Non-contact full-field dynamic strain reconstruction of rotating blades under multi-mode vibration

Abstract

Dynamic strain measurements of rotating blades have attracted significant attention in the turbomachinery design, testing, and service stages. Measuring the blade full-field strain using traditional strain gauges (SGs) is difficult. Too many SGs may add damping to the measured blades, thereby lowering the peak strain that should have been experienced. The strain level was then underestimated for the blades without SGs. A non-contact displacement measurement technique, called blade tip timing (BTT), is promising for replacing SGs but requires effective displacement-to-strain transformation. The transformation under blade single-mode vibration has been studied in recent years. Although the multi-mode vibration of rotating blades is increasingly common, it is usually ignored. In contrast to single-mode vibration, when the blade is subjected to multi-mode vibration, the peak stress changes in both the temporal and spatial domains. This causes difficulties in predicting the blade stress limit and fatigue life. This study proposes a full-field dynamic strain reconstruction method for rotating blades under multi-mode vibration. Based on the BTT-measured displacement, the proposed method enables the full-field dynamic strain reconstruction of the blade in the time domain. First, the multi-mode displacement response of the rotating blades was measured using the BTT system. Second, a least-squares decoupling model for the multi-mode response was established. The blade tip displacement response was decoupled, and the multi-mode vibration parameters were identified, including the frequency, amplitude, and phase. Third, an analytical transform relationship between the tip displacement and full-field strain was derived based on the blade mode shapes. The blade full-field dynamic strain was reconstructed in the time domain using the decoupled displacement response and a displacement-to-strain transmissibility matrix. Finally, the full-field strain at different instants was visualised using a blade finite element model. The proposed method is validated on a rotor with five blades through both numerical simulations and spinning experiments. The reconstructed strain was compared with the result measured by the SG. The average strain relative errors of the five blades were within 7.1%. The peak stress is predicted, and the critical positions on the blade under multi-mode vibration are marked, which can provide valuable knowledge for blade fatigue life prediction and health monitoring.