# Deformation Characteristics of Mechanical Seal Face under Alternating Loads
## 1 Introduction  
As an important device in the propulsion systems of deep-sea submersibles, the mechanical seal plays a vital role in the stability, reliability, and safe operation of deep-sea submersibles. In extreme marine environments, the mechanical seal is susceptible to alternating loads whose magnitude and direction vary periodically with time. The periodic intermittent frictional contact problem of the seal face occurs under alternating loads, and a moving heat source is generated on the seal face, resulting in thermal shock. Repeated thermal shocks and the synergy effect of the locally varying contact pressure and friction force cause the failure of the mechanical seal due to the deformation and wear aggravation of the seal face. Therefore, it is necessary to research the deformation of the seal face to establish the coupling deformation characteristics under alternating loads and improve the sealing performance of the mechanical seal. In the field of fluid seals, many scholars have completed a great deal of work on the deformation of the mechanical seal. For example, [PERSON] et al. [1] studied the deformation of the seal ring based on the finite element method and found that the thermal deformation of the seal ring was larger than that of force deformation. [PERSON] et al. [2] focused on the time-varying effect of the deformation and contact pressure of the seal face during the start-stop stage of the mechanical seal. [PERSON] [3, 4] and [PERSON] et al. [5] investigated the influence of the deformation of the seal ring on the performance of the mechanical seal based on the thermal-elasto-hydrodynamic model. [PERSON] et al. [6, 7] established an axisymmetric model of the mechanical seal and presented that the seal face would appear to form a convergent gap based on the thermal-mechanical coupling effect. [PERSON]'s team [8, 9] established the thermal-structural coupling model of the mechanical seal using finiteelement software and studied the deformation characteristics of the seal face based on high-speed dry friction. [PERSON] et al. [10] investigated the coupling deformation of the deep-sea mechanical seal using the separation method, and [PERSON] et al. [11] used the integral coupling method to investigate the thermal-mechanical coupling characteristics of the mechanical seal ring. [PERSON] et al. [12] analyzed the coupling effect of the thermal deformation of the seal face of the mechanical seal based on the finite element method (FEM). Many researchers have contributed to the deformation characteristics of the mechanical seal face and successfully solved related problems using computational fluid dynamics (CFD). However, there are still some limitations due to the complexity of the problem and many simplified assumptions, and most research is performed in a steady state. There are few studies on the deformation of the mechanical seal face based on marine transient conditions, especially on the deformation characteristics of the seal face under alternating loads. Although some scholars have researched the thermal-mechanical coupling characteristics of the mechanical seal face under alternating loads [13], they did not consider the effect of thermal deformation. Later, some scholars focused on the thermal-mechanical coupling effect of the seal face [14]. However, the actual operation state of the mechanical seal under variable working conditions has not been considered, and research on mechanical seals under continuous alternating fluctuation conditions is still relatively scarce. The authors studied the temperature distribution of the mechanical seal face in the previous work and the temperature distribution presented the alternating transient characteristics under alternating loads [15].