## 1 Introduction
However, whether the centroid distribution of the irregular tooth end milling cutter with an equal overall eccentricity is the same or not, as well as the influence of the centroid distribution of the irregular tooth end milling cutter on the tool vibration characteristics and dynamic performance are rarely mentioned by scholars and need to be studied further. Finite element analysis has been continuously developed and improved since the 1960s. It has attracted a great deal of attention from scholars because of its high degree of reduction and accurate calculations [17; 18; 19]. Modal analysis and harmonic response  
Figure 1: Optimization of helical flute of irregular tooth end milling cutter [15]. analysis are two commonly used and effective methods for investigation of the dynamic characteristics of tools [20]. Modal analysis aims to discretize the vibration problem of an elastic continuum into a multi-degree-of-freedom system with finite node displacements as a generalized coordinate system [21]. Harmonic response analysis is mainly based on the excitation of the external load, and then the response of the structure under the excitation is determined, which provides an important reference for the dynamic characteristic analysis and structural optimization of the structure [22]. The advantages of the finite element method in the process of tool research and development are as follows: (a) using finite element method to analyze and predict the natural frequency, vibration mode, and stiffness of cutting tools can reduce the number of tests on the finished products and effectively reduce the research and development cycle; (b) data information, which are inconvenient to collect from the actual machining process can be obtained by analyzing the dynamic characteristics of the cutting tool through simulations; (c) the finite element simulation makes data generation more intuitive, convenient, and accurate, and reduces the cost of research and development [23]. [PERSON] et al. [24] established cemented carbide tool models, with and without coatings, and performed finite element simulation analyses to conclude that cemented carbide tools with coatings can reduce the cutting force and cutting temperature. [PERSON] et al. [25] carried out modal analyses of a milling cutter and milling system components, and proposed generalized equations for predicting static and dynamic characteristics of milling system components. [PERSON] [26] conducted finite element modal analyses on an insert milling cutter, and concluded that the total deformation of the cutter was minimal when the axial front angle and radial front angle of the cutter are \(5^{\circ}\) and \(-5^{\circ}\), respectively, and the working frequency reached 10,012 HZ. [PERSON] et al. [27] analyzed the harmonic response of tools with different lengths using the finite element method, and found that the excitation of specific tool modes was the prerequisite for realizing the maximum efficiency of the vibration milling process. [PERSON] [28] used the finite element method to study the suppression effects of two different clamps on the deformation of TC4 thin-walled parts, and the conclusion proved that the total deformation of parts was reduced by 24.3% and the maximum principal stress was reduced by 61.5% using the clamping fixture. It can be seen that the use of the finite element method to explore the dynamic characteristics of irregular tooth end milling cutter is an effective research method. In summary, scholars have accomplished some research achievements on flutter suppression mechanism and the design criteria of irregular tooth end milling cutters, such as angle design optimization, milling force waveform, mass eccentricity, and so on. Through previous studies, it can be known that reducing mass eccentricity makes the centroid of the end milling cutter approach the infinitesimal, which can effectively solve the problem of the dynamic characteristics of irregular tooth end milling cutters being limited by their structure.