## 1 Introduction  
Aluminum-based composite material is a high-quality composite material composed of an aluminum metal matrix and a certain volume fraction of silicon carbide particles [1]. Various thermal expansion coefficients can be obtained by adjusting different volume fractions. This unique characteristic makes SiCp/Al widely used in many important technical fields such as aerospace, microelectronic packaging, and high-speed rail [2, 3]. There are many technical methods derived from the processing of composite materials. Among them, the elliptical vibration processing method attracts significant attention due to its high efficiency processing, easy heat dissipation, and low cutting force [4, 5]. The vibration of the elliptical vibration cutting in the horizontal and vertical directions causes the chip to have a velocity component in the vertical direction. At this time, the friction behavior of the tool-cutting interface becomes more complicated, thereby preventing the elliptical vibration processing technology from being widely used in precision composite processing [6, 7]. Friction and wear are the main behaviors of the tool-chip interface. The prediction of friction force is usually characterized by the cutting force model [1]. The cutting force reflects the cutting characteristics and determines the cutting state of the workpiece surface [8]. Many scholars have made efforts to establish accurate prediction models in composite material cutting. On the one hand, several important experimental techniquesare used to determine the normal and shear stress distribution on the rake face, in order to determine the existence of the shear force [9], such as the photoelastic tool [10], the force measurement of the separation tool plan [11; 12]. On the other hand, the research methods of cutting force are mainly divided into two categories: one is to establish a mathematical model and study the effect on cutting force by changing the model parameters, the other is to obtain the cutting force directly through cutting experiments and then change the experimental parameters and study the effect on cutting forces. [PERSON] et al. [13] performed mechanical analysis and modeling of two-body abrasive wear particles under multiple contact conditions, and predicted the critical wear value. [PERSON] et al. [14] used a four-group force and torque measuring instrument to achieve real-time measurement of cutting force. However, the cutting force is not modeled and analyzed. [PERSON] et al. [15] used an energy-based method to predict cutting forces. [PERSON] et al. [8] established a model to predict the cutting force of AMCM during machining, taking into account the \(G\) force and particle breakage caused by the presence of abrasive reinforcement in the three force component composites such as chip formation force and ploughing force. In the above model, the time-varying of friction coefficient and cutting force of abrasive-reinforced particles has not been considered. Chip-tool interface friction is governed by multiple friction components and determines the amount of machining force. Although great progress has been made in studying the friction characteristics between cutting tool-chip, there are still many unresolved problems. Most scholars only choose a single friction model for simulation and analysis, without analysis of every friction component systematically. However, the AMCM contains multiple friction groups, which will cause errors in the prediction results. This effect is more valuable in precision machining. To sum up, this paper proposes a new friction force prediction model based on three-phase friction theory and EVC intermittent cutting, which takes into account compound friction and single friction behavior that traditional models ignore. The friction model system analyzes the friction characteristics of the tool-chip interface under complex conditions. This paper establishes the tool-chip interface (TCI) cutting force prediction model of EVC cutting AMCM based on TPF theory.