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Evaluating the Performance Parameters for the Journal Bearings by Using the Graphical and Analytical Methods

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Abstract

This paper illustrates evaluating performance parameters for the journal bearing design by using three different methods. In the first approach, Raimondi and Boyd Charts (Graphical) method will be used. The second approach represents the first analytical method called Reynold equations tables, which can be used by utilizing familiar equations connected by other values. The second analytical method by Reason and Narang (Combined Solution Method) requires using the empirical equation and tables. Finally, the error percentage for all performance parameters for the analytical methods will be compared with the graphical to show which method is more precise. The main goal of obtaining the precise procedure for the journal bearing performance parameters evaluation is to determine the exact temperature rise in journal bearing and the average temperature of the oil film inside the journal bearing. By knowing these temperatures, the designers can select the best type of lubricant oil and bearing material to avoid bearing failure
SSRG International Journal of Mechanical Engineering (SSRG-IJME) volume 2 Issue 10October 2015
ISSN: 2348 8360 www.internationaljournalssrg.org Page 1
Evaluating the Performance Parameters for the Journal Bearings
by Using the Graphical and Analytical Methods
Graduate Student: Yasir D. Mahdi1, Adj. Professor: George V. Bauer2
1Graduate Student at University of New Haven \ Tagliatela College of Engineering \ Department of Mechanical\Civil &
Environmental Engineering \ United States of America
Mechanical Engineer in North Refineries Co.\ Ministry of Oil in Iraq
Scholarship Student at the Higher Committee for Education Development in Iraq
2 Adj. Professor at University of New Haven \ Tagliatela College of Engineering \ Department of Mechanical\Civil &
Environmental Engineering \ United States of America
ymahd2@unh.newhaven.edu
Abstract
This paper illustrates evaluating performance parameters
for the journal bearing design by using three different
methods. In the first approach, Raimondi and Boyd Charts
(Graphical) method will be used. The second approach
represents the first analytical method called Reynold
equations tables, which can be used by utilizing familiar
equations connected by other values. The second analytical
method by Reason and Narang (Combined Solution Method)
requires using the empirical equation and tables. Finally, the
error percentage for all performance parameters for the
analytical methods will be compared with the graphical to
show which method is more precise. The main goal of
obtaining the precise procedure for the journal bearing
performance parameters evaluation is to determine the exact
temperature rise in journal bearing and the average
temperature of the oil film inside the journal bearing. By
knowing these temperatures, the designers can select the best
type of lubricant oil and bearing material to avoid bearing
failure.
Keywords
Journal Bearings, Lubricant oil, Sommerfeld No.,
Reynolds Equation, Temperature Rise, Combined Solution,
and Leakage Flow Rate.
I. INTRODUCTION
Clearly, the lubricant film performance illustrates the
key factor in the journal bearings design. So, many equations
and theories govern the design and operational conditions of
the lubricant film. The aim of its design is to produce a journal
bearing working in all operational conditions without any
interruptions due to some error in design performance
parameters. There are two basic aspects of the journal bearing
design analysis [1]:
1. The first aspect refers to the basic analysis of the
journal bearing load capacity, friction, and
lubrication flow rate as a function of load, speed, and
any other controlling parameters. This aspect can be
found when the lubricant film geometry is defined
and then the Reynolds equation is applied to find
pressure filed, load capacity, and other parameters.
2. The second aspect relates to practical or operational
problems, such as the method of lubricant supply and
bearing design to avoid the vibration and cavitation
or to allow misalignment and frictional heating of the
lubricant.
One of the most important equations governing the
pressure in the lubricant film is Reynolds Equation, which
represents the simplification of the Reynolds’s paper in 1886
[2]. To apply this equation to the lubricant film, many
assumptions should be considered [3][5]:
1. The lubricant flow between the rotating surfaces
should be laminar.
2. The bearing and the journal surfaces should be
parallel to neglect the film curvature.
3. Pressure variation across the lubricant film thickness
should be zero.
4. The internal force and inertial force should be
neglected because they are very small compared
with the viscosity and pressure forces.
Now, the equation can be written: ……. (1)
Many works and methods have been examined and
designed over centuries from theories, experiments, and
practices to manufacture the optimum design for the journal
bearings. By studying the key parameters affecting journal
bearing performance, Researchers have tried to improve
models leading to a more perfect performance during the
operation of the journal bearing [2].
In 1883, Towers was sponsored by the Institution of
Mechanical Engineering to experiment with the friction in
journal bearings. Towers examined many materials in his
experiments such us cork and wooden plugs by placing these
materials in the loaded zone of the journal bearing crown to
stop up the lubricant hole. As a result of his experiment, he
found that the oil under considerable pressure removes the
plugs from the oil path (hole). This experiment showed the
SSRG International Journal of Mechanical Engineering (SSRG-IJME) volume 2 Issue 10October 2015
ISSN: 2348 8360 www.internationaljournalssrg.org Page 2
first attempt to investigate the hydrodynamic film pressure of
the lubricant oil [2].
In 1886, Reynolds submitted his papers to the Royal
Society. Reynolds described the principle by showing that the
converging wedge-shaped for the lubricant film was very
essential to develop the pressure within the film layer.
Equation (2) represents the simplified version of Reynolds
equation in a 2-D analysis. These papers represent the
classical method for the journal bearing design especially after
many.
II. EVALUATING PERFORMANCE PARAMETERS FOR THE
JOURNAL BEARING:
The graphical method represents the way to calculate the
performance parameters for the journal bearing. This method
had been developed by Raimondi and Boyd which illustrates
the most famous method by using the relationships between
the Sommerfeld No. (The dimensionless bearing characteristic
number S) and minimum film-thickness variable, the
temperature-rise variable, the friction variable, the flow
variable, the flow ratio, and the attitude angle. This method
stayed convenient till the middle of the last century when the
analytical and empirical methods have been found.
Journal Bearing and Bearing Notation [4], [6]
. (4)
Where,
:- Clearance (in)
:- Journal Radius (in)
:- Lubricant Viscosity (reyn)
:- Revolution per sec.
:- Load per unit projected area (lbf\in2 or Psi)
…………(5)
: Load (lbf)
L: JB length (in)
D: JB Diameter (in)
By using the charts below, journal bearing performance
parameters can be evaluated:
Relationship between Sommerfeld No. and the Minimum Film
Thickness [3], [4], [6]
Relationship between Sommerfeld No. and the coefficient of
friction [3], [4], [6]
Relationship between Sommerfeld No. and the minimum film
pressure ratio [3], [4], [6]
SSRG International Journal of Mechanical Engineering (SSRG-IJME) volume 2 Issue 10October 2015
ISSN: 2348 8360 www.internationaljournalssrg.org Page 3
Relationship between Sommerfeld No. and the position of
minimum film thickness [3], [4], [6]
Relationship between the position of maximum film pressure
and the film terminating [3], [4], [6]
Relationship between the Sommerfeld No. and the flow
variable [3], [4], [6]
Relationship between the Sommerfeld No. and the flow ratio
[3], [4], [6]
The results which evaluated by using the Raimondi and Boyd
Charts have an error percentage. Moreover, using charts for
calculating the journal bearings performances required many
interpolations and extrapolations process which makes this
method very tedious. The journal bearings performance
parameters have been coded, tabled and become easy to
calculated for both short and long journal bearings [7]. Table
(1) shows the analytical method for evaluating the
performance parameters for the journal bearings by solving
Reynold’s Equation. Table (1)
Performance Parameters
Equation
Sommerfeld No.
Lubricant Oil Leakage
Flow Rate (in3/sec)
Lubricant Oil Inlet Flow
Rate (in3/sec)
Minimum Lubricant Oil
Film Thickness
Friction Force (lbf)
Power Loss (Btu/sec)
Temperature Rise
(oF)
From the table directly
Reason and Narang have found a new technique
which can be used for journal bearing design in both long
journal bearings and short journal bearings. This way can be
utilized to design the journal bearings which are effected by
steady load. According to the new technique, pressure and
other parameters can be evaluated by using the combined
solution approximation table (2) which includes several
SSRG International Journal of Mechanical Engineering (SSRG-IJME) volume 2 Issue 10October 2015
ISSN: 2348 8360 www.internationaljournalssrg.org Page 4
equations which depend on the value of the Sommerfeld No.,
Ic, Is, ɛ, and (Values of empirical table[4].
Table (2)
III. CASE STUDY
Determine the performance parameters of a steadily loaded
full journal bearing.
Given Data:
D=3 in , L=1.5 in
N=4000 RPM, W= 1000 lbf
Inlet Temp. = 120 , C=1.5*10-3 in, Lubricant oil is SAE 20
ρ= 0.03 lbm/in3, C* = 0.40 Btu/lbm oF
JB performance parameters at initial condition when the Inlet
Temp. = 120 : Table (3)
Parameters
Method
rad
Raimondi and Boyd
charts
70
25.2
3.95
Analytical Method
69.837
27.8826
3.948
Combined Solution
69.8902
25.7646
3.96783
Table (4)
Parameters
Method
(oF)
Error (%)
Raimondi and Boyd
charts
0.42
208
------
Analytical Method
0.4188
198.4779
4.578%
Combined Solution
0.41793
204.587
1.64%
JB performance parameters at normal operation
condition when the lubricant film temperature:
………… (6)
Table (5)
Parameters
Method
oF
Reyn *10-6
Raimondi and Boyd
charts
224
0.67
0.201
0.718
Analytical
Method
219.23895
0.778
0.2334
0.687
Combined
Solution
220.7935
0.7626
0.2286
0.666
Table (6)
Table (7)
Performance
Parameters
Equation
Sommerfeld No.
Where
, use top sign for max. flow
, use bottom sign for min. flow
Parameters
Method
rad
Raimondi and Boyd
charts
5.12
0.8
44
5.75
Analytical Method
5.097
0.795
41.738
6.293
Combined Solution
5.3367
0.537
43.33
6.2911
Parameters
Method
oF
Error (%)
Raimondi and Boyd
charts
38.438
--------
Analytical Method
51.054
-32.68%
Combined Solution
40.177
-4.524%
SSRG International Journal of Mechanical Engineering (SSRG-IJME) volume 2 Issue 10October 2015
ISSN: 2348 8360 www.internationaljournalssrg.org Page 5
Chart (1)
IV. CONCLUSION
It is obvious that using different methods to obtain the
journal bearing performance parameters have many
advantages because it will show the researchers which method
is very precise to use in journal bearings design. In this paper,
the comparison between the two analytical methods and the
graphical method, which it evaluation results represent the
research guide reference, showed that the results which came
from the combined solution approximation method have less
error percentage than the analytical method. According to the
table (4), the error percentage between the temperature rise at
the initial conditions illustrate that the value of all methods are
approximately close but the combined solution approximation
method have the more precise evaluation due to the few error
rate (1.64%) comparing with the guide reference results. As
well as, table (7) and chart (1) show the same results which
they proof that the combine solution approximation method is
the perfect way to calculate the performance parameters for
the journal bearings with the minimum error rate (-4.524%,
1.64%). While, the analytical method recorded error rate
(-32.68%, 4.578%).
V. ACKNOWLEDGEMENT
This study is underpinned by the Higher Committee of
Education Development in Iraq (HCED) the sponsor
governance of the scholarship to study M.Sc. of Mechanical
Engineering at the University of New Haven. Also Thanks for
the corporation of Dr. Samuel Bogan Daniels MSME Program
coordinator. As well as, that is my pleasure to thank Dr. Ravi
Gorthala for his advice during my thesis and preparation.
VI. REFERENCES
[1] G. Stachowiak and A. W. Batchelor, “H y d r o d y n a m
i c l u b r i c a t i o n,” in Engineering Tribology, 4th
Editio., MA, USA: Elsevier , Butterworth-Heinemann,
2014, pp. 105210.
[2] E. H. Smith, Ed., Mechanical Engineer’s Reference
Book, 12th ed. Oxford, London, Boston:
Butterworth,Heinemann, 2013.
[3] R. C. Juvinall and H. Saunders, “Fundamentals of
Machine Component Design,” Journal of Mechanisms
Transmissions and Automation in Design, vol. 105, no. 4.
JOHN WILEY & SONS, INC., Wiley, p. 929, 2011.
[4] K. L. Edwards, Standard handbook of machine design,
Second Edi., vol. 17, no. 3. New York, San Francisco,
Washington, D.C. Auckland Bogota Caracas Lisbon
London Madrid Mexico City Milan Montreal New Delhi
San Juan Singapore Sydney: McGraw-Hill, 1996.
[5] P. K. Kundu, Fluid mechanics., 5th Editio. Oxford; MA:
Academic Press, Inc., 2012.
[6] R. Budynas, Mechanical Engineering Shigley’s
Mechanical Engineering Design, Eighth Edi. McGraw-
Hill, 2008.
[7] M. Khonsari, “Journal Bearing Design and Analysis,” in
Tribology Data Handbook An Excellent Friction,
Lubrication, and Wear Resource, E. R. Booser, Ed. CRC
Press, 1997, p. 1120.
SSRG International Journal of Mechanical Engineering (SSRG-IJME) volume 2 Issue 10October 2015
ISSN: 2348 8360 www.internationaljournalssrg.org Page 6
Yasir Dhaif Mahdi: Currently he
is Graduate student at the
University of New Haven, USA.
He received his B.Sc. degree in
Mechanical Engineering from
University of Tikrit in 2007. Since
2007, he had worked as a
Mechanical Engineer in ARADET
Co. for petrochemical industry. Then, in 2008, he has started
work in North Refineries Co.\ Ministry of Oil in Iraq as a
Mechanical Engineer in Projects Engineering Corps for three
years and Maintenance Engineering Corps for two and half
years. He participated in many national and international
courses such as in Japan, Czech Republic, Turkey, and
Lebanon.
George Bauer has over 22
years of structural analysis
experience with strong finite
element, composite, fatigue and
fracture analysis skills. George
has performed analysis and
design consulting work in a
variety of industries including
aerospace, civil, and consumer
products. Some of George's past consulting projects include
durability analysis of aerospace mechanically fastened joints,
composite structural part delamination and growth evaluation,
detailed thermal analysis of air and conduction cooled circuit
boards and included components, and detailed thermal
transient structural analyses of ball grid array packages
including fatigue evaluation of electrical connections. George
customizes, develops and instructs CAE Associates' full
lineup of ANSYS training courses and provides ANSYS
technical support to our customers. George also teaches Finite
Element courses at Fairfield University and the University of
New Haven as an adjunct professor.
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Article
Contenido: Parte I Fundamentos: 1) Perspectiva general del diseño en ingeniería mecánica; 2) Análisis de cargas; 3) Materiales; 4) Esfuerzos en los cuerpos elásticos; 5) Deformación elástica, deflexión y estabilidad; 6) Teorías de las fallas, factores de seguridad y confiabilidad; 7) Impacto; 8) Fatiga; 9) Daño a la superficie. -- Parte II Aplicaciones: 10) Sujetadores roscados y tornillos de potencia; 11) Remaches, soldadura y unión con adhesivos; 12) Resortes; 13) Lubricación y cojinetes deslizables; 14) Rodamientos; 15) Engranes rectos; 16) Engranes helicoidales, cónicos y tornillos sinfín; 17) Ejes de transmisión y partes asociadas; 18) Embragues y frenos; 19) Miscelánea de componentes de maquinaria.
Fluid mechanics., 5th Editio. Oxford
  • P K Kundu
P. K. Kundu, Fluid mechanics., 5th Editio. Oxford; MA: Academic Press, Inc., 2012. [6] R. Budynas, Mechanical Engineering Shigley's Mechanical Engineering Design, Eighth Edi. McGraw- Hill, 2008.
Journal Bearing Design and Analysis," in Tribology Data Handbook An Excellent Friction, Lubrication, and Wear Resource
  • M Khonsari
M. Khonsari, "Journal Bearing Design and Analysis," in Tribology Data Handbook An Excellent Friction, Lubrication, and Wear Resource, E. R. Booser, Ed. CRC Press, 1997, p. 1120.