Performance evaluation of a lever-assisted optimized tuned mass damper inerter in mitigating edgewise vibration of wind turbine blade

Abstract

A Lever-assisted Tuned Mass Damper Inerter (LTMDI), comprising a lever mechanism with a fulcrum and a spanning inerter, coupled with a Tuned Mass Damper (TMD), is introduced to mitigate the edgewise vibration of wind turbine blades. The equations of motion for the coupled blade-LTMDI-tower system are derived using the Euler–Lagrangian approach. The turbulent aerodynamic loads on the blade are calculated using the modified Blade Element Momentum theory. Closed-form expressions for optimal tuning frequency and damping ratio of LTMDI are derived from a simplified 2-DOF blade-LTMDI model using the classical fixed-point theory. These expressions also verify the corresponding formulas for blade with TMDI and TMD reported in the existing literature. Numerical studies are conducted using the National Renewable Energy Laboratory (NREL) 5-MW horizontal axis wind turbine. A comprehensive analysis in both time and frequency domains is performed to evaluate the control effectiveness of LTMDI for both the 2-DOF and full wind turbine models, with results compared to those obtained using TMDI and TMD. Results reveal that TMD is the most effective at reducing blade response, while TMDI excels in minimizing the stroke length of the mass block, and LTMDI performs between these two extremes. To systematically compare the overall performance of these devices, a normalized performance index is proposed, which incorporates peak, RMS, and peak-to-peak displacements of both blade tip and mass block. It is observed that LTMDI effectively serves as a trade-off between TMD and TMDI, providing a consistent and uniform performance regardless of whether the focus is on reducing blade response or minimizing the stroke length of the mass block. Therefore, LTMDI emerges as the optimal choice, offering a comprehensive solution that effectively addresses both blade and mass block responses, and demonstrating significant potential for application in wind turbine blades.