## 1 Introduction  
With the increasing complexity of product structures in industry fields, such as automobile, machine tools, and aerospace, the quality consistency and machining accuracy of key parts is constantly improving, and high-performance tool products are urgently needed to meet machining needs. End milling cutters have attracted the attention of scholars because of their good processing quality, processing efficiency, and economical efficiency [1, 2]. Their dynamic characteristic are the key factor affecting the quality of milling. The structure design of an end milling cutter, based on dynamic characteristics, is the key to improve machining quality and machining efficiency and reduce machining costs [3, 4, 5]. The conventional end milling cutter can easily cause vibrations and affect the machining quality and efficiency because the milling force waveforms of each cutter tooth are exactly the same [6]. In order to improve tool performance, [PERSON] [7] came up with the idea of a variable pitch end milling cutter in 1965. It was found that an irregular tooth end milling cutter can obviously reduce vibrations in the milling process. Since then, research on the structural design and dynamic characteristics of irregular tooth end milling cutter has been widely performed by scholars. [PERSON] [8] found that an end milling cutter with a variable helix could reduce workpiece deformation more effectively than the variable pitch end milling cutter. [PERSON] [9] put forward a new structural design method based on the optimization of a pitch angle distribution of an irregular tooth end milling cutter, and experiments showed that a reasonably designed irregular tooth end milling cutter can improve stability in the milling process. [PERSON] et al. [10] used the eigenvalue clustering method to analyze the stable and unstable boundaries, and this mathematical method could obtain a more reasonable pitch angle distribution and cutting parameters. [PERSON] et al. [11] used two algorithms to optimize the angle of a variable helix end milling cutter to suppress flutter. Through the above research, it was found that the milling stability of the irregular tooth end milling cutter is better than that of the ordinary end milling cutter, and the machining quality of the parts could be effectively improved by optimizing the structure design of the irregular tooth end milling cutter. However, the structure of the variable pitch angle and helix angle will lead to an uneven mass distribution of the irregular tooth end milling cutter, which will lead to its poor stability compared with some high-performance equal pitch and helix end milling cutters in high-speed milling [12]. Therefore, the eccentricity and centroid distribution caused by the asymmetric structure of the irregular tooth end milling cutter cannot be ignored [13; 14]. Our team put forward a helical flute design method for irregular tooth end milling cutters, based on dynamic balance accuracy, which aims at minimum eccentricity and eliminates the principle error of dynamic balance design caused by uneven distributions of cutter pitch, as shown in Figure 1[15]. The overall eccentricity of the end milling cutter approaches infinitesimal. According to the formula of unbalancing of rotating body and accuracy of dynamic balance:  
\[U=m\times e \tag{1}\]  
\[G=\frac{1}{3}\pi\cdot n\cdot e\cdot 10^{-4} \tag{2}\]  
where \(U\) is the unbalanced amount of the revolving body (kg\(\cdot\)mm); \(m\) is the mass of the revolving body (kg); \(e\) is the mass eccentricity of the rotor (mm); \(n\) is the rotation speed (rpm). \(G\) is the dynamic balance accuracy (mm/s) [16]. When the eccentricity approaches infinitesimal, a higher dynamic balance accuracy can be achieved and the cutting stability can be improved.