THERMOHYDRODYNAMIC ANALYSIS OF A JOURNAL BEARING USING CFD AS A

TOOL

Presented By

Mukesh Kumar ME 4th Semester

(Roll No.:5146409006)

Under Guidance of

Prof. Sanjeev Shrivastava (Associate Professor)

Department of Mechanical Engineering Shri Shankaracharya Group of Institutions

Faculty of Engineering and Technology Junwani, Bhilai (C.G.)

Objective of this thesis:

In this project work of Cuppilard et al [7] has been reproduced with a three-dimensional journal bearing model and using ANSYS Fluent 12.0 as a CFD analysis tool. Cupillard et al considered a two-dimensional model journal bearing and they did not consider effect of temperature on the property of fluid in the fluid film during simulation and thus the effects of property changes were not carried forward in performance parameters of dimpled journal bearing.

Here in this present work a thermohydrodynamic simulation has been done on a three-dimensional journal bearing, that is, effect of temperature has been considered.

To incorporate temperature effect in the simulation an User Defined Function (UDF) has been written and hooked up with the Fluent software.

Introduction:

Bearing and its types Tribology is the word derived from Greek word ‘Tribos’, means rubbing process. Tribology mainly deals with technique of lubrication and mechanism of friction and wear. The loss of input energy in any mechanism is mainly due to friction and lubrication is the most efficient way to reduce friction. From this point of view the subject tribology has immense importance. Through research and development in the field of tribology if mechanical systems can be run more with higher efficiency then in turn it will save huge money and can contribute significantly in the progress of the human society. For this reason the subject tribology has been the subject of extensive research for many a decades.

In a mechanical system bearing has an important role to play. A bearing is a system of machine elements whose function is to support an applied load by reducing friction between the relatively moving surfaces. The load may be radial or axial or combination of these. Bearings are classified according to the direction of applied load. If the bearing supports radial loads, it is called radial or journal bearing. On other hand, a thrust bearing supports a thrust or axial load. Some bearing can support both radial as well as axial load and they are known as conical bearings. In the clearance space of a bearing a substance called lubricant is introduced. Any substance which has some amount of viscosity is known as lubricant. The most common lubricants are oils and greases.

Contd….

There are mainly two common types of bearing are used in practice. They are rolling element and fluid film bearings. If two mating surfaces during operated conditions are completely separated by fluid film, such a type of lubrication is called fluid film lubrication. Fluid film bearings are lubricated by hydrodynamic flow which is generated by relative surface motion and/or external pressurization. A fluid film bearing operating on the principle of hydrodynamic lubrication is called ‘self-acting’ bearing, in which the load is supported due to wedging effect of the fluid caused by the relative tangential motion between two surfaces.

Contd….

Hydrodynamic journal bearings are considered to be a vital component of all rotating machinery. It is used to support radial loads under high speed operating conditions. Journal bearing may be divided into full journal bearing, where the contact angle of the bushing with the journal is 360º, and partial journal bearing, in which the contact angle is either 180º or less. Full (360º) journal bearings are widely used bearing in industrial machinery. These bearings are widely used bearings in industrial machinery. These bearings can take up rotating load. The partial journal bearings have limited applications and are used when the direction of radial loads does not change. Figure below shows the full and partial journal bearings.

Contd….

Fig1: Full Journal Bearing.

Contd….

Fig2: Partial Journal Bearing.

Contd….

Besic Laws of Tribology Journal bearing is a hydrodynamic load bearing. In the journal bearing, the lubricant in between the journal and bearing rotates with the journal and supports the load. Due to the physical configuration of journal bearing a wedge shaped fluid film is created as shown in the figure below-

Contd….

Fig3: Fluid film development in a journal bearing.

Now this wedge shaped fluid film obeys the laws of- Conservation of mass flow Conservation of momentum in X, Y and Z directions Conservation of energy Besides these the lubricants physical property obeys the equation of states. Now if the fluid obeys the Newtonian laws of viscosity then we have to modify the above conservation laws as shown below. Mass flow conservation Rate of increase of mass in the fluid element = Net rate of flow of mass into fluid element.

Contd….

Equ.- 1

Conservation of momentum Rate of increase of momentum in the fluid particle in any particular direction = Sum of forces on the fluid particle in that direction. For X-Direction For Y-Direction For Z-Direction

Contd….

Equ. (2)

Conservation of energy Rate of increase of energy of a fluid particle = Net rate of heat added to the fluid particle + Net rate of work done on the fluid particle If Newton’s laws of viscosity are imposed on the momentum conservation equations then following equations are generated which are called Navier-Stoke’s equations:

Contd….

Contd….

and if we combine viscous equations with energy conservation equation, we get―

Where,

Formation of FEA model of the problem: A journal bearing of following dimensions and fluid properties has been considered for the study. The dimensions and properties of lubricant used as per the work of Cupillard et al (Reference [7]).

Length of the bearing (L) 133mm

Radius of Shaft (Rs) 50mm

Radial Clearance (C) 0.145mm

Eccentricity ratio(ε) 0.61

Angular Velocity (ω) 48.1 Rad/sec

Lubricant density (ρ) 840 Kg/m3

Viscosity of the lubricant (η) 0.0127 Pas

Contd….

According to the above topological data other derived data would be like― I. Radius of Bearing (Rb) : (Rs + C) = 50.145mm II. Attitude angle (φ) : 68.4⁰. (as per reference [7]) III. Eccentricity (e) : (ε × C) = (0.61 × 0.145) =0.08845mm. Now details for cavitation model are as follows as per reference [7].

Lubricant vapour saturation pressure 20 Kpa.

Ambient pressure 101.325 Kpa.

Density of lubricant vapour 1.2 kg/m3

Viscosity of lubricant vapour 2×10-5 Pas.

Assumed vapour bubble dia 1×10-5 m

Schematic diagram a smooth journal bearing:

Contd….

To proceed in this analysis, first a 3-dimensional bearing has been generated in GAMBIT 2.3.16. Figures below show the 3d-geometry and meshed geometry in GAMBIT.

Contd….

Next the 3-D model of the journal bearing has been meshed using QUAD element. Figure below shows the meshed view of the journal bearing.

Contd….

After generating meshed volume in GAMBIT next following boundary conditions have been fixed.

Contd….

SL

NO. BOUNDARY NAME BOUNDARY TYPE

1 Middle cross-sectional plane SYMETRY

2 End plane of the bearing PRESSURE OUTLET

3 Journal surface WALL

4 Bearing surface WALL

After assigning boundary name and types of the flow region the file has been exported as ‘.msh’ and then has been imported to the ‘Fluent’ software for CFD simulation. In Fluent, data regarding chemical and physical properties of lubricant oil and properties of lubricant vapor, which have been mentioned before, have been fed into the software. Here, following mathematical parameters have been set in the software.

Contd….

Pressure-

Velocity

Coupling

Discretization Methods

Pressure Density Momentum Vapor

SIMPLE PRESTO Second

order

Second

Order First order

After simulation pressure distribution on journal surface has been found out as contour representation. Figure below depicts the stress distribution starting from the mid plane that is plane of symmetry of the bearing.

Contd….

Figure below expresses the pressure distribution starting from a cross-sectional plane at a distance of 10% of total bearing length from the plane of symmetry.

Contd….

The above pressure distribution on Journal surface of a Journal Bearing has been generated without considering the effect of temperature. The above result is very much in compliance with the work of S Cupillard, S Glavatskih, and M J Cervantes presented in reference [7]. But in their work Cupillard et. al. simulated a journal bearing with 2-Dimensional flow region. So, their work does not say about the pressure distribution along the length of bearing. In this work simulation has been done in 3-Dimensional flow region representing the actual lubricant flow of inside the bearing. So, the work presented in this thesis depicts more accurate pressure distribution in all 3-Dimensions. In next chapter it will be shown that value of maximum pressure in pressure distribution on journal surface becomes less if we consider temperature effects.

Contd….

To include the effect of temperature on the properties of the bearing oil in ANSYS a very beautiful mechanism is there in ANSYS software. This mechanism is known as “UDF” method. Full form of UDF is ‘User Defined Function’. By this method one can append a governing function which would control the variation of any property of the fluid with respect to pressure or temperature or both. Here in this project following relation has been used to control the viscosity as a function of temperature and pressure. This equation has been adapted from the reference [1]. The above equation has been appended to the ANSYS Fluent software through a C-Program with a ‘udf’ header file. The program has been shown below.

Contd….

#include "udf.h"

DEFINE_PROPERTY(cell_viscosity,c,t)

{

real mu_lam;

real temp = C_T(c,t);

real pr = C_P(c,t);

mu_lam = 0.0127*exp(0.000000213345*(pr-101345))*exp(0.029*(temp-293));

return mu_lam;

}

Contd….

In above program we have used two terms α and β which are the pressure and temperature coefficient of viscosity and value of these quantities are 21.3345x10-8 m2/kg and 0.029/°K. After appending this program to Fluent and analyzing it we get the following pressure distribution.

Contd….

Result and discussion: From the above result it is clear that temperature created from the frictional force increases decreases the viscosity of the lubricant and lesser viscosity decreases the maximum pressure of the lubricant inside the bearing. For this reason it is recommended that when any analysis of journal bearing is done to measure its performance always thermohydrodynamic analysis should be used. Because considering the thermal effect on lubricant property actual value of performance parameters can only be obtained. Now when the thermal analysis is done on the journal bearing temperature distribution has been obtained along the journal surface. Figure below represents the temperature variation of oil along the journal surface.

Contd….

Conclusion and future scope: The investigation carried out in this project leads to a very important conclusion. Thermohydrodynamic analysis of bearing gives the actual prediction of different performance parameters correctly. So whatever modification done on a bearing and then CFD simulation is done, it is mandatory to consider thermal effects on the chemical properties of the lubricant in the flow region. This reassessment of Cupillard et al [7] work shows that whatever result regarding the pressure distribution Cupillard et al got in their work did not depict actual value because they considered the isothermal case which is not practical. The actual pressure distribution considering adiabatic case has been shown in this work which is very near to the practical scenario.

References:

1) W. F. Hughes, F. Osterle, “Temperature Effects in Journal Bearing Lubrication”, Tribology Transactions, 1: 1, 210 — 212, First published on: 01 January 1958 (iFirst).

2) T. P. Indulekha, M. L. Joy, K. Prabhakaran Nair, “Fluid flow and thermal analysis of a circular journal bearing”, Wairme- und Stoffubertragung 29(1994) 367-371.

3) S. A. Gandjalikhan Nassab, M S Moayeri, “Three-dimensional

thermohydrodynamic analysis of axially grooved journal bearings”, Proc Instn Mech Engrs Vol 216 Part J: J Engineering Tribology, December 2001, Page: 35-47.

4) Prakash Chandra Mishra, “Thermal Analysis of Elliptic Bore Journal Bearing”, Tribology Transactions, 50: 137-143, 2007.

5) Wei Wang, Kun Liu, Minghua Jiao, “Thermal and non Newtonian analysis on mixed liquid- solid lubrication”, Tribology International 40 (2007) 1067-1074.

6) K.P. Gertzos, P.G. Nikolakopoulos, C.A. Papadopoulos, “CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant”, Tribology International 41 (2008) 1190– 1204.

7) S Cupillard, S Glavatskih, and M J Cervantes, “Computational fluid dynamics analysis of a journal bearing with surface texturing”, Proc. IMechE, Part J: J. Engineering Tribology, 222(J2), 2008, page 97-107.

8) E. Feyzullahoglu, “Isothermal Elastohydrodynamic Lubrication of Elliptic Contacts”, Journal of the Balkan Tribological Association, Vol. 15, No 3, 438—446 (2009).

9) Samuel Cupillard, Sergei Glavatskih, Michel J.Cervantes, “3D thermohydrodynamic analysis of a textured slider”, Tribology International 42 (2009) 1487–1495.

10) Ravindra R. Navthar et al., “Stability Analysis of Hydrodynamic Journal Bearing using Stiffness Coefficients”, International Journal of Engineering Science and Technology Vol.2 (2), 2010, page 87-93.

11) Majumder B. C. ‘Introduction to Tribology of Bearings’, A. H. Wheeler & Co publication.

12) Verseteeng H. K. & Malalasekera W. ‘An Introduction to Computational Fluid Dynamics’, Longman Scientific & Technical publication.

Contd….

7) Niyogi P., Chakrabarty S. K., Laha M. K. ‘Introduction to Computational Fluid Dynamics’, Pearson Education publication.

8) Sheshu P. ‘Textbook of Finite Element Analysis’, Prentice Hall of India publication.

9) Cengel A. Yunus, ‘Fluid Mechanics’, McGraw-Hill publication.

10) Help documentation of ‘GAMBIT 2.3.16’ Software.

11) Help documentation of ‘Fluent 6.3.26’ Software.

12) Help documentation of ‘Matlab 7.0’ Software.

Contd….

THANK YOU