DISTORTION OF A THRUST PAD EARING ON ELASTIC SUPPORT
by
NOWESAR MOHAMED ABDEL GAWAD ASHOUR
Thesis submitted in fulfilment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY, DELHI
NEW DELHI
JUNE 1989
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Acc.
DEDICATED TO
MY PARENTS MY FAMILY
CERTIFICATE
It is hereby certified that, except where the work of others has been specifically quoted, this thesis is entirely the result of candidate'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 for any degree.
The results contained in this thesis have not been submitted, in part or in full, to any other university or institute for the award of any degree or diploma.
Dr. K. Athre
Assistant Professor
Department of Mechanical Engineering
Indian Institute of Technology,Delhi New Delhi
Dr. S. Biswas
Associate Professor ITMME Centre
ACKNOWLEDGEMENT
I would like to thank Head, Department of Mechanical Engineering, Indian Institute of Technology Delhi, for providing the facilities to carry out this work.
I wish to express my sincere gratitude to Dr. K. Athre, Assistant Professor, Department of Mechanical Engineering and Dr. S. Biswas, Associate Professor, Industrial Tribology Machine Dynamics and Maintenance Engineering Centre, for their valuable guidance and encouragement throughout the work.
Thanks are also due to Dr. Y. Nath, Assistant Professor, Department of Applied Mechanics for useful suggestions and to Mr. K.
K. Chaturvedi of Bharat Heavy Electricals Ltd. for fruitful discussion.
I would like to record my thanks to the Governments of India and Egypt for providing funding through the bilateral cultural exchange programme (Indo-A.R.E.) for this work.
I wish to record my appreciation to Mr. K. N. S. Swamy, Research Scholar, ITMME Centre for his cooperation and to Mr. A. Sharma and Mr.
Ashok of ITMME Centre for word processing of the manuscript.
fil
N.M. Ashour
ABSTRACT
This investigation pertains to analysis of elastic and thermal dist on effects on thrust bearing having elastic support.
The background on the subject and literature survey are given in Chapter 1. The elastic deflection formulation for rectangular pad geometry for isoviscous fluid is reported in Chapter 2. The same for the sector thrust pad has been given in Chapter 3. The solution procedure and computational aspects I, methods employed are contained in Chapter 4. Chapter 5 contains the results obtained for rectangular and sector shaped pad for the stated conditions. The discussion on the results also follows in the same chapter.
The consideration of thermal distortion needed estimation of temperature profile of thrust pad. This required formulation of pressure generating equation for lubricant viscosity varying with temperature, the energy equation and implementation of viscosity- temperature relationship. These are included in Chapter 6.
The results of elastic and thermoelastic distortions alongwith new approach to solution of such problems are given in the chapter 7. The analysis based on thick plate theory has also been attempted by the author and is contained in this chapter. The conclusions and suggestions for future work follow in Chapter 8.
The results of investigation indicates that solution techniques are very important for obtaining theoretical results. It is also observed that thermal effects on the distortion of pad could be overbearing when compared to elastic bending. The results based on thick plate theory indicates the similar trend although the magnitude of maximum deflection is slightly more for the case studied when compared to thin plate results.
NOMENCLATURE
a Minimum film thickness (m)
B Width of pad across direction of flow (m) b Amount of taper (m)
D Rigidity of pad material (N.m)
Cv Specific heat of the lubricant (Joules /kg°C) E Modulus of elasticity (N/m2 )
H,11* Nondimensional film thickness H2,H
0 Nondimensional minimum film thickness h Film thickness (m)
h2,ho. Minimum film thickness (m)
hp Film thickness along pitch line (m) Spring stiffness per area (N/m3 )
RA Thermal conductivity of babbit lining (watts/m°C) KB Thermal conductivity of parent material (watts/me C) L Length of pad, along direction of flow (m)
M Number of grid points along direction of flow N Number of grid point across direction of flow P,P* Nondimensional pressure
p Pressure (N/m2 )
R Nondimensional radius (r/ro )
Rcp Center of pressure across direction of flow RI,R1 Inner radius of the pad (m)
Ro ,R 2 Outer radius of the pad (m)
R. . Nondimensional radius at any point i,j I')
ro Outer radius (m)
r. . Radius at any point i,j T
1,3
Oil temperature (°C)
CONTENTS
ABSTRACT
NOMENCLATURE ii
CHAPTER 1 INTRODUCTION AND LITERATURE SURVEY 1
1.1 Introduction 1
1.2 Literature Survey 8
CHAPTER 2 ANALYSIS OF RECTANGULAR PAD THRUST BEARING 16 ON ELASTIC SUPPORT
2.1 Introduction 16
2.2 Governing Equation for Pressure 16 2.2.1 Pressure estimation 16 2.2.2 Estimation of film thickness 18 2.2.3 Load calculation 20 2.3 Governing Equation for Deflection 20 2.3.1 Basic equation 21 2.3.2 Boundary conditions 21 2.4 Finite Difference Formulation for 22
Rectangular Pad
CHAPTER 3 ANALYSIS OF SECTOR SHAPED PAD ON ELASTIC 24 SUPPORT
3.1 Introduction 24
3.2 Governing Equations for Pressure Estimation 24 3.2.1 Pressure estimation 24 3.2.2 Estimation of film thickness 27 3.2.3 Load calculation 30 3.2.4 Formulation for sector pad considering 31 '
pitch and roll motion and viscosity variation with temperature
3.3 Governing Equation for Bending Analysis 33 ,
3.3.1 Basic equation 34
3.3.2 Finite difference formulation for 37 sector pad
CHAPTER 4 SOLUTION PROCEDURE 43
4.1 Introduction 43
4.2 Successive Approximation(Gauss-Seidel Method) 43
4.3 Matrix Method 44
CHAPTER 5 NUMERICAL RESULTS 53
5.1 Introduction 53
5.2 Pressure Profile 54
5.3 Input Parameters for Matrix/Iterative Method 56 5.4 Results from Iterative Technique 59 5.5 Results from Matrix Approach and Discussion 59
CHAPTER 6 FORMULATION OF THERMAL EFFECTS ON PAD 130
6.1 Introduction 130 6.2 Governing Equations for Sector Pad 132 6.2.1 Reynolds equation 132 6.2.2 Fil■ geometry 132 6.2.3 Energy equation 133 6.2.4 Equation of state 133 6.3 Finite Difference Formulation 134 6.3.1 Reynolds equation 134 6.3.2 Energy equation 134 6.4 Numerical Procedure 137 6.5 Conduction Equation 139 6.5.1 Nondimensional approach 144 6.5.2 Finite difference formulation 142 6.5.3 Computational methodology 142
CHAPTER 7 COMPREHENSIVE SOLUTION PROCEDURE 145
7.1 Introduction 145
7.2 Elastic Distortion with Viscosity Variation 146 7.3 Thermoelastic Distortion 151 7.4 Nonlinear Solution Technique 151 7.5 Results and Discussion 156
7.5.1 Input parameters 156 7.5.2 Effect of variation of viscosity 157 7.5.3 Effect of thermoelastic distortion 157 7.5.4 Non-linear method 159
7.6 Discussion 159
CHAPTER 8 CONCLUSIONS AND SCOPE FOR FURTHER WORK 193
REFERENCES 197
APPENDIX A A-1
APPENDIX B B-1
APPENDIX C
C-1
APPENDIX D D-1
APPENDIX E E-1
APPENDIX F F-1
APPENDIX G
C- 1
APPENDIX H H-1
