## 1 Introduction  
Under the trend of increasingly tight global connectivity, the environment and political landscape of Arctic waters have undergone complex changes with the developments in the 21 st century [1]. The Arctic has not only enormous economic value but also very important military value. For China, it holds an important geostrategic position. Currently, the Arctic has become a new channel for maritime trade, a new space for resource development, and a new battlefield for great power games [2]. A rudder device is of great significance for the maneuverability and vitality of underwater vehicles. Under the action of low Arctic temperatures and long-term alternating loads, the efficiency of the rudder decreases, and the underwater vehicle turns slowly [3]. The fatigue life of its rudder mechanism has been severely tested, and once a brittle fracture occurs, it will cause irreparable losses. Underwater vehicles in our country have experienced rudder stem breakage accidents, and the designed lifespan of such rudders is generally approximately 3000 h [4]. However, the fatigue problem of the rudder stem mechanism at low temperatures has not been given sufficient attention. Therefore, studying the fatigue performance of underwater vehicle rudder mechanisms at low polar temperatures is of great research significance and practical value. Fatigue damage is one of the main forms of mechanical structure failure. Fatigue damage occurs in a variety of equipment and is very common. If the equipment is damaged and not subject to timely maintenance and replacement, then this often causes unpredictable consequences, so fatigue issues have attracted wide attention. When a material or a structure is subjected to frequent alternating loads, even if the stress is lower than the yield limit, fatigue of the structure or damage could occur. Fatigue failure is the main form of failure for parts working under variable stress. When a component fails due to fatigue fracture, the variable stress it experiences is much smaller than the static stress value during static tensile fracture. The vast majority of machines or parts in mechanical operation work under alternating loads; thus, fatigue analysis of parts and component structures is essential, and fatigue analysis is related to the type of load, stress-strain characteristics, fatigue limit, fatigue _S-N_ curve, and other characteristics. The rudder of an underwater vehicle consists of an elevator and a rudder, and the rudder device is mainly arranged outside the pressure-resistant steering engineering room and pressure-resistant shell. An elevator is a device for underwater vehicles to maintain and change depth and is mainly divided into a front elevator and a tail elevator. The rudder blades of the first elevator are symmetrically arranged on both sides of the front or command room enclosure, with a smaller rudder surface and less rudder force. The rudder blades of the tail elevator are symmetrically arranged on the front (or rear) surface of the shaft propeller. The rudder blade surface is larger than that of the front rudder and is directly affected by the water flow of the propeller, generating a greater rudder force. It is the main elevator for underwater operation. The mechanical part of the rudder is used alone with the electrical control part of the steering subsystem or in conjunction with the tail elevator to maintain or change the depth and pitch attitude of the underwater vehicle [5]. Functionally speaking, the rudder is used to change or maintain the heading of underwater vehicles, while the elevator is mainly used to change or maintain the depth of underwater vehicles during navigation. The working principle is to change the attitude or state of underwater vehicles through the action of the rudder force and torque, thereby changing the force and achieving the goal of changing or maintaining the heading and depth [6]. Essentially, the control of the entire rudder device belongs to the position servo control system.