Effect of balance weight on dynamic characteristics of a rotating wind turbine blade

Abstract

Iron pellets are often added in blades to maintain moment balance in the design process of a wind turbine. The balance weight will change the natural vibration characteristics of the wind turbine blade. Resonant frequencies may appear for this reason, so it is necessary to study the effects of balance weight on the dynamic characteristics of a blade. In this paper, the wind turbine blade, after the weight balance process, is modeled as an Euler-Bernoulli beam with lumped masses. A mathematical model for a rotating nonuniform blade with a lumped mass on an arbitrary section is established, while nonlinear partial differential equations governing the coupled extensional-bending-bending vibration are obtained by applying the Hamiltonian principle. The associated modal problem is obtained from the governing equations, and then the differential form of the modal problem is transformed to integral form based on Green's functions (structural influence functions). A direct numerical approach is applied to calculate natural frequencies and vibrating modes. The effects of the mass and position of the balance weight and the rotating speed on the natural frequencies and mode shapes of the blade are discussed.

A method to select correcting faces of a double-face dynamic balancing rotor

“…In theory, any unbalance of rigid rotor can be corrected by two correcting faces, 13 and the correcting result can be taken as the linear superposition of the correcting effect from two correcting faces. The overall amplitudes of correcting vectors will be minimum when two correcting faces are respectively selected in their sensitive area.…”

“…ZX Dong et al 12 analyzed that the balancing plane positions had a great effect on pathological characteristics of influence coefficient and the interference of dynamic errors could be reduced by selecting locating parameter properly. In 2016, L Li et al 13 discussed the effects of the mass and position of the balancing weight and the rotating speed on the natural frequencies and mode shapes of the blade.…”

Dynamic Modeling and Response of a Rotating Cantilever Beam with a Concentrated Mass

“…where = ∫ 0 ( 2 / ) ( 2 / ) . From (14), the ordinary differential equations can be rewritten into matrix form as…”

“…Zhang et al [13] present experimental verifications of vibration suppression for a cantilever beam bond with a piezoelectric actuator by an adaptive controller. Li et al [14] discuss the effects of the mass and position of the balance weight added in blades on the natural frequencies and mode shapes of the blades. By using the dynamic stiffness matrix method, Banerjee [15] studies the free vibration of axially loaded composite Timoshenko beams and applies his method to composite wings and helicopter blades.…”

Experimental and numerical modal analysis of the first and second stage compressor blades

“…Thus, attaining reliable and accurate results from this method requires high-precision design and implementation of boundary conditions. So far, according to the importance of modal analyses of blades, several efforts have been made to evaluate the natural frequencies of blades (Bhat et al, 1996;Li et al, 2016;Marugabandhu & Griffin, 2003;Sinha & Turner, 2011;Wang et al, 2014;Yang et al, 2014). In this regard, Kim and Lee (2014) have studied modal characteristics and fatigue strength of compressor blades.…”