# Deformation Characteristics of Mechanical Seal Face under Alternating Loads
## 3 Results
### Alternating Working Conditions
#### 3.2.2 Alternating Rotational Speed  
The thermal-mechanical coupling deformation trend of the seal ring under alternating rotational speed is close to that under alternating medium pressure. The contact also occurs at the inner diameter of the seal face and a tapered gap appears at the outer diameter of the seal face. The coupling deformation of the end face of the rotating ring is also larger than that of the stationary ring. Figure 7 describes the axial displacement of the end face of the rotating ring along the radial direction under alternating rotational speeds with different amplitudes and periods. The coupling deformation trends of the end face of the rotating ring are all in a convex shape like that of the alternating medium pressure. With the increase in the amplitude of the alternating rotational speed, there is little change in coupling deformation at the inner diameter, but the axial displacement at the outer diameter increases gradually as  
Figure 6: The axial displacement of the end face of the rotating ring along the radial direction under alternating medium pressure with different amplitudes and periods: (**a**) Different amplitude \(M\); (**b**) Different period \(\Gamma\). shown in Figure 7a. The main reason is that the friction heat of the seal face increases with the increase in the amplitude of the alternating rotational speed, and the temperature difference between the inner and outer diameters of the seal face increases gradually. When the amplitude \(M\) is 0.1, the maximum axial displacement of the end face of the rotating ring \(\mid\Delta l\mid\) is about 0.865 \(\upmu\)m. If \(M\) is 0.5, the corresponding maximum axial displacement \(\mid\Delta l\mid\) is about 0.91 \(\upmu\)m. As the amplitude increases, the taper angle on the outer diameter of the end face is also increased due to the increased temperature difference between the inner and outer diameters of the seal face. Compared with the results of the alternating medium pressure, the maximum coupling deformation of the end face of the rotating ring under alternating rotational speed is larger based on the same amplitude. The effect of alternating rotational speed on the coupling deformation of the seal face is more significant than that of alternating medium pressure. In Figure 7b, although the coupling deformation trend of the end face for different periods is in a similar convex shape, there is no obvious difference in coupling deformation of the end face as the period of the alternating rotational speed increases, especially in coupling deformation at the inner diameter of the end face. Compared with the results of alternating medium pressure with different periods, the axial displacement at the outer diameter of the end face is slightly different. When the period \(\Gamma\) is 1.6 s, the maximum axial displacement of the end face \(\mid\Delta l\mid\) is about 0.85 \(\upmu\)m. If the \(\Gamma\) is 3.2 s, the maximum axial displacement \(\mid\Delta l\mid\) increases slightly by about 0.87 \(\upmu\)m. If the alternating period \(\Gamma\) continues to increase, there is no obvious difference in the maximum axial displacement of the end face due to the temperature distribution and contact state of the seal face reaching a steady state. According to the above-mentioned results, it can be concluded that the influence of the alternating amplitude on the coupling deformation of the seal face is more significant than that of the alternating period. When the working condition fluctuates alternately, the coupling deformation of the end face is larger than that in the stable working condition. The end face tends to be squeezed at the inner diameter side, and there is a tapered gap at the outer diameter of the seal face. Under alternating working conditions, the mechanical seal is in a state of high-frequency vibration, and the seal ring has a weak ability to resist and suppress alternating disturbance, which is prone to instability, especially for the instantaneous variation in rotational speed.