DEFORMATION AND HEAT TRANSFER EFFECTS IN CONVENTIONAL AND WATER-COOLED
SPRING-SUPPORTED TILTING-PAD THRUST BEARINGS
by
KAUSHAL KISHORE CHATURVEDI
INDUSTRIAL TRIBOLOGY, MACHINE DYNAMICS AND MAINTENANCE ENGINEERING CENTRE
submitted in fulfilment of the requirements of degree of
DOCTOR OF PHILOSOPHY
to the
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
NEW DELHI
JULY, 1994
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DEDICATED TO My parents
Dr. S. Biswas Professor and Head ITMME Centre
CERTIFICATE
It is hereby certified that, except where the work of others has been specifically quoted, this thesis is the result of the candidates's own investigation under our guidance.
It is also certified that this thesis has not already been accepted in substance for any degree, and is not being concurrently submitted in candidature of any degree.
The results contained in this thesis have not been submitted, in part or in full, to any other university or institute for award of any other degree or diploma.
2
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Dr. K. Athre
Associate Professor Deputy General Manager Department of Mechanical Fracture Mechanics Engineering Laboratory
Indian Institute of Technology, Delhi BHEL, Vikasnagar
New Delhi Hyderabad
S J.4
Dr. S. . Roy
ACKNOWLEDGEMENT
I wish to express my profound sense of gratitude to Prof. S.
Biswas, Head, ITMMEC, Dr. K. Athre, Associate Professor, Department of Mechanical Engineering, IIT, Delhi and Dr. S. K.
Roy, Deputy General Manager, Fracture Mechanics Laboratory, BHEL, Corp. R&D, Hyderabad, for invaluable guidance and constant encouragement provided to me.
I thank Professor Y. Nath, Department of Applied Mechanics, IIT, Delhi, for advice and useful discussions.
I am thankful to the management of Bharat Heavy Electricals Ltd., for sponsoring me for the Ph. D. programme.
Thanks are due to Shri T. Ramakrishana, for preparing the figures and graphs.
I am grateful to my friends and relatives, particularly my younger brother Mr. D. K. Chaturvedi and his wife, Mrs. Renu Chaturvedi, whose warmth and affection made my stay at Delhi, pleasant.
Finally, I wish to record profound appreciation to my wife, Kirti, for her patience, encouragement and support, and to my daughters, Mitali and Shefali, for forbearing lack of attention from me during the difficult periods of work.
0:10N4 - K. K. Chaturvedi
ABSTRACT
The work reported here pertains to the thermoelastic deformation in large spring-supported conventional and water-cooled tilting-pad thrust bearings. It includes the following :
The background on the subject and the literature survey are given in Chapter I.
Formulation of the shape of the oil film for a flat pad has been done. The procedure for solution of the coupled Reynolds equation, energy equation and viscosity temperature relationship has been developed. A search procedure for finding value of the film shape parameters and the minimum oil film thickness for a given load and location of the centre-of-pressure has been developed. These are described in Chapter 2.
The conduction of heat in the thrust pad affects the operating temperature of the bearing. Solution of the Fourier equation of conduction, boundary conditions for the surfaces exposed to oil, the coefficients of the convective heat transfer, dissipation of the heat through the runner, thrust pad, by convection in the oil film and in the inter-pad gap are described in Chapter 3.
Analysis of deformation in the thrust pad is dealt with in Chapter 4. Solution of the biharmonic equation of bending of
plate with the boundary conditions for edge reactions, bending twisting and equivalent thermal bending moments is described.
The conduction of heat in the water-cooled thrust bearing is given in Chapter 5. A two-dimensional analysis of conduction has been solved by the local linearization method. In case of the sector pad, the solution has been obtained by the lumped parameter technique.
The deformation of the anisotropic plate model of the water-cooled thrust pad has described in the Chapter 6.
Treatment of the biharmonic equation of bending of plate, the boundary conditions and thermal bending effects have been dealt with here.
The solution procedure and the computer program developed have been described in Chapter 7. The results are given for two large thrust bearings. These include the elastic and thermoelastic deformations in these bearings.
The conclusions and the scope for further work are given in Chapter 8.
It has been shown that the thermal deformation is predominant in large thrust bearings. The provision of water-cooling is effective in reducing the thermal deformation by a large extent. The residual elastic deformation can be reduced by the modified spring support configuration proposed herein. Thus, it has been established that the provision of water-cooling and optimization of the spring support configuration are very effective in reducing the thermoelastic deformation of a large thrust bearing.
ii
CONTENTS
ABSTRACT
LIST OF FIGURES iii
LIST OF TABLES vii
NOMENCLATURE ix
CHAPTER 1 INTRODUCTION AND LITERATURE SURVEY 1 - 36
1.1 INTRODUCTION 1
1.2 LITERATURE SURVEY 10
CHAPTER 2 FINITE SECTOR-SHAPED THRUST BEARING 37 - 74 2.1 SHAPE OF THE OIL FILM 37
2.2 REYNOLDS EQUATION 45
2.3 ENERGY EQUATION 54
2.4 VISCOSITY-TEMPERATURE RELATIONSHIP 59 2.5 SEARCH FOR FILM SHAPE PARAMETER AND THICKNESS 61
CHAPTER 3 DISSIPATION OF HEAT IN THE THRUST SEGMENT 75 - 100 3.1 FOURIER EQUATION OF CONDUCTION 75 3.2 CONVECTION OF HEAT FROM THE THRUST SEGMENT 89 3.3 HEAT DISSIPATION THROUGH THE RUNNER 91 3.4 HEAT DISSIPATION IN THE GAP BETWEEN THE PADS 95
CHAPTER 4 DEFORMATION OF THE THRUST PAD 101 -124 4.1 SUPPORT PRESSURE FIELD 101 4.2 BIHARMONIC EQUATION OF BENDING OF PLATE 105
4.3 BOUNDARY CONDITIONS 108
4.4 THERMAL DEFORMATION OF THE THRUST PAD 113
CHAPTER 5 HEAT TRANSFER IN WATER-COOLED THRUST•BEARING 125 -170 5.1 ARRANGEMENT OF WATER-COOLING IN THRUST PAD 125 5.2 TWO-DIMENSIONAL ANALYSIS OF HEAT TRANSFER IN
WATER-COOLED BEARING 127
5.3 RESULTS AND DISCUSSION 139 5.4 THREE-DIMENSIONAL ANALYSIS OF HEAT TRANSFER
IN THRUST BEARING 143
CHAPTER 6 THERMOELASTIC DEFORMATION OF WATER-COOLED TILTING PAD THRUST BEARING
6.1 WATER-COOLED THRUST BEARING
6.2 GOVERNING EQUATION FOR DEFORMATION OF RECTANGULAR ANISOTROPIC PLATE
6.3 BOUNDARY CONDITIONS FOR RECTANGULAR ORTHOTROPIC PLATE
6.4 GOVERNING EQUATION FOR DEFORMATION OF ORTHOTROPIC SECTOR-SHAPED PLATE
6.5 BOUNDARY CONDITIONS FOR THE WATER-COOLED SECTOR-SHAPED THRUST PAD
171 - 193 171
173
176
178
181
6.6 THERMAL STRESSES IN THE WATER-COOLED THRUST
BEARING 185
CHAPTER 7.0 SOLUTION PROCEDURE, RESULTS AND DISCUSSION 194 - 223 7.1 SOLUTION PROCEDURE AND PROGRAM DETAILS 194
7.2 INPUT DATA 200
7.3 RESULTS AND DISCUSSION 203 7.3.1 EFFECT OF FILM SHAPE ON THE PRSSURE
DISTRIBUTION 203
7.3.2 EFFECT OF WATRER-COOLING ON THE TEMPERATURE
DISTRIBUTION 203
7.3.3 EFFECT OF WATER-COOLING ON THE THERMOELASTIC
DEFORMATION 205
7.3.4 EFFECT OF THE SPRING SUPPORT CONFIGURATION ON THE
ELASTIC DEFORMATION 206
CHAPTER 8.0 CONCLUSIONS AND SCOPE FOR FURTHER WORK 224 -228
8.1 CONCLUSIONS 224
8.2 SCOPE FOR FURTHER WORK 227
REFERENCES 229 - 235
APPENDICES
APPENDIX A : CONVERSION OF THE REYNOLDS EQUATION TO THE
FINITE DIFFERENCE FORM A- 1 APPENDIX B : GEOMETRY OF THE THRUST PAD WITH A UNIFORM GAP B - 1 APPENDIX C : DERIVATIVES IN THE FINITE DIFFERENCE FORM C - 1
