## 1 Introduction  
The milling cutter of a helical-edge has been widely used in high-speed and high-precision manufacturing, especially in side milling. The ever-changing interaction between the helical edge and workpiece causes the milling force to fluctuate rapidly and complexly, which has a great influence on machining quality and efficiency [1]. Therefore, the force fluctuation characteristics were studied and used as an indicator, such as tool wear [2], surface quality [3] and parameter monitoring [5]. In order to avoid the effect of force fluctuations in the high-speed and high-precision milling, a small cutting width or depth should be used, while feed speed and other processing parameters should be reduced [6; 7; 8]. However, this reduces productivity and limits the potential processing improvement. To this end, studying the force generation mechanism of a helical-edge cutter and revealing the force fluctuation behavior in high-speed and high-precision machining have great research value. Most of the studies on the milling force are based on the force prediction model proposed by [PERSON] [9; 10; 11]. The most representative theoretical modeling method is to apply the oblique cutting theory. The force of the milling cutter can be dispersed into a series of micro-elements along the axial direction, where each micro-element is considered as an oblique cutting process. Then, the milling force can be calculated by force superimposed on each micro-element. Accordingly, the study of milling force can be divided into two parts. The first one is the research on the supplement of a milling force model [12; 13; 14]. The related literature shows that many enhanced force models have been proposed and they have been mainly focused on improving the accuracy and the scope of the application [15; 16]. However, although the force fluctuation in the milling process is also a very important characteristic, the existing milling force models lack a good description of force fluctuation characteristics. This study supplements the force model description from the mentioned aspect. Another part is the study on the milling force model to reveal the influence of different parameters on force fluctuation characters. The parameters can be roughly divided into two categories: cutter parameters and processing parameters [17; 18]. [PERSON] [19] studied the influence of the mentioned parameters on the milling force, such as cutter geometrical parameters (helix angle and rake angle) and milling parameters (axial depth of cut, radial depth of cut, feed rate per tooth and cutting speed. The research results showed that the axial depth of cut, radial depth of cut and cutter helix angle were the main affecting factors of the engagement angle of the milling force. In addition, [PERSON], [PERSON] and [PERSON] [20] considered the influence of tool runout, minimum chip thickness, elastic recovery, ploughing area, entry and exit angles. [PERSON] [21] supplemented the study of the edge number parameter and the cutter diameter parameter and pointed out that an ideal force distribution should be as continuous as possible. The ideal selection of the cutter and processing parameters can not only reduce the surface error, but also make it possible to achieve a high finishing accuracy in semi-finishing. Although the previous studies have considered the effects of individual changes in each parameter on force characteristics, the mathematical relationship between various parameters and the intensity of milling force fluctuation, such as combined changes in the axial depth of cut, helix angle and tool radius, have still not been revealed and explained clearly. After years of research, scholars aimed to summarize the characteristics and rules of force fluctuations and tried to define a comprehensive theorem. [PERSON] [22] studied the relationship between the characteristics of the milling force curve, axial depth of cut, radial depth of cut and helix angle.