Full-field dynamic strain reconstruction of blade from limited displacement data

Blade vibration monitoring based on blade tip-timing (BTT) makes it possible to capture vibration parameters of rotor blades in a non-contact way. However, for high cycle fatigue (HCF) analysis and life evaluation of the blade, the measured displacement is far from adequate and should be transformed into the dynamic strain of some critical points to reflect the service condition of the blade. In this paper, a method based on the modal reduction and expansion for reconstructing full-field dynamic strain from blade-tip limited displacement data is proposed. Firstly, the displacement-strain response transmissibility matrix which establishes the mapping relation between the vibration displacement and strain, is derived using mode shapes of the blade. Secondly, the displacement signals of few blade-tip points are recorded by BTT. Thirdly, the full-field dynamic strain is expanded by combining the displacement-strain response transmissibility matrix with the limited displacement data. Finally, a simulated rotor blade subjected to impact excitation is used to demonstrate the merit of the proposed dynamic strain reconstruction approach. Numerical simulation results show that the proposed method can effectively reconstruct the full-field dynamic strain of blades from limited displacement data when the multi-mode vibration occurs. It should be noticed that not only the principal strain but also the shear strain of any points within the blade can be accurately reconstructed.