## 1 Introduction  
High energy efficiency milling cutters are widely used in the manufacturing of heavy machine tools and aircraft components. The energy consumption of the main cutting force of the cutter is an important indicator for revealing the cutting process of the milling cutter and evaluating the cutting energy efficiency of the milling cutter [1]. During the intermittent cutting process, the main cutting force of the milling cutter random changes under the effects of the vibration and impact between cutter and workpiece. The energy consumption of the main cutting force of the milling cutter thus changes dynamically, which would lead to difficulty in precisely predicting and controlling energy consumption in the cutting process [2]. The instantaneous multi-tooth cutting method of the high energy efficiency milling cutter determined that the main cutting force energy consumption of the milling cutter was composed of the instantaneous main cutting force energy consumption of each tooth participating in the cutting. The instantaneous energy consumption distribution of the main cutting force on the cutting edge of the cutter tooth was the key to revealing the dynamic characteristics of the energy consumption of the main cutting force of the high energy efficiency milling cutter [3]. The non-straight tooth structures, such as helical teeth commonly used in high-efficiency milling cutters, varies the instantaneous cutting speed vector direction of each point on the cutting edge [4]. At the same time, affected by milling vibration and tooth error, the main section of the milling cutter and the instantaneous cutting behavior of the cutter teeth are in an unstable state in the workpiece coordinate system space [5]. As a result, the instantaneous cutting contact relationship between the tool tooth and the workpiece is constantly changing, which causes the magnitude and direction of the instantaneous main cutting force at each point on the cutting edge of the cutter tooth to change continuously, rendering the instantaneous main cutting force relationship between the cutter teeth uncertain [6]. The energy consumption of the main cutting force of the milling cutter by multiplying the result of the composition cutting force of the tooth of the milling cutter or the main cutting force of the milling cutter obtained through experiments with the cutting speed of the milling cutter was calculated [7]. Based on the response of the maximum or average value of the energy consumption of the main cutting force to the cutting parameters, the factors affecting the energy consumption of the main cutting force of the milling cutter were identified [8]. The above method assumed that the instantaneous cutting behavior of each tooth of the milling cutter had the same change characteristics. It was impossible to reveal the instantaneous bias of the main section of the milling cutter and the changes of the instantaneous cutting speed vector and the instantaneous main cutting force vector at each point on the cutting edge, as well as its influence on the energy consumption of the cutter tooth and the instantaneous main cutting force of the milling cutter. Thus, it is necessary to conduct in-depth research. Establishing the correct cutter-workpiece engagement and cutting force model is the prerequisite for revealing the dynamic characteristics of the main cutting force energy consumption [9]. In recent years, [PERSON] [10] used the contact behavior of the cutter and a workpiece to predict the simulation model of the milling force, which was consistent with the experimental results of several combinations of the predicted cutting forces and the cutter postures and feed rates; [PERSON] [11,12] studied the changing law of cutting forces and established an empirical model of cutting forces on cutting parameters; [PERSON] [13] proposed a new cutting force prediction model based on non-uniform rational basis splines and finite element methods, and established a single-insert cutting force model using NURBS interpolation.