


ARTICLE 

Year : 2011  Volume
: 1
 Issue : 1  Page : 1623 

Performance of Asymmetric SlotEntry Hybrid Journal Bearing Operating with NonNewtonian Lubricant
HC Garg
Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar  125001, India
Date of Web Publication  4Jan2011 
Correspondence Address: H C Garg Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar  125001 India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09768580.74533
Abstract   
This article presents the theoretical investigations of the rheological effects of the lubricant on the performance of asymmetric slotentry hybrid journal bearing system. Finite element method (FEM) has been used to solve the Reynolds equation governing the flow of lubricant in the bearing clearance space along with the restrictor flow equation. The nonNewtonian lubricant has been assumed to follow the cubic shear stress law. The simulated results of bearing characteristics parameters in terms of minimum fluid film thickness and bearing flow have been presented for the wide range of values of nonlinearity factor and external load. The computed results reveal that the variation of viscosity due to nonNewtonian behavior of the lubricant affects the performance of slotentry hybrid journal bearing system quite significantly. Keywords: Hybrid, journal bearing, nonnewtonian lubricant, slotentry
How to cite this article: Garg H C. Performance of Asymmetric SlotEntry Hybrid Journal Bearing Operating with NonNewtonian Lubricant. J Eng Technol 2011;1:1623 
How to cite this URL: Garg H C. Performance of Asymmetric SlotEntry Hybrid Journal Bearing Operating with NonNewtonian Lubricant. J Eng Technol [serial online] 2011 [cited 2019 Mar 25];1:1623. Available from: http://www.onlinejet.net/text.asp?2011/1/1/16/74533 
1. Introduction   
In recent times, the nonrecessed slotentry hybrid journal bearings are being used under severe conditions of high speed and heavy load. The continual growth of technological advances and industry's expanding demands for higher speed applications and the ability of hydrostatic/hybrid journal bearings to support heavy loads have necessitated the study of performance of these bearings in detail under more realistic conditions. In slotentry type the restrictors are formed by a slotted shim fabricated into the bearing. The slotentry bearing need finer filtration to prevent gradual silting of the slot restrictors. The asymmetric slotentry journal bearing configuration having 6 holes per row is shown in [Figure 1]. Shires and Dee ^{[1]} proposed the idea of slotentry bearing originally for a purely hydrostatic bearing application. Slotentry bearings are originally developed by Dee and described by Dee and Shires ^{[2]} . Rowe et al. ^{[3]} showed that when hole and slotentry journal bearings are compared with recessed hydrostatic and hydrodynamic bearings on load basis alone, the slotentry journal bearing has superior performance to the recessed hydrostatic bearing for a given supply pressure. The advantages of the slotentry journal bearing over axial groove hydrodynamic bearings were also demonstrated. From the studies and initial experimental results, Rowe and Koshal ^{[4]} found that there are areas of operation where slotfeed journal bearings have considerable advantages over recessed bearings. Slotentry bearings are more suitable for heavily loaded conditions, including high dynamic loading. Ives and Rowe ^{[5]} theoretically analyzed the slotentry bearings of various symmetrical and asymmetrical inlet port configurations by finite difference method. Cheng and Rowe ^{[6]} presented a computerized selection method for externally pressurized journal bearings, including the slotentry journal bearing with respect to bearing type, configuration, fluid feeding device, bearing material, and production techniques. Sinhasan and Sah ^{[7]} studied the effect of nonNewtonian lubricants on the performance characteristics of orificecompensated hydrostatic journal bearing. It has been found that the effect of nonlinearity factor on the maximum pressure, minimum film thickness, bearing flow, and attitude angle under constant load are only marginal. The nonNewtonian characteristic of the lubricant is not beneficial from the damping point of view. The critical journal mass and threshold speed also have low values for the nonNewtonian lubricants than for the corresponding bearing with Newtonian lubricants. Sharma et al. ^{[8]} studied the combined effect of nonNewtonian lubricant behavior and bearing shell flexibility on the performance of an orificecompensated multirecess hydrostatic/hybrid journal bearing system. The computed results demonstrate that the loss in bearing performance due to the pseudoplastic effect of the nonNewtonian lubricant can be mitigated by a proper selection of parameters, such as the deformation coefficient and nonlinearity factor or power law index. Garg et al. ^{[9]} presented a comprehensive review of the developments in the design and application of hydrostatic and hybrid journal bearing systems and concluded that more extensive research is needed, both analytically and experimentally, to consider the extension of these bearings into high speed applications. Duvedi et al. ^{[10]} carried out the theoretic analysis of capillarycompensated nonrecessed holeentry hybrid journal bearing lubricated with nonNewtonian lubricant. Garg et al. ^{[11]} found that change in viscosity of lubricant due to nonNewtonian behavior and rise in temperature affect the performance of the holeentry hybrid journal bearing system quite significantly. Nagaraju et al. ^{[12]} investigated the combined influence of surface roughness, nonNewtonian behavior of lubricant, and thermal effects on the performance of a holeentry hybrid journal bearing system. Garg et al. ^{[13]} studied the performance of a capillarycompensated holeentry journal bearing system and found that the value of minimum fluid film thickness reduces due to the decrease in viscosity because of the consideration of thermal effects and the nonNewtonian behavior of the lubricant. This reduction in the value of may be compensated to maintain the designed value of by taking suitable values of restrictor design parameter.  Figure 1: SlotEntry hybrid journal bearing geometry and coordinate system (a) Asymmetric configuration, and (b) Coordinate system
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To the best of the author's knowledge, no study which considers the influence of nonNewtonian behavior of the lubricant on the performance of asymmetric slotentry hybrid journal bearing is yet available in the literature. The present work is aimed to study the performance characteristics of slotentry hybrid journal bearings considering the variation of viscosity due to nonNewtonian behavior of the lubricant. In the analysis, required governing equation, that is, generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space, and the equation of flow of lubricant through slot restrictor, have been solved using the finite element method and a suitable iterative technique. The nonNewtonian lubricant is assumed to follow the cubic shear stress law. The performance characteristics in terms of maximum pressure, minimum fluid film thickness, bearing flow, attitude angle, and eccentricity ratio for a wide range of values of nonlinearity factor and external load are presented. The results presented in this article are expected to be quite useful to the bearing designers.
2. Analysis   
The analysis presented in the following subsection uses finite element method to model the complete journal bearing system operating with nonNewtonian lubricants. The mathematical model, which includes the viscosity variation due to nonNewtonian behavior of the lubricant, involves solution of Reynolds equation.
2.1 Reynolds Equation for Fluid Domain
The generalized Reynolds equation governing the laminar flow of incompressible lubricant between the clearance space of journal and bearing considering variable viscosity and usual assumptions in the nondimensional form is written as ^{[14]} :
Where and are the crossfilm viscosity integrals and given by the following relations:
2.2 Restrictor Flow Equations
The flow of the lubricant through a slot restrictor is expressed as ^{[15],[16]} :
The above equation is reduced to a nondimensional form and expressed as ^{[15],[16]}
The parameter is called as slotrestrictor design parameter and is defined as
Where is the land width ratio and k is the number of rows of slots in a bearing. The slot width ratio (SWR) is the ratio of actual slot width α _{s} to the maximum possible slot width (α _{s}) _{max} as given below
2.3 NonNewtonian Model
Most of the nonNewtonian oils follow the behavior, which is represented by cubic shear law ^{[17]} . The constitutive equation for cubic shear law is described in a nondimensional form as
Here, is known as the nonlinearity factor. The viscosity of nonNewtonian lubricant is described by the apparent viscosity and is defined as the function of shear strain .
In the nondimensional form, the shear strain rate at a point in the fluid film is the function of velocity gradients and , and is expressed as
Where,
2.4 Boundary Conditions
The boundary conditions used for the lubricant flow field are described as follows:
 Nodes situated on the external boundary of the bearing have zero relative pressure with respect to atmospheric pressure.
 The nodal flows are zero at the internal nodes except those situated on slots and external boundaries.
 Flow of the lubricant through the restrictor is equal to the bearing input flow at slot.
 At the trailing edge of the positive region according to SwiftStieber cavitation condition.
3. Solution Procedure   
The flow chart of an iterative scheme used to obtain the converged solution for slotentry hybrid journal bearing system operating with a nonNewtonian lubricant has been shown in [Figure 2]. The Reynolds equation with restrictor equation is solved after satisfying appropriate boundary conditions to yield the pressure distribution in the flow field. The solution for the Newtonian lubricant is obtained as the initial trial solution to be used for the nonNewtonian case. The element fluidity matrix and flow vectors are generated and assembled using the usual assembly procedure in the subroutine FLUID. In this subroutine the crossviscosity integrals and fluid film viscosity can be computed for both Newtonian and nonNewtonian lubricants. The values of crossviscosity integrals and are obtained at each Gaussian point using numerical integration (Simpson's rule). The shear strain rate is computed using Eq. (4). For the continuity of the flow between the restrictor and the bearing, the system equation is modified accordingly. The subroutine BOUNDRY modifies the system equation for specified boundary conditions. The modified system equation is solved for the nodal pressure in subroutine SOLVER using the Gaussian elimination technique. In BLOCK NON_NWTN the iterative procedure is terminated when the difference in the nodal pressures at each node in the successive iteration becomes less than the predefined tolerance of ZO ≤ 0.001 for nonNewtonian solution. The pressure field for the lubrication flow field for Newtonian and nonNewtonian lubricants can be obtained as shown by BLOCK PRES. The journal center equilibrium is established by an iterative method shown by BLOCK EQM. The nodal pressure is thus obtained after achieving journal center equilibrium position. The performance characteristics are computed.
4. Results and Discussions   
The analysis and solution algorithms as described in the previous sections have been used to compute the performance characteristics of slotentry hybrid journal bearing system operating with nonNewtonian lubricant for representative values of the bearing geometric and operating parameters as shown in [Table 1]. The performance characteristics are computed for the values of concentric design pressure ratio, β* = 0.5, and slot width ratio, SWR = 0.25.
To check the validity of the analysis, the results for a tworow slotentry nonrecessed journal bearing (disregarding nonNewtonian behavior of the lubricant) with 6 slots per row are compared with the available results of Rowe et al. ^{[18]} . The computed results of load carrying capacity corresponding to different eccentricity ratios shows a good agreement with maximum percentage deviation of about 2% as shown in [Figure 3].  Figure 3: Comparison of load carrying capacity of symmetric slotentry journal bearing
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4.1 Maximum Pressure
The variation of maximum pressure with external load for asymmetric slotentry hybrid journal bearing is shown in [Figure 4]. It is clear from the figure that the value of increases with an increase of external load . This is due to the fact that to support more load, the journal runs at higher eccentricity and reduces film thickness and thus the pressure is increased. It is clear from the figure that at constant external load , maximum pressure decreases with increase in the nonlinearity factor of the lubricant.
4.2 Minimum Fluid Film Thickness
From [Figure 5] it may be observed that the combined effect of the increase in the external load and the nonlinearity factor is to reduce the value of minimum fluid film thickness . The maximum reduction of around 16% (at = 1.50) is observed for when the bearing is operating with nonNewtonian lubricant with =1.0 as compared with = 0.0.
4.3 Bearing Flow
The variation in the bearing flow with an external load for various values of is shown in [Figure 6]. The effect of increase of load on bearing flow is marginal. For constant load the bearing flow increases due to the decrease in viscosity because of the rise in nonlinear behavior of the lubricants.
The maximum increase of around 23.9% (at = 0.50) is observed, when the bearing is operating with nonNewtonian lubricant with =1.0 as compared with =0.0.
4.4 Attitude Angle ( φ) and Eccentricity Ratio (ε)
The effect of the variation of viscosity due to nonlinear behavior of the lubricants on attitude angle ( φ) and eccentricity ratio (ε) for the different values of the external load ( = 0.501.50) is presented in [Figure 7] and [Figure 8]. For a given value of load, the value of attitude angle ( φ) decreases with increase in the nonlinearity factor of the lubricant. The maximum reduction of around 9% (at = 0.50 ) is observed, when the bearing is operating with nonNewtonian lubricant with = 1.0 as compared with = 0.0. The combined effect of the increase of the external load and the nonlinearity factor is to increase the value of eccentricity ratio (ε).
5 Conclusions   
On the basis of the above results obtained using the theoretic analysis and solution algorithm presented in this article, the following conclusions are drawn.
 The viscosity of the lubricant decreases due to increase in the nonlinearity factor of the lubricant. The effect of the decrease in the viscosity of the lubricant is to reduce the minimum fluid film thickness for the bearing with the given operating and geometric parameters. Such reduction in the value of should be accounted while designing a bearing to maintain a safe design value of .
 It is found that there is an increase in the oil requirement for a hybrid journal bearing with the specified operating and geometric parameters, when the viscosity of the lubricant decreases due to the nonNewtonian behavior of the lubricant. The percentage increase in the value of is observed to be of the order of 23.7% operating with nonNewtonian lubricant having =1.0 as compared with =0.0 at 1.0, W=1.0, Ω =0.25, and λ=1.0, β*=0.5.
 The effect of the decrease in the viscosity of the lubricant due to nonNewtonian behavior of the lubricant diminishes the attitude angle ( φ) and enhances the eccentricity ratio (ε).
6. Nomenclature   
6.1 Dimensional Parameters
6.2 NonDimensional Parameters
6.3 Subscripts and Superscripts
References   
1.  G. L. Shires, and C. W. Dee, "Pressurized Bearings with Inlet Slots," Gas Bearing Symposium, U K: Proc. of the Southampton University; pp. 7, 1967. 
2.  C. W. Dee, and G. L. Shires, "The Current State of the Art of Fluid Bearings with Discrete Slot Inlets," Trans. ASME, Journal Lubrication Technology, Vol. 93, no. 2, pp. 441, 1971. 
3.  W. B. Rowe, D. Koshal, and K. J. Stout, "SlotEntry Bearings for Hybrid Hydrodynamic and Hydrostatic Operation," Journal of Mechanical Engineering Science, Vol. 18, no. 2, pp. 73, 1976. 
4.  W. B. Rowe, and D. Koshal, "Investigation of Recessed Hydrostatic and SlotEntry Journal Bearings for Hybrid Hydrodynamic and Hydrostatic Operation," WEAR, Vol. 43, pp. 55, 1977. 
5.  D. Ives, and W. B. Rowe, "The Effect of Multiple Sources on Performance of Heavily Loaded Pressurized High Speed Journal Bearings," Proc. IMECHE, TribologyFriction, Lubrication and Wear, C199, pp. 121, 1987. 
6.  K. Cheng, and W. B. Rowe, "A Selection Strategy for the Design of Externally Pressurized Journal Bearings," Tribology International, Vol. 28, pp. 465, 1995. 
7.  R. Sinhasan, and P. L. Sah, "Static and Dynamic Performance Characteristics of an Orifice Compensated Hydrostatic Journal Bearing with NonNewtonian Lubricants," Tribology International, Vol. 29, no. 6, pp. 515, 1996. 
8.  S. C. Sharma, S. C. Jain, and R. Sinhasan, "Static and Dynamic Performance Characteristics of Orifice Compensated Hydrostatic Flexible Journal Bearings with NonNewtonian Lubricants," STLE Tribology Trans., Vol. 44, no. 2, pp. 242, 2001. 
9.  H. C. Garg, H. B. Sharda, and V. Kumar, "On the Design and Development of Hybrid Journal Bearing: A Review," Tribotest (John Willey), Vol. 12, no. 1, pp. 1, 2006. 
10.  R. K. Duvedi, H. C. Garg, and V. K. Jadon, "Modelling and Analysis of NonRecessed HoleEntry Hybrid Journal Bearing for NonNewtonian Lubricants," Lubrication Science, Vol. 18, pp. 187, 2006. 
11.  H. C. Garg, V. Kumar, and H. B. Sharda, "NonNewtonian and Thermal Effects in Constant Flow Valve Compensated Symmetric HoleEntry Hybrid Journal Bearing," Lubrication Science (John Willey), Vol. 19, no. 4, pp. 269, 2007. 
12.  T. Nagaraju, S. C. Sharma, and S. C. Jain, "Influence of Surface Roughness on NonNewtonian Thermohydrostatic Performance of a HoleEntry Hybrid Journal Bearing," ASME, Journal of Tribology, Vol. 129, pp. 595, 2007. 
13.  H. C. Garg, V. Kumar, and H. B. Sharda, "Thermohydrostatic Analysis of HoleEntry Hybrid Journal Bearing with nonNewtonian Lubricant," Industrial Lubrication and Tribology, Vol. 61, no. 1, pp. 11, 2009. 
14.  D. Dowson, "A Generalized Reynolds Equation for fluid film Lubrication," International Journal of Mechanical Engineering Science, Vol. 4, pp. 159170, 1962. 
15.  S. C. Sharma, V. Kumar, S. C. Jain, Sinhasan, and M. A. Subramanian, "Study of Slotentry Hydrostatic/Hybrid Journal Bearing Using FEM," Tribology International, Vol. 32, no. 4, pp. 185, 1999a. 
16.  S. C. Sharma, S. C. Jain, and N. M. M Reddy, "Influence of Elastic Effects on the Performance of SlotEntry Journal Bearings," Tribology International, Vol. 32, no. 10, pp. 537, 1999b. 
17.  S. C. Sharma, S. C. Jain, and P. L. Sah, Effect of NonNewtonian Behaviour of Lubricant and Bearing Flexibility on the Performance of SlotEntry Journal Bearing," Tribology International, Vol. 33, pp. 507, 2000. 
18.  W. B. Rowe, S. X. Xu, F. S. Chong, and W. Weston, "Hybrid Journal Bearings with Particular Reference to HoleEntry Configurations," Tribology International, Vol. 15, pp. 339, 1982. 
Authors   
Dr. Hem ChanderGarg is an Associate Professor and Chairman in Mechanical Engineering Department, Guru Jambheshwar University of Science and Technology, Hisar, Haryana (State Government), since September 16, 2004. He worked as Lecturer in Mechanical Engineering Department, Beant College of Engineering and Technology, Gurdaspur, Punjab (State Government), from July 30, 1997 to September 15, 2004. He also worked as Visiting Associate Professor in Tokyo University of Science, Japan, from October 1, 2009 to November 29, 2009. Dr. Garg has also visited USA for research Purpose. His area of specialization is Tribology, Lubrication and Design. He has published a number of research papers in international/national journals. He is a reviewer of Journal of Tribology (ASME), Tribology International (Elsevier), and Journal of Engineering, Design and Technology (Emerald). He is a life member of Tribology Society of India (TSI).
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
[Table 1]
