# Modal Verification and Strength Analysis of Bladed Rotors of Turbine in Rated Working Conditions
## 3 Results and Discussion
### Analysis of Aerodynamic Force of TRT Rotor  
In the aerodynamic analysis, the stress resulting from the centrifugal force of rotation and the aerodynamic force through the flow channel and the stress distribution positions when the TRT rotor is actuated will be discussed. To investigate the stress behavior of the TRT moving blade in working conditions resulting from the centrifugal force of rotation and the aerodynamic force of the driving system, the FEM is used for analyzing centrifugal and aerodynamic forces. To make the analysis condition match the actual situation, axial and radial constraints are applied to the bearing, and the rotational degree of freedom of the shaft is maintained. The contact pair is set between the blade and shaft in the dovetail slot aiming to determine the contact stress intensity on the dovetail slot when the blade receives a centrifugal force in centrifugal action. To analyze the maximum air pressure on the windward side of the moving blade when the TRT rotor system is in operational condition, the operating load parameter of the moving blade must be obtained at first. According to the data provided by steelworks, the generating power of the TRT system is correlated with the blast furnace inlet air pressure and the variable guide vanes opening. The result is shown in Figure 16.  
The CFD analysis result of the TRT flow field provided by steelworks shows the pressure on the 1 st stage and 2 nd stage moving blade faces, and the maximum pressure on the blade face is used as the loading condition of aerodynamic analysis. The TRT flow field analysis result is shown in Table 4.  
Figure 16: Operation conditions of inlet pressure, stationary blades’ opening, and power. When the aerodynamic force parameter of actuation is obtained, the maximum load when the TRT rotor blade is in operation condition can become known. However, when the TRT rotor is in operation, the moving blade cuts the flow fields of various flow channels, so when each blade bears aerodynamic force, it does not bear a constant external force but bears a periodic simple harmonic external force. The working condition of this system is a constant speed of 3600 rpm, so the periodic function of the aerodynamic force of the moving blade is cos (60 \(\times\) number of stationary blades). As the number of stationary blades is unequal to the number of moving blades, the aerodynamic force on the moving blade will have a phase difference. The law of phase difference repetition can be known by calculating the greatest common factor between the number of moving blades and the number of stationary blades. The phase difference of aerodynamic force between flow channels is calculated by Equations (7) and (8). The calculation results are shown in Figures 17 and  
According to the CFD analysis result of the TRT flow field provided by steelworks (Table 4), when the inlet pressure is 1.77 kg/cm\({}^{2}\) and the stationary blades' opening is 100%, the harshest working condition of the TRT moving blade is formed. Therefore, the  
Figure 18: The phase difference of the 2 nd stage moving blade. \begin{table}
\begin{tabular}{c c c c} \hline
**1 st Stage Moving** & **Phase Angle** & **2 nd Stage Moving** & **Phase Angle** \\
**Blade (\#)** & **(Degree)** & **Blade (\#)** & **(Degree)** \\ \hline
1 & 0 & 1 & 0 \\
2 & 6.67 & 2 & 0.71 \\
3 & 13.33 & 3 & 1.42 \\
4 & 0 & 4 & 2.13 \\
5 & 6.67 & 5 & 2.84 \\
6 &  
maximum pressure on the 1 st stage and 2 nd stage moving blades in this condition is set as the aerodynamic condition of the rotor blade. The air loads of two blades (amplitude of simple harmonic external force) are 1 st stage blade 0.21 MPa, 2 nd stage blade 0.16 MPa. When the amplitude of simple harmonic external force and the phase difference of aerodynamic force in various flow channels are obtained, the parameters are substituted in Equation (7) to obtain the function of simple harmonic external force on each moving blade.