VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. NON-NEWTONIAN EFFECTS OF OAD CARRYING CAPACITY AND FRICTIONA FORCE USING RABINOWITS FUID ON TE PERFORMANCE OF INCINED MUTI-STEPPED COMPOSITE BEARING Nisha and Sundarammal Kesavan Deartment of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India E-Mail: nisha.s@ktr.srmuniv.ac.in ABSTRACT The theoretical investigations on different tye of non-newtonian fluid called as Rabinowitsh Fluid on the steady characteristics of inclined multisteed comosite bearings has been analysed. ere the modified Reynolds s closed form exressions are obtained using MATAB Iterative method. The erformance characteristics of different bearings such as lane inclined Slider, comosite taered land; steed bearing and comosite taered concave bearings are established using the exressions. According to the results, the influences of Rabinowitsh fluid on the bearing characteristics rovide an influence in the ressure and therefore which will lead to increase in load carrying caacity. Keywords: inclined multi-steed comosite bearings, non-newtonian lubricants, rabinowitsh fluid. INTRODUCTION Moving arts are searated using the ubricant in a system. This searation leads to less friction, Fatigue on the surface (stress limit), less heat generation, noise in an oerating system and vibrations. ubricants hel to achieve this in most of the ways. The most common way is to forma hysical barrier, or in general way a thin layer of lubricant which hels to searate the moving arts. We can name this rocess as hydrolaning or the friction loss when a car tire got searated due to moving through standing water from the surface of road. This rocess is called ydrodynamic ubrication. When the surface ressure or temerature is high, the fluid film becomes much thinner and the lubricants hel the forces to transmit between the surfaces. In, Udaya P Singh and Ram S Guta studied omotoy Analysis of Curved Slider Bearings using Rabinowitsch Fluid as the ubricant. e concluded that the bearing characteristics vary with the non Newtonian Pseudolastic and Dilatant behavior of the fluid changes deending on the slider Curvature. To study the non linear behavior of various Non- Newtonian lubricants, Rabinowitch fluid model has been taken into account which is a different tye of Non- Newtonian model. For various value of k, Rabinowitch fluid model can be alied to establish the different behaviours of fluid. For k= the behaviour will be Newtonian, for k> it will be the seudo lastic fluids and for k<, the dilatants fluids. Stress-strain relation who holds for one dimensional fluid flow is as follows: u xy k xy y () Where μdescribes the shear rate with zero viscosity, k denotes the non linear factor resonsible for the Non- Newtonian effect of the fluid. In Aug, Jaw Ren in studied the Non-Newtonian squeeze film characteristic between arallel annular disks. A theoretical analysis has been made by Naduvinamani Neminath Bhujaa and Rajashekar Marea in May found that the existence of a critical value for rofile arameter at which the dynamic coefficient attains maximum. In field like agriculture, Automotive, Construction, Marine, Railroad and material handling equiment needs a long wear and low maintenance matters the most. In such field Comosite Bearings are used. It has an advantage like high-load carrying caacity/high shock load caacity, self lubricating design or model, and low coefficient of friction, a resistant to temerature. The hysical and mechanical roerties of this comosite material make it an excellent bearing material comosite bearing achieve their finished dimensions using traditional machining system. This gives the designer a high degree of flexibility to roduce a finished art which is erfectly aligned to the alication. In 99, N.M Bujurke,.P Patil studied the orous slider bearing with coule stress fluid. Similarly, N. B. Naduvinamni, Siddangouda found that the load carrying caacity decrease as ste height increases in Mar 9. FORMUATION OF TE PROBEM Figure- shows a schematic diagram of the squeeze film geometry under consideration. It consists of two surfaces searated by a lubricant. Along the length, the axis x has been taken while along the lubricant film, y axis is taken. ower lane moving with a velocity along x- axis in its own late. Different bearing hysical configuration has been shown in Figure-. It consists of two surfaces searated by fluid called Rabinowitch fluid. The length has been taken as x-axis while y-axis is across lubricant film. 84
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. Above schematic diagram reresents Figure-. Inclined multi steed comosite bearing. Figure-.,.. Plane slider bearing. Figure-.,.5. Comosite taered land bearing. Figure-.4. Comosite taered concave bearing. With reference to Figure-, the film thickness is defined as: m s x h h The total film thickness over the interval is defined as: h d x m x h d x m h d x m x h d x h m 4 4 m 4 x () Where h m is minimum film thickness and h s is slider rofile function. The basic equation under the assumtion of ydrodynamic ubrication governing Incomressible flow of Non-Newtonian Rabinowitsch fluid is given by: u v () x y xy x y y (4) (5) The velocity comonents having the boundary condition are as follows: u U, v at y u, v V at y h (6) On integrating equation (4) with resect to y with subject to the boundary condition (6) and using equation (), the velocity comonent exression is obtained in the form: U y k g C u y yh k g C U h.5k g h (7) Where 4 C.5y.5hy.75h y.5h y & C y.5hy.75h y g x 85
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. Using the relevant boundary condition (6) in continuity equation () for y, the Non-Newtonian Rabinowitsh fluid Reynolds s tye equation is obtained in the form: 5.66 h.5k h U h h x x x x t (8) By using the non-dimensional arameters h x h s h, x, hs hm l h m h h hm m m, t, hm Ul d l k U,, h U h m m (9) The multi-steed comosite bearing dimensionless film thickness for is obtained as from ()and (9) h x h h x m s Where is the dimensionless wedge arameter of the slider rofile? The Reynolds s tye equation for Rabinowitsh fluid is obtained in the form: d 5 d d dhs dhm h.5h dx dx dx dx d () is the non-linear factor resonsible for Non- Newtonian effects and denotes the dimensionless squeeze number. The dimensionless minimum film thickness and film ressure can be obtained as h m i e e i () () On substituting in equation () and on neglecting the higher order terms of ε, the steady state characteristics resectively are obtained in the form: d 5 d d d d.66.5 dx dx dx dx dx Where () x x x x x x 4 4 x 4 4 (4) at x, And ressure is continuous at x & x 4 (5) (6) Substituting of the above condition into equation () results in the following two equations containing &.666 d d d dx dx dx (7) d 5 d d 6.67 dx dx dx (8) x gives On integrating the equation (7) with resect to.666 d dx (9) d Where is the film thickness at which = dx Integration of equation (9) and the use of boundary equation (5) give, 86
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. x x dx x c x c dx x c x c x c dx x 4 c x x c dx 4 x 4 () A B Where 4 dx dx dx A dx dx dx B 4 On integrating equation (8) and using (9) gives the following results: 87
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. x x 7 dx x x c 7 c 7 dx x x c 7 c 7 x dx x x c 7 4 c 7 STEADY STATE OAD CARRYING CAPACITY On integrating the steady film ressure over the film region, the steady load carrying caacity of the bearing is obtained as follows:.5 4.5 x dx W 4 x x dx dx () W B dx x () Dimensionless Work load exression is in the form: FRICTION The Frictional Force alied on the bearing sliding surface is given by:.5 Ff B x dx xy y () x = 4 4 4 dx dx 4 x dx COEFFICIENT OF FRICTION C F f W RESUTS AND DISCUSSIONS Figure- shows the variation of non dimensional steady film ressure with non dimensional coordinate x for different bearing geometries under has been consideration. The highest film ressure observed for inclined steed bearing as comared to other bearing geometries. 88
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. Figure- shows the variation of non dimensional steady film ressure with non dimensional coordinate x for various values of non linear arameter α. It is found that as the arameter values increases the ressure increases gradually and reaches the maximum when α=.5. Figure-4 shows the variation of steady film ressure in a non dimensional form with non dimensional coordinate system x for different negative values of non linear arameter α. It has been seen that unlike in the case as mentioned above, it shows a varying distribution, it increases and reaches a stagnated oint ( oint of maxima) and decreases instantly with the increase in value of α. Figure-5 shows the variation of load carrying caacity W in a non dimensional form with dimensionless coordinate x for various bearing geometries. It has been seen that inclined steed bearing shows the maximum eaks. The effect is advantageous in bearings subjected to load. It hels in inducing the fatigue loading. The danger of fatigue failure of the bearing is reduced. Figure-6 shows the variation of non-dimensional load carrying caacity W with non linear arameter α for different bearing geometries. It has been found that with the increase of non linear arameter, the bearing characteristics can be seen clearly, the weight age should be more in inclined steed bearing region whereas the less weightage should be given to comosite taered concave art. Figure-7 shows the variation of load carrying caacity W in a non-dimensional form with dimensionless coordinate system x for different non linear arameter α. It can be seen that as we increase the value of non linear arameter, the load caacity increases. The higher load caacity resents ossible metal to metal contact at low seeds and reduces wear of the bearing. Figure-8 shows the variation of coefficient of Friction C with dimensionless coordinate x for different values of non linear arameter α<, α= & α> has been lotted. As the values of non linear arameter decreases, the coefficient of friction increases, this means that the direction of the force does not affect the direction the hysical quantity. Figure-9 shows the variation of coefficient of Friction C with non linear arameter α for different bearing geometries. The arameter which affect the erformance of the bearing are the non linear arameter, the comosite bearing shows the maximum characteristics. Figure-. The variation of non-dimensional film ressure with x for different bearing geometries with.5,.5,.45 and 4.65. Figure-. The variation of non-dimensional film ressure with x for different values of α with.5,.5,.45 and 4.65. Figure-4. The variation of film ressure in a nondimensional form with x for different negative values of α with.5,.5,.45 and 4.65. 89
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. Figure-5. Variation of non-dimensional load carrying caacity W with dimensionless coordinate x for distinct bearing geometries. Figure-8. Variation of coefficient of Friction C with dimensionless coordinate x for different values Of non linear arameter α. Figure-6. Variation of non-dimensional load carrying caacity W with non linear arameter α for different bearing geometries. Figure-9.Variation of coefficient of Friction C with non linear arameter α for different bearing geometries. CONCUSIONS Based on the study, this aer redicts the non- Newtonian effects on inclined multi-steed Comosite slider bearing for Non-Newtonian fluid model named as Rabinowitch fluid model. The following conclusions can be drawn on the basis of the results obtained. Figure-7. Variation of non-dimensional load carrying caacity W with dimensionless coordinate x for different non linear arameter α. a) The highest film ressure has been found for the inclined steed bearing than the other geometries. α b) As we increase the stes we have found that the multi steed bearings seems to show the largest ressure distribution than any other geometry. We conclude that multi steed bearing in the resence of Rabinowitsh fluid control a motion by controlling the vectors of normal forces that the moving arts bears. This bearing design gives the maximum efficiency, reliability, durability and erformance, a maximum outcomes and allow the demands of this alication for further studies. It has a long life unless like years (comosite bearing). 8
VO., NO., FEBRUARY 8 ISSN 89-668 6-8 Asian Research Publishing Network (ARPN). All rights reserved. c) In summary, there are three observations resulting from the above numerical results. First, it is imortant to kee track of the work load. Without it, imortant bearing characteristics will be ignored. Deending uon the bearing characteristics we need to give the load. The second thing is the consequence of friction i.e. wear, which is resonsible for oor erformance or erformance degradation and/or damage to comonents of the bearing systems. In any of the system, the flow of material shows an increase in energy density, because initial hase of the transformation and dislacement of the material demand acceleration of material and high ressure. Or in general way we can say we can't deform a solid material using direct contact without alying a high ressure. Somewhere along the rocess must acceleration and deceleration take lace, i.e., the high ressure must be alied on all the sides of the deformed material for more effect. Due to hase transformation, the flowing material will immediately exhibit energy loss and will have reduced ability to flow if ejected from high ressure into low ressure. Coefficient of friction hels to holds the high ressure and energy density in the contact zone and decreases the amount of energy or friction force. And the last one is effect of coefficient of friction on the bearing characteristics. The material combinations of sliding surfaces, along with the lubricant should rovide a low friction coefficient for reducing damage and lower running cost. The characteristic of the bearing should be like it must not fatigue, flatten, or slit under these loads. If the bearing load resistance is too low, the bearing can flatten which ultimately results in abnormal function of the bearing system. REFERENCES [] Stokes V.K. 966. Coule stresses in fluids. The hysics of fluids. 9, Vol. 966, 79-7. [] amrock B.J. 994. Fundamentals of fluid film lubrication. st edition, New York, Mc Graw-ill. [] Murti P.R.K. 974. Analysis of Porous slider bearing. Wear. 8: -5. [4] ughes W.F. 96. The magneto hydrodynamic finite ste slider bearing. Journal of Basic Engineering. 85: 9-6. [5] Pinkus O. and Sterlicht B. 96. Theory of hydrodynamic lubrication. McGraw ill, New York. [6] Ramanaiah.G. 979. Slider bearings lubricated by fluids with coule stress. Wear. 5: 7-6. 8