# Modal Verification and Strength Analysis of Bladed Rotors of Turbine in Rated Working Conditions
## 1 Introduction
[11] used a vibration exciter to analyze the natural frequency of a cracked blade and found that when the blade has a crack, the natural frequency of the structure will change, and the position of the crack will change, and the blade vibration amplitude will also change. The longer the crack length, the greater the drop in the natural frequency of the structure. In addition to using vibration exciters for operating modal analysis of the blade structure, the EMA is also a common method to explore the dynamic characteristics of the structure. [PERSON] et al. [12] used experimental modal analysis to explore the dynamic characteristics of Kaplan Turbine blades, and compared them with the frequency results of the Theoretical Modal Analysis (TMA) based on FEM to improve the reliability of the finite element model. [PERSON] [13] used experimental modal analysis methods to explore the dynamic characteristics of large turbines. After knowing the dynamic behavior of the system, using the disturbance behavior of the jet airflow to the blades, the frequency that may be excited by the external force is established, and is helpful to the discussion of blade failure analysis. From previous studies, it can be known that the failure behavior of blades is mostly caused by initial defects. Under the external excitation of the structure, cracks are generated at the defects, and the cracks grow gradually. Therefore, understanding the structural dynamic characteristics of the blade is an important point that cannot be ignored in the rotor structure. The Campbell diagram is a method used to evaluate the dynamic characteristics of the axial flow turbine blade disc structure. The Campbell diagram can effectively determine whether the structure will resonate at the working speed. Toexplore the structural mode of the system resonance, [PERSON] et al. [14] proposed a Singh's Advanced Frequency Evaluation (SAFE) diagram, which integrates the structural modes and resonance frequency information to determine the structural modes that may be excited. [PERSON] et al. [15] used Campbell diagrams and SAFE diagrams to discuss the dynamic characteristics of the impeller. The results indicated that for the conditions under which the structural mode is excited, except for the same natural frequencies of the structure, the excitation phase of the external force needs to be consistent with the structural modes; otherwise, the structure will not resonate with the excitation. To monitor the moving blades of the turbine effectively, some rotor systems will be equipped with a Blade Tip Timing (BTT) system. The BTT technology can be used to measure the displacement of the tip of the rotor blade, and then analyze the dynamic characteristics of the rotor blade during operation. [PERSON] et al. [16] used the BTT system to monitor the blade dynamics and found abnormal blade vibration during the experiment. After shutting down the inspection, they found that the blade heel was cracked, which indicated that the BTT system was effective in monitoring the dynamic characteristics of the blade. In the past studies, more attention was paid to the dynamic characteristics of the blades, and the simplified equivalent blisk/blade model was used for discussion. In this paper, a more complete model verified by EMA is used to implement strength analysis of the bladed disks of the turbine in rated working conditions. We firstly performed EMA on the practical TRT rotor, and then used modal verification technology to verify and update the finite element model. The centrifugal force analysis is employed to explore the centrifugal force that the TRT rotor structure bears during operation, evaluate the strength of the structure, and verify the stress generated by the centrifugal force at the blade and the analytical solution. In addition to the dynamic characteristics of the blade itself, we also pay attention to the contact behavior at the dovetail groove of the blade.