Modern
Lubrication Theory
Dr. Luis San
Andrés, LSanAndres@tamu.edu
Note to the reader:
Since
1994, Prof. San Andrés taught this course 14 times (every other year). In the
early 2000s, what seemed novel is (in 2022) presently commonplace. Hence, the “modern”
qualification should be taken as “current.”
At times when
using the lecture notes in a journal paper, thesis, report, etc., the question
arises on the stability (longevity) of the URL site hosting these notes. This
lecture material can also be found at the permanent URL: http://oaktrust.library.tamu.edu/handle/1969.1/93197
The site will be
stable forever! To reference a particular lecture note in an archival
publication please follow the example below:
San Andrés, L., 2010, Modern Lubrication Theory, “Experimental Identification of Bearing
Force Coefficients,” Notes 14, Texas A&M
University Digital Libraries, http://oaktrust.library.tamu.edu/handle/1969.1/93197 [access date]
OBJECTIVE: To introduce the
fundamental physical principles of the classical theory of hydrodynamic
lubrication and to review the latest advances and applications to high speed,
externally pressurized, turbulent flow bearings and seals with process fluids.
To provide guidance on the important aspects of modern lubrication theory and
novel applications. The class material emphasizes the understanding of physical
principles and the effects of fluid film bearings on the dynamics of rotating
machinery.
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Size |
Author San Andrés, L. |
Content |
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2018 |
(new) NOTE SETS 2018 |
Download below - Index |
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Download |
13.4 MB |
(~600 pages) September 2012, (All Notes 0-16) Pdf
portfolio – needs acrobat |
All
material below is copyrighted by Dr. Luis San Andrés. Do NOT distribute or modify the material listed
below without express permission from the author.
Index To Lecture Notes 2018 click on
link to download pdf file - LINKS TO MATHCAD PROGRAMS (Highlighted)
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Notes |
Content |
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1 |
Introduction to
Hydrodynamic Lubrication (16 p) The
basic laws of friction. Fluid Film Bearings. Basic Operational Principles.
Hydrodynamic and Hydrostatic Bearing Configurations. Example of rotordynamic
study. Performance objectives. Appendix. Microturbomachinery
Applications (23 p) |
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1 |
The fundamental assumptions and equations of lubrication theory (15 p) The fundamental
assumption in Lubrication Theory. Derivation of thin film flow equations from
Navier-Stokes equations. Importance of fluid
inertia effects in thin film flows. Some fluid physical properties |
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2 |
Classical Lubrication
Theory (10 p) Derivation
of Reynolds equation for laminar flow bearings. Boundary conditions and types
of liquid cavitation. Appendix. One dimensional
slider bearing, Rayleigh (step) bearing and circular plate squeeze film
damper A historical ASME landmark:
The Kingsbury bearing. (35 p) MATHCAD program for evaluation of 1D
Slider bearing performance(PDF) MATHCAD program for evaluation of 1D
Tilting pad bearing performance(PDF) |
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3 |
Kinematics of motion in
cylindrical journal bearings (10 p)
Reynolds
equation for cylindrical journal bearings. Kinematics of motion and film
thickness. Distinction between fixed and rotating coordinates. The pure
squeeze velocity vector. Examples of journal motion. MATHCAD
program for display of pressure field in short length journal bearings. |
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4 |
Static load
performance of plain journal bearings (21 p)
The long and short bearing models. Pressure field and fluid film forces on short length journal bearings. Equilibrium condition, load capacity and the Sommerfeld number. Includes Appendix. Simple lumped parameter thermal analysis MATHCAD
program for calculation of equilibrium eccentricity in a short length journal
bearing. |
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5 |
Dynamics
of a simple rotor-fluid film bearing system (45
p) Includes Appendix showing practical bearing configurations (advantages and
disadvantages) Appendix.
Physical
interpretation of dynamic forces for circular centered whirl (14 p) Equations
of motion of a rigid rotor. The concept of force coefficients. Derivation of
stiffness and damping coefficients for the short bearing. Stability analysis
and the effect of cross-coupled stiffness. Effect of rotor flexibility on
stability and imbalance response. MATHCAD program for evaluation of
static and dynamic forced performance of rigid rotor supported on short
length journal bearings(PDF) MATHCAD program for evaluation of transient
response of a point rotor supported on journal bearings Mathcad file |
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6 |
Liquid cavitation
in fluid film bearings (27 p)
Appropriate
boundary conditions for a sound cavitation model. The basics of a universal
cavitation model (algorithm). A
discussion on dynamic cavitation: air ingestion and entrapment. MATHCAD program for calculation of
pressure fields in 1-D bearing. Universal cavitation model ( Single point
relaxation). Mathcad file |
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7 |
Thermal
analysis of finite length journal bearings including fluid inertia (59 p) Evaluation
of dynamic force coefficients in finite length bearings using a perturbation
of the flow equations. Finite Element models: basic equations and their
solution. Gives
explanation about pad offset and preload. FORTRAN
program for prediction of static load and force coefficients in multiple pad
bearings (request Dr. San
Andres for a copy). |
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8 |
Turbulence
flow in thin film bearings : Characteristics and
Modeling (27 p)
The
nature of turbulence. Turbulence equations in thin film flows. Turbulence
flow models. The bulk-flow model of turbulence, Hirs’
and Moody’s friction factors. MATHCAD program for prediction of shear
factors for turbulent flows in thin film regions. Mathcad file |
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9 |
Fluid
inertia and turbulence in fluid film bearings (24 p)
When
fluid inertia effects are important. Bulk-flow model for inertial flows.
Turbulence and inertia in short length journal bearings and open end dampers. MATHCAD program- Laminar flow short
journal bearing with fluid inertia effects.Mathcad file MATHCAD program for prediction of
threshold speed of instability and imbalance response of a rigid rotor
supported on turbulent flow short length journal bearings (no fluid inertia).
Mathcad file |
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10 |
A thermohydrodynamic
bulk-flow model for fluid film bearings (24 p)
The
complete set of bulk-flow equations for the analysis of turbulent flow fluid
film bearings. Importance of thermal effects in process fluid applications. A
CFD method for solution of the bulk-flow equations. |
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11 |
High pressure
floating ring seals (17p) Floating ring seals for
compressors: leakage and force coefficients, seal lock up and effect on
rotor stability, recommendations to reduce seal cross-coupled
effects High pressure long oil
seals (12p) Long oil seals as pressure
barriers in industrial mixers: leakage and force coefficients,
effect on rotor stability, recommendations for grooved seals with reduced leakage
and lesser cross-stiffnesses. MATHCAD
program for prediction of force coefficients in turbulent flow short length
annular pressure seals. |
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12 |
(a) Annular pressure (damper) seals
(19 p) The mechanism of centering stiffness in seals. Force coefficients for short-length pressure seals. Design of annular seals: swirl brakes, impact on rotordynamics. MATHCAD program for prediction of leakage and force coefficients for short
length annular seal Mathcad file (b) Hydrostatic journal
bearings (18
p) Hydrostatic
bearings in modern applications. The principle of hydrostatic lubrication.
Effects of recess volume-fluid compressibility on force coefficients for
operation at low and high frequencies. Applications of hydrostatic bearings PRESENTATION:
Damper
Seals and Hydrostatic Bearings for Pump Applications
(64 p) MATHCAD
program for prediction of frequency dependent force coefficients in 1-D
hydrostatic bearings. |
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13 |
Squeeze
Film Dampers (SFDs) (22
p) Appraisal
of the art. Design considerations. Force Coefficients. Lubricant cavitation
and air entrainment in SFDs. Response of a Rigid Rotor Supported on
open-ended SFDs. (*) Digital video clips showing air entrainment in a SFD available at http://rotorlab.tamu.edu MATHCAD program: prediction of
imbalance response of rigid rotor supported on short length SFDs with fluid
inertia effects. (Zipped Mathcad file) |
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14 |
Experimental identification of bearing force coefficients (42 p) A method for identification: Instrumental Variable Filter method. Includes an example of system parameter identification (Hybrid Brush Seal) MATHCAD
program implementing impedance and IVF methods for identification of
parameters in a 2DOF mechanical system. (Zipped
Mathcad file) |
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15 |
Gas
film lubrication (58
p) Introduction
to gas bearings: slider and radial rigid bearings – limits of operation. A
little about foil bearings. Gas Bearings
for oil-free MTM (87
p) Appraisal of the art.
Technical Presentation to IFToMM Rotordynamics
Conference, |
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16 |
Analysis
of tilting pad bearings (30
p) The fundaments of analysis
– Incomplete document. Draft and presentation. |
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17 |
Selected Technical papers (get me now) Pinkus, O., 1987, “The Reynolds Centennial: A
Brief History of the Theory of Lubrication,” ASME Journal of Tribology, Vol.
109, pp. 1-20. Szeri, A., 1987, “Some Extensions of the
Lubrication Theory of Osborne Reynolds,” ASME Journal of Tribology, Vol. 109,
pp. 21-36. San Andrés, L., 1989, “Approximate Design of Statically Loaded
Cylindrical Journal Bearings”, ASME Journal of Tribology, Vol. 111, pp.
391-393. Allaire, P., and R.D. Flack, 1981, “Design of Journal Bearings
for Rotating Machinery,” Proceedings of the 10th Turbomachinery
Symposium, pp. 25-45. Zeidan, F., and B. Herbage, 1991, “Fluid Film Bearing
Fundamentals and Failure,” Proceedings of the 20th Turbomachinery
Symposium, pp. 161-186. Braun, M.J, and Hannon, W.M, 2010, “Cavitation formation and modeling for
fluid film bearings: a review,” Proc. IMechE Vol. 224
Part J: J. Engineering Tribology,
JET772, pp. 839-871. Klitt, P., and J.W. Lund, 1986, “Calculation
of the Dynamic Coefficients of a Journal Bearing Using a Variational
Approach,” ASME Journal of Tribology, Vol. 108, pp. 421-425. |
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17 |
San Andrés, L., 2012, “Extended Finite
Element Analysis of Journal Bearing Dynamic Forced Performance to Include
Fluid Inertia Force Coefficients,” Proc. ASME 2012 International Mechanical
Engineering Congress & Exposition, November 9-15, 2012, Houston, Texas, IMECE2012-87713 Paper Hirs, G.G., 1973, “A Bulk-Flow Theory for Turbulence in
Lubricant Films,” ASME Journal of Lubrication Technology, pp. 137-146. Hashimoto, S., S. Wada, and M. Sumitomo, 1988, “The Effects of
Fluid Inertia Forces on the Dynamic Behavior of Short Journal Bearings in Superlaminar Regime,” ASME Journal of Tribology, Vol.
110, pp. 539-547. San Andrés, L., 1990, “Turbulent Hybrid Bearings With Fluid
Inertia Effects,” ASME Journal of Tribology, Vol. 112, pp. 699-707. Launder, B.E., and M. Leschziner, 1978,
“Flow in Finite-Width, Thrust Bearings Including Fluid Inertia Effects,” ASME
Journal of Lubrication Technology, Vol. 100, pp. 330-338. Chupp, R.E., Hendricks, R.C., Lattime,
S.B., and Steinetz, B., 2006, “Sealing in
Turbomachinery,” AIAA J. Propulsion and Power, Vol. 22, 2, pp. 313-349 Childs, D.W. and
Vance, J.M., 1997, “Annular Gas Seals and Rotordynamics of Compressors and Turbines,”
Proceedings of the 26th Turbomachinery Symposium, pp. 201–220, September. Zeidan, F., L. San Andrés, and J.M. Vance, 1996, “Design and
Application of Squeeze Film Dampers in Rotating Machinery,” Proc. of the 25th
Turbomachinery Symposium, pp. 169-188. Diaz, S.E., and San Andrés, L., 2001, “Air
Entrainment Versus Lubricant Vaporization in Squeeze Film Dampers: An
Experimental Assessment of Their Fundamental Differences,” ASME Journal of Engineering for Gas
Turbines and Power, Vol. 123, pp. 1-7. Della Pietra,
L., and Adiletta, G., 2002, “The Squeeze Film Damper over
Four Decades of Investigations. Part I: Characteristics and Operating
Features,” Shock and Vibration Digest, Vol.
34, No. 1, pp. 3-26. Adiletta, G., and Della Pietra,
L., 2002, “The Squeeze
Film Damper over Four Decades of Investigations. Part II: Rootordynamic
Analysis with Rigid and Flexible Rotors,” Shock
and Vibration Digest, Vol. 34, No. 2, pp. 97-126. Diaz, S., and L. San Andrés, 1999, "A Method for
Identification of Bearing Force Coefficients and its Application to a Squeeze
Film Damper with a Bubbly Lubricant,” STLE Tribology Transactions, Vol. 42,
4, pp. 739-746. Tiwari, R., Lees, A.W., and Friswell,
M.I., 2004, “Identification of Dynamic Bearing Parameters: A Review,” The Shock and Vibration Digest, Vol. 36, No. 2, pp.
99-124. Tiwari, R., Manikandan, S., and Dwivedy, S.K. , 2005, “A Review of the Experimental
Estimation of the Dynamic Parameters of Seals,” The Shock and Vibration Digest, Vol. 37, No. 4, pp.
261–284 |
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18 |
Other
References with Useful Information (paper copy only, ask your
course instructor) Tribological Design Data Guide, Part 1: Bearings,
1995, The Institution of Mechanical Engineers, Tribology Group, Tribological Design Data Guide, Part 2:
Lubrication, 1995, The Institution of Mechanical Engineers, Tribology Group, |
Recommended
Tribology Journals
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Impact factor |
2015 or
last 5 years |
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Journal of Tribology |
1.236 |
(Transactions of the ASME). Published quarterly by
the American Society of Mechanical Engineers, |
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Journal of Eng
Gas Turbines Power |
1.095 |
(Transactions of the ASME) |
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Tribology Transactions |
1.418 |
(Journal of the Society of Tribologists
and Lubrication Engineers). Published quarterly by STLE, |
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Wear |
2.323 |
Published by Elsevier Science B.V. Sequoia SA, |
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Tribology Letters |
1.758 |
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Tribology International |
2.352 |
Published bimonthly by Butterworth Heinemann, |
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Journal of Engineering Tribology |
0.631 |
(Proceedings of the
Institution of Mechanical Engineers, Part J). Published quarterly by Mechanical
Engineering Publications Ltd. |
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Lubrication Engineering |
0.53 |
(STLE magazine). Published monthly by STLE |
Recommended
reference books
Childs, D., Turbomachinery Rotordynamics, J. Wiley Pubs., 1993, Chps. III & IV.
Szeri, A., Fluid Film Lubrication,
Hamrock, B., Fundamentals of Fluid Film Lubrication, McGraw-Hill, Inc., 1994.
Flitney, R., 2007, Seals and Sealing
Handbook, 5th
Ed., Elsevier BH.
Stahley, J.S, 2005, Dry Gas Seals
Handbook, PennWell
Corp.
Khonsari, M. and E.R. Booser, 2001,
Applied Tribology, John Wiley Pubs.
Williams, J.A., 1994, Engineering Tribology, Oxford
University Press, New York
Szeri, A., Tribology, 1980, McGraw Hill Co., Taylor &
Francis (reprint).
Moes, H., 2000, Lubrication and Beyond, U of Twente Press.
Hutchings, I. M., 1992, Tribology: Friction and Wear
of Engineering Materials, Edward Arnold Ltd.
Pinkus, O., 1990, Thermal Aspects of Fuid
Film Tribology, ASME Press.
Arnell, R. D., Davies, P. R., Halling,
J. and Whomes, T. L., 1991, Tribology, Principles and
Design Applications, Macmillan Education Ltd.
Johnson, K. L., 1985, Contact Mechanics, Cambridge
University Press.
Landsdown, A. R. and Price, A. L., 1986, Materials to Resist
Wear, Pergamon.
Neale, M.J., 1993, Tribology Handbook: Lubrication;
Bearings; Drives and Seals, Butterworth Heinemann.
Cameron, A., 1971, Basic Lubrication Theory, Longmans.
Recommended
URL resources (right-click
to open in new tab)
MIT Open Course Tribology Advanced
Fluid Mechanics
http://www.rotordynamics.org/ Search for Conference papers – good stuff!
Fluid film lubrication (the fundaments) Wikipedia
Fluid film bearing manufacturers (nice pictures of cool products and
applications) – Links may no longer be current
Kingsbury Bearings Waukesha Bearings Orion Bearings
(John Crane)
NASA
Oil-free turbomachinery Program
Air bearings: New Way Air Bearings
Foil Gas Bearings: http://www.neuros.com/ http://www.miti.cc/ http://www.rddynamics.com/
TRIBOLOGY
SOFTWARE http://www.tribology-abc.com/calculators/window.htm
Disclaimer: Dr. San Andrés does NOT endorse any of the
commercial sites listed above. The links are merely
resources for your learning