# Study on Influence of Multi-Parameter Variation of Bladed Disk System on Vibration Characteristics
## 4 The Influence of Detuning Parameters on Bladed Disk System Is Analyzed
### Analysis on the Influence of Structural Changes of Bladed Disk System  
#### 4.3.1 Modal Analysis of Disk and Bladed Disk System  
The 1 st, 3 rd, 4 th, and 6 th-order low-order modes of the disk and blade disk system were extracted respectively for comparison, as shown in Figure 10. Among them, the first and fourth order of the disk and bladed disk system have the phenomenon of stress root. As can be seen from Figure 10 disk and modal vibration mode of the bladed disk system have the same trend, in the figure, in turn, show the section line m = 1, radial expansion, the section line m = 2 corresponding to the vibration mode of the figure, the 6 th order modes are different. The 6 th order of the disk is the mode pattern diagram of the pitch line m = 3, the bladed disk system is the mode of disk static, blade vibration, and as mentioned earlier, the bladed disk system's 6 th order to 23 rd order for irregular blade vibration. As the number of nodes increases, the amplitude of vibration increases gradually, but the  
Figure 8: Modal frequency of bladed disk system under different working conditions. Figure 9: Modal frequency deviation of blade-disk system in different working conditions. amplitude of radial expansion is less than the amplitude of node m = 1. The mass of the bladed disk system is larger than that of the disk, which leads to the reduction of the modal frequency of the bladed disk system. The bladed disk system can be regarded as the result of an increase in the diameter of the disk on the basis of the original disk. With the increase of the diameter of the blade disk system, the amplitude of the corresponding vibration mode will increase compared with the amplitude of the original disk. As the diameter of the bladed disk system increases, the amplitude of the corresponding vibration mode will be higher than that of the original disk. After the 6 th stage of the disc, it continued to develop according to the trend that the number of nodal lines and nodal circles increased alternately. By contrast, the modal frequency was basically unchanged from the 6 th to the 23 rd stage of the bladed disc system. 3.2 The Influence of the Quality Change of Single Blade on the Modal Frequency of the Bladed Disk System  
For the disk system studied in this paper, the blade at the top of the plane was selected for the study. The counterweights with the same mass of 1.7 g were added to the upper, middle and lower positions of the blade keyway for modal analysis. Then, the upper end of  
Figure 10: Contrast between disk and bladed disk system vibration mode (**A**) 1 st low-order mode (**B**) 3 rd low-order mode (**C**) 4 th low-order mode (**D**) 6 th low-order mode. the blade keyway was fixed, adding 5.1 g of counterweight, and compared with the above working conditions. The typical modal modes of the above four working conditions and the initial state of the bladed disk system (without counterweight) were extracted, as shown in Figure 11. Each column, from top to bottom, was a single blade keyway without weight, a counterweight with 1.7 g at the top, middle and bottom, and a counterweight with 5.1 g at the top. It can be seen from Figure 9 that the frequency deviation of 6 th, 7 th and 8 th modes is large when mass changes, so the three modes are extracted for comparison. It can be concluded from Figure 11 that the modes of the 6 th, 7 th and 8 th order of the bladed disk system are all impeller static and blade vibration. At this point, the amplitude of blade vibration is much greater than the amplitude of the dominant vibration of the previous 5 th-order disk. The vibration amplitude of the counterweight added to the tip of the blade is larger, and the corresponding vibration frequency is slightly smaller. The larger the mass at the same position, the smaller the modal frequency and the larger the maximum amplitude. Figure 11: Mode vibration contrast of bladed disk system mass change (**A**) 6 th mode (**B**) 7 th mode (**C**) 8 th mode.