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Hydrostatic, Aerostatic, and

Hybrid Bearing Design

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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

AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO

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Butterworth-Heinemann is an imprint of Elsevier

The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB 225 Wyman Street, Waltham, MA 02451, USA

First published 2012

Copyright Ó 2012 Elsevier Inc. All rights reserved.

The right of W. Brian Rowe to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangement with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website:www.elsevier.com/permissions

This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library Library of Congress Number: 2012932618

ISBN: 978-0-12-396994-1

For information on all Butterworth-Heinemann publications visit our website atwww.elsevierdirect.com

Printed and bound in the United States 12 13 14 15 10 9 8 7 6 5 4 3 2 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

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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

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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

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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

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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

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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

References

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