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Analysis of linear bending vibrations of rotating composite wind turbine blade and its software simulation

Number of pages: 107 File Format: word File Code: 32603
Year: 2014 University Degree: Master's degree Category: Facilities - Mechanics
Tags/Keywords: Bending vibrations - Campbell diagram - Composite wind turbine - Frequency analysis - Limited components - Natural frequencies - Rotating wind turbine - Vibration analysis - Wind turbine blades
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  • Summary of Analysis of linear bending vibrations of rotating composite wind turbine blade and its software simulation

    Dissertation for M.Sc degree

    Mechanical Engineering Orientation - Applied Design

    Abstract

    Today's modern wind turbines tend to vibrate a lot due to their elastic, long and thin structure. Therefore, all components of wind turbines should be subjected to vibration and modal analysis in the design stages, and their natural frequencies should be reviewed with turbine excitation frequencies. The vibration study of wind turbines is located in several main fields, and the study of wind turbine blade vibrations as the main components of the turbine is a part of these fields.

    In this research, the frequency analysis of wind turbine blades is discussed using Abaqus finite element software and based on the two theories of Timoshenko beam and Euler-Bernoulli beam. The natural frequencies of the wind turbine blades are calculated in two states, non-rotating and rotating, for different metal and composite materials, and the sensitive areas are determined according to the Campbell diagram. The nature and behavior of the studied composite materials is isotropic and linear elastic. Also, in this research, the effect of various parameters such as layering of composite materials, blade shell thickness, hub radius and rotational speed on natural frequencies is investigated. Finally, the transient response of the system under a pressure shock is checked. To confirm the accuracy and correctness of the results obtained from the vibration analysis of the wind turbine blade in Abaqus software, the results of a rotating single beam are compared with the codes written in MATLAB software, which are derived from the finite element method.

    Key words: rotating wind turbine blade, finite element method, natural frequencies, diagram Campbell

    1-1 Preface

    With the increasing expansion of human societies and the development of different societies, the need for energy resources is increasing. On the other hand, the fossil resources in the world are running out, these resources are limited in terms of size and quantity, and they are also considered to pollute the environment. Therefore, in the past years, the tendency to use new and renewable sources of energy has increased, one of the cheapest and most accessible of which is wind energy. Examining the amount of use of this energy in recent years is a good indication of its importance and position in energy supply in the world.

    Currently, wind energy has had the highest growth rate among different energy sources with an average annual growth of more than 26% since 1990. However, the global potential of wind energy is still not fully exploited. Historically, the wind energy market has been mainly under the control of five countries: Germany, Spain, the United States of America, India and Denmark.

    However, in recent years, many developed and developing countries have sought to develop the use of wind energy, and several countries outside of Europe and the United States have already taken initial steps to develop large-scale commercial wind energy markets. Political goals for wind energy have been established in 45 countries, including 10 developing countries. In recent years, China alone has set its goal to produce 30 gigawatts of wind power by 2020, while the potential of using wind energy in this country and other countries is much higher than the figures mentioned. The following charts contain information on the development of wind turbines in the past years. 1-1-1 Vertical axis wind turbines Vertical axis wind turbines consist of two main parts: a main component that faces the wind and other vertical components that are placed perpendicular to the wind direction. These turbines include parts of various shapes that collect the wind and cause the rotation of the main axis. The construction of these turbines is very simple, but they have low efficiency. In this type of turbines, on one side of the turbine, the wind is absorbed more than on the other side and causes the system to find an anchor and rotate. One of the advantages of this system is that it does not depend on the wind direction.

    1-1-2 Horizontal axis wind turbines

    Horizontal axis wind turbines are more common than the vertical axis model and are also more complex and expensive in terms of technology. Their construction is more difficult than the vertical type, but they are very efficient. These types of turbines have the ability to produce electrical energy at low speeds and have the ability to adjust the direction of the wind.

    Horizontal axis wind turbines are divided into single-blade, two-blade, three-blade and multi-blade categories. As shown in Figure 1-4. Although single-bladed horizontal axis wind turbines have lower construction costs and lower raw material requirements; They are not used much. Because in order to balance the weight of a single blade wind turbine, these blades need a balance weight on the opposite side of the hub [1]. Also, these turbines need more wind speed to produce the same output power compared to three-bladed wind turbines. Two-bladed wind turbines have almost the same problems as single-bladed wind turbines and receive less energy than three-bladed wind turbines. Multibladed wind turbines are often used as water pumping mills and are not used to generate much electricity. Therefore, most of the current commercial wind turbines are three-bladed.

    (images and diagrams are available in the main file)

    Abstract

    The current modern wind turbines incline to vibration very much due to their elastic, long and thin structures. Therefore, all of the wind turbines' components must be analyzed from vibrational and modal aspects in all of the design's steps. Then their natural frequencies should be checked with the turbine's exciting frequencies. Vibrational investigation of the wind turbine is occurred in several main fields that the wind turbine blade's vibrational analysis is a part of these fields.

    In this study, the frequency analysis of wind turbine blade is performed by the finite element software Abaqus and based on the Euler-Bernoulli beam theory and Timoshenko beam theory. Then the frequencies of the wind turbine blade are computed in rotating and non-rotating states for different metal and composite materials and then the critical regions are determined due to the Campbell diagram. In this study, the properties and behavior of the composite materials are isotropic and linear elastic respectively. Furthermore, in this study the effects of different parameters such as the composite lamination, blade's thickness, hub's radius and rotating velocity on the natural frequencies are discussed. Eventually, the transient response of the system under pressure impulse is analyzed. In order to validate the results from the wind turbine blade's vibrational analysis in Abaqus, the results from a cantilever beam are compared with the codes that are written in Matlab software.

    Keywords: Rotating wind turbine blade; Finite element method; Natural Frequency; Campbell diagram.

  • Contents & References of Analysis of linear bending vibrations of rotating composite wind turbine blade and its software simulation

    List:

    Table of Contents .. viii

    List of Figures .. xi

    List of Tables .. xiv

    Symbols, Signs and Indices. xv

    Summary.. 1

    Chapter One: Introduction. 2

    1-1 Preface 2

    1-2 Types of advanced wind turbines. 4

    1-2-1 Vertical axis wind turbines. 4

    1-2-2 Wind turbines with horizontal axis. 5

    1-3 Wind power plants. 7

    1-4    Horizontal axis wind turbine power. 8

    1-5    Horizontal axis wind turbine components. 9

    1-6 Horizontal axis wind turbine blades. 11

    1-6-1 Airfoil of wind turbine blade. 12

    1-6-2      Forces on the airfoil. 13

    1-6-3       Wind turbine blade structure structure. 14

    1-6-4       Wind turbine blade internal structure. 15

    1-6-5 Wind turbine blade materials. 16

    1-7 Forces acting on a horizontal axis wind turbine. 18

    1-7-1       Aerodynamic forces. 18

    1-7-2       Gravitational forces. 19

    1-7-3 Centrifugal forces. 19

    1-7-4       Gyroscopic forces. 20

    1-7-5      Wind turbulence 20

    1-7-6       Wind profile changes 21

    1-8    An introduction to horizontal axis wind turbine vibrations. 22

    1-8-1      Excitation forces and vibrational degrees of freedom. 23

    1-8-2       Vibrations of thin wind turbine blades. 25

    1-9 Wind turbine blade dynamic card (Campbell chart) 27

    1-10 History of the works done in the field of wind turbine blade dynamic analysis. 28

    1-11 Current work and project objectives. 31

    1-11-1 Characteristics of the studied wind turbine. 32

    1-12 The content of the next chapters. 33

    Chapter Two: Governing theories. 34

    2-1 Formulation of bending vibrations of rotating beam lips. 35

    2-1-1 Changing the position of arrow points. 36

    2-2    Tymoshenko's beam theory. 37

    2-2-1 Shear correction factor. 40

    2-3 Calculation of kinetic and strain energies. 42

    2-4    Hamilton's principle. 44

    2-4-1 Virtual changes of kinetic energy. 44

    2-4-2 Virtual changes of strain energy. 45

    2-4-3       Virtual changes of potential energy caused by loads applied to the system. 45

    2-4-4       Differential equations of motion of the system for the state of lips. 47

    2-5 Discretization of the equations of motion. 48

    2-5-1      Calculation of the functions of the figure. 48

    2-6 Formulation of lip bending vibrations based on Euler-Bernoulli beam theory. 61

    2-7    Formulation of bending vibrations of swinging beam. 63

    2-7-1 Changing the position of arrow points. 63

    2-7-2 Calculation of kinetic and strain energies. 65

    2-7-3       Differential equations of motion of the system in bouncing mode. 67

    2-7-4 Discretization of motion equations. 68

    2-8 Formulation of bouncing bending vibrations based on Euler-Bernoulli beam theory. 72

    Chapter three: analysis of wind turbine blade vibrations with the help of software and extraction of modal parameters. 73

    3-1    Modeling method and software analysis. 74

    3-1-1 Finite element software method 74

    3-1-2 Abaqus finite element software. 75

    3-2 Assumptions used in using software 75

    3-3 Software analysis process. 76

    3-3-1       Wind turbine blade modeling. 76

    3-3-2 Definition of material properties. 76

    3-3-3 Determining the type of solution. 76

    3-3-4 Definition of boundary conditions and loading. 77

    3-3-5 Meshing or networking. 78

    3-4 Validation. 81

    3-5    Results of wind turbine blade software analysis. 86

    3-5-1 Frequency analysis of wind turbine blades. 86

    3-5-2 93

    3-5-4 Investigating the effect of layering of composite materials on natural frequencies 93

    3-5-5 Investigating the effect of rotational speed on natural frequencies. 97

    3-5-6 Investigating the effect of wind turbine blade thickness on natural frequencies. 98

    3-5-7 Investigating the effect of rotor hub radius on natural frequencies.99

    3-5-8       Checking the transient response of the system under a pressure shock. 100

    Chapter Four: Conclusions and Suggestions 103

    4-1 Conclusion. 103

    4-2    Proposals. 105

    Source:

    1- 

    ]1[ Seyed Habib Emami al-Arizi, "An analysis of the vibration behavior of the tower and the power transmission system of the 660 kW wind turbine based on modal analysis", Master's thesis, Department of Aerospace Engineering - Aeronautical Structures, Faculty of Mechanical and Aerospace Engineering, Malik Ashtar University of Technology, Isfahan, Isfahan 2013.

    ]2[Alireza Shushtri, Shiva Grossi, "Modeling and investigation of the effects of different geometrical parameters on the natural frequencies of wind turbine blades, the second annual clean energy conference", Kerman International Center for Advanced Science and Technology and Environmental Sciences, July 21-22, 2011.

    ]3[Mohammed Kankarani Farahani, Mona Ain al-Qadati, Abbas Bahri, Hamidreza Lari, "Frequency analysis of wind turbine rotors" 2 MW using the finite element method", 28th Tehran International Electricity Conference, November 13-15, 2013. 4. Peyman Hajheidari, "Vibration analysis of rotating beams with graded performance characteristics", master's thesis, Applied Design Mechanics, Faculty of Mechanics, Isfahan University of Technology, Isfahan 2013. 5. Mustafa Ghayor, Heshmat Elah Mohammad Khanlou, "Fundamentals of mechanical vibrations", Isfahan University of Technology Publishing Center, Isfahan University of Technology, 1382. [p>

    ]6 [S. S. Rao, translated by Bahram Pousti, "Mechanical Vibrations", Motafkaran Publications, Tehran, 2016.

    ]7[ M. Craig, translated by Alireza Inteziri, "Dynamics", Nofardazan Publishing House, Tehran 2017.

    ]8 [K. Kav. Avtar, translated by Amir Pashaei, "Mechanics of Composite Materials", Jihad University Press, Isfahan Branch, Isfahan 1389.

    ]9 [Mohammed Mahdi Darvishi, Yusuf Tarzjamshidi, Mohammad Salhi, Rabia Razmjoui, "Mechanical analysis using Abaqus software", Afrang Publishing House, Tehran 1391.

    ]10[Mohammed Farzin, Seyed Dibajian, Asghar Mahdian, Mohammad Hosseini Farid, "Getting to know and how to use ABAQUS software", Jihad University Press, Isfahan Industrial Unit, Isfahan 1391.

    [11] http://www.suna.org.ir/fa/home.

    [12] A. Namiranian, "3D Simulation of a 5 MW wind turbine", Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden. 2011.

    [13] K. Cox, A. Echtermeyer, "Structure design and analysis of a 10MW wind turbine blade", Journal of Energy Procedia 24 (2012) 194-201.

    [14] S. K. Chakrapani, "Investigation of ply wavainess in wind turbine blades: Experimental and numerical analysis", Iowa State University, Ames, Iowa 2011.

    [15] E. Hau, "Wind turbine, Fundamentals, Technologies, Application, Economics", Third translated edition, Munich, Germany, 2013.

    [16] M. E. Bechly and P. D. Clausen, "Structural design of a composite wind turbine blade using finite element analysis", Computers & Structural Vol. 63, No. 3, pp. 639-646, 1997. [17] K. Y. Maalawi, H. M. Negm, "Optimal frequency design of wind turbine blades", Journal of Wind Engineering and Industrial Aerodynamics 90 (2002) 961-986.

    [18] M. Jureczko, M. Pawlak, A. Mezyk, "Optimization of wind turbine blades", Journal of Materials Processing Technology 167 (2005) 463-471. [19] J.B. Gunda, A.P. Singh, P.S. Chabra, R. Ganguli, "Free vibration analysis of rotating tapered blades using Fourier-p super element", J. Structural Engineering and Mechanics, Vol. 27, No. 2 (2007). Zeng, "An experimental study of rotational effects on modal parameters of rotating wind turbine blades", Proceedings of the 8th International Conference on Structure Dynamics, EURODYN 2011.

    [22] Y. Li, L. Li, Q. Liu, H. Lv, "Dynamic characteristics of lag vibration of a wind turbine blade", Acta Mechanica Solida Sinica, Vol. 26, No. 6, December, 2013.

    [23] http://lagerwey.com/.

    [24] http://grabcad.com/.

Analysis of linear bending vibrations of rotating composite wind turbine blade and its software simulation
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