A study on the performance of a magnetic fluid based hydrodynamic short porous journal bearing

Transcription

1 Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 / pp (UDC: 6.8.5) A tudy on the performance of a magnetic fluid baed hydrodynamic hort porou journal bearing N.S.Patel, D.P.Vakharia, G.M.Deheri 3 *. Mechanical Engineering Department, Faculty of Technology, Dharminh Deai Univerity, Nadiad-38700, Gujarat, India. - nimehp@yahoo.co.in. Mechanical Engineering Department, Sardar Vallabhbhai National Intitute of Technology, Surat , Gujarat, India. - dpvakharia@yahoo.com 3. Mathematic Department, Sardar Patel Univerity, Vallabh Vidyanagar, Anand- 3880, Gujarat, India. - gm.deheri@rediffmail.com *Correponding Author: nimehp@yahoo.co.in Keyword: Magnetic fluid, Hydrodynamic, Porou journal bearing, Preure, Friction. Abtract: An endeavour ha been made to invetigate the performance of a hydrodynamic hort porou journal bearing under the preence of a magnetic fluid lubricant. The aociated Reynold equation for the fluid preure i olved with appropriate boundary condition. To get the fluid film preure leading to the calculation of the load carrying capacity.further, friction i computed. Reult preented in graphical form indicate that the magnetic fluid turn in a better performance of the bearing ytem compared to the cae of the conventional lubricant. It i clearly een that the load carrying capacity increae nominally while the co-efficient of friction decreae ignificantly. Beide, it i een that the bearing can upport a load even in the abence of flow. Thi tudy may offer an additional degree of freedom from deign point of view in term of the form of the magnitude of the magnetic field.. Introduction: Porou oil bearing find extenive ue in the indutry becaue of their low cot and little oil requirement. Theoretical reearch on thee bearing wa firt initiated by [Morgan and Cameron 957]. [Chattopadhyay and Majumdar 984] conducted a theoretical invetigation in to the performance characteritic of finite hydrotatic porou oil journal bearing with tangential velocity lip at the porou interface. It wa found that the effect of velocity lip on the performance of hydrotatic porou oil bearing wa ignificant for lower value of permeability for uitable value of lip parameter. It wa concluded that for all practical purpoe the effect of lip might be neglected.

2 Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 9 [Bujurke and Naduvinamani 99] preented a tudy on the performance characteritic of a narrow porou journal bearing lubricated with couple tre fluid. It wa etablihed that the journal bearing with couple tre a lubricant provided ignificant load capacity and enured coniderable reduction in the coefficient of friction a compared with vicou lubricant. [Baka 999] calculated the hydrodynamic load carrying capacity of porou journal bearing. The calculated load carrying capacity howed that the hort bearing aumption gave more implified olution than the infinite long bearing aumption. [Elharkawy and Guedour 00] obtained a numerical olution for the hydrodynamic lubrication of finite porou journal bearing uing a modified Brinkman-extended Darcy model. It wa hown that the dimenionle permeability parameter had a ignificant effect on the performance parameter of finite porou journal bearing epecially, at higher eccentricity ratio. Further, it wa concluded that the load carrying capacity and friction factor decreaed with the increae in the permeability parameter, however, the attitude angle increaed. [Durak 003] experimentally invetigated the behavior of porou bearing under different lubricant and lubricating condition. The experimental reult obtained in thi tudy indicated that the correct election of the lubricant and uitable running condition were very important on the tribological characteritic of porou bearing. Further, it wa clear from the experimental reult that the change in friction coefficient wa more table and in maller magnitude under table loading than that of periodic loading. [Grabovki 005] olved the problem of an infinite journal bearing having an iothermal compreible lubricant and a porou buh enuring the optimum load carrying capacity. Recently, [Patel et al.0] analyzed the performance of a hydrodynamic hort journal bearing under the preence of a magnetic fluid lubricant. The reult preented in graphical form uggeted that the bearing ytem regitered an improved performance due to the magnetic fluid lubricant a compared to the conventional lubricant. In addition, it wa oberved that the coefficient of friction decreaed ignificantly.. Analyi: The configuration of the bearing which i infinitely hort in Z-direction i preented in Figure.The journal having radiu R j rotate inide a bearing and the pace between the journal and the bearing i filled with a magnetic fluid. If the journal i infinitely hort, the preure gradient p z i much larger than the preure gradient p x, a a reult of which the later can be neglected. The magnetic field i oblique to the tator a in [Agrawal 986] and it magnitude i given by H B = B k z z where, k i a contant to uit the dimenion and the trength of the magnetic field [Bhat 003].

3 30 N.S.Patel et al: A tudy on the performance Fig.. Configuration of the problem In 964 Neuringer and Roenweig developed a imple model to tudy the teady flow of magnetic fluid in the preence of lowly changing external magnetic field. The model conited of the following equation: ( q. ) q p q o ( M. ) H. q 0 () () H 0 (3) M H (4).( H M ) 0 where ρ i the fluid denity, q =(u,v,w) i the fluid velocity in film region, p i the film preure, i the fluid vicoity, o i the permeability of free pace, M i the magnetization vector, H i the external magnetic field and i the magnetic uceptibility of the magnetic particle. Uing equation (3) and (4), equation () become (5) H 0 ( q. ) q p q (6) Thi how that an extra preure term 0 H i introduced into the Navier-Stoke equation when magnetic fluid i ued a a lubricant. The lubricant film i taken to be iovicou, incompreible and the flow i laminar. Thu, the modified Reynold equation for

4 Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 3 magnetohydrodynamic hort journal bearing under the uual aumption [Bhat and Deheri 99], [Bhat 978] and [Agrawal 986] turn out to be d H o 6u dh p. 3 dz h R d Introduction of the lip and poroity parameter in the equation (7) lead to d dz o H p h The aociated boundary condition are 3 4 h h 6u * H p 0 at z = +B/ and -B/, d h. h d ( h) R (7) dp dz 0 Introduction of the dimenionle quantitie Z z B, S h at z = 0. * R *, P p,, 3 u h kb R o u pave the way for expreion of the preure ditribution in dimenionle form a * B P 3 C in The load carrying capacity in x direction i given by Z 3 co 4 w X B 0 ( ) ( ) 0 pcorddz Thu, the dimenionle load carrying capacity in x direction i obtained from c u B Wx w 3 x (4 ) ( ) The load carrying capacity in z direction i given by w Z B 0 0 pin Rddz Therefore, the non-dimenional load carrying capacity in z direction i obtained from (8) (9) (0) ()

5 N.S.Patel et al: A tudy on the performance 3 z w z u B c W 3 ) ( ) ( * () Therefore, the reultant load carrying capacity i given by * x z W W W (3) The friction force i determined by LRd h u f 0 which render the non dimenional friction force a ULB C f F (4) Latly, the coefficient of friction i given by W F 3 * (5) 3. Reult and dicuion: Setting µ* to be equal to zero thi invetigation reduce to the performance of a porou journal bearing in the abence of lip. Further, it i clear that in the abence of magnetization thi tudy become eentially the analyi of a porou journal bearing with lip velocity. A cloe look at equation () and (7) ugget that the effect of magnetization i quite ignificant. In addition, the combined effect of poroity and lip turn in a relatively advere effect on the behavior of the bearing ytem. Beide, it i noticed from equation (9) that the friction decreae due to the magnetic fluid lubricant. It i revealed that the bearing ytem regiter an improved performance a compared to that of the correponding bearing ytem working with

6 Preure Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 33 conventional lubricant. However, the reult are preented graphically to tudy and analyze the performance characteritic. Fig: dealing with the preure profile with repect to angle θ, indicate that the preure increae marginally with repect to the magnetization parameter. Thi i due to the fact that the magnetic preure add to the one generated by the magnetic force developed due to the magnetic particle upended in the lubricant. Fig: 3, 4, 5 indicate that the preure increae ubtantially with repect to Z, B/C and eccentricity ratio repectively. If B/C i le than more fluid pae through the gap between journal and bearing and therefore more preure develop. Increae in eccentricity ratio increae the convergent region of fluid film between the bearing and the journal which again increae the preure. Alo, Fig: 6, how that the effect of lip parameter on the preure profile i almot negligible. Fig: 7 indicate that the preure decreae with increaing value of ψ. Fig: 8-7 are another way of repreentation of the preure ditribution with repect to z, B/C and ε. Fig: 8, indicate that the load carrying capacity decreae ignificantly due to the lip when lower value of eccentricity ratio i taken in to conideration. It i alo een from thi Figure that the effect of lip i almot negligible for higher range of lip parameter. It i oberved from Fig: 9 that poroity tend to decreae, the load carrying capacity ignificantly for higher value of eccentricity ratio, however, thi decreaing effect reduce for lower value of eccentricity. It i manifet in Fig: 0 that magnetization increae the load carrying capacity marginally for the lower value of poroity. Fig: - how that the effect of magnetization i negligible on the load carrying capacity with repect to the eccentricity while load carrying capacity increae a uual with increaing value of eccentricity. Fig: 3, how that the magnetization decreae the friction coniderably while the friction decreae with the decreaing value of the lip parameter. Thu, for a better performance due to magnetization thi lip hould be kept minimum. From Fig: 4 it i clear that the coefficient of friction decreae coniderably for lower value of eccentricity ratio. Further, it i oberved that even lower to moderate value of eccentricity ratio caue reduced coefficient of friction. Finally, it i clearly viible from Fig: 5 that the poroity effect on the friction profile with repect to magnetization i negligible for lower value of poroity. But, it i intereting to note that the friction decreae coniderably due to the magnetization. In addition, coefficient of friction i relatively le for moderate value of poroity. θ µ*=0 µ*=0.00 µ*=0.0 µ*=0. Fig.. Non-dimenional preure ditribution P veru θ for different value of magnetic parameter µ*

7 Preure Preure Preure 34 N.S.Patel et al: A tudy on the performance θ z=0 z=0. z=0. z=0.3 z=0.4 Fig. 3. Non-dimenional preure ditribution P veru θ for different value of Z θ B/C=500 B/C=750 B/C=000 B/C=50 B/C=500 Fig. 4. Non-dimenional preure ditribution P veru θ for different value B/C ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 θ Fig. 5. Non-dimenional preure ditribution P veru θ for different value of ε

8 Preure Preure preure Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 35 θ / =0. / =0.5 / =.0 / =.5 / =.0 Fig. 6. Non-dimenional preure ditribution P veru θ for different value of / Z ψ=0.0 ψ=0.000 ψ=0.00 ψ=0.0 ψ=0. Fig. 7. Non-dimenional preure ditribution P veru Z for different value of ψ Z B/C=500 B/C=750 B/C=000 B/C=50 B/C=500 Fig. 8. Non-dimenional preure ditribution P veru Z for different value of B/C

9 Preure Preure Preure 36 N.S.Patel et al: A tudy on the performance Z / =0. / =0.5 / =.0 / =.5 / =.0 Fig. 9. Non-dimenional preure ditribution P veru Z for different value of / z ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 Fig. 0. Non-dimenional preure ditribution P veru Z for different value of ε Z θ=0 θ=45 θ=90 θ=35 θ=80 Fig.. Non-dimenional preure ditribution P veru Z for different value of θ

10 Preure Preure Preure Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 37 B/C / =0. / =0.5 / =.0 / =.5 / =.0 Fig.. Non-dimenional preure ditribution P veru B/C for different value of / B/C ψ=0.0 ψ=0.000 ψ=0.00 ψ=0.0 ψ=0. Fig. 3. Non-dimenional preure ditribution P veru B/C for different value of ψ B/C ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 Fig. 4. Non-dimenional preure ditribution p veru B/C for different value of ε

11 Preure Preure Preure 38 N.S.Patel et al: A tudy on the performance B/C=500 B/C=750 B/C=000 B/C=50 B/C=500 Fig. 5. Non-dimenional preure ditribution P veru ε for different value of B/C ψ=0.0 ψ=0.000 ψ=0.00 ψ=0.0 ψ=0. Fig. 6. Non-dimenional preure ditribution P veru ε for different value of ψ / =0. / =0.5 / =.0 / =.5 / =.0 Fig. 7. Non-dimenional preure ditribution P veru ε for different value of /

12 Load Load Load Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 39 / ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 Fig. 8. Load veru / for different value of ε ψ ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 Fig. 9. Load veru ψ for different value of ε µ* ψ=0.0 ψ=0.000 ψ=0.00 ψ=0.0 ψ=0. Fig. 0. Load veru µ* for different value of ψ

13 µ Load Load 40 N.S.Patel et al: A tudy on the performance µ* ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 Fig.. Load veru µ* for different value of ε ε Fig.. Load veru ε for different value of µ* µ*=0 µ*=0.00 µ*=0.0 µ*=0. µ*= µ* / =0. / =0.5 / =.0 / =.5 / =.0 Fig. 3. Coefficient of friction veru μ for different value of /

14 µ µ Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 4 µ* ε=0. ε=0.3 ε=0.5 ε=0.7 ε=0.9 Fig. 4. Coefficient of friction veru µ* for different value of ε µ* ψ=0.0 ψ=0.000 ψ=0.00 ψ=0.0 ψ=0. Fig. 5. Coefficient of friction veru µ* for different value of ψ 4. Concluion: Thi invetigation tend to ugget that the performance of the bearing ytem can be improved ignificantly with a proper choice of eccentricity ratio by conidering a uitable magnetic trength. Thi article offer ome meaure for minimizing the advere effect of poroity and lip by the poitive effect of magnetization. Of coure here the lip deerve to be kept at minimum. Nomenclature: B Breadth of bearing (mm) H Strength of magnetic field (A m - ) p Lubricant preure (N/m ) P Dimenionle preure w Load carrying capacity (N) F Dimenionle friction force Co-efficient of friction W Dimenionle load carrying capacity 0 Permeability of free pace (kg m - A - )

15 4 N.S.Patel et al: A tudy on the performance magnetic uceptibility * Dimenionle magnetization parameter Lubricant vicoity (N.S/m ) R Journal radiu (m) e Eccentricity (m) c Radial clearance(m) ε Eccentricity ratio(=e/c) ψ Permeability parameter Permeability(m ) H Porou layer thickne (m) h Film thickne(m) lip parameter =α/ α lip coefficient Dimenionle lip parameter

16 Journal of the Serbian Society for Computational Mechanic / Vol. 6 / No., 0 43 Извод Студија о перформансама хидродинамичког кратког порозног цилиндричног лежаја са магнетним флуидом N.S.Patel, D.P.Vakharia, G.M.Deheri 3 *. Mechanical Engineering Department, Faculty of Technology, Dharminh Deai Univerity, Nadiad-38700, Gujarat, India. - nimehp@yahoo.co.in. Mechanical Engineering Department, Sardar Vallabhbhai National Intitute of Technology, Surat , Gujarat, India. - dpvakharia@yahoo.com 3. Mathematic Department, Sardar Patel Univerity, Vallabh Vidyanagar, Anand- 3880, Gujarat, India. - gm.deheri@rediffmail.com *Correponding Author: nimehp@yahoo.co.in Резиме Уложен је труд да би се испитале перформансе хидродинамичког кратког порозног цилиндричног лежаја под присуством магнетног флуида подмазивача. Одговарајућа Рејнолдсова једначина за притисак флуида је решена са граничним условима да би испитао притисак флуида филма у односу на рачунање носивости. Даље је анализирано и рачунање трења. Резултати који су представљени графички указују на то да магнетни флуид показује боље перформансе код лежајних система у поређењу са уобичајеним подмазивачем. Јасно се види да се носивост повећава док се коефицијент трења значајно смањује. Осим тога, види се и да лежај може да поднесе оптерећење чак и у одсуству протока. Ова студија може да пружи додатни поглед са дизајнерске тачке гледишта у виду јачине магнетног поља. Књучне речи: Магнетни флуид, хидродинамички, порозни цилиндрични лежај, притисак, трење. Reference: Agrawal V (986). Magnetic fluid baed porou inclined lider bearing, WEAR, 07, Baka Ern o (999). Calculation of the hydrodynamic load carrying capacity of porou journal bearing, periodica polytechnica er. Mech. Eng., 46, NO., 3 4. Bhat M (003). Lubrication with a magnetic fluid, Team Spirit (India) Pvt. Ltd. Bhat M (978). Hydrodynamic lubrication of a porou compoite lider bearing. Japanee Journal of AppliedPhyic, 7, Bhat M, Deheri G (99). Squeeze film behavior in porou annular dic lubricated with magnetic fluid, Wear, 5, 3-8. Bujurke N, Naduvinamani N (99). On the performance of narrow porou journal bearing lubricated with couple tre fluid. Acta Mech., 86, 79 9.

17 44 N.S.Patel et al: A tudy on the performance Chattopadhyay A, Majumdar B (984). Steady tate olution of finite hydrotatic porou oil journal bearing with tangential velocity lip. Tribology international, DURAK Ertugrul (003). Experimental Invetigation of Porou Bearing Under Different Lubricant and Lubricating Condition. KSME International Journal, 7(9), Elharkawy A, Guedouar L (00). Hydrodynamic lubrication of porou journal bearing uing a modified Brinkman-extended Darcy model, Tribology International, 34, Grabovkii V I (005). Optimum porou journal bearing enuring maximum load capacity, Fluid Dynamic, 4(), Morgan V, Cameron A (957). Mechanim of lubrication in porou metal bearing, Proc. Conf. Lubrication and Wear. Intitution of Mechanic M Engineer, London, Neuringer J, Roenweig R (964). Phy Fluid, 7, 9-7. Patel N, Vakharia D, Deheri G (0). A Study on the Performance of a Magnetic-Fluid-Baed Hydrodynamic Short Journal Bearing. ISRN Mechanical Engineering, 7 page.