## 1 Introduction  
With the opening of the Arctic channel, especially the Arctic Northeast channel, and the development of Arctic resources, there has been increased global focus on icebreakers, ice-class ships, and other ice-going ships used to open the channel for polar navigation ships. The propulsion system of ice-going ships is their most important part and is, therefore, becoming increasingly researched. Compared with conventional regional navigation ships, the stern propeller of polar navigation ships is more prone to damage. The propeller is typically exposed on the outer side of the hull. When a ship sails in an icy area, it often causes broken ice to submerge and slide along the hull surface [1, 2]. The proximity of the propeller to the ice causes ice-propeller contact, which generates a strong ice load on the propeller surface. In order to remove ice traps when the ice-going ship are operating astern in the ice-breaking mode, the propeller needs to continuously mill sea ice at a high speed, which induces a large pulsating load on the blade surface. Under extreme conditions, the edge area and tip of the blade are deformed or damaged; consequently, the propeller's thrust is reduced and the maneuverability of the ship will be limited, which will pose a great threat to the normal navigation of ice-going ships. Therefore, research on the load and bearing force of the propeller in the ice-propeller milling process is of great significance. In recent years, researchers have carried out a series of theoretical and experimental studies on the ice-propeller milling process. [PERSON] et al. [3] and [PERSON] [4] examined the complex ice-water-propeller coupling process; the total load on the propeller during ice-propeller milling in water is called a mixed load, which has three components: ice milling load, separable hydrodynamic load, and inseparable hydrodynamic load. Among them, the ice milling load refers to the ice load on the propeller when only ice and propeller participate in the milling action. The ice-propeller milling test is mainly carried out in air without considering the influence of water. The separable hydrodynamic loads refer to the open-water hydrodynamic loads of the propeller. The inseparable hydrodynamic loads are the loads at which ice blockage, proximity effect, and cavitation influence the hydrodynamic performance of the propeller. The following are some examples of experimental research conducted in this field. [PERSON] et al. [5] introduced a laser sensor on a full-scale ship to measure mixed loads at different positions of the blade. [PERSON] et al. [6] and [PERSON] et al. [7] conducted ice-water propeller milling experiments in an ice tank. The effects of variations in the milling depth, pitch distribution, and advance coefficient on the mixed loads of highly skewed propellers were measured, and the destruction phenomenon of the blade during the milling process was observed. The results showed a positive linear relationship between the mean value of the mixed load and milling depth; the former increases first and then decreases with an increase in the advanced coefficient. [PERSON] et al. [8] carried out a milling experiment on an ice-water propeller in an ice tank and determined the variation law of the mixed load (time-domain curve, mean value, and extreme value) of the propeller and blade based on geometric parameters, advance coefficient, angle of attack, milling depth, and other important factors. [PERSON] et al. [9] performed a frozen ice-propeller milling experiment in air, analyzed the bearing force characteristics of the ice milling loads of the propeller, and compared it with the calculation of the theoretical model. The results showed that the estimated value of the periodic ice milling loads of the propeller could be used to analyze the fatigue strength of the propulsion system or to numerically estimate the vibration characteristics of ice-going ships.