Abstract
High-speed blades form core mechanical components in turbomachines. Research concerning online monitoring of operating states of such blades has drawn increased attention in recent years. To this end, various methods have been devised, of which, the blade tip-timing (BTT) technique is considered the most promising. However, the traditional BTT method is only suitable for constant-speed operations. But in practice, the rotational speed of turbomachine blades is constantly changing under the influence of external factors, which lead to unacceptable errors in measurement. To tackle this problem, a new BTT method based on multi-phases is proposed. A plurality of phases was arranged as evenly as possible on the rotating shaft to determine the rotation speed. Meanwhile, the corresponding virtual reference point was determined in accordance with the number of blades between consecutive phases. Based on these reference points, equations to measure displacement due to blade vibrations were deduced. Finally, mathematical modeling, numerical simulation and experimental tests were performed to verify the validity of the proposed method. Results demonstrate that the error in measurement induced when using the proposed method is less than 1.8 %, which is much lower compared to traditional methods utilized under variable-speed operation.
Correction to: An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems
