## 1 Introduction  
The axial flux permanent magnet motor (AFPMM) features a compact motor structure that differentiates it from conventional designs. In both industrial and everyday applications, motors serve as essential energy conversion devices, transforming electrical energy into mechanical energy and driving various types of equipment. With the rapid growth of modern industrial production, the demand for motors with higher performance is steadily increasing. Permanent magnet synchronous motors (PMSMs), known for their excellent dynamic response and high power density, have attracted significant attention in various fields both domestically and internationally [1]. Mechanical dogs, as an advanced robotic technology, require efficient, compact, and responsive power sources to support their complex movements and tasks. Axial flux motors have become an ideal power choice for mechanical dogs, enhancing their performance and making them more agile and efficient when executing tasks. To meet the stringent performance requirements of specialized applications, such as in aircraft, motors with optimized structures and superior performance are essential [2]. Among commercially available motors, radial flux motors are the most common. However, the axial flux motor introduced in this paper is designed to be compact, flat, and highly efficient in heat dissipation [3,4]. These characteristics make it particularly suitable for use in transportation [5, 6, 7], wind energy [8, 9, 10], and aviation. In the field of unmanned aerial vehicles, where installation space for motors is limited, the axial flux motor offers an effective solution. Additionally, its relatively simple control system reduces the complexity of development, enhancing its application potential. Permanent magnet motors, characterized by their high power density and efficiency, have become ideal actuators for applications such as electric vertical take-off and landing vehicles. In 1991, Japanese researchers applied the AFPMM to the wheel hubs of new energy vehicles to drive the car, creating a prototype vehicle capable of reaching a top speed of 311 km/h. In 1992, [PERSON] and [PERSON] developed a ring-wound motor, realizing the application of an AFPMM in wind power generation [11]. In 1998, researchers such as [PERSON] from Shanghai University simulated the magnetic field of a dual-stator axial flux permanent magnet generator using a three-dimensional scalar finite element method and conducted a preliminary design and analysis of the motor. In 2002, American researchers [PERSON] and [PERSON] developed a novel AFPMM with dual-side rotors, achieving relatively high air gap flux density [12]. In 2006, [PERSON] and [PERSON] from Beijing Jiaotong University, based on Maxwell's electromagnetic equations, used the method of separation of variables to analyze the distribution of the air gap magnetic field in axial flux permanent magnet brushless DC motors. In 2008, [PERSON], [PERSON], and other researchers analyzed the impact of variations in winding configurations on the performance of axial flux coreless motors [13]. In 2009, [PERSON] and [PERSON], based on the structure and operating principles of the flux-switching axial flux permanent magnet wind generator, developed a three-phase, 12/10-pole flux-switching axial flux permanent magnet wind generator, which was applied in a direct-drive variable-speed constant-frequency wind power generation system. In 2010, [PERSON] and [PERSON] analyzed the positioning torque of Axial Flux Flux-Switching Permanent Magnet (AFFSPM) motors rapidly by combining analytical and finite element methods, achieving an efficient reduction of the detent torque in these motors. In 2013, [PERSON] and [PERSON] from Pakistan applied numerical and analytical algorithms to axial motor research for the first time. Their work involved modeling an axial flux coreless generator for a direct-drive low-speed wind turbine, along with dynamic system simulations [14].