# Modal Verification and Strength Analysis of Bladed Rotors of Turbine in Rated Working Conditions
## 3 Results and Discussion
### Analysis of Centrifugal Force of TRT Rotor
#### 3.2.2 Centrifugal Force Analysis Results  
The stress intensity on the wingspan of the blade when the blade works at 3600 rpm is calculated in the analytic solution result. To explore the contact stress on the TRT moving blade further, the computer-aided analysis software is used for centrifugal force analysis. 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; the purpose is to know the contact stress intensity on the dovetail slot when the blade is pulled by centrifugal force in centrifugal action. When the shaft speed is 3600 rpm, the stress on the TRT rotor is shown in Figure 12.  
The average stresses on various sections of the 1 st stage and 2 nd stage moving blades in the simulation are extracted, and the simulation result is compared with the analytic solution. The two results have coincident trends and almost identical intensity, so the finite element model is reliable. The two stresses are compared in Figure 13.  
To estimate the difference between the stress results of the analytic solution and analysis, the errors in the two results are calculated, respectively. The mean error of the 1 st stage moving blade is 0.20%; the root mean squared error of the 1 st stage moving blade is 4.98%. The error mean of the 2 nd stage moving blade is 2.12%; the root mean squared  
Figure 12: Stress result of TRT rotor centrifugal force analysis.  
Figure 13: Comparison diagram of analytic solution and simulation of centrifugal stress on TRT blade.  
error of the 2 nd stage moving blade is 2.90%. The errors in the simulation and analytic solution are less than 5%, so the analysis result is reasonable.  
When the coincidence of the simulation calculation result and the analytic solution is confirmed, the maximum stress on the shaft is not in the wingspan of the blade, but in the first section dovetail slot of the blade. As shown in Figure 14, when the 1 st stage moving blade of the TRT rotor is extracted for discussion, it is found that the maximum stress of the 1 st stage moving blade occurs in the first section dovetail slot; the stress value is 259.21 MPa.  
As shown in Figure 15, the maximum stress occurs in the first section dovetail slot of the 2 nd stage blade. The maximum stress of the 2 nd stage moving blade is 286.21 MPa; it is the region of the TRT rotor bearing the maximum stress.  
According to the overall centrifugal force analysis result, the maximum stress occurs in the inner side of the dovetail slot of the 2 nd stage blade; the stress value is 286.21 MPa. The maximum stress is lower than the yield stress (735 MPa), so the structure will not have plastic deformation under the effect of centrifugal force.  
Figure 14: Stress result of centrifugal force analysis of the 1 st stage moving blade.  
Figure 15: Stress result of centrifugal force analysis of the 2 nd stage moving blade.