A novel method for the determination of blade vibration stress considering the change in blade tip timing sensing position

Blade Tip Timing (BTT) technology is concerned with the estimation of turbomachinery blade stress. The stress is determined from BTT data by relating the measured tip displacement to the stress via Finite Element (FE) models based on the sensing position. However, the correlation of BTT data with FE predictions involves a number of uncertainties. One of the main ones is the effective positions detected by sensors may deviate from their nominal position due to the blade deformation, which will yield deceptive calibration factors. To deal with this problem, a novel method based on the amplitude ratio and virtual displacement optimization under the distance constraints of sensors installed in different axial positions is proposed to determine the accuracy calibration factors and sensing positions. It realizes the identification of sensing positions without the information of static deformation, and overcomes the inapplicability of the corrected displacement to bending modes. Both synchronous and asynchronous vibrations of five typical vibration modes are discussed to illustrate the applicability of this method. The results show that this method has better performance than traditional method. The prediction errors of bending modes are reduced from 20~30% to 7%, and the maximum error of other modes is reduced from 72% to 23%. In addition, sensitivity analysis is performed to investigate the influence of vibration levels and mode shape inaccuracies. Results demonstrate the great potential of this method in vibration stress determination.