###### Abstract  
Ultra-precision milling with an aerostatic high-speed spindle and a single-crystal diamond micro-tool is promising for the fabrication of miniaturized complex parts. While tool chatter occurring in milling processes has a substantial effect on the machined surface formation, a fundamental understanding of the tool chatter behavior in ultra-precision milling is essentially required for achieving an ultra-high surface finish. In this paper, through a combination of finite element simulations and experimental validations, the machining mechanisms of the ultra-precision diamond micro-milling of a copper workpiece are revealed, in which the tool chatter behavior and its correlation with the machined surface morphology are emphatically studied. Specifically, the correlation between the tool chatter and the transient depth of cut is analytical established. Subsequently, we first establish a finite element model of diamond micro-milling with the consideration of milling tool deformation and material removal to reveal the tool chatter behavior during the milling process. Furthermore, a corresponding micro-milling experiment is also conducted to validate the simulation results in terms of the milling force, chip profile and morphology of machined surfaces. Finally, the effect of spindle speed on the milling process in particular tool chatter is investigated by FE simulations, through which a linear relationship between the spindle speed and microscopic roughness Rz of a machined surface is obtained. The research findings provide a theoretical basis for understanding the origination of tool chatter in the diamond micro-milling process, as well as the rational selection of machining parameters for suppressing the tool chatter. ultra-precision micro-milling; diamond milling tool; tool chatter; finite element simulation 202212121968202212196820221212196820  
tool chatter inevitably exists in the micro-milling process [6]. A considerable amount of literature has documented that tool chatter has an important effect on the machined surface quality and tool wear in milling processes [7]. Large efforts have been made in the investigations of chatter stability prediction [8], chatter detection [9] and chatter suppression [10]. Although the kinematics of ultra-precision micro-milling are similar to conventional milling, the utilization of an aerostatic high-speed spindle and a diamond micro-tool leads to different tool chatter behavior and an associated correlation with the machined surface quality in the micro-milling process, which inhibits the promotion of the machining capability of the micro-milling. It is extremely difficult to explore the tool chatter in the micro-milling experimental process due to the significantly reduced machining feature size. Numerous studies have investigated the characteristics of tool chatter from an experimental perspective. [PERSON] et al. analyzed the fluctuation of the machined surface profile to determine the stability and severity of tool chatter during milling using a serrated end mill [11]. [PERSON] et al. showed through experimental studies that the variation in the acoustic emission signal has an excellent detection performance for the severity of tool chatter during milling [12]. [PERSON] et al. detected chatter frequencies by analyzing the accelerations of the milling tool shank in two vertical directions in the plane perpendicular to the spindle [13]. However, due to the characteristics of a high frequency and a small amplitude of tool chatter in ultra-precision milling, it is extremely difficult to directly monitor tool chatter in the milling experiments. In recent decades, considerable finite element (FE) simulations of milling processes have been conducted to provide important insights into the fundamentals of tool chatter in the micro-milling process. [PERSON] et al. analyzed the influence of tool holder coating modes on the tool chatter behavior of a single-point milling tool by FE simulation, which is capable of capturing the tool damping ratios [14].