A Review of Tilting Pad Bearing Theory

A theoretical basis for static and dynamic operation of tilting pad journal bearings (TPJBs) has evolved over the last 50 years. Originally demonstrated by Lund using the pad assembly method and a classic Reynolds equation solution, the current state of the art includes full thermoelastohydrodynamic solutions of the generalized Reynolds equation that include fluid convective inertia effects, pad motions; and thermal and mechanical deformations of the pads and shaft. The development of TPJB theory is reviewed, emphasizing dynamic modeling. The paper begins with the early analyses of fixed geometry bearings and continues to modern analyses that include pad motion and stiffness and damping effects. The development of thermohydrodynamic, thermoelastohydrodynamic, and bulk-flow analyses is reviewed. The theories of TPJB dynamics, including synchronous and nonsynchronous models, are reviewed. A discussion of temporal inertia effects in tilting pad bearing is considered. Future trends are discussed, and a path for experimental verification is proposed.

[1]  N. O. Myklestad A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams , 2012 .

[2]  Paul E. Allaire,et al.  The Effect of Tilting Pad Journal Bearing Dynamic Models on the Linear Stability Analysis of an 8-Stage Compressor , 2012 .

[3]  Jason C. Wilkes Measured and Predicted Transfer Functions Between Rotor Motion and Pad Motion for a Rocker-Back Tilting-Pad Bearing in LOP Configuration , 2011 .

[4]  Dara W. Childs,et al.  Tilting-Pad Bearings: Measured Frequency Characteristics Of Their Rotordynamic Coefficients , 2011 .

[5]  P. Allaire,et al.  Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads , 2010 .

[6]  Adolfo Delgado,et al.  Identification and Prediction of Force Coefficients in a Five-Pad and Four-Pad Tilting Pad Bearing for Load-on-Pad and Load-Between-Pad Configurations , 2010 .

[7]  Paul E. Allaire,et al.  Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis (GT2009-60269) , 2010 .

[8]  Paul E. Allaire,et al.  Identification methods and test results for tilting pad and fixed geometry journal bearing dynamic coefficients – A review , 2009 .

[9]  Paul E. Allaire,et al.  Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis , 2009 .

[10]  D. Childs,et al.  Measurements Versus Predictions for the Rotordynamic Characteristics of a Five-Pad Rocker-Pivot Tilting-Pad Bearing in Load-Between-Pad Configuration , 2009 .

[11]  D. Childs,et al.  Static Performance Characteristics and Rotordynamic Coefficients for a Four-Pad Ball-in-Socket Tilting Pad Journal Bearing , 2009 .

[12]  Dara W. Childs,et al.  Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration , 2008 .

[13]  D Bonneau,et al.  Thermohydrodynamic lubrication analysis for a dynamically loaded journal bearing , 2007 .

[14]  D. Childs,et al.  Rotordynamic coefficients measurements versus predictions for a high-speed flexure-pivot tilting-pad bearing (load-between-pad configuration) , 2006 .

[15]  D. Childs,et al.  Frequency Dependency of Measured and Predicted Rotordynamic Coefficients for a Load-On-Pad Flexible-Pivot Tilting-Pad Bearing , 2006 .

[16]  Paul E. Allaire,et al.  Thermohydrodynamic Modeling of Leading-Edge Groove Bearings under Starvation Condition , 2005 .

[17]  J. C. Nicholas Lund’s Tilting Pad Journal Bearing Pad Assembly Method , 2003 .

[18]  Michel Fillon,et al.  Transient Thermoelastohydrodynamic Analysis for Safe Operating Conditions of a Tilting-pad Journal Bearing During Start-up , 2000 .

[19]  Jean Frene,et al.  Transient Thermoelastohydrodynamic Study of Tilting-Pad Journal Bearings—Comparison Between Experimental Data and Theoretical Results , 1997 .

[20]  Jean Frene,et al.  Comparison between three turbulent models : application to thermohydrodynamic performances of tilting-pad journal bearings , 1996 .

[21]  Dara W. Childs,et al.  Thermohydrodynamic Analysis of Process-Liquid Hydrostatic Journal Bearings in Turbulent Regime, Part II: Numerical Solution and Results , 1995 .

[22]  Luis San Andrés,et al.  Thermohydrodynamic analysis of fluid film bearings for cryogenic applications , 1995 .

[23]  Dara W. Childs,et al.  Thermohydrodynamic Analysis of Process-Liquid Hydrostatic Journal Bearings in Turbulent Regime, Part I: The Model and Perturbation Analysis , 1995 .

[24]  John C. Nicholas,et al.  Tilting Pad Journal Bearing Pivot Design For High Load Applications. , 1995 .

[25]  Hyun Cheon Ha,et al.  Inlet pressure effects on the thermohydrodynamic performance of a large tilting pad journal bearing , 1995 .

[26]  Dara W. Childs,et al.  A TEST APPARATUS AND FACILITY I TO IDENTIFY THE ROTORDYNAMIC COEFFICIENTS OF HIGH-SPEED HYDROSTATIC BEARINGS , 2022 .

[27]  J. Nicholas Tilting Pad Bearing Design. , 1994 .

[28]  Alan Palazzolo,et al.  Dynamic Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility Model , 1993 .

[29]  Dara W. Childs,et al.  A Parameter Identification Method for the Rotordynamic Coefficients of a High Reynolds Number Hydrostatic Bearing , 1993 .

[30]  Lloyd E. Barrett,et al.  Exact dynamic reduction of tilting-pad bearing models for stability analyses , 1993 .

[31]  Jean Frene,et al.  Experimental Study of Tilting-Pad Journal Bearings—Comparison With Theoretical Thermoelastohydrodynamic Results , 1992 .

[32]  C. Ettles The analysis of pivoted pad journal bearing assemblies considering thermoelastic deformation and heat transfer effects , 1992 .

[33]  M. F. White,et al.  The Subsynchronous Dynamic Behavior of Tilting-Pad Journal Bearings , 1992 .

[34]  S. Taniguchi,et al.  A Thermohydrodynamic Analysis of Large Tilting-Pad Journal Bearing in Laminar and Turbulent Flow Regimes With Mixing , 1990 .

[35]  Alan Palazzolo,et al.  A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part I—Single Pad Analysis , 1990 .

[36]  Alan Palazzolo,et al.  A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part II—Assembled Bearing and System Analysis , 1990 .

[37]  Waldemar Dmochowski,et al.  Measurement and Calculation of the Dynamic Operating Characteristics of the Five Shoe, Tilting Pad Journal Bearing , 1990 .

[38]  G. Hopf,et al.  Investigations on Large Turbine Bearings Working Under Transitional Conditions Between Laminar and Turbulent Flow , 1989 .

[39]  D. Brugier,et al.  Influence of Elastic Deformations of Turbo-Generator Tilting Pad Bearings on the Static Behavior and on the Dynamic Coefficients in Different Designs , 1989 .

[40]  R. G. Kirk,et al.  Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs , 1988 .

[41]  Lloyd E. Barrett,et al.  Analysis of Tilting Pad Journal Bearings With Heat Transfer Effects , 1988 .

[42]  Paul E. Allaire,et al.  The Eigenvalue Dependence of Reduced Tilting Pad Bearing Stiffness and Damping Coefficients , 1988 .

[43]  Jorgen W. Lund,et al.  The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing , 1987 .

[44]  Hiromu Hashimoto,et al.  Performance Characteristics of Large Scale Tilting-pad Journal Bearings , 1985 .

[45]  Paul E. Allaire,et al.  Frequency Effects in Tilting-Pad Journal Bearing Dynamic Coefficients , 1983 .

[46]  Keith E. Rouch,et al.  Dynamics of Pivoted-Pad Journal Bearings, Including Pad Translation and Rotation Effects , 1983 .

[47]  R. G. Kirk,et al.  Four Pad Tilting Pad Bearing Design and Application for Multistage Axial Compressors , 1982 .

[48]  Andras Z. Szeri,et al.  Linear force coefficients for squeeze-film dampers , 1982 .

[49]  V. N. Constantinescu,et al.  Operating Characteristics of Journal Bearings in Turbulent Inertial Flow , 1982 .

[50]  Paul E. Allaire,et al.  A pad perturbation method for the dynamic coefficients of tilting-pad journal bearings , 1981 .

[51]  C. M. McC. Ettles,et al.  The Analysis and Performance of Pivoted Pad Journal Bearings Considering Thermal and Elastic Effects , 1980 .

[52]  A. Szeri,et al.  A Thermohydrodynamic Analysis of Journal Bearings , 1979 .

[53]  G. J. Jones,et al.  Geometry Effects in Tilting-Pad Journal Bearings , 1979 .

[54]  Paul E. Allaire,et al.  Stiffness and Damping Coefficients for the Five-Pad Tilting-Pad Bearing , 1979 .

[55]  Chin‐Hsiu Li The Effect of Thermal Diffusion on Flow Stability Between Two Rotating Cylinders , 1977 .

[56]  Vinay Kumar Elastic and damping properties of partial porous journal bearings of finite length and arbitrary wall thickness taking film curvature and slip flow into account , 1976 .

[57]  J. W. Lund,et al.  The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings , 1975 .

[58]  J. M. Conway-Jones,et al.  Plain Bearing Damage , 1975 .

[59]  J. Berry Some Friction and Lubrication Problems in the Metalworking of the Superalloys , 1975 .

[60]  S. Galetuse,et al.  On the Possibilities of Improving the Accuracy of the Evaluation of Inertia Forces in Laminar and Turbulent Films , 1974 .

[61]  Duncan Dowson,et al.  Turbulent Lubrication Theory—Application to Design , 1974 .

[62]  G. G. Hirs A Systematic Study of Turbulent Film Flow , 1974 .

[63]  G. G. Hirs A Bulk-Flow Theory for Turbulence in Lubricant Films , 1973 .

[64]  V. N. Constantinescu On the Influence of Inertia Forces in Turbulent and Laminar Self-Acting Films , 1970 .

[65]  C. Ng,et al.  A Theory for Turbulent Fluid Films and Its Application to Bearings , 1967 .

[66]  F. K. Orcutt The Steady-State and Dynamic Characteristics of the Tilting-Pad Journal Bearing in Laminar and Turbulent Flow Regimes , 1967 .

[67]  K. K. Schwarz Some Problems of Rotor Dynamics , 1966 .

[68]  E. J. Gunter Dynamic stability of rotor-bearing systems , 1966 .

[69]  C. Pan,et al.  A Linearized Turbulent Lubrication Theory , 1965 .

[70]  J. W. Lund,et al.  ATTENUATION OF BEARING TRANSMITTED NOISE. VOLUME I. SPRING AND DAMPING COEFFICIENTS FOR THE TILTING-PAD JOURNAL BEARING , 1964 .

[71]  O. Pinkus,et al.  Theory of Hydrodynamic Lubrication , 1962 .

[72]  B. Sternlicht Elastic and Damping Properties of Cylindrical Journal Bearings , 1959 .

[73]  V. Constantinescu On Turbulent Lubrication , 1959 .

[74]  W. Philipzik Zur hydrodynamischen Theorie der Schmiermittelreibung , 1956 .

[75]  Charles Hummel,et al.  Kritische Zahlen als Folge der Nachgiebigkeit des Schmiermittels im Lager , 1926 .

[76]  O. Reynolds I. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil , 1886, Proceedings of the Royal Society of London.

[77]  HighWire Press Philosophical Transactions of the Royal Society of London , 1781, The London Medical Journal.