Research On Multl-Mode Coupled Vibration Of Wind Turbine Blades

The multi-mode coupled vibration of a wind turbine blade is systematically investigated in this dissertation. The emphasis of this work is put on the influence of the coupling (including extension-bending coupling, mode coupling among different modes of the same vibration, bending-torsion coupling, bending-bending coupling) on aeroelastic stability, dynamic characteristics, nonlinear dynamical behavior and stability of the blade.In Chapter 1, the background and significance of this work is illustrated. From the aspects of blade modeling, aeroelastic stability, dynamic characteristics, nonlinear dynamical behavior and stability, a review on the past researches and the main problem in these aspects is presented, and then a brief statement on the research plan of this dissertation is given.By comprehensively considering the effects of geometric nonlinearity, asymmetry of section, inclined installation of blade, eccentricity of mass center from shear center, offset between aerodynamic center and shear center, coning angle, pre-twist angle of blade section, structural damping, gravitational loading and aerodynamic loading, a set of nonlinear partial differential equations governing the coupled extension-flap-lead/lag-feather vibration is established based on the Hamiltonian principle in Chapter 2. The accuracy and usability of this model is verified by previous models. Finally, the solution of the governing equations is discussed.The aeroelastic stability of the blade subjected to the coupled, nonlinear vibration is investigated in Chapter 3. In order to describe the nonlinear effects on aeroelastic stability, the blade deformation is expressed as the superposition of static displacement and dynamic displacement. The nonlinear terms are linearized based on this separation and the aeroelastic problem is transformed to a complex modal problem. The assumed-modes method is intruded to solve the associated complex modal problem. The influence of design parameters on the static deformation of the blade and the effect of the flap-lead/lag coupling on aeroelastic stability are analyzed. Results show that the flap-lead/lag coupling can improve the aeroelastic instability of the blade through pitch angle. However, this coupling can cause instability when pitch angle is large.The dynamic characteristics of the coupled vibration of the blade subjected to unsteady aerodynamic forces are investigated in Chapter 4. The numerical variational method based on Green function is introduced to the research of the modal problem of blade vibration. The effects of coupling and balance weight on natural frequencies and mode shapes are emphasized. Results show that the flap-lead/lag coupling dramatically affects bending frequencies at high rotating speed. Flapwise and edgewise bending frequencies all increase with increasing rotating speed due to the centrifugal stiffening effect. The effects of the balance weight on frequencies and vibrating modes are tiny when it is placed near the blade root. The balance weight brings about marked changes of bending frequencies and vibrating modes when it is placed near the blade tip. Balance weights have little influence on the centrifugal stiffening effect.The nonlinear dynamical behavior and stability of the blade with coupled extension-flap vibration in super-harmonic resonance is researched in Chapter 5. The method of multiple scales is used to obtain the steady state, resonant response of the blade, and the stability of motion is judged from the eigen-values of the Jacobian matrix. Due to the influence of nonlinearity, the super-harmonic resonance peak can’t appear at σ=0. A method to estimate the functional dependence of the detuning parameter (corresponding to resonance peak) on designing parameters is introduced in this chapter, and then the variation of dynamic response and stability with designing parameters and aerodynamic effects is discussed. This method can be generalized in other resonance cases. Results show that the axial extension mainly generates the static deformation of the blade, so the influence of the axial extension on the flap motion is mainly on bending frequencies through the centrifugal stiffening effect. The influence of the flap motion on the dynamic displacement of the axial extension is very little even in super-harmonic resonance. By using a concrete computational model, the evolution of the resonance response with aerodynamic damping for different designing parameters is analyzed. Results show that the resonance response is harmonic (whose period is the same with excitation force) and stable when aerodynamic damping is large. Instable multi-period motion appears with decreasing aerodynamic damping. The resonance response will become quasi-harmonic with further decrease of damping.The coupled flap-lead/lag nonlinear vibration is investigated in Chapter 6. The 1:2 internal resonance that often appears at lower modes of flap and lead/lag motion is considered. By applying the Galerkin truncation to the nonlinear governing equations, the equations of dynamic displacements are obtained. The nonlinear principal mode transformation is used to decouple linear stiffness terms, and then a 2-degree-of-freedom generalized motion system with decoupled linear elastic restoring forces is derived. The method of multiple scales is employed to derive the steady state resonance response, and the effects of designing parameters, wind speed, geometric nonlinearity and aerodynamic nonlinearity on resonance response and stability are discussed. Results show that there exist trivial motion and mix-mode motion for the coupled nonlinear vibration of blade. In normal operating condition, the trivial motion is stable and mix-mode motion is unstable. There is a sub-critical bifurcation in blade motion with respect to wind speed. The mix-mode response disappears and the trivial response becomes unstable with increasing wind speed. This bifurcation can cause serious destroy for blade. Weakening nonlinearity can increasing the critical wind speed, this can improve the stability of blade.The influence of the coupling among higher and lower flapwise modes on nonlinear dynamical behavior and stability of the blade with both external and internal resonances is studied in Chapter 7. The external resonance is a primary resonance that appears at the first flapwise mode; it can cause severe damage to blade. The internal resonance happens at the first two flapwise modes; it can enhance the energy transfer between two modes, and change blade dynamics in primary resonance. The method of multiple scales is applied to derive the dynamic responses of the blade in combination resonance (CR) and pure primary resonance (PPR). The effect of the internal resonance (i.e. modal coupling) on external resonance is analyzed by comparing the results of CR and PPR. The influence of external excitation, damping and nonlinearity on two resonances and the influence of designing parameters including setting angle, coning angle, inflow ratio on resonance response and stability are discussed. Results show that internal resonance can suppress the vibration and instability that introduced by external resonance. Therefore, controlling external resonance behavior by using internal resonance mechanism is reasonable.Finally, the research content, research methods and research results of this work are summarized, and a brief plan for future studies is given.