Study On Dynamic Characteristics Of Large Horizontal Axis Wind Turbine Blades

As one of the main components of the wind turbine,the blades bear the complex force and the main wind load.So it is very important to ensure its safe operation and good aerodynamic effect.In this study,the dynamic characteristics of wind turbine blades are studied.In this paper,the dynamic characteristics of wind turbine blades are studied,including free vibration characteristics,stability analysis and aerodynamic response of blades.(1)A differential equation of motion for bending vibration of a variable cross-section rotating cantilever beam in a rotating plane is established.By analyzing the geometric characteristics of the wind turbine blades,a model of variable cross-section(variable stiffnessvariable density)rotating cantilever beam is established to describe the dynamic behavior of the wind turbine blades.Based on Euler Bernoulli beam theory and distributed parameter system theory,one-dimensional distributed parameter system beam theory of variable axial force is established.Based on the theory of variable axial force beam and considering the gravity,aerodynamic force and inertia force of blades,the governing equations and boundary conditions of bending vibration of variable cross-section rotating beam im the rotating plane are established.(2)The vibration characteristics and stability of a rotating beam with constant cross-section are studied.By reducing the order of the model,the differential equation of the transverse vibration of a rotating beam with constant cross-section is obtained.The dimensionless governing equations of the transverse vibration of a rotating beam with constant cross-section are obtained.The assumed displacement solution of the governing equation is introduced to separate variables from the governing equations.The complex eigenvalue equation of the transverse vibration of a rotating beam with constant cross-section is obtained by discretization of the differential quadrature method.The complex eigenvalue equation is solved,and the curves of complex frequency with rotation speed,ratio of width to length,ratio of height to length,hub radius,modulus of elasticity and bulk density are obtained.The influence of various parameters on vibration characteristics and stability is analyzed,and the critical value and instability form of transverse vibration instability of constant cross-section rotating cantilever beam are determined.(3)The vibration characteristics and stability of wind turbine blades are studied.The linear variable cross-section assumption is introduced into the governing equation of the transverse vibration of the variable cross-section rotating beam,and the differential equation of the free vibration of the wind turbine blades in the rotating plane is obtained.The dimensionless governing equations of blades free vibration are obtained by introducing dimensionless parameters.The complex eigenvalue equation of the system is obtained by the of separating variables method and differential quadrature method.Based on the solution of complex eigenvalue equation,the effects of rotating speed,hub radius,variable density coefficient and variable stiffness coefficient on the vibration characteristics of rotating blades are obtained.The results show that with the increase of rotation speed,the system will enter into flutter instability state from stable state.If the radius of hub is reduced properly,the stability of blade will be enhanced.The critical instability velocity of NERL 5-MW wind turbine blade is obtained by using the physical parameters of the actual blade.(4)The dynamic characteristics of wind turbine blades under aerodynamic load are studied.Based on the theory of blade momentum,the aerodynamic loads on the blades of a wind turbine at constant wind speed are derived.Based on the assumption of linear variable cross-section and one-dimensional distributed parameter beam theory,the governing equations for transverse forced vibration of wind turbine blades are established.The governing equation of forced vibration is transformed into dimensionless form by introducing dimensionless quantity.Based on the method of undetermined function,the dimensionless special solution equation of forced vibration of blade is obtained.The differential quadrature method is used to separate variables from the dimensionless special solution equation,and the differential quadrature scheme of the special solution equation is obtained.The dimensionless aerodynamic response curve of wind turbine blade is obtained by using the numerical calculation software.Based on the differential quadrature method,the governing equation of the free vibration of the wind turbine blades are solved,and the first three dimensionless modes of the free vibration of the system are obtained.By combining the general displacement solution of free vibration with the special displacement solution of forced vibration,the three-dimensional surface figure of dimensionless aerodynamic displacement of wind turbine blades is obtained.The results show that the displacement response of the blades increases with the increase of the wind speed.