fige. Schematic of a cank and slide mechanism and notations Paamete Vale TABLE I. a 8 b 10 CONSTANT PARAMETERS i 4 o 4.1 L 10 ϕ& (pm) 1500 υ (cm /s) The govening eqation of the poblem in cylindical coodinate system has been deived sing a nmbe of assmptions. At fist, the flid flow is assmed to be lamina and in each cank angle, velocity pofiles ae assmed to be homogenos along the piston. Additionally, the oil paticles ae tansfeed only in the diection of piston movement and the movement of paticles in othe diections is negligible. Finally, oil tempeate and viscosity ae nealy constant since the dissipated powe is calclated fo one cycle ding the steady state pefomance of the ecipocating compesso o othe facilities. Ths, the simplified fom of Navie-Stokes eqation [0-] can be deived fo the poblem in one dimension as follows: 1 ϕ& g = (1) υ ϕ υ The thid tem of (1) is local acceleation, while convective acceleation of piston is tifling. Accoding to Fig., fo downwad motion of piston, bonday conditions ae [3]: cosϕ (i ) = s& = a ϕ& sin ϕ 1 ; (o ) = 0 (,3) b sin ϕ a Then, sbstitting s fo ϕ gives s& = = a sin ϕ 1 s ϕ ϕ& cosϕ b s sin ϕ a (4) Intenational Jonal of Mechanical and Indstial Engineeing (IJMIE), ISSN No , Volme-1, Isse-3, 01 80

3 III. SOLUSION METHODS A. Estimation of dissipated powe sing nonlinea oil velocity pofile The discetized comptational domain is shown in Fig. 3. In this fige, the diffeent cank angles show the diffeent positions of piston along cylinde and the piston cose is divided into eight eqal pats only to show the velocity pofiles clealy in Fig. 4 and 5 in specified cack angles. Howeve, in nmeical soltion of the poblem, the piston cose is divided into 8000 eqal pats. Then, discetized eqation fo each node of the gid can be deived sing finite diffeence method fo eqally-spaced gid as: Thee is no need to the initial condition o bonday condition fo ϕ o s since when (5) is applied on nodes at ϕ =0 and I ϕ I =180, it can be solved independent of ϕ. Afte calclating velocity pofile, shea stess ove the entie ote sface of piston can be estimated sing the law of viscosity fo Newtonian flids as follows: (Fig. 3) I,1 I, τ = μ (8) Δ Then, dissipated powe which is podct of shea foce and piston velocity can be calclated as: cosϕi PI = a ϕτ & I(πi L)sin ϕi 1 (9) b sin ϕ I a Theefoe, by integating the dissipated powe in each cank angle, the aveage dissipated powe fo half of a cycle becomes: 1 π M 1 PI PI 1 P = P dϕ = ( ϕi 1 ϕi ) (10) π I 1 = Fige 3. Coodinates and gids in the domain between piston and cylinde I,J 1 I,J 1 I,J 1 I,J 1 I,J ( Δ) I,J Δ aϕ& cosϕ I 1,J I I,J g sin ϕi 1 = (5) υ b Δs υ sin ϕ I a In which ϕ I is the cank angle coesponding to the position I along the piston cose. The bonday conditions given by (,3) can be witten in the discetized fom as: I, N = 0 ; fo I=1,,...,M (6) cosϕi fo I=1,,...,M (7) I,1 = aϕ& sin ϕi 1 ; b sin ϕi a Intenational Jonal of Mechanical and Indstial Engineeing (IJMIE), ISSN No , Volme-1, Isse-3, Finally, the dissipated powe in vetical state of piston and cylinde is calclated by aveaging the dissipated powes in the pwad and downwad motions of piston. B. Estimation of dissipated powe sing linea oil velocity pofile Fo validation of eslts of nonlinea oil pofile, the linea oil pofile is sed. Accoding to Fig. 4, the linea oil pofile is given by o = s& (11) o i Also, sing the law of viscosity fo Newtonian flids, the dissipated powe is calclated as follows: s& πμi L P = τ(π L)s& = μ (πil)s& = s& (1) o i o i Integating (1) fo half of a cycle gives the aveage dissipated powe as following: μ P = π La ϕ& cosϕ i sin ϕ 1 dϕ (13 ) o i 0 b sin ϕ a To calclate the dissipated powe in case of linea oil pofile, thee is no diffeence between pwad and downwad motions of the piston becase the gavity tem does not exist.

4 Fige 4. Linea velocity pofile IV. DESCUSSION AND RESULTS Fo half of the cycle, when cank angle changes between 0 and 180 (Fig. ), the nonlinea velocity pofiles ae shown fo downwad and pwad motion of piston in Fig. 5 and 6 espectively. velocity pofile ding a piston cose. When the piston and cylinde ae in hoizontal position, the vales of the velocity pofiles ae between the vales of velocity pofiles in pwad and downwad motions of piston. The dissipated powe was fond to be watts fo downwad motion of piston and watts fo pwad motion of piston and watts fo hoizontal state of piston and cylinde which is oghly the aveage of the vales of dissipated powe in downwad and pwad motions of piston. In Fig. 5, when ϕ = 30.75, it can be seen that the diagam has a minimm which is de to high momentm of flid when piston is going to be stopped at ϕ = 0 (Fig. ). Fig. 7 shows gid independency of the nmeical eslts. The velocity pofiles in this fige ae given fo the piston cose at ϕ = 66.4 as a test case. It can be seen that the velocity pofiles fo M=6000 and M=8000 ae nealy coincident and the maximm diffeence between these two cases is less than %. Fige 7. Gid independency of the eslts in adial diection Fige 5. Velocity pofiles fo downwad motion of piston (angle φ is in degee) Reslts show that the dissipated powe calclated sing nonlinea velocity pofile is moe than that of linea velocity pofile. As illstated in Fig. 8, fo a specified ϕ and s&, Δ N < Δ L whee Δ denotes Δ fo nonlinea velocity N pofile and Δ denotes Δ fo linea velocity pofile. The L law of viscosity fo Newtonian flids implies that Δ has invese elationship with shea foce, and dissipated powe. As shown in Fig. 8, in case of linea velocity pofile, Δ is highe than that of nonlinea velocity pofile. Theefoe, the shea foce and powe fo linea velocity pofile shold be less than those of nonlinea velocity pofile. In fact, the dissipated powe is estimated watts fo linea velocity pofile and watts fo nonlinea velocity pofile. Fige 6. Velocity pofiles fo pwad motion of piston (angle φ is in degee) In these figes, cank angles ae coespond to eqally divided piston cose to illstate the ate of change of the Intenational Jonal of Mechanical and Indstial Engineeing (IJMIE), ISSN No , Volme-1, Isse-3, 01 8

5 Fige 8. Compaison of the eslts of linea and nonlinea oil velocity pofiles V. CONCLUSION Dissipated powe, which is an impeative facto in installation, design, analysis, and optimization of ecipocating compessos, pesses, pmps, and othe facilities, cased by oil viscosity has been evalated in this pape. To find the amont of dissipated powe, nonlinea and linea oil velocity pofiles assmed between piston and cylinde and sing nmeical and analytical methods espectively, eslts of these two appoaches wee compaed with each othe. In addition, sing the finite diffeence method, the effect of the geometical paametes and oil popeties on dissipated powe can be analyzed. In the case of nonlinea oil velocity pofile, the shea stess and dissipated powe in pwad motion of piston wee highe than those in downwad motion of piston. Indeed, the dissipated powe fo downwad motion of piston ( watts) was less than that of hoizontal state of piston and cylinde ( watts) and it was less than the dissipated powe fo pwad motion of piston ( watts). Fthemoe, the dissipated powe fo a cycle in hoizontal position of piston and cylinde was nealy eqal to the aveage of dissipated powe in pwad and downwad motions of piston. These slight diffeences wee de to the low weight of oil film and all of the diffeences between dissipated powes wee physically acceptable. Moeove, accoding to Fig. 8, dissipated powe which is calclated sing linea velocity pofile shold be less than that of nonlinea velocity pofile which was consistent with the eslts. The diffeence between the eslts of linea and nonlinea velocity pofiles is pimaily fnction of cleaance between piston and cylinde and this fact is descibed in Fig. 8. a b L VI. cank length (m) connecting od length (m) piston length (m) NOMENCLATURE M nmbe of gid points in s diection N nmbe of gid points in diection P dissipated powe (W) p pesse (pa) P aveage dissipated powe fo half of cycle (W) adial coodinate (m) adis of piston (m) i adis of cylinde (m) o s piston path (m) s& linea velocity of piston (m s -1 ) oil velocity pofile in z diection (m s -1 ) IJ th node velocity (m s -1 ) I,J z vetical coodinate (m) Δ ϕ finite diffeence in ϕ diection (deg) Δ finite diffeence in diection (m) ϕ cank angle (deg) ϕ& angla velocity of cank (ad s -1 ) θ angla coodinate (deg) μ oil dynamic viscosity (N s m - ) υ oil kinematic viscosity (m s -1 ) τ shea stess (pa) REFERENCES [1] M. Razaghi, Analysis, comptation and soltion of Navie-Stokes Eqations fo the stdy of dissipated powe that cased by consmed oil and also ate of oil consmption in ecipocating systems withot oil ing and with cank and slide dive. Bachelo thesis, KIAU, 009. [] D.F. Li, S.M. Rohde, and H.A. Ezzat, An atomotive piston lbication model,. ASLE Tans., vol. 6, 1983, pp [3] D. Zh, H.S. Cheng, T. Aai, and K. Hamai, A nmeical analysis fo piston skits in mixed lbication pat: basic modeling, ASME J. of Tibol., vol. 114, 199, pp [4] D. Zh, Y.Z. H, H.S. Cheng, T. Aai, and K. Hamai, A nmeical analysis fo piston skits in mixed lbication pat : defomation consideation, ASME J. of Tibol., vol. 115,1993, pp [5] K. Gommed and I. Etsion, Dynamic analysis of gas lbicated ecipocating ingless piston: basic modeling, ASME J. of Tibol., vol. 115, 1993, pp [6] K. Gommed and I. Etsion. Paametic stdy of the dynamic pefomance of gas lbicated ingless piston, ASME J. of Tibol., vol. 116, 1994, pp [7] I. Etsion and K. Gommed, Impoved design with non-cylindical pofile of gas lbicated ingless piston, ASME J. of Tibol., vol. 117, 1995, pp [8] A.T. Pata, J.R.S. Fenando and F.Fagotti, Dynamic analysis of piston seconday motion fo small ecipocating compesso, ASME J. of Tibol., vol. 1, 000, pp [9] T.J. Kim, Nmeical analysis of the piston seconday dynamics in ecipocating compessos, KSME Int. J., vol. 17, 003, pp [10] Y. Jeng, Theoetical analysis of piston-ing lbication pat 1: flly flooded lbication, STLE Tibol.Tans., vol. 35, 199, pp [11] A. Ronen, I. Etsion, and Y. Kligeman, Fiction-edcing sfacetexting in ecipocating atomotive components, STLE Tibol. Tans., vol. 44, 001, pp Intenational Jonal of Mechanical and Indstial Engineeing (IJMIE), ISSN No , Volme-1, Isse-3, 01 83

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