## 1 Introduction and Literature Review
The ISO 484 standard clearly defines the manufacturing tolerance grades for marine propellers and, thus, facilitates quality control with respect to geometric accuracy and consistency. Adhering to the standard ensures high overall reliability and performance in the manufacturing process. Regarding the efficiency of CNC machining, another study classified propeller blade surfaces into elliptical and hyperbolic regions on the basis of curvature characteristics. Machining deviations and efficiency were further analyzed using ball-end and flat-end milling tools. The method was demonstrated to effectively support tool selection and optimization of machining paths, thereby improving both the quality and productivity of complex blade surface machining [7]. The vibrational behavior of propellers during underwater operation exerts a notable effect on their service life and performance. To address this issue, [PERSON] et al. [8] proposeda noncontact vibration measurement technique based on a laser Doppler vibrometer. This technique enables the acquisition of accurate vibration responses under both fixed and tracking operation modes without interfering with blade motion. The scholars also compared the measured results with those generated from finite element simulations, and the findings confirmed the high accuracy and practical applicability of the technique in both air and water environments. The process of casting marine propellers often results in nonuniform deformation at the edges of the propeller blades. Conventional manual finishing methods are time-consuming and not conducive to consistent machining accuracy. To resolve this problem, [PERSON] and [PERSON] [9] proposed an innovative two-stage proximity machining approach. This method leverages the ability of cylindrical cutters to maintain line contact with curved surfaces, meaning that the entire surface of a propeller can be machined in a single-clamp setup. It is particularly suitable for propellers with large projected surface areas, greatly enhancing machining efficiency and surface quality. [PERSON] and [PERSON] [7] applied the first and second fundamental forms in combination with mathematical surface models to conduct in-depth geometric analyses of propeller surfaces. Their investigation into key geometric properties--including the normal curvature, principal curvature, and first and second principal directions--provides a crucial theoretical foundation for programming CNC machining paths in propeller manufacturing. [PERSON] et al. [10] developed a cost-effective precision caliper system designed for measuring the surface contours of outboard marine engine propeller blades. The system has a simple structural design and clear operating principles. Through practical testing and error verification, this system was demonstrated to have stable and accurate measurement capability. [PERSON] et al. [11] further developed an automated grinding system that integrates laser vision with robotic compensation technologies. This system utilizes feature-based point cloud modeling and compensation algorithms to automatically plan grinding paths and dynamically adjust blade edge thickness. The approach greatly enhances machining consistency and efficiency. Post-grinding results showed that the dimensional standard deviation was maintained within the range of 0.04-0.08 mm. Therefore, the system meets precision tolerance requirements and has strong applicability and automation potential. For high-speed underwater propulsion devices, cavitation not only causes structural damage but also substantially reduces propulsion efficiency. To address this issue, [PERSON] et al. [12] proposed an inverse design process that combines the constraint regions method, Kriging surrogate modeling, and the multiobjective particle swarm optimization algorithm. Their method has three optimization objectives: blade thrust, energy consumption, and the maximum size of cavitation cavities.