ACTIVE VIBRATION CONTROL OF ROTOR 4..
USING SMART MATERIALS saaA
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by
ARAVINDHAN T S
Department of Mechanical Engineering
Submitted
in fulfillment of the requirements of the degree of Doctor of Philosophy
to the
Indian Institute of Technology, Delhi New Delhi - 110116, India
June, 2006
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Certificate
This is to certify that the thesis entitled "Active Vibration Control of Rotors Using Smart Materials" being submitted by Aravindhan T S to the Indian
Institute of Technology, Delhi for the award of the degree of Doctor of Philosophy is a record of bona fide research work carried out by him under my supervision and guidance. This thesis has been prepared in conformity with the rules and regulations of the Indian Institute of Technology — Delhi, New Delhi.
The thesis work, in my opinion has reached the requisite standard fulfilling the requirements for the degree of Doctor of Philosophy. 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. Kshitij Gupta) Professor,
Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi, India.
Acknowledgements
I am grateful to my thesis supervisor, Prof. K. Gupta, for his constant support and encouragement during the course of this work. The interest shown by him with this research work had been a great inspiration for me.
I thank. Dr. S.P.Singh, for allowing me to use the Vibration Research Laboratory during the entire course of my research. In addition, I would like to thank Dr. S.P.Singh, Dr. A.K.Darpe and Dr. J.K.Dutt for the fruitful discussions about various topics in my tenure.
I would also like to thank the SRC members Prof. K. Athre (SRC chairman), Dr. S.P.Singh, and Prof. S.K.Gupta for their valuable comments that helped me to outline and improve the contents of the thesis.
I acknowledge the strong moral support of Prof K.Gupta, Dr. A.K.Darpe, and Dr. S.P.Singh for their good wishes and encouragement throughout the period.
I am indebted to thank Mr. K.N.Madhu of Vibration Research Laboratary for his constant help at many instances, which cannot be expressed in mere words. He has been a great support. I also thank Mr. Gamdur Singh and Mr. Ram Vilas Bhatt.
In addition, I thank my co-researchers, graduate and postgraduate students in the Vibration Research Laboratory for their affection and time, shared with me.
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I also would like to thank my friends, Ganesan, Hariharan, Karthikeyan, Balamurugan, Raj Kumar, Naveen, Manu and various others, without whom, I couldn't rejuvenate myself.
Special thanks are due to my parents, and the rest of my family for supporting me throughout the years. They are the people responsible for what I am.
I /
Aravindhan T S
Indian Institute of Technology Delhi, New Delhi, India
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Abstract
In the present work, application of two smart materials, namely shape memory alloy (SMA) and magnetorheological (MR) fluid for rotor vibration control is explored. First a single degree of freedom system is analysed to study the effect of SMA and MR fluid damper individually, and then the simulations are repeated to find the feasibility of using the two smart materials simultaneously. Three different types of excitations, i.e., harmonic base, forced and unbalance excitations are analysed. For SMA, switching time and switching rate analyses are carried out for different damping values and an optimum switching time and switching rate is established. It is observed that for an effective stiffness switching strategy, the damping in the system should be low. Application of MR damper alone for rotor vibration control at resonance and at frequencies above 1.4146)n is analysed. Effect of step change and a gradual change in MR fluid damper voltage which alters system damping, is studied. Further analysis on combined effect of two materials reveals that the combination of SMA and MR fluid damper is not effective.
Effectiveness of MR fluid damper for two degrees of freedom system representing a rigid rotor and supports under unbalance excitation is analysed.
Three cases are considered, when MR damper is parallel to bearing stiffness, parallel to the support stiffness, and when at both the locations. Simulations are also carried out for two degrees of freedom system accounting for shaft flexibility. The same three configurations as above are repeated. Theoretical
analysis establishes the effectiveness of MR fluid damper for two degree of freedom system.
A MR damper is designed and fabricated for the present study. Finite element analysis is carried out in ANSYS® to determine the current density required to generate a sufficiently strong magnetic field for the MR fluid. The fabricated MR damper is tested and an ANFIS model is trained to predict the damper force required for theoretical analysis. The experimental rotor model is analyzed using finite element method in Matlab. The ANFIS MR damper model trained is used in this simulation. MR fluid damper is placed at a distance of L/6 from bearing end.
The applied voltage across the MR damper is held constant for one simulation, as in experiments. Various voltages are applied to achieve required level of current in the MR damper coils.
Experimental results are obtained for three different current levels. The measurements are obtained by using a data acquisition program developed with the aid of LabVIEW®. Response of the system when coasting up and down the resonance region is acquired, and waterfall as well as envelope plots are obtained. MR damper is used only in the vertical direction with constant voltage applied to its coils. Experimental results show considerable reduction in peak vertical amplitude as the current in the MR damper is increased.
The present work establishes the feasibility of using multiple smart materials for rotor vibration control. However the analysis shows that SMA and the MR fluid damper do not provide an ideal combination. Theoretical analysis highlights the effectiveness of switching strategy approach for stiffness control using SMA as
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well as damping control using MR fluid damper. Effectiveness of an MR fluid damper is demonstrated on an experimental setup.
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Contents
Chapter 1 Introduction and Literature Survey 1
1.1 Introduction 1
1.2 Literature Survey 7
1.2.1 Balancing 9
1.2.2 Rotor Passive Control 12
1.2.3 Rotor Active Control 15
1.2.4 Semi-active Control 18
1.3 Scope and Objectives of the Present Work 22
1.4 Organization of Thesis 24
Chapter 2 Smart Materials 29
2.1 Introduction 29
2.2 Smart Structures 29
2.3 Smart Materials 30
2.3.1 Shape Memory Alloys 31
2.3.2 Constitutive MOdels of SMA 34
2.3.3 Engineering Application of SMA 36
2.3.4 Magnetorheological Fluids 38
2.3.5 Dynamic Models of MR damper 42
2.3.6 Engineering Applications of MR dampers 47
2.4 MR Damper Modeling 48
Chapter 3 Application to Single Degree of Freedom System 55
3.1 Introduction 55
3.2 Simulations Approach 55
3.3 Base Excitation 56
3.3.1 Instantaneous Switching 59
3.3.2 Gradual Switching 61
3.4 Forced Excitation 69
3.4.1 Instantaneous Switching 71
3.4.2 Gradual Switching 74
3.5 Unbalance Excitation 78
3.6 Magnetorheological Fluids 85
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3.7 MR with SMA 90
3.8 Conclusions 93
Chapter 4 Application to Two Degree of Freedom System 95
4.1 Introduction 95
4.2 Two Degree of Freedom 95
4.2.1 System Model 95
4.2.2 Simulation 96
4.2.3 Results and Discussions 98
4.2.4 Step Analysis 104
4.3 Two degree of freedom with shaft flexibility 107
4.3.1 System Modeling 107
4.3.2 Simulation 110
4.3.3 Results and Discussions 111
4.4 Conclusions 120
Chapter 5 MR Damper Design 123
5.1 MR Damper Basics 123
5.2 Types of MR Dampers 123
5.3 Magnetic Circuit Design 126
5.4 Magnetic Circuit Analysis 131
5.4.1 2D Axi-symmetric Model 131
5.5 MR Damper Fabrication 134
5.6 Theoretical Modeling 137
5.7 Modeling Outline 138
5.8 Conclusion 144
Chapter 6 Finite Element Analysis of Rotor System 147
6.1 Introduction 147
6.2 Model of the Rotor System 147
6.3 Numerical Analysis• 150
6.4 Magnetorheological Damper at L/6 151
6.5 Conclusion; 156
Chapter 7 Experimental Results 157
7.1 Experimental Setup 157
7.2 Measurement and Data acquisition 158
7.3 Experimental Results 160
7.4 Conclusions 170 Chapter 8 Conclusions and Future Work 171
8.1 Conclusions 171
8.2 Scope for Future Work 177
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