INTERFACE DAMPING IN BLADE
ATTACHMENT REGION
A THESIS SUBMITTED TO THE
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
for the Award of the Degree of
DOCTOR OF PHILOSOPHY
BY
MOHAMMED ABDUL WASAY USMANI
DEPARTMENT OF MECHANICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
APRIL, 1986
CERTIFICATE
This is to certify that the thesis entitled "INTERFACE
DAMPING IN BLADE ATTACHMENT REGION" being submitted
by Mr. M. A . W. Usmani to the Indian Institute of Technology,
Delhi (India) for the award of the Degree of Doctor of Philosophy
in Mechanical Engineering Department, is a record of bonafide
research work carried out by him under our supervision and
guidance. The thesis work, in our opinion, has reached the
standard fulfilling the requirements for the Doctor of Philosophy
Degree. The research report and the results presented in this
thesis have not been submitted in part or full to any other
University or Institute for the award of any degree or diplorra .
•s
,e(
Prof. C. V. Ramakrishnan
Prof.J.S.Rao
Department of Applied Mechanics
Department of Mechanical Engineering
Indian Institute of Technology, Delhi.Indian Institute of Technology,
Delhi.
ACKNOWLFDUMFNTS
The author wishes to express his deep sense of gratitude
and indebtness to Prof. J.S. Rao of Mechanical Engineering
Department and Prof. C.V. Ramakrishnan of Applied Mechanics
Department for their inspiring technical guidence, active supervision
and constant help at all stages of the research work.
The author also wishes to place on record his sincere
heart felt thanks to Prof. J.A. Munir, Prof. S.R. Khan, Prof. S.H.
Mohsin, Dr. S. Tarique Jilani and Iqbal Mian of Mechanical
Engineering Department of Aligarh Muslim University for their
help and encouragement.
In this research work which has spanned over a long .
duration, it is impossible to acknowledge the help of all my
colleagues and friends. However special thanks to Mr. I.A. Khan
who made my stay comfortable at I.I.T. during the closing stages
of this work.
Thanks are also due to Mr. B.B. Arora, Mr. N.C. Saraswat
and Mr. Ashok Vashistha for their assistance in the preparation
of this thesis.
Words can not express my gratitude to Afroze, my wife,
for her help, encouragement, understanding and patience during
my preoccupation with the research activity.
Samina, Rafey and
Uzma my children deserve special thanks as they were deprived
of the usual attention due to author's absence from home.
,()C i
M.A.W. Usmani
ABSTRACT
-------Energy dissipation is a major blade design criterion
since damning limits the blade resonant amnlituies an(: stresses
which may develop under steady oneratini7 conditirIns ',7ith harmonic
forcing input. T3lade damning is therefore a desirable structural
nronerty which helps to reduce the nossihility of blade damage
from metal fatigue.
7\ major contribution of damning in a free
standing blade arises from the interface.slin that take niece
in the blade root junction. This thesis is concerned 4ith the
estimation of damning in the blade disk junction.
The nresent work addresses the nroblem of evaluation of
root damning using analytical and exnerimental nrocedures.
To study the nroblem analytically, the finite element method
has been made use of and to simulate the blade - root behaviour,
the dynamic contact nrohlem under the action of centrifugal
force and a lateral load is analysed using a time marching
nrocedure.
71 general nurnose comnuter nrogram consisting of a main
nrogram and twenty eight other segments has•been develoned.
The program is very efficient since only the equations
corresponding to the contact nodes, loaded noded and the nodes
which leave contact are set un at every iterative sten within
a. time interval. The nrogram is canahle of handling inclined
contact surfaces and the nresence of clearances.
(iv)
k free vibration analysis of a blade with ?striddle-T
type root junction has been ,nade to deter-line the lcflrath'lic
decrernent at successive ti'''e stens.
To estimate the true
behaviour, the initial disnlace,rents have been obtaini by
solving static contact nroble-I. The amain-( ratio has been
obtained as a function of centrifugn.1 load and ti') dis-)lacements.
A test rig to determine the damning of a blade-root
is designed and fabricated uqinr thermal_ coolinct to si.)-lulate
the centrifugal load. The tests can be carried out in air
as well as in vacuum. 7xperiments have been conducted to
estimate blade damning and atter-1--)ts have been made to correlate
it with the theoretical investi-lations !nentioned earlier.
While the qualitative trend is 17ound to be alricrht, there is
considerable deviation from the theoretical nrediction on
account of the oractical conditions in which the blade is
mounted.
The thesis ends with a detailed summary of conclusions
and suggestions for future research.
(v )
1TE'1T S
i
Certificate
Acknowledgements
Abstract'
Contents
CliiVnE
List of Pigures
ix
List of Photogranhs
xii
List of 'Symbols
xiii
-1
INT7ODUCTION AND LTTE”ATTME sur2VEm1-15
1.1 Introduction
1
1.2 general Tteview of 'Thee Vibration2
Analysis of Turbine 731ades
1.3 Pole of namning in Iribration and Analytical
Methods of Determining It.
1.3.1 Source of D,amning in steam Turbine
91ading
1.4 review of Work .on T)amninq of. Turbomachine3
Blades
1.5 Finite Element Analysis or Contact problem12
1.6 Scone of present Invstigations13
1.7 organisation of the Thesis14
CHAPTEP -2
ANALYSTS OF STATIC CONTACT T",(VIT,T7416-4 3
2:1 Introduction
16
2.2 The Finite Element method 17
2.2.1 Ouadratic Tsonr)rametric Elements22
(vi)
R
age
2.3 Method of Analysis of Static Contact 7)roblem 22
2.4 Analysis of 31ade Root-Disk Junction28
For Centrifugal Force
2.4.1 Finite Element Discretization29
2.4.2 Boundary Conditions30
2.4.3 Results of Analysis of Blade-Disk30
Assembly.
2.4.3.1 Results of T-Root Junction31
2.4.3.2 Results of Straddle T-root31
Junction
2.5 Conclusions
31
CHAPTER -3
MODELLING OF DYNAMIC CONTACT PROBLE
44-60
3.1 Introduction
44
3.2 Governing 77untion7
44
Wilson-0 Method
47
3.4 Derivation of the (;overninrr Equations
49
for the Subregion
3.5 Simulation of Openinl
52
3.6 Simulation of Slip
53
3.7 Contact Along Inclined Surfaces54
3.8 Efficient Computation of Condensed Equations 55
3.9 Numerical Procedure
57
3.10 Conclusions
59
CHAPTER -4
DEVELOPMENT OF COMPUTER PP0GRAM
61-81
4.1 Introduction
61
Page
4.2 General Organisation of the Program61
4.2.1 Data Processor
62
4.2.2 Flexibility Matrix Analyser63
'4.2.2.1 Computation of Element64
Property Matrices
4.2.2.2 Computation of Load Vector66
4.2.2.3 Comoutation of P-IS For66
Dynamic Terms
4.2.2.4 - Static Condensation And67
Inversion
4.2.3 Contact Solver
68
4.2.4 Elastic 71nalyser
69
4.3 Test Problems And Results 70
4.3.1 Cantilever Under Suddenly Apnlied70
Load
72
4.3.2 Suddenly 7\pplied Load in a
Cantilever with part of the body
having high rigidity
4.3.3 Dynamic Modelling of. Joint 0nening72
and Closing and Slip
CHAPTER -5
FINITE ELEMENT MODELLING OF ROOT DAMPING82-106
5.1 Introduction
82
5.2 Finite Element Modelling 82
84
5.3 Response of A. Cantilever. Ilade Under
Suddenly Aoolied Load
85
5,4 Effect of Centrifugal Load
87
5.5 Effect of. Coefficient of Eriction
88
5.6 Effect of Lateral Load
(viii)
Page
5.7 Effect of Root qeometry
go
5.8 Discussion and Conclusions90
CHAPTER -6
EXPERIMENTAL STUDIES ON ROOT DAMPINry107-15Z
6.1 Introduction
107
6.2 Methods of Damnin7 Estimation in Dlade Root107
.6.2.1 Logarithmic Decrement Method107
6.2.2 Half Rower (3anftiidth) Method109
6.3 Exnerimental Setun
109
6.4 Details of Test Rig
110
6.4.1 Dimensional Mismatch112
6.5 Instrumentation
113
6.5.1 Measurements for Centrifuclal Meld113
6.5.2 Measurements of Transient Decay114
6.5.3 Instrumentation for Excitation115
in Vacuum
6.6 Discrintion of the Nssembled Setun115
6.7 Test Procedure
115
6.8 Test in Tir
117
6.9 Test in Vacuum
118
.6.10 Results and Discussions
119
CHAPTER -7
CONCLUSION
153-155
•
7.1 Scone of_' qork and Sucr7estion for Future154
Research
REFERENCES
156-167
APPENDIX
168-169