FERROFLUID LUBRICATION OF A SLIDER BEARING WITH A CIRCULAR CONVEX PAD

Analysis was done of a slider bearing with its stator having a circular convex pad surface, using a ferrofluid lubricant with a Jenkins model to describe its flow. Expressions were obtained for dimensionless pressure, load capacity, friction on the slider, the coefficient of friction and the position of the centre of pressure. The pressure was little affected by either the crown height or the material parameter. However, i t increased considerably with increasing values of the field strength. The load capacity increased with increasing values of the field or film thickness ratio and decreasing values of the material parameter. The friction force on the slider decreased when the film thickness ratio increased. However, i t increased after a certain value of the film thickness ratio when either the field strength or the material parameter increased. The coefficient of friction increased with increasing values of the material parameter or decreasing values of the film thickness ratio or the field strength. The position of the centre of pressure shifted towards the outlet when the film thickness ratio increased. It shifted towards the inlet when either the field strength or the material parameter increased only after the film thickness ratio attained a certain value.


INTRODUCTION
A bearing with an impermeable stator and an impermeable slider with a convex pad surface was studied by Abramovitzl.He found its performance better than that of a plane slider.Vinay Puri and Pate12 generalized the above analysis by taking the stator -to have a porous facing of uniform thickness backed by a solid wall.They found that such a bearing had more load capacity, friction and coefficient of friction than the corresponding bearing with a plane slider.
A ferrofluid is a suspension of solid magnetic particles of subdomain size in a liquid carrier.Agrawa13, Paras Ram and Verma4studied inclined porous slider bearing with a ferrofluid lubricant using Neuringer-Rosensweig model and Jenkins model respectively to describe the flow.They found that magnetization increased the load capacity of the bearing without altering the friction on the slider.Jenkins considered material property also, thus generalizing the Neuringer-Rosensweig model.Recently, Shah and Bhat5v6 considered the effect of magnetic fluid lubricant on the squeeze film between curved porous rotating circular plates and two curved annular plates and found that ferrofluid lubricant was more advantageous than the conventional lubricant.
In the present paper the convex slider bearing with a ferrofluid lubricant whose flow is described by Jenkins was studied.

Formulation of t h e Problem
The impermeable bearing consists of a stator with a circular convex pad surface with crown height 6 and a slilder moving with a uniform velocity U in the x-direction.
The film thickness h is taken as where B is the bearing breadth, h, and h, are the minimum and maximum film thicknesses.
Assuming steady flow of the lubricant with no slip condition at the boundaries, no end effects and no side effects, the equation governing the film pressure p is deduced form Ram and Verma4 as where p is the fluid density, 6 is the fluid viscosity, aZ is the material constant of Jenkins model, P is the magnetic susceptibility of the fluid particles, H is the magnitude of the external magnetic field R and p, is the free space permeability.If z is the stress and u is the fluid velocity in the x-direction, the shear-stress relation is We take a magnetic field H of strength H inclined at an angle 4 with the x-axis.It vanishes at the inlet and outlet of the bearing so that it attains its maximum at the middle of the bearing as p does, thus enhancing the latter.The inclination @ does not appear in eq. ( 2) and can be obtained as in Ram and Verma4.Thus, we rl~fine K being a quantity chosen to suit the dimensions of both sides and the value of H. Let us introduce the dimensionless quantities -Xhh:p

Solution
Solving eq.( 6) under the boundary conditions we obtain The load capacity W, friction on the slider I?, coefficient of friction f and the position of centre of pressure X are defined as where L is the bearing length.
They are expressed in non-dimensional forms as

RESULTS AND DISCUSSION
Expressions for dimensionless pressure 3 , load capacity W, friction on the slider F, the coefficient of friction f and for the position % of thk centre of pressure are given by eqs.(lo), ( 12) -(15).
In the reference^^-^, both the magnetization parameter and material parameter include K, the field strength.As per the referees suggestion to make the material parameter independent of K, we define it by the equation so that ? is independent of K. Then Let us take the representative values of Bhat7 as,

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to compute the values of the bearing characteristics p, W, F, r a n d which are displayed in tabular form and graphical forms in Tables 1-7 and Figs.2-5.
The values corresponding to K=O and B=0 in the above represent the results for a c~r,ventional lubricant obtained by ~brimovitzl and those for a ferrofluid lubricant flowing following the Neuringer-Rosensweig model respectively.
From Table 1 we see that is symmetrical about the line g 0 . 5and attains a maximum there.Moreover, p is not much affected by the crown height 6.   2 p is not much affected by the material parameter p. From Fig. 2 p' increases considerably for increasing values of the field strength K.For a ten-fold increase in K, there is a ten-fold increase in p.
From Fig. 3 % increases for increasing values of K or a.It can be considerably increased by increasing K.  3 F decreases when a increases.However, it increases when K increases provided a > a,, 1.8 < a, < 1.9.

,Table 3: f i ' vs K for various values of a
From Fig. 4 ?decreases with increasing values of a or K.   increases accordingly as a ;a,, 1.9 < a,< 2.0.

Table 5: $ vs B for various values of a
From Table 6 ?decreases or increases accordingly as a or p increases.

Table 6: f v s B for various valu,es of a
From Table 7 the position of the centre of pressure shifts towards the outlet when a increases.However, it shifts towards the outlet or inlet accordingly as a 2 a,, 1.8< a,<1.9, when p increases

CONCLUSION
The pressure and load capacity of the bearing can be increased considerably by increasing the strength of the external magnetic field.However, they are not much affected by the material parameter.

Figure 1 :
Figure 1: Slider Bearing with a circular Convex Pad Surface

Figure 4 :
Figure 4: vs K for various values of a for 8 = 0.35, = 2 . 7 7~1 0 .~From Fig.5the position of the centre of pressure shifts towards the outlet when K increases.But shifts towards the inlet when a > a,, 1.8 < a, < 1.9.

Table 4 : W vs p for various values of a
From Table5decreases when a increases.It decreases or increases when B