## 1 Introduction  
Nickel-based superalloys, with their good high-temperature strength, oxidation, and corrosion resistance, have become a material with significant development potential [1; 2; 3]. These alloys are widely used in aerospace, defense, nuclear power manufacturing, and petrochemical industries [4; 5; 6; 7]. However, GH4169 has poor cutting performance, mainly characterized by high strength, high plasticity, and severe work hardening, and it is one of the difficult-to-machine materials [8]. With the continuous improvement of the machining quality and accuracy requirements for precision mechanical parts in the machinery manufacturing industry [9], the machining morphology of workpieces has become increasingly complex. The standards for surface roughness, surface topography, cutting forces, cutting temperatures, and tool wear of workpieces also need to be improved [10]. The machining of GH4169 is mainly by cutting, in which the surface morphology is a crucial indicator for assessing the quality of the workpiece, which directly affects the performance of the part [11; 12]. Due to the unique physical properties of GH4169, conventional cutting methods (CC) can cause significant work-hardening phenomena. This not only leads to higher cutting forces and cutting temperatures but also shortens the service life of the tool and seriously reduces the surface quality of the workpiece [13]. These problems limit the broad application of GH4169 to a certain extent. Ultrasonic elliptical vibratory cutting (UEVC) technology demonstrates significant process advantages in these challenges,which effectively reduces cutting forces [14, 15] and cutting temperatures through its unique intermittent cutting method and reduces the deformation of the diamond tool during nano cutting, thus improving the surface quality of the workpieces [16], prolonging the tool life [17], and minimizing the machined surface defects. These technological advances not only enhance the machining stability and machining efficiency but also improve the overall quality of the product. High-quality machined surfaces are critical to the performance of mechanical parts. The ultrasonic elliptical vibratory cutting technique, initially proposed by [PERSON] [18] and [PERSON] [19], is an effective method for improving surface machining quality. [PERSON] et al. [20] utilized ultrasonic elliptical vibration for machining, compared the cutting performance with conventional cutting methods, and showed that ultrasonic elliptical vibration reduces the cutting forces and improves the surface quality irrespective of the material of the workpiece and tool. [PERSON] [21] and others measured and compared the roughness of ultrasonic and conventional machining and showed that ultrasonic vibration can effectively improve surface quality by as much as 25-50%. [PERSON] et al. [22], to enhance the machinability of Inconel 718, proposed the application of an ultrasonic elliptical vibratory cutting method on the base surface; the study concluded that on the surface of the workpiece of the conventional cutting, one would witness the presence of small particles, while the ultrasonic elliptical vibratory cutting machining of the surface of the particles is almost nonexistent. The surface quality is better than conventional cutting. [PERSON] [23] tested the cutting performance of nickel-based superalloys using an ultrasonic elliptical vibration device installed on a general machine tool. By comparing it with ordinary cutting technology, the study not only demonstrated the advantages of ultrasonic elliptical vibration cutting in improving the surface morphology of the workpiece but also analyzed the influence of the cutting parameters on the surface roughness. The results showed that ultrasonic elliptical vibratory cutting significantly improves the performance of nickel-based superalloys, machining surface quality, and machining efficiency. In addition, [PERSON] et al.