Modern Lubrication Theory: Lecture Notes 2016  Instructor: Dr. Luis San Andrés,


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At times when using the 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:

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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,  [access date]



Note to the prospective course instructor:

For teachers interested in using these set of lecture notes for classroom instruction; I could release to your attention the presentations I use in my lectures. These are abridged pdf files with larger fonts and power point presentations. Please request these presentations from Dr. San Andrés.  


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.


Instructor: Dr. Luis San Andrés, MEOB 118, Phone: 862-4744, LSanAndres@

Class Time:    PETR 104  MWF 3:00-3:50 pm  
Office hours:  MW 2:00– 3:00 pm MEOB 117 or by appointment


EXAMS:                          1: Design of  simple thrust and journal bearings,    (FRI Oct 7)   

2: Rotordynamic and Bearings,                               (FRI Nov 18)


GRADING:   Group Assignments                             40%

                        Weekly (individual) quizzes                10%

                        First Exam                                           15%                                                         

                        Second Exam                                      15%     

                        Class Project                                        30%     (proposal due by FRI Oct 14)

                                                                                    110%      (*)    

Notes:       University justification required for missing Exams. All background material on prerequisites is responsibility of each student.
Project topic approved by instructor on F Oct 21, Project report & presentation on Monday December 5.







Author San Andrés, L.



0 B



Everything you need to know to get an A


13.4 MB 

Modern Lubrication Theory

Notes Portfolio (~600 pages) September 2012,

(All Notes 0-16)         



UPDATED (new) Individual NOTE SETS 2016 below



32.6 MB 

Reading assignments

Link will be removed on 09/02

for contents see L17



Pdf portfolio – need acrobat




References:      Childs, D., Turbomachinery Rotordynamics, J. Wiley Pubs., 1993, Chps. III & IV.

Szeri, A., Fluid Film Lubrication, Cambridge University Press, 2011.

Hamrock, B., Fundamentals of Fluid Film Lubrication, McGraw-Hill, Inc., 1994.

Selected journal papers (mandatory reading) listed in Index of Notes (pages 7-ff Syllabus).


All material is copyrighted by Dr. Luis San Andrés. Do NOT distribute or modify the material listed below without express permission from the author.

Index To Course Notes 2016  (Fall)
click on link to download pdf file  - LINKS TO MATHCAD PROGRAMS (Highlighted)




1 new

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. Applications of Tribology in the 21st  century  (8 p)

Appendix. Microturbomachinery Applications (23 p)



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



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)

(Zipped Mathcad file)


MATHCAD program for evaluation of 1D Tilting pad bearing performance(PDF)

(Zipped Mathcad file)



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.


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.


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)


Hydrodynamic fluid film bearings and their effect on the stability of rotating machinery (Presentation in pdf form) (42 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)

 (Zipped Mathcad file)

MATHCAD program for evaluation of transient response of a point rotor supported on journal bearings Mathcad file


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  


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 (distribution limited).



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


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


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.



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.


Appendix (to notes 11 & 13). A Linear Fluid Inertia Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Grooved Oil Seal Rings  (34p)


MATHCAD program for prediction of force coefficients in turbulent flow short length annular pressure seals.


(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.


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 

MATHCAD program: prediction of imbalance response of rigid rotor supported on short length SFDs with fluid inertia effects. (Zipped Mathcad file)



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)


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, Seoul, Korea (Sept, 2010)



Analysis of tilting pad bearings (30 p)

The fundaments of analysis – Incomplete document. Draft and presentation.
Appendix A primer to tilting pad bearings  (33 p)




Selected Technical papers

(reading assignments


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.


Lund, J.W., 1987, “Review of the Concept of Dynamic Coefficients for Fluid Film Journal Bearings”, ASME Journal of Tribology, Vol. 109, pp. 37-41.


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.


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



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, UK.


Tribological Design Data Guide, Part 2: Lubrication, 1995, The Institution of Mechanical Engineers, Tribology Group, UK.



Recommended Tribology Journals


Impact factor

2015 or last 5 years

Journal of Tribology


(Transactions of the ASME). Published quarterly by the American Society of Mechanical Engineers, 22 Law Drive, Box 2300, Fairfield, NJ 07007-2300, USA.

Journal of Eng Gas Turbines Power


(Transactions of the ASME)

Tribology Transactions 


(Journal of the Society of Tribologists and Lubrication Engineers). Published quarterly by STLE, 840 Busse Highway, Park Ridge, Illinois, USA



Published by Elsevier Science B.V. Sequoia SA, PO Box 851, 1001 Lausanne, Switzerland. ISSN 0043-1648


Tribology Letters



Tribology International


Published bimonthly by Butterworth Heinemann, Linacre House, Jordan Hill, Oxford, OX2 8DP.


Journal of Engineering Tribology


(Proceedings of the Institution of Mechanical Engineers, Part J). Published quarterly by Mechanical Engineering Publications Ltd.

Lubrication Engineering


(STLE magazine). Published monthly by STLE


Recommended reference books 

Szeri, A., 2011, Fluid Film Lubrication, Cambridge University Press

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.

Hamrock, B.J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill Book Co., Singapore

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 

MIT Open Course Tribology    Advanced Fluid Mechanics  Search for Conference papers – good stuff!


Fluid film lubrication (the fundaments) Wikipedia


Fluid film bearing manufacturers (nice pictures of cool products and applications)

Lufkin-RMT Bearings                  Bearings+                                              

Kingsbury Bearings                      Waukesha Bearings             Orion Bearings (John Crane)             


NASA Oil-free turbomachinery Program                                                  


Air bearings: New Way Air Bearings        

Foil Gas Bearings:      



Disclaimer: Your lecturer does NOT endorse any of the commercial sites listed above. These are merely resources