# Dynamic Behavior of Twin-Spool Rotor-Bearing System with Pedestal Looseness and Rub Impact
## 3 Analysis
### Dynamic Analysis of the System with Coupled Failure
A looseness failure occurs at bearing 1 (node 2) with a loosening gap of 0.5 mm, a loosening damping of 400 N \(\cdot\) s/m, and a loosening stiffness of 10 \(\times\) 10\({}^{7}\)\(\sim\)0.1 \(\times\) 10\({}^{7}\) N/m to simulate the evolution from no fault to a severe looseness failure, a rub impact gap of 1.6 mm and a rub impact stiffness of 6 \(\times\) 10\({}^{6}\) N/m to simulate the rub impact fault of the No. 4 LP compressor. The spectrum of each node with different loosening stiffness is shown in Figure 21 for the system affected by looseness failures and looseness-rub coupled failure and operated at a rotational speed of 1034 rad/s with a rotational speed ratio of \(-\)1.3. Figure 19: Shaft centerline orbit and spectrum of the LP compressor at 560 rad/s. (**a**) Shaft centerline orbit (loose failure). (**b**) Spectrum (loose failure). (**c**) Shaft centerline orbit (looseness–rub failure, the red line indicates the initial gap). (**d**) Spectrum (looseness–rub failure). Figure 20: Shaft centerline orbit and spectrum of the LP compressor at 1034 rad/s. (**a**) Shaft centerline orbit (loose failure). (**b**) Spectrum (loose failure). (**c**) Shaft centerline orbit (looseness-rub failure, the red line indicates the initial gap). (**d**) Spectrum (looseness-rub failure). Figure 21: Spectrum of the twin-spool rotor-bearing system affected by the looseness–rub failure at different loosening stiffness (rotating speed is 1034 rad/s). (**a**) Translational displacement at the fan (loose failure). (**b**) Translational displacement at the fan (looseness–rub failure). (**c**) Rotational displacement at the LP compressor (loose failure). (**d**) Rotational displacement at the LP compressor (looseness–rub failure). (**e**) Translational displacement at the HP compressor (loose failure). (**f**) Translational displacement at the HP compressor (looseness–rub failure). (**g**) Translational displacement at the HP turbine (loose failure). (**h**) Translational displacement at the HP turbine (looseness–rub failure). Figure 21a,b show the frequency spectrum of the fan during the effects of looseness failure and looseness-rub coupled faults, respectively. It can be seen from the figure that the main frequency of the fan vibration is \(f_{L}\) in the case of slight looseness failure, and as the loosening stiffness decreases, the frequency spectrum around 80 Hz has a high percentage of spurious waves, and there is a frequency component close to \(\frac{3}{2}f_{L}\); when the loosening is coupled with the rub impact, the rub impact leads to an increase in the low-frequency component around 80 Hz, and enhances the frequency component of \(\frac{3}{2}f_{L}\). The subharmonic vibration at the fan following a significant looseness failure is particularly noteworthy. In this case, the vibration is primarily characterized by the \(f_{b}\) component. The frequency spectrum of response at the LP compressor is similar to that at the fan, except that there is no subharmonic vibration at the LP compressor, and the \(f_{b}\) frequency component is relatively small. Figure 21c,d show the spectrum of the rotational displacement response of the LP compressor, respectively. Compared with the translational displacement, the vibration response of the rotational displacement is more susceptible to coupled faults, and as the degree of faults becomes higher, the \(f_{b}\) and \(\frac{3}{2}f_{L}\) components in the frequency spectrum increase rapidly and eventually exceed the \(f_{L}\) frequency component. The vibration response at the LP turbine is similar to that of the LP compressor. The frequency spectrum of the response at the HP compressor is shown in Figure 21e,f. The spectrum of the HP compressor contains both LP and HP rotor frequencies, \(f_{L}\) and \(f_{H}\), when there is no fault, and there are obvious \(2f_{L}\) and \(3f_{L}\) multiplier components in the spectrum just after the system has been loosened.