THERMOHYDRODYNAMIC ANALYSIS OF PLAIN JOURNAL BEARING WITH MODIFIED VISCOSITY - TEMPERATURE EQUATION

Transcription

1 INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN (Print), ISSN (Print) ISSN (Online) Volume 5, Issue 11, November (14), pp IAEME: Journal Impact Factor (14): (Calculated by GISI) IJMET I A E M E THERMOHYDRODYNAMIC ANALYSIS OF PLAIN JOURNAL BEARING WITH MODIFIED VISCOSITY - TEMPERATURE EQUATION Kanifnath Kadam, S.S. Banwait, S.C. Laroiya National Institute of Technical Teachers Training & Research, Sector 6, Chandigarh ABSTRACT The purpose of this paper is to predict the temperature distribution in fluid-film, bush housing and ournal along with pressure in fluid-film using a non-dimensional viscosity-temperature equation. There are two main governing equations as, the Reynolds equation for the pressure distribution and the energy equation for the temperature distribution. These governing equations are coupled with each other through the viscosity. The viscosity decreases as temperature increases. The hydrodynamic pressure field was obtained through the solution of the Generalized Reynolds equation. This equation was solved numerically by using finite element method. Finite difference method has been used for three dimensional energy equations for predicting temperature distribution in fluid film. For finding the temperature distribution in the bush, the Fourier heat conduction equation in the non- dimensional cylindrical coordinate has been adopted. The temperature distribution of the ournal was found out using a steady-state unidirectional heat conduction equation. Keywords: Journal Bearings. Reynolds Equation, Thermohydrodynamic Analysis, Viscosity- Temperature Equation. 1. INTRODUCTION A Journal bearing is a machine element whose function is to provide smooth relative motion between bush and ournal. In order to keep a machine workable for long periods, friction and wear of mating parts must be kept low. The plain ournal bearings are used for high speed rotating machinery. This high speed rotating machinery fails due to failure of bearings. Due to the heavy load and high speed, the temperature increases in the bearing. For prediction of temperature and pressure distribution in bearing, accurate data analysis is necessary. An accurate thermo hydrodynamic 31

2 analysis is required to find the thermal response of the lubricating fluid and bush. Therefore, a need has been felt to carry out further investigation on the thermal effects in ournal bearings. By considering thermal effects B. C. Maumdar [1] obtained a theoretical solution for pressure and temperature of a finite full ournal bearing. D. Dowson and J. N. Ashton [] computed a solution of Reynolds equation for plain ournal bearing configuration. Operating characteristics were evaluated from the computed solutions and results were presented graphically. The optimum design obective was stated explicitly in terms of the operating characteristics and was minimized within both design and operative constraints. J. Ferron et al. [3] solved three dimensional energy, three dimensional heat conduction equation. They computed mixing temperature by performing a simple energy balance of recirculating and supply oil at the inlet. H. Heshmat and O. Pinkus [4] recommended that the mixing occurs in the thin lubricant layer attached on the surface of the ournal. This implies that no mixing occurs inside the grooves. An excellent brief review of thermo hydrodynamic analysis was presented by M. M. Khonsari [5] for ournal bearings. H. N. Chandrawat and R. Sinhasan. [6] simultaneously solved the generalized Reynolds equation along with the energy and heat conduction equations. They studied the effect of viscosity variation due to rise in temperature of the fluid film. Also they compared Gauss- Siedel iterative scheme and the linear complementarity approach. M. M. Khonsari and J. J. Beaman [7] presented thermohydrodynamic effects in ournal bearing operating with axial groove under steady-state loading. In this analysis, the recirculating fluid and the supply oil was considered. S. S. Banwait and H. N. Chandrawat [8] proposed a non-uniform inlet temperature profiles and for correct simulation. They considered the heat transfer from the outlet edge of the bush to fluid in the supply groove. L. Costa et al. [9] presented extensive experimental results of the thermohydrodynamic behavior of a single groove ournal bearing. And developed the influence of groove location and supply pressure on some bearing performance characteristics. M. Tanaka [1] had shown a theoretical analysis of oil film formation and the hydrodynamic performance of a full circular ournal bearing under starved lubrication condition. Sang Myung Chun and Dae-Hong Ha [11] examined the effect on bearing performance by the mixing between re-circulating and inlet oil. M. Tanaka and K. Hatakenaka [1] developed a three-dimensional turbulent thermohydrodynamic lubrication model was presented on the basis of the isothermal turbulent lubrication model by Aoki and Harada, this model was different from both the Taniguchi model and the Mikami model. P. B. Kosasih and A. K. Tieu [13] considered the flow field inside the supply region of different configurations and thermal mixing around the mixing zone above the supply region for different supply conditions. Flows in the thermal mixing zone of a ournal bearing were investigated using the computational fluid dynamics. The complexity and inertial effect of the flows inside the supply region of different configurations were considered. M. Fillon and J. Bouyer [14] presented the thermohydrodynamic analysis of plain ournal bearing and the influence of wear defect. They analyzed the influence of a wear defect ranging from 1% to 5% of the bearing radial clearance on the characteristics of the bearing such as the temperature, the pressure, the eccentricity ratio, the attitude angle or the minimum thickness of the lubricating film. L. Jeddi et al. [15] outlined a new numerical analysis which was based on the coupling of the continuity. This model allows to determine the effects of the feeding pressure and the runner velocity on the thermohydrodynamic behavior of the lubricant in the groove of hydrodynamic ournal bearing and to emphasize the dominant phenomena in the feeding process. S. S. Banwait [16] presented a comparative critical analysis of static performance characteristics along with the stability parameters and temperature profiles of a misaligned non-circular of two and three lobe ournal bearings operating under thermohydrodynamic lubrication condition. U. Singh et al. [17] theoretically performed a steady-state thermohydrodynamic analysis of an axial groove ournal bearing in which oil was supplied at constant pressure. L. Roy [18] theoretically obtained steady state thermohydrodynamic analysis and its comparison at five different feeding locations of an axially grooved oil ournal bearing. Reynolds equation solved simultaneously along with the energy 3

3 equation and heat conduction equation in bush and shaft. B. Maneshian and S. A. Gandalikhan Nassab [19] presented the computational fluid dynamic techniques. They obtained the lubricant velocity, pressure and temperature distributions in the circumferential and cross film directions without considering any approximations. B. Maneshian and S. A. Gandalikhan Nassab [] determined thermohydrodynamic characteristics of ournal bearings with turbulent flow using computational fluid dynamic techniques. The bearing had infinite length and operates under incompressible and steady conditions. The numerical solution of two-dimensional Navier Stokes equation, with the equations governing the kinetic energy of turbulence and the dissipation rate, coupled with then energy equation in the lubricant flow and the heat conduction equation in the bearing was carried out. N. P. Mehata et al. [1] derived a generalized Reynolds equation for carrying out the stability analysis of a two lobe hydrodynamic bearing operating with couple stress fluids that has been solved using the finite element method. N. P. Arab Solghar et al. [] carried out experimental assessment of the influence of angle between the groove axis and the load line on the thermohydrodynamic behavior of twin groove hydrodynamic ournal bearings. Mukesh Sahu et al. [3] used computational fluid dynamic technique for predicting the performance characteristics of a plain ournal bearing. Three dimensional studies have been done to predict pressure distribution along ournal surface circumferentially as well as axially. E. Suith Prasad et al. [4] modified average Reynolds equation that includes the Patir and Cheng s flow factors, cross-film viscosity integrals, average fluid-film thickness and inertia term. This was used to study the combined influence of surface roughness, thermal and fluid-inertia on bearing performance. Abdessamed Nessil et al. [5] presented the ournal bearings lubrication aspect analysis using non-newtonian fluids which were described by a power law formula and thermohydrodynamic aspect. The influence of the various values of the non- Newtonian power-law index,, on the lubricant film and also analyzed the ournal bearing properties using the Reynolds equation in its generalized form. The aim of this work is to predict the pressure and temperature distribution in plain ournal bearing. Thermohydrodynamic analysis of a plain ournal bearing has been presented with an improved viscosity-temperature equation. The equation has been modified by authors to predict the proper relation between viscosity and temperature for forecasting the correct temperature in plain ournal bearing. The pressure and temperature distribution in the ournal bearing which was almost equal to the temperature obtained by experimental results of Ferron J. et al. [3]. The results have been validated by comparison with experimental results of Ferron J. et al. [3]. and show good agreement.. GOVERNING EQUATIONS In this present work three dimensional energy equation, heat conduction and Reynolds equation were considered for analysis of thermohydrodynamic analysis of a plain ournal bearing. This bearing having a groove of 18 extent at the load line. The geometric details of the ournal bearing system are illustrated in Fig 1. Single axial groove has been used for supplying fluid to the bearing under, negligible pressure. The model based on the simultaneous numerical solution of the generalized Reynolds and three dimensional energy equations within the fluid-film and the heat transfer within the bush body..1 Generalized Reynolds Equation Navier derived the equations of fluid motion for a viscous fluid. Stokes also derived the governing equations of motion for a viscous fluid, and the basic equations are known as Navier- Stokes equations of motion. The Reynolds equation is a simplified version of Navier-Stokes equation. A partial differential equation governing the pressure distribution in fluid film lubrication is known as the Reynolds equation. This equation was first derived by Osborne Reynolds. The hydrodynamic pressure and the velocity field within fluid flow were accurately described through the 33

4 solution of the complete Navier-Stokes equations. This has provided a strong foundation and basis for the design of hydrodynamic lubricated bearings. This paper is to deal with the finite element analysis of Reynolds equation. It will show how the finite element technique is used to form an approximate solution of the basic Reynolds equation. The analysis has been incorporated in a computer programme and results from it were presented. A Reynolds equation in the following dimensionless form governs the flow of incompressible isoviscous fluid in the clearance space of a ournal bearing system. This equation in the Cartesian coordinate system is written as, 3 3 (1) p p F h h F + h F = h h + α β β α t 1 α F where the non-dimensional functions of viscosity F, F1 and F are defined by, dz z z F1 F = ; F1 = dz ; and F z dz = F () The non-dimensional functions of viscosity F, F1 and F report for the effect of variation in fluid viscosity across the film thickness. And non dimensional minimum film thickness is given by, h = 1 X cosα Z sinα (3) The above equation (1) was solved to satisfy the following boundary and complementarity conditions: i. On the bearing side boundaries, ( β = ± λ), p = (4) ii. On the supply groove boundaries, p = p s (5) iii. In the positive pressure region, Positive pressures will be generated only when the fil thickness is thin, Q =, p > (6) iv. In the cavitated region, p Q <, p =, = α (7) Solution of Eq. (1) with above boundary and complementary conditions gives pressure at each node.. Viscosity-Temperature Equation for predicting temperature distribution in bearings The viscosity of fluid film was extremely sensitive to the operating temperature. With increasing temperature the viscosity of oils falls rapidly. In some cases the viscosity of oil can fall by about 8% with a temperature increase of 5 C. From the engineering viewpoint it is important to know the viscosity value at the operating temperature since it determines the lubricant film thickness 34

5 separating two surfaces. The fluid viscosity at a specific temperature can be either calculated from the viscosity-temperature equation or obtained from the viscosity-temperature ASTM chart...1 Viscosity-Temperature Equations There were several viscosity-temperature equations available; some of them were purely empirical whereas others were derived from theoretical models. The Vogel equation was most accurate. In order to keep a machine workable for long periods, friction and wear of its parts must be kept low. For effective lubrication, fluid must be viscous enough to maintain a fluid film under operating conditions. Viscosity is the most important property of the fluid, which utilized in hydrodynamic lubrication. The coefficient of viscosity of fluid and density changes with temperature. If a large amount of heat is generated in the fluid film, the thickness of fluid film changes with respect to temperature and viscosity. The viscosity of oil decreases with increasing temperature. Hence, the change in viscosity cannot be ignored. Due to viscous shearing of fluid layer, heat is generated; as significance, high temperatures may be anticipated. Under this condition the fluid can experience a variation in temperature, so that it is necessary to predict the bearing temperature and pressure. Therefore, a need has been felt to carry out further investigations on analysis of the thermal effects in ournal bearings, so the viscosity-temperature relation given by Ferron J. et al. [3] has been modified. The viscosity is a function of temperature and it was assumed to be dependent on temperature. The viscosity of the lubricant was assumed to be variable across the film and around the circumference. The variation of viscosity with the temperature in the non-dimensional two degree equation was described by Ferron J. et al. [3]; this equation was expressed as, = = k k1 Tf + k T (8) f The authors modified and developed a two degree viscosity-temperature relation in to three degree polynomial viscosity-temperature relation. This modified equation as illustrated below, 3 = = k k1 Tf + k Tf k3 T (9) f J. Ferron et al. [3] used the viscosity coefficients, k = 3.87, k 1 = 3.64, k =.777 while the authors considered the following modified viscosity coefficients, k = 3.186, k 1 =.4817, k = and k 3 =.366. The polynomial equation was found out for getting improved results. Results obtained from viscosity-temperature equation which was developed by authors gives good results when compared with experimental results of J. Ferron et al. [3]. This temperature distribution in plain ournal bearing shows very slight variation between temperature obtained by authors and temperature obtained by J. Ferron et al. [3]. At different load the computed maximum bush temperature and pressure are nearly equal for 15,, 3 and 4 rpm. The authors have found during their investigation that the developed viscosity-temperature equation gives very close values of the maximum bush temperature when compared with the experimental results of J. Ferron et al. [3] at all above speeds. To verify the validity of the above equations and the computer code, the results from the above analysis was compared with experimental values of J. Ferron et al. [3] bearing..3 Three dimensional energy equation for temperature distribution in bearing The solution of energy equation needs the pressure field established from solution of Reynolds equation. It is very important to carry out a three-dimensional analysis to accurately predict the temperature distribution in bearings. Accurate prediction of various bearing characteristics, like 35

6 temperature distribution, is very important in the design of a bearing. The heat flows inside the solid parts, such as the bearing and the shaft, and finally dissipates in the air. The total amount of heat that flows out by convection and conduction is equal to the total amount of heat generated. Temperature distribution in fluid-film is given by three-dimensional energy equation. Fluid temperature has been obtained by solving the following three-dimensional energy equation which has been modified using thin-film approximation and changing the shape of the fluid film into a rectangular field, Tf Tf 1 T Tf ( h h u w z u ) f D u v +ν + = e + + P α β z z z e h α z (1) The non-dimensional effective inverse Peclect number ( P e ) and Dissipation number ( D e as follows, ) are k f Pe =, De = ω ( C p ρ ω c ) ( C p ρ Tr c ) (11) Values of the non-dimensional velocity components in circumferential and axial direction are as follow, z z p 1 1 u = h z F d z z d z + d z α F F (1) p z z F z v = h d z d z β 1 F (13) The continuity equation is partially differentiated with respect to z to determine the nondimensional radial component of velocity ( w ) as, w u v u h + h z + = z α β z z α z (14) Integrate the above equation with finite difference method considering the following boundary conditions, h w = at z = and w = at z = 1 α (15) The three dimensional energy equations have been solved with the following boundary conditions, (i) On the fluid ournal interface ( z = 1) T f = T (16) (ii) On the fluid bush interface ( z = ), T = T (17) f b 36

7 .4 Thermal analysis of heat conduction equation for Bush-Housing Heat conduction analysis was performed to determine the bush temperatures. The Fourier heat conduction equation in the form of non-dimensional cylindrical coordinate form has been solved for the temperature distribution in the bush and is given below, Tb 1 Tb Tb 1 T b = r r r β r α (18) Using following boundary conditions, heat conduction equation was solved. i. On the interface of fluid bush z r R1 Continuity of heat flux gives, ( =, = ), k T b f f b r = r R c h z = 1 z = k T (19) ii. On the outer part of the bush housing ( r = R ), The free convection and radiation hypothesis gives, T h b ab = Tb r R T r k a r R b = = R () iii. On the lateral faces of the bearing ( ) β =± λ, T b hab R = Tb T β a kb β λ =± β =± λ (1) iv. At the outlet edge of bearing pad, free convection of heat flow from bush to fluid in the supply groove gives, Tb hfb R = ( Tb Ts ) kb α α = α e () α = Circumferential coordinate of the outlet edge of bearing. e v. At the inlet edge of the bearing ( α = α ) and at the fluid supply point on the outer surface, i Tb r = R = (3) Ts In addition, a free convection of heat between fluid and housing has been assuming, Tb hfb R T T α = α = α i kb ( b s ) (4) Where α i = circumferential coordinate of the inlet edge of bearing. 37

8 .5 Heat conduction equation for Journal For finding the temperature distribution in ournal, the following assumptions were made, i. Conduction of heat in the axial direction. ii. Journal temperature does not vary in radial or circumferential direction at any section. iii. Heat flows out of the ournal from its axial ends. Hence the following steady state unidirectional heat conduction equation was used for a ournal, T k y A q y + = (5) Where q = the heat input to the element ( q y) ; y = the length of element. Above equation reduces to the following non-dimensional form, π T β + q = (6) where q is the non-dimensional heat input to ournal per unit length, π f k q = c k 1 h T z f dα (7) The above equations have been solved with the following boundary condition, At the axial ends, i.e. β λ = ±, T ha R = T T β k a β = ± λ β = ± λ (8).6 Thermal mixing of fluid in a groove It was not possible for the experimenters to maintain the inlet fluid temperature at a constant value. Because of low supply pressures and high fluid viscosities, the inlet fluid temperature would rise. Thermal mixing analysis of hot recirculating and incoming cold fluid from supply groove was used to calculate the fluid temperature at the inlet of the groove. Energy balance equation is used to estimate the mean temperature of the fluid in a groove. In this work, the overall energy balance equation is expressed in terms of mean temperature, T m, Q Tm = Qre Tre + Qs Ts (9) Where T re - recirculating hot fluid, For the unit length of bearing, 1 ( ) Q = h u d z (3) Qs Q Qre = (31) 38

9 1 ( L ) Qre = C h u d z 1 ( L ) Tre Qre = C h u T f d z (3) (33) Mean temperature T related to the assumed temperature distribution, m Tf ( z) across the fluid film at the inlet of the bearing pad as below, 1 ( ) Tm = T f z d z (34) 3. SOLUTION PROCEDURE The overall solution scheme for thermohydrodynamic analysis of plain ournal bearing is depicted in Fig. The non dimensional coefficient of viscosity has been found out. Reynolds equation solved by finite element method for obtaining pressure distribution in the fluid-film by iterative technique. The negative pressure nodes were set to zero and attitude angle was modified till convergence was achieved. Pressure and temperature fields for the initial eccentricity ratio have been recognized. The load capacity of the ournal bearing was calculated by iterative method. Values of the fluid film velocity components were calculated in circumferential, axial and radial directions. Coefficient of contraction of fluid-film was determined. Coefficient of contraction was assumed as unity in positive pressure zone. The mean temperature of the fluid was calculated. By using finite difference method three dimensional energy equation was solved for temperature distribution in fluid-film. Heat conduction equation was solved for determination of temperature distribution in bush housing. The above procedure was repeated till convergence was achieved. One dimensional heat conduction equation was used for temperature distribution in ournal. The ournal temperature was revised after obtaining the converged temperature for fluid and bush. The energy and Fourier conduction equations were simultaneously solved with revised ournal temperature. All the above steps were repeated until the convergence was achieved. Using modified non dimensional viscositytemperature relation the non dimensional viscosity was found out and modified until convergence was achieved. After convergence achieved the temperature of fluid, bush and ournal was found. For the next value of the eccentricity ratio once the thermohydrodynamic pressure and temperature have been established. The data used for computation of pressure and temperature in fluid, bush and ournal were depicted in Table RESULTS AND DISCUSSION Numerical calculations were performed by writing a computer program in C. The nondimensional governing equations were discretized for numerical solution. The global iterative scheme was used for solving these equations. A mesh discretization for fluid film and bush with 68 nodes in the circumferential direction, 16 nodes in the axial direction and 16 nodes across the film thickness and 16 nodes across the radius of bush thickness. For thermohydrodynamic analysis of plain ournal bearing the input parameters has been taken from Table 1. The present data was assumed for aligned plain ournal bearing. It was assumed that temperature of fluid equal to temperature of bush at the fluid bush interface. Journal temperature is also equal to temperature fluid at the fluid ournal interface. The condition of mixing the recirculating fluid with the supply fluid was also considered. Fig. 3 and Fig. 4 depicts the distribution of the maximum bush temperature obtained with different eccentricity ratio for different speeds of plain ournal bearing. The 39

10 experimental results of J. Ferron et al. [3] were nearly equal to theoretical results of authors as per the modified viscosity-temperature equation. Fig. 5 and Fig. 6 predict the circumferential temperature distribution in the mid-plane of fluid-bush interface. Theoretical predictions and experimental results of J. Ferron et al. [3] exhibit a similar pattern, the predicted maximum temperature value and their locations are reasonably very close to the measured values of J. Ferron et al. [3]. Pressure variation in mid plane of plain ournal bearing for various speeds and loading conditions were shown in the Fig. 7 and Fig. 8. In the authors developed model pressure distribution was very close to the experimental values given by J. Ferron et al. [3]. The mean ournal temperature has been computed along axial direction. Fig. 9 depicts load versus mean ournal temperature at and 4 rpm for two different loads as 4N and 6N respectively. The radial temperature was negligible in the present work. Journal temperature along axial direction of the ournal varies by about one degree for rpm and very close to the 4 rpm at 4 N and 6 N loads respectively. A theoretical result predicted by authors modified viscosity-temperature equation gives good agreement as compared with published experimental results of J. Ferron et al. [3]. 5. CONCLUSIONS On the basis of results and discussions presented in the earlier sections, the following maor conclusions are drawn: The developed viscosity-temperature equation for this work is more appropriate. The maximum pressure is noted at minimum film thickness of fluid. The temperature of fluid-film increases with increase in load and speed of shaft. Due to thermal effects the eccentricity ratio, attitude angle and side flow also changes. The effect of mixing of recirculating and supply temperatures of lubricant in the groove is quite important. Heat transfer from the outlet edge of the bush to fluid in the supply groove must be considered for correctly simulating the actual conditions. At higher speed and heavy load, developed model of viscosity-temperature predicts accurate values for temperature in fluid, bush and ournal. The authors have found during their investigation that the developed equation gives very close values of the maximum fluid and bush temperature when compared with the experimental results of J. Ferron et al. [3] at different speeds and loads respectively. REFERENCES [1] B. C. Maumdar, The thermohydrodynamic solution of oil ournal bearings, Wear, 31, 1975, [] D. Dowson and J. N. Ashton, Optimum computerized design of Hydrodynamic Journal Bearings, International Journal of Mech. Sciences, 18, 1976, 15-. [3] J. Ferron, J. Frene. and R. A. Boncompain, A study of thermohydrodynamic performance of a plain ournal bearing Comparison between theory and experiments, ASME Journal of Lubrication Technology, 15,1983, [4] H. Heshmat. and O. Pinkus, Mixing inlet temperature in hydrodynamic bearings, ASME Journal of Tribology; 18,1986, [5] M.M. Khonsari, A review of thermal effects in hydrodynamic bearings, Part II: ournal bearing, ASLE Transaction, 3(1), 1987,

11 [6] H.N. Chandrawat and R. Sinhasan, A comparison between two numerical techniques for hydrodynamic ournal bearing problems, Wear, 119, 1987, [7] M.M. Khonsari. and J.J. Beaman. Thermohydrodynamic analysis of laminar incompressible ournal bearings, ASLE Transaction,; 9(), 1987, [8] S.S. Banwait. and H.N. Chandrawat, Study of thermal boundary conditions for a plain ournal bearing, Tribology International, 31, 1998, [9] L. Costa, M. Fillon, A. S. Miranda. and J. C. P. Claro, An Experimental Investigation of the Effect of Groove Location and Supply Pressure on the THD Performance of a Steadily Loaded Journal Bearing, ASME Journal of Tribology, 1,, 7-3. [1] M. Tanaka, Journal bearing performance under starved lubrication, Tribology International, 33,, [11] Sang Myung Chun and Dae-Hong Ha, Study on mixing flow effects in a high-speed ournal bearing, Tribology International, 34, 1, [1] M. Tanaka and K. Hatakenaka, Turbulent thermohydrodynamic lubrication models compared with measurements, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 18, 4, [13] P.B. Kosasih and A. K.Tieu, An investigation into the thermal mixing in ournal bearings, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 18, 4, [14] M. Fillon and J. Bouyer, Thermohydrodynamic analysis of a worn plain ournal bearing. 4, Tribology International, 37, [15] L. Jeddi, M. El.Khlifi, and D. Bonneau, Thermohydrodynamic analysis for a hydrodynamic ournal bearing groove, I Mech. E, Part J: J. Engineering Tribology Proceeding, 19, 5, [16] S.S. Banwait, A Comparative Performance Analysis of Non-circular Two-lobe and Threelobe Journal Bearings, IE (I) I Journal-M,; 86, 6, -1. [17] U. Singh, L. Roy. and M. Sahu, Steady-state thermo-hydrodynamic analysis of cylindrical fluid film ournal bearing with an axial groove, Tribology International 41, 8, [18] L. Roy, Thermo-hydrodynamic performance of grooved oil ournal bearing, Tribology International, 4, 9, [19] B. Maneshian and S.A. Gandalikhan Nassab, Thermohydrodynamic Characteristics Of Journal Bearings Running Under Turbulent Condition, IJE Transactions A: Basic,; (),9, [] B. Maneshian. and S. A. Gandalikhan Nassab, Thermohydrodynamic analysis of turbulent flow in ournal bearings running under different steady conditions, Engineering Tribology proc. Part J, I Mech E, 3, 9, [1] N.P. Mehta, S.S. Rattan and Raiv Verma, Stability analysis of two lobe hydrodynamic ournal bearing with couple stress lubricant, ARPN Journal of Engineering and Applied sciences, 5, 1, [] A. Arab Solghar, F.P. Brito, J. C. P. Claro. and S.A. Gandalikhan Nassab, An experimental study of the influence of loading direction on the thermohydrodynamic behavior of twin axial groove ournal bearing, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 5, 11, [3] Mukesh Sahu, Ashish Kumar Giri and Ashish Das, Thermohydrodynamic Analysis of a Journal Bearing Using CFD as a Tool, International Journal of Scientific and Research Publication, (9), 1,

12 [4] E. Suith Prasad., T. Nagarau and J. Prem sagar, Thermohydrodynamic performance of a ournal bearing with 3d-surface roughness and fluid inertia effects, International Journal of Applied Research in Mechanical Engineering (IJARME) ISSN, (1), 1, [5] Abdessamed Nessil, Salah Larbi, Hacene Belhaneche and Maamar Malki Journal Bearings Lubrication Aspect Analysis Using Non-Newtonian Fluids, Advances in Tribology 13, 1-1. [6] Prof. Amit Aherwar, Prof. Rahul Bapai and Prof. Md. Saifullah Khalid, Investigation to Failure Analysis of Rolling Element Bearing with Various Defects, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue, 1, pp , ISSN Print: , ISSN Online: [7] Dr.R.Uday Kumar and Dr.P.Ravinder Reddy, Influence of Viscosity on Fluid Pressure in Hydroforming Deep Drawing Process, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue, 1, pp , ISSN Print: , ISSN Online: Nomenclature A Cross-sectional area of the ournal ( π R ) c Radial clearance, (m); c = c / R CL Coefficient of contraction, C L is unity in positive pressure region C p D D e ( ) ( ) 1 1 C L = u h t dz u h α dz e Specific heat of fluid, (J/kg C) Diameter of Journal, (m) Dissipation number e Journal Eccentricity, (m); ε = e / c F, F1, Non dimensional Integration functions of Viscosity F h Thickness of fluid-film,(m); h = h / c h Convective heat transfer coefficient ab bush, (W/ m C) h Convective heat transfer coefficient a of ournal, (W/m C) h fb k, k 1 k, k 3 Convective heat transfer coefficient from bush to fluid in groove, (W/m C) Coefficient of Viscosity k, k Thermal conductivity of fluid, f b bush and ournal, (W/m C) k L Length of bearing, (m) p Pressure, p = p ps (N/ m ) ps Supply pressure, (N/ m ) P Peclet number, e 4

13 q Heat input per unit length Q Fluid-flow, (m 3 s /s) r Radial coordinate; r = r / R R Radius of ournal, (m) Inner and outer radius of bush, m R, R R1 = R / R, R = R / R 1 r 1 Q = Q ( ω c R 4 ) T Reference temperature, ( C) T Ambient temperature, ( C); = / a b T T T a a r T Bush temperature, ( C); T = T / T f b b r T Fluid film temperature, ( C); = / T T f T T f r Journal temperature,( C); T = T / T r T s Supply temperature, ( C); T = T / T t u, v, w s s r Time ; t = t / ω Fluid velocity components, in circumferential, axial and radial u = u, v = v, w = w ( ω / R) ( ω / R) ( ω / R) directions respectively (m/s) Cartesian Coordinate in circumferential, axial and radial direction, x, y, z z = z / h X, Z Coordinates of ournal centre, (m); X = ε sin φ, Z = ε cosφ α Circumferential cylindrical coordinate; x R β Axial cylindrical coordinate; y R ε Eccentricity ratio; λ Aspect ratio; L D φ Attitude angle (degrees) Viscosity of fluid, (N.s/m ); Reference viscosity of fluid,(n-s/m ) ρ Mass density of fluid, (kg/m 3 ) ω Angular speed of the ournal, (rad/s) 43