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Procedía Engineering 105 (2015) 225 - 231

Procedía Engineering

www.elsevier.com/locate/procedia

6th BSME International Conference on Thermal Engineering (ICTE 2014)

Transient Analysis Of 3-Lobe Bearings Considering Surface Roughness Effect For A Gas Turbine

Nabaran Biswasa*,Prasun Chakrabortib

a*Department ofMechanicalEngineerig, NITAgartala,Jirania,Tripura-799046,India bDepartment of Mechanical Engineerig, NIT Agartala,Jirania,Tripura-799046,India

Abstract

The performance of a 3-lobe bearing is investigated by means of three-dimensional computational fluid dynamics analysis. Surface roughness effects were included in the computation of unsteady transient analysis of 3-lobe bearing, taking into account gravity. Each of the lobes is placed at a distance of 120 degree. In this paper K-Epsilon turbulence model is used. The 3-lobe bearing is designed in Gambit software, the journal is modeled as a "moving wall" with an absolute rotational speed of 6000 rpm. Design parameters like L/D ratio, total pressure distribution, surface roughness and lubricant flow properties like turbulent viscosity and velocity magnitude are considered for the analysis The flow is simulated using Ansys Fluent software.

©2015The Authors.PublishedbyElsevierLtd.Thisisan open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of organizing committee of the 6 th BSME International Conference on Thermal Engineering (ICTE 2014) Keywords: 3-lobe; viscosity; pressure; wall shear stress; surface roughness.

1. Introduction

A bearing is a system of machine elements which supports another moving machine element; it permits relative motion while carrying the load. Lubricant applied load for reducing friction between the relatively moving surfaces. As modern science and technology is developing, one discovered that the lubricant is affected by the gap of bearing. The interaction degree between the lubricant and solid surface influences the lubrication property of the bearing clearly. Dr G. Bhushan, Dr S. S. Rattan, DrN. P. Mehta [5] worked on "Effect of Pressure Dams and Relieftracks on the Performance of a Four-lobe Bearing" .Their main findings are the following- the presence of pressure dams and relief cracks on the performance of an ordinary four lobe bearing. The generation of pressure and their

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of organizing committee of the 6th BSME International Conference on Thermal Engineering (ICTE 2014) doi: 10.1016/j.proeng.2015.05.098

circumferential variation in the upper half of a bearing primarily affect the stability of a rotor bearing system. In qualitative terms, the proportion of hydrodynamic load generated in upper half with respect to load generated in lower half is one of the deciding factors as to how stable a bearing would be. The magnitude and pressure generated in the lobes of the four-lobe bearing without and with dam indicate that the latter would provide a relatively smoother operation of the bearing. A four-lobe pressure dam bearing operates in the higher range of eccentricity ratios compared to an ordinary four-lobe bearing. There is a marginal increase in the dimensionless friction coefficient when pressure dams are incorporated in an ordinary four-lobe bearing. The stability of an ordinary four-lobe bearing increases when pressure dams and relief-tracks are incorporated in it.

F.A Martin and A.V. Ruddy [6] worked on "The effect of manufacturing tolerances on the stability of profile bore bearings". Their main findings are - the introduction of new quantities of speed independent of the clearance and clearance independent of speed. They gave a more precise analysis to problem than quantities like M' and W' which arise due to various factors and are not independent of machining allowances. The method could be well implemented for 4-lobe bearing. The tighter bearing tolerances results to higher instability at increased condition of speed and turbulence as there is no chance of loss of thermal quantities over them. They categorised the tolerances in two distinct parts like tolerances on the shaft and the tolerances on the bearing itself. Both these clearances play a distinct role in the instability in the bearings caused at very high speeds. The importance of considering the tolerances is based on the fact that tighter tolerances result in the higher instability like vibrations, overheat and wear and tear.

Raghunandana. K. [7] worked on "Inverse Design Methodology for the Stability Design of Elliptical Bearings Operating with Non-Newtonian Lubricants". They considered lubrication as Newtonian in nature which incidentally allowed error in calculation of various critical parameters. This study provided steady state results for different L/D and eccentricity ratios in the form of empirical equations Hence the simulation with the various data and with the aid of computational methods various factors like oil film density and oil film viscosity could be found out for various NON-NEWTONIAN fluids and for BINGHAM plastics too.

J.D Knight and L.E. Barrett [8] worked on "An Approximate Solution Technique for Multilobe Journal Bearings Including Thermal Effects, with Comparison to Experiment". They proposed an approximate solution method for multilobe journal bearings that includes thermal effect. Comparison of solutions obtained by the variable viscosity method to effective viscosity solutions after Lund and Thomsen illustrates discrepancies in operating eccentricity and stiffness coefficients between the two approaches. They also derived a very good co-relation between the variable viscosity solutions and experimental measurements reported by Tonnesen and Hansen of eccentricity, pressures, and temperatures in a two-axial groove bearing.

Nomenclature

Cp Specific heat(Kg-K)

L/D Length/Diameter ratio

T Temperature (°C)

RPM Revolution per minute

Subscripts

Avg Average

Max Maximum

2. Objective

The scope of this work is to design 3 lobe bearing and to analyze the various flow parameters which arise due to the motion of the shaft at rpm of 6000 and surface roughness 0.9 is considered. By using Gambit the design of 3-lobe bearing is done and analysis part is done in FLUENT.

3. Methodology

The main objectives in this stage are:-

• To find the pressure distribution across the various parts of the oil media as well as the shaft in an unsteady condition.

• In this study six time steps 10, 30,50,70,90 and 110 seconds are taken and L/D ratio as 0.25,0.5. After 110 seconds the unsteady condition becomes steady. The properties do not change with time after 110 seconds.

4. Equations

The steady, conservative form of Navier-Stokes equations in two dimensional forms for the incompressible flow of a constant viscosity fluid is as follows Continuity:

dX dY X- momentum:

d(UU) ^ d(VU) _ dPn ^ 1 ,d2U ^ d2U. dX dY ~ dX RP W2 dY2'

Y- momentum:

d(UV) d(VV) dX dY

Where,

dPn | l ,d2V | d2V, dX RP ^ax2 dY2

D D n pu^2

.. u .. v puxD

,U =—,V=—, Re^"^—

In the present study, a three-dimensional numerical study of unsteady, static pressure across the various parts of the oil media as well as the shaft of the 3-lobe bearing is done.

5. Meshing in Gambit (a standard modeling tool)

The part of the oil flooded region is meshed using GAMBIT. The model is exported to fluent for post analysis and results.

Fig .1. The 4-D view of the meshedpart

6. Grid arrangement

The mesh file obtained from the Gambit was exported to Ansys Fluent for subsequent analysis. The mesh file was linked to Fluent and subsequently its grid checking result was surfaced as error free. Eventually it is assumed for formation one default surface at the boundary of the shaft and oil surface.

The rest of the surfaces were defined in the similar manner. The following conditions were assigned to the various components-

Table 1. Defining the various walls and interfaces

Zone Type

Fluid wall interface Interior

Fluid Fluid

Wall 1 Inlet Pressure

Wall 2 Outlet Pressure

Wall 3 Wall

7. Boundary condition for fluid

Physical properties of the fluid (SAE 50) like specific heat, thermal conductivity, viscosity and density were taken as 2270 kg-K, 0.62 W/m-K, 0.044 kg/m-s and 899 kg/m3 respectively. Various parameters considered are given below -

Table 2. Defining the boundary conditions for wall

Property Value

Gauge TotalPressure 101325(Pascal)

Supersonic Pressure O(Pascal)

Direction Specification Method Normal to the

Temperature

boundary 300(k)

The wall was considered to be stationary with no slip condition and Marangoni stress. The wall thickness was considered to be negligible. The thermal conditions are illustrated below:-

Table 3 . Defining conditions for wall

Property Value Nature

Temperature 300(K) Constant

Heat Generation Rate 0(W/m3) Constant

Steel was considered as wall material whose properties like density, specific heat and thermal conductivity are taken as 8080 kg/m3, 509.48 J/kg-K and 11.27 W/m-K respectively.

8. Results and Discussion

The results obtained for a bearing with the following parameters are presented here: L/D ratios are 0.25 and 0.5, radial clearance = 0.05mm, journal speed (n) = 6000 rpm and surface roughness 0.9. The transient variations of oil pressure are studied. In this study six time steps 10, 30,50,70,90 and 110 seconds are taken respectively for unsteady analysis. After 110 seconds the unsteady condition becomes steady. It is observed that the properties do

not change much with time after 110 seconds. The results are further iterated for a value of 1000 for convergence criterion ofO.l. The results converged in 441 iterations.

Residuals

-continuity x-velocily —y-velocity --z-velocity —energy -k 1e+08 le+06 le+04 -

1e+02 -

le+00 -

1e-02 -i

1B-04 -1e-06 - 1B-08 -

0 50 100 150 200 250 300 350 400 450

Iterations

Fig.2. Convergence plot for scaled residuals @ 6000 rpm .1. Fluent analysis oftotalpressure at 6000 rpm, roughness=0.9 andL/D=0.25

Fig.3. Contours(a),(b),(c),(d),(e),(f) are total pressure @ 6000 rpm after 10,30,50,70,90 and 110 sec respectively when surface roughness 0.9.

The total pressure predominates near the shaft surface when the surface roughness is 0.9 where the total pressure comes into picture due to rotation of the shaft. For rotation of the shaft in 6000 rpm the maximum total pressure distribution is same. The value is 1.31e+07pascal.

8.2. Fluent analysis for totalpressure at 6000 rpm, roughness=0.9 and L/D=0.5

Fig.4. Contours(a),(b),(c),(d),(e),(f0 are total pressure @ 6000 rpm after 10,30,50,70,90 and 110 sec respectively when surface roughness 0.9

When the surface roughness is 0.9 then total pressures also predominates near the shaft surface due to rotation of the shaft. For rotation of the shaft in 6000 rpm the maximum total pressure distribution is same. The value is 1.30e+07pascal.

9. Conclusion

The contours of the bearing exhibit distinct pattern to surface critical values of pressure near the interface of the wall and the surface of the shaft. It is observed after 441 iterations the critical pressure gets stabilized. Transient dynamic behavior of thin film lubricated journal bearing system is studied and presented. From pressure plots, it is observed that the maximum pressure, the bearing can withstand is increasing with increase in roughness value. The maximum pressure is noted at minimum oil film thickness. Transient dynamic behavior of thin film lubricated journal bearing system have been studied and presented. From pressure plots, it is observed that the total pressure increases when roughness increases.

References

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[2] F.A Martin and A.V. Ruddy, The effect of manufacturing tolerances on the stability of profile bore bearings, (1984) 494-499.

[3] Raghunandana. K., Inverse Design Methodology for the Stability Design of Elliptical Bearings Operating with Non-Newtonian Lubricants, World Congress on Engineering and Computer Science, October 24-26, 2007

[4] J.D Knight, L.E. Barrett, An Approximate Solution Technique for Multilobe Journal Bearings Including Thermal Effects, with Comparison to Experiment, 26(4) (1983) 501-508.

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[13] J. D. Knight, L. E. Barrett, An Approximate Solution Technique for Multilobe Journal Bearings Including Thermal Effects, with Comparison to Experiment, Tribology Transactions, 26 (4) (1983) 501-508.

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[18] F.A Martin, A.V. Ruddy, The effect of manufacturing tolerances on the stability of profile bore bearings, (1984) 494-499.