Thermohydrodynamic Instability in Fluid-Film Bearings

J. K. Wang, PhD, PE has over 20 years' academic and industrial experience in the design and vibration analysis of high-speed rotating machinery associated with fluid film bearings. Dr. Wang currently works as the Director of Engineering and Product Development of reciprocating and centrifugal pumps business units for TSC Group. He received his bachelor and master degrees from Xi'an Jiaotong University, and his doctoral degree from Louisiana State University. He is a professional engineer registered in the state of Texas, a certified Category IV Vibration Analyst, and Category IV Vibration Consultant listed by Vibration Institute. He holds the membership of ASME, ASM, SPE, and AISC. M. M. Khonsari holds the Dow Chemical Endowed Chair at Louisiana State University (LSU). He is holder of several US patents, has authored over 250 archival papers, 50 book chapters and special publications, and three books. Professor Khonsari is the recipient of several research awards including the ASME Mayo Hersey Award, Burt Newkirk Award, the STLE Presidential Award awards for his contributions to tribology. He is the Editor-in-Chief for ASME Journal of Tribology. Professor Khonsari is a fellow of American Society of Mechanical Engineers (ASME), Society of Tribologist and Lubrication Engineers (STLE), and American Association for the Advancement of Science (AAAS).

• Preface xiAcknowledgements xiii1 Fundamentals of Hydrodynamic Bearings 11.1 Reynolds Equation 31.1.1 Boundary Conditions for Reynolds Equation 61.1.2 Short Bearing Approximation 71.1.3 Long Bearing Approximation 71.2 Short Bearing Theory 81.2.1 Analytical Pressure Distribution 81.2.2 Hydrodynamic Fluid Force 91.2.3 Static Performance of Short Journal Bearings 111.3 Long Bearing Theory 131.3.1 Analytical Pressure Distribution of Long Journal Bearings 131.3.2 Hydrodynamic Fluid Force of Long Journal Bearings 171.3.3 Static Performance of Long Journal Bearings 191.4 Finite Bearing Solution 26References 282 Governing Equations for Dynamic Analysis 292.1 Equation of Motion 292.2 Decomposition of the Equations of Motion Based on Short Bearing Theory 312.2.1 Laminar Flow Simplification 332.3 Decomposition of the Equations of Motion Based on Long Bearing Theory 342.4 Summary 37References 373 Conventional Methods on System Instability Analysis 393.1 Linearized Stiffness and Damping Method 413.1.1 Derivation of Linearized Bearing Stiffness and Damping Coefficients 413.1.2 Instability Threshold Speed Based on the Linearized Stiffness and Damping Coefficients 483.2 Nonlinear Method 513.2.1 Brief Description of Trial-and-Error Method 513.2.2 Illustration of the Trial-and-Error Method 513.2.3 Comparison Between Different Types of Fluid-Film Boundary Conditions 54References 564 Introduction to Hopf Bifurcation Theory 594.1 Brief Description of Hopf Bifurcation Theory 604.2 Shape and Size and Stability of Periodic Solutions 614.3 Definition of Orbital-Asymptotically Stable with an Asymptotic Phase 62References 625 Application of HBT to Fluid-Film Bearings 635.1 Application I: Prediction of Stability Envelope 645.1.1 Definition of Stability Envelope 645.1.2 Equations of Motion 665.1.3 Application of Hopf Bifurcation Theory to the Equations of Motion 675.1.4 Numerical Investigation of the Stability Envelope Rs 695.1.5 Illustrative Case Study 705.2 Application II: Explanation of Hysteresis Phenomenon Associated with Instability 745.2.1 Introduction 745.2.2 Definition of Hysteresis Phenomenon Associated with Instability 755.2.3 Experimental Investigation 775.2.4 Relationship between Hysteresis Phenomenon and Subcritical Bifurcation 815.2.5 Case Studies 83References 886 Analysis of Thermohydrodynamic Instability 916.1 Inlet Temperature Effects 916.1.1 Theoretical Prediction 926.1.2 Experimental Studies 976.1.3 Explanation of Newkirk and Lewis’s Experimental Results 1046.1.4 Design Guidelines for Improving System Stability Based on Oil Supply Temperature 1046.2 Effects of Inlet Pressure and Inlet Position 1056.2.1 Equations of Motion with Consideration of Inlet Pressure and Position Effects 1066.2.2 Influence of Oil Inlet Pressure on the Instability Threshold Speed 1086.2.3 Influence of Oil Inlet Position on the Instability Threshold Speed 1106.2.4 Design Guidelines on Inlet Pressure and Inlet Position 1116.3 Rotor Stiffness Effects 1126.3.1 Equations of Motion of a Flexible Rotor 1136.3.2 Effects of Rotor Flexibility 1176.3.3 Comparison with the Results Based on Rigid-Rotor Model 1206.3.4 Experimental Verification 1216.3.5 Application Examples 1226.3.6 Design Guidelines on Rotor Stiffness 1286.4 Worn Bearing Bushing Effects 1296.4.1 Wear Profile Model 1296.4.2 Dynamic Pressure Distribution in Worn Journal Bearing 1326.4.3 Hydrodynamic Fluid Force in Worn Journal Bearing 1336.4.4 Example Showing the Worn Bearing Bushing Profile and Its Pressure Profile 1356.4.5 Bearing Bushing Wear Effect on System Stability 1366.5 Shaft Unbalance Effects 1396.5.1 Equation of Motion with Shaft Unbalance 1406.5.2 Decomposition of the Equations of Motion with Shaft Unbalance 1426.5.3 Numerical Solution of the Equations of Motion 1446.5.4 Example Showing Shaft Unbalance Effects on Journal Orbits 1456.6 Turbulence Effects 1476.6.1 Governing Equations for Turbulent Flow 1476.6.2 Effects of Turbulence on the Dynamic Performance 1536.6.3 Effects of Turbulence on the Shape and Size and Stability of the Periodic Solutions 1546.7 Drag Force Effect 1606.7.1 Dynamic Fluid Forces in Journal Bearings 1606.7.2 Equations of Motion 1626.7.3 Effects of Drag Force on the Hopf Bifurcation Profile 163References 165Appendix A: Derivation of the Dynamic Pressure for Long Journal Bearing 169Reference 171Appendix B: Integrals Used in Section 1.3 173References 174Appendix C: Curve-fitting Functions for Long Journal Bearings 175Reference 177Appendix D: Jacobian Matrix of the Equations of Motion 179Reference 181Appendix E: Matlab Code to Evaluate Rotor Shaft Unbalance Effects 183E1 Main Code 183E2 Functions 189E2.1 Function whirl_ fullflexiblewithunbalance.m 189E2.2 Function kshaft.m 190Appendix F: Nomenclature 193Index 197