Hydrostatic, Aerostatic, and
Hybrid Bearing Design
Hydrostatic, Aerostatic, and
Hybrid Bearing Design
W. Brian Rowe DSc, FIMechE
Emeritus Professor of Mechanical Engineering, Liverpool John Moores University and Consulting Engineer, Court Cottage, Moult Hill, Salcombe, Devon, TQ8 8LF, UK
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First published 2012
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ISBN: 978-0-12-396994-1
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Contents
Preface ...xi
Usual Meaning of Symbols ... xiii
Chapter 1: Application ... 1
1.1 Introduction... 1
1.2 What are Hydrostatic, Hybrid, and Aerostatic Bearings? ... 2
1.3 When are Hydrostatic, Hybrid, and Aerostatic Bearings Employed? ... 7
1.4 Bearing Selection... 9
1.5 Bearing Categories ... 12
1.6 Commercial Applications... 16
1.7 Materials and Manufacture... 18
1.8 Aerostatic Bearings... 22
1.9 How to Read and Use the Book... 23
References... 23
Chapter 2: Basic Flow Theory ... 25
2.1 Introduction... 25
2.2 Viscosity... 25
2.3 Density and Consistent Units ... 27
2.4 Compressibility... 27
2.5 Viscous Flow Between Parallel Plates ... 28
2.6 Combined Pressure- and Velocity-Induced Viscous Flow in a Two-Dimensional Nonparallel Film ... 32
2.7 Flow Through Restrictors... 33
2.8 Recess Pressure and Pressure Ratio... 37
2.9 Bearing Load ... 39
2.10 Use of Normalized Data... 42
2.11 Aerostatic BearingsdSummary of Relationships ... 44
References ... 48
Further Reading... 48
Chapter 3: Power, Temperature Rise, and Shape Optimization ... 49
Summary of Key Design Formulae ... 49
3.1 Introduction... 49
3.2 Pumping Power Hp... 49
3.3 Friction Power Hf... 50
3.4 Power Ratio K... 50
3.5 Temperature Rise DT... 51
3.6 Minimum Power as an Optimization Criterion... 53
3.7 Minimum Power for Low-Speed Bearings (K ¼ 0) ... 53
3.8 Minimum Power for High-Speed Recessed Bearings ... 54
3.9 Speed Parameter Shand Optimum Value Sho... 57
3.10 Optimization of Plain Nonrecessed Hybrid Bearings... 63
References ... 63
Chapter 4: Pads: Area and Flow Shape Factors (A and B)... 65
Summary of Key Design Formulae ... 65
4.1 Pad Shapes and Shape Factors ... 65
4.2 Virtual Recesses and Dispersion Losses ... 65
4.3 Circular Pads... 70
4.4 Square Pad Data ... 71
4.5 Rectangular Pad Data ... 72
4.6 Annular Recess Circular Pad Data... 72
4.7 Conical Pad Data ... 73
4.8 Spherical Pad Data ... 75
4.9 Multi-Recess Circular Pad Data... 76
4.10 Multi-Recess Rectangular Pad Data... 77
4.11 Data for Rectangular Pad with Radiussed Recess Corners ... 78
4.12 Data for Any Shape with Thin Constant Land Width... 79
4.13 Annular Multi-Recess Pad Data... 79
Chapter 5: Flow Control and Restrictors ... 83
Summary of Key Design Formulae ... 83
5.1 Introduction... 83
5.2 Bearing Film Stiffness... 84
5.3 Hydrostatic Circuit Design and Sealing... 85
5.4 Load and Stiffness of Capillary-Controlled Pads ... 86
5.5 Flow Control Mechanisms ... 90
5.6 General Stiffness Laws for Hydrostatic and Aerostatic Bearing Pads ... 102
5.7 Aerostatic Bearings and Flow Control... 104
References ... 109
Appendix: Tabular Design Procedures for Restrictors and Worked Examples... 110 vi Contents
Chapter 6: Basis of Design Procedures ... 115
6.1 Introduction... 115
6.2 An Acceptable Range for Design Pressure Ratio... 115
6.3 Zero- and Low-Speed Hydrostatic Bearings... 116
6.4 Zero- and Low-Speed Aerostatic Bearings... 117
6.5 Optional Size Limits and Tolerances for Film Thickness ... 118
6.6 High-Speed Bearings... 119
6.7 Specification for ISO Limits and Fits ... 122
6.8 Tolerance Grades for Hydrostatic and Aerostatic Bearings ... 122
References ... 124
Chapter 7: Plane Hydrostatic and Aerostatic Bearings ... 125
Summary of Key Design Formulae ... 125
7.1 Use of the Design Charts ... 125
7.2 Choice of Land Width... 125
7.3 Flow Variation with Film Thickness... 126
7.4 Load Variation with Film Thickness... 126
7.5 Stiffness Variation with Film Thickness ... 127
7.6 Single-Pad Bearings... 127
7.7 Equal Opposed-Pad Bearings... 138
7.8 Unequal Opposed-Pad Bearings... 146
7.9 Complex Arrangements of Pads (Capillary Controlled)... 147
Appendix: Tabular Design Procedures ... 154
Chapter 8: Partial Journal Bearings ... 167
Summary of Key Design Formulae ... 167
8.1 Recessed Partial Journal Bearings ... 167
8.2 Partial Journal Bearings with a High-Pressure Supply Groove... 174
Reference... 178
Chapter 9: Recessed Hydrostatic Journal Bearings ... 179
Summary of Key Design Formulae ... 179
9.1 Introduction... 179
9.2 Flow ... 181
9.3 Load ... 186
9.4 Power, Power Ratio, and Temperature Rise ... 191
9.5 Land-Width Ratios and Concentric Pressure Ratio ... 192
9.6 Selection of Tolerances for Bearing Film Clearance... 192
9.7 Selection of Supply Pressure, Viscosity, and Clearance... 193
9.8 Bearing Film Stiffness... 197
References ... 202 Contents vii
Appendix 1: Derivation of Journal Bearing Stiffness by an Approximate
Analytical Method ... 202
Appendix 2: Tabular Design Procedure... 204
Chapter 10: Plain Journal Bearings... 207
Summary of Key Design Formulae ... 207
Part A. Hydrostatic/Hybrid Plain Journal Bearings... 207
10.1 Introduction... 207
10.2 Selection of Bearing Configuration... 208
10.3 Power Ratio, K... 210
10.4 Concentric Hydrostatic Pressure Ratio, b... 210
10.5 Bearing Clearance and Clearance Limits... 210
10.6 Hydrostatic Load Support ... 213
10.7 Hybrid Slot-Entry Bearings... 215
10.8 Hybrid Hole-Entry Bearings ... 218
10.9 Size of Slot and Hole-Entry Ports... 219
10.10 Summary of Hydrostatic and Hybrid Load Support... 220
10.11 Concentric Hydrostatic/Hybrid Flow ... 220
10.12 Power and Temperature Rise... 222
Part B. Aerostatic Plain Journal Bearings... 225
10.13 Introduction to Aerostatic Journal Bearings ... 225
10.14 Concentric Aerostatic Pressure Ratio, Kgo... 225
10.15 Aerostatic Clearance and Clearance Limits... 226
10.16 Aerostatic Load Support... 226
10.17 Concentric Aerostatic Flow... 227
10.18 Hybrid Aerostatic Journal Bearings ... 229
10.19 Materials and Surface Texture for Journal Bearings ... 231
References ... 231
Appendix: Tabular Design Procedures ... 232
Chapter 11: The Yates Bearing ... 239
Summary of Key Design Formulae ... 239
11.1 Introduction... 239
11.2 Principle of Operation ... 241
11.3 Basic Parameters for the Yates Bearing... 242
11.4 Hydrostatic Design Procedure... 250
11.5 Aerostatic Yates Bearings... 255
11.6 Aerostatic Design Procedure ... 256
References ... 258
Chapter 12: Conical Journal Bearings... 259
Summary of Key Design Formulae ... 259
12.1 Application... 259
12.2 Basic Parameters... 262
12.3 Single-Cone Bearings ... 264
12.4 Complementary-Cone Spindle Bearings... 265
12.5 High-Speed Design... 269
12.6 Design Procedure for a Complementary-Cone Hydrostatic Bearing ... 269
12.7 Design Procedure for a Complementary-Cone Aerostatic Bearing ... 272
References ... 274
Chapter 13: Spherical Bearings ... 275
Summary of Key Design Formulae ... 275
13.1 Application... 275
13.2 Basic Parameters... 277
13.3 Central-Recess Spherical Bearing... 279
13.4 Annular-Recess Spherical Bearing... 282
13.5 Single Multi-Recess Spherical Bearings... 283
13.6 Opposed Multi-Recess Spherical Bearings... 283
Reference... 287
Chapter 14: Dynamics... 289
Summary of Key Design Formulae ... 289
14.1 Introduction... 289
14.2 Static Loading... 290
14.3 Dynamic Loading ... 291
14.4 Squeeze Film Damping ... 292
14.5 Compressibility in Hydrostatic and Aerostatic Bearings... 293
14.6 Dynamic Model of a Thrust Pad... 294
14.7 Hydrostatic Thrust Pad with Thin Lands... 297
14.8 Journal Bearings: Equations of Motion ... 301
14.9 Journal Bearings in the Concentric Condition... 303
14.10 Eccentric Journal Bearings... 311
References ... 313
Chapter 15: Experimental Methods and Testing ... 315
15.1 Introduction... 315
15.2 Flat-Pad Rig... 316
15.3 Cylindrical Journal Bearing Rig... 318
15.4 Publications on Experimental Behavior... 322
References ... 322
Index ... 325
Preface
The special qualities of pressurized hydrostatic, aerostatic, and hybrid bearings afford a simple and convenient solution to many bearing problems experienced with particular machines. Sometimes, the best method of achieving a specified performance is to use a hydrostatic bearing, an aerostatic bearing, or a hybrid bearing. However, the designer is not always experi-enced in hydrostatic and aerostatic lubrication, and has difficulty obtaining authoritative guid-ance presented in a simple manner.This book has been written with this problem in mind and is based on the author’s personal experience over many years in bearing design and testing, in running courses on this subject for industry, and in writing articles for the technical press.
Theory is kept to an elementary level in the design sections and the book offers a useful intro-duction for engineers who have left academic study behind. A basic theory chapter refreshes relevant principles of fluids. The book is also useful to students of engineering design and lubri-cation. There is growing awareness in universities and colleges of the importance of tribology for reliability and effectiveness of all moving devices and mechanisms. This book covers important sectors of thin-film lubrication and machine design.
Acknowledgements are due to many valued colleagues, particularly Dr J. P. O’Donoghue, Dr K. J. Stout, Dr D. A. Koshal, Dr F. S. Chong, Professor K. Cheng, Professor W. Weston, and Dr D. Ives, main colleagues with whom analysis, computing, and experimental investigation were developed. A considerable volume of experimental work undertaken over the years has contrib-uted to understanding where theory fits with reality and, more importantly, where it diverges. Great care has been paid to ensure accuracy in the design guidance given in this book. But, however carefully the text has been checked, some readers may find ambiguity. The technique of presenting and explaining principles wherever possible, followed by procedures and ex-amples, allows the reader to cross-check intentions and overcome such problems.
W. Brian Rowe
Consulting Engineer and Emeritus Professor of Mechanical Engineering Liverpool John Moores University 2012 xi