## 1 Introduction  
With global warming and the application of new technologies, the rich oil, gas, and mineral resources in the Arctic are expected to be developed, and new ocean transportation routes are expected to be opened. The unprecedented melting of Arctic ice provides new opportunities for shipping by decreasing the distance for commercial traffic between Asia and Europe by up to 40% [1]. The Arctic Channel will also become a convenient channel. It is its shipping value that determines the strategic military value of the Arctic. Seventy-three percent of the Arctic Ocean is covered by ice. The ice layer up to several meters thick can effectively prevent the penetration of electromagnetic waves. Even the most advanced satellites have difficulty tracking and monitoring submarines. The huge noise generated by the frequent breaking of sea ice can interfere with sound waves, thus damaging the tracking of underwater monitoring systems so that submarines can move freely under the ice without being detected. The efficiency of long-range backscatter radar for detecting submarines is greatly reduced due to the frequent interference of the ionosphere in polar regions. Therefore, the Arctic is the \"ideal hiding place\" for submarines [2]. The Arctic is foggy, the visibility is low, and the channel is winding and tortuous and changes with sea ice movement. When a submarine sails on the Arctic surface, it needs to change the course frequently to use the ice water channel and thin ice area. When sailing in an ice area, the submarine speed is low, the steering efficiency is reduced, and the submarine turns slowly [3]. Submarines mainly rely on the rudder stock mechanism located in the nonwatertight area between the pressure hull and the submarine shell for lifting. After the actual investigation of our research team, large pieces of ice floes are unable to enter the area where the rudder stock mechanism is located, while smaller ice floes have little effect on this structure. Unlike in pressure hull, the rudder stock mechanism will be directly exposed to extremely cold temperatures. Therefore, low temperature is the most important factor affecting the fatigue life of submarine rudder stock mechanism in the Arctic environment. Under the action of Arctic low temperatures and long-term alternating loads, the fatigue life of the submarine rudder stock mechanism is severely tested. The fatigue life of the rudder stock due to the ship roll motion under random sea waves was examined by [PERSON] et al., but temperature conditions lower than the normal operating temperature were not included in the calculation model [4]. [PERSON] et al. presented a comprehensive review of the current state-of-the-art high-cycle fatigue strength assessment methods for steel structures subjected to subzero temperatures and provided an overview of how to account for temperature effects on the fatigue strength when designing steel structures [5]. They also experimentally analyzed the effect of subzero temperatures on the fatigue strength of butt-welded normal and high strength steel structures [6]. [PERSON] et al. studied the low-temperature mechanical properties and low-temperature fatigue properties of polar icebreaker steel and concluded that the yield strength, tensile strength, and other static properties increase to varying degrees with decreasing temperature, the plasticity of the steel decreases, and the britteness increases [7]. In conclusion, research on the fatigue of polar ships mainly focuses on the fatigue of hull structures under ice loads and low temperature loads, while research on the low temperature fatigue of machinery outside the sealed cabin is scarce. In recent years, with the continuous development of computer technology and the wide application of finite element calculations, it is very common for scholars to combine fatigue analysis software (FE safe, nCode DesignLife, etc.,) with different fatigue design methods for fatigue analysis [8; 9; 10; 11; 12; 13].