# Deformation Characteristics of Mechanical Seal Face under Alternating Loads
## 3 Results  
### Stable Working Conditions  
According to the mentioned geometric and numerical model, the steady-state analysis is performed first. Since the axial displacement of the seal ring has a great influence on the seal performance of the mechanical seal, the axial deformation characteristics of the seal ring under different working conditions are the main focus. Figure 2 presents the contour graph of the axial deformation of the seal ring under the default working parameters (working medium pressure \(p\) = 400 kPa, rotational speed \(n\) = 3600 rpm and \(p_{\text{sp}}\) = 200 kPa). From Figure 2, there are similar trends between thermal deformation and thermal-mechanical coupling deformation. Due to the temperature gradient distribution of the seal ring, mainly concentrated near the seal face, and because the temperature gradient along the axial direction is larger than that along the radial direction [15], the thermal deformation of the seal ring is also mainly concentrated near the seal face. The thermal deformation at the inner diameter of the seal face is greater than that at the outer diameter. This is because the friction heat is mainly concentrated on the inner diameter side of the seal face, and the convective heat transfer coefficient on the inner diameter side of the seal ring is relatively smaller than that on the outer diameter. Under the thermal-mechanical coupling effect, the inner diameter side of the seal face is extruded, while the outer diameter side is in a non-contact state and there is a divergent cone. Figure 2: Contour diagram of the axial deformation of the seal ring. In addition, since the thermal conductivity of the rotating ring is smaller than that of the stationary ring, the temperature gradients of the rotating ring are larger than that of the stationary ring. Thus, the thermal deformation of the whole rotating ring is larger than that of the stationary ring. Therefore, the thermal deformation can be diminished by adopting seal ring materials with larger thermal conductivity. In addition, the elastic modulus of the rotating ring is smaller than that of the stationary ring, so the thermal-mechanical coupling deformation of the whole rotating ring is also larger than that of the stationary ring. The axial displacement of the end face of the rotating ring along the radial direction under the default working parameters is presented in Figure 3. The dotted line describes the thermal deformation, and the solid line represents the thermal-mechanical coupling deformation. It can be intuitively seen that the maximum deformation of the end face of the rotating ring occurs at the outer diameter, while the minimum deformation occurs at different locations. Compared with the thermal deformation, the thermal-mechanical coupling deformation is in a convex shape, and the maximum displacement is about 0.538 \(\upmu\)m smaller than that of the thermal deformation at about 0.718 \(\upmu\)m. In Figure 3, the minimum deformation of the rotating ring is located near the middle diameter of the end face based on the thermal-mechanical coupling effect. However, the minimum thermal deformation occurs at the place that approaches the inner diameter of the end face. This indicates that the position near the middle diameter of the end face is prone to wear under the thermal-mechanical coupling effect, while the inner diameter region of the end face is prone to wear if the thermal effect is only considered. Furthermore, the deformation of the end face of the rotating ring is slightly reduced under the thermal-mechanical coupling effect. This is because the thermal deformation caused by the friction heat is dominant in the operation process of the seal ring, and the deformation caused by mechanical force is opposite to the trend of thermal deformation.