## 1 Introduction
Under a certain ice condition and considering the effect of periodic ice milling loads of the propeller, hull vibration increased by 3-4 times. [PERSON] et al. [10] conducted an impact test between smaller chunks of ice and propeller, and measured the mixed load on the blades in an ice-water mixed environment by installing a six-degrees-of-freedom mechanical sensor at the connection between the hub and blade root. The test results showed that the highly dynamic forces during an impact can change rapidly in amplitude as well as direction. [PERSON] et al. [11] measured the changes in the ice milling load and mixed load during the milling process of an ice propeller in an ice tank; however, the test results mainly provided support for numerical calculations, and the difference in the influence of the ice milling load and mixed load was not discussed. [PERSON] et al. [12] performed an ice-water propeller milling test in an ice tank under the typical navigation mode and discussed the change in the propeller mixed load when the propeller was milling with a columnar layer and granular layer of ice. [PERSON] et al. [13] carried out a collision test between smaller chunks of ice and propeller by using multiple high-speed video acquisition devices and propeller hydrodynamic performance measuring devices. The results showed that there are different impact modes in ice-propeller collision such as single and multiple times, which have strong randomness and uncertainty and different effects on the hydrodynamic performance of a propeller. Unfrozen model ice is widely used in the ice-water-propeller coupling process owing to its stable mechanical properties, sturdiness, good repetition, etc. [PERSON] et al. [14] and [PERSON] et al. [15; 16] developed an ice-water propeller milling test using Styrofoam in a cavitation tunnel. The time domain and mean value curves of the mixed load on the propeller were presented. The results showed that propeller thrust decreased whereas torque increased during the ice-propeller milling process, which is the result of cavitation and ice-blade milling. Cavitation caused severe vibration, noise, and fatigue problems in the propeller and related equipment. [PERSON] et al. [17] conducted an ice-propeller contact test using model ice made of expanded polystyrene and paraffin; they measured the ice milling load of a propeller in air and verified the feasibility of the model ice to carry out an ice-propeller milling test. [PERSON] et al. [18] used phenolic foam panels as non-frozen model ice to measure the ice milling load and mixed load on the propeller under different propeller rotational speeds, ice pushing speeds, ice milling depths, and inflow velocities in water and air; however, they did not analyze the relationship between the ice milling load and mixed load. Next, we discuss some examples of theoretical research on ice-propeller milling. [PERSON] et al. [19] and [PERSON] et al. [11] predicted the mixed load acting on the propeller by using the panel method program PROPELLA in combination with the semi-empirical estimation formula for the ice force, which was verified experimentally. [PERSON] et al. [20] proposed a cohesive element method by using elastoplastic softening constitutive model based on the LS-DYNA software and predicted the ice milling load during the ice-propeller milling process. At the same time, the numerical simulation of the collision between smaller chunks of ice and blade was also carried out. The results showed that the ice loads were significantly affected by the five factors. Ice loads tended to increase by decreasing the rotational speed, increasing the initial ice speed and the contact area, and changing the rotational direction from clockwise to counterclockwise. [PERSON] et al. [21,22] and [PERSON] et al. [23] established a numerical model of ice-propeller milling based on the peridynamic method and continuous contact detection theory and predicted the ice milling load, the shielding effect, and blade pressure distribution of the propeller.