## 1 Introduction  
During the cutting process of high-feed milling cutters, the friction and wear on the tooth flank shows a non-linear variation due to vibration and cutter tooth errors [1], which directly affects the milling cutter's service life and quality of the processed surface. Studying the instantaneous wear depth, instantaneous wear volume, and dynamic relationship between the friction energy consumption on the tooth flank [2; 3] and obtaining the property of the instantaneous wear distribution on the tool flank is of guiding significance to reveal the formation and evolution of the wear process on the tool flank of the high-feed milling cutter.  
Recently, in the study of wear on the tooth flank of the milling cutter, [PERSON] described the cutter's wear mechanism experimentally using SEM and EDS [4]; [PERSON] investigated the work of the cutter geometry angle, milling speed, and feed rate of the flank wear, respectively [5; 6; 7]. [PERSON] obtained a model of incremental wear of the tool flank of the tool under five factors based on orthogonal experiments [8]; [PERSON] constructed the wear curves of different types of cutters and predicted the wear states and validated them by experiments [9]; [PERSON] improved the precision of the tool's wear estimation by constructing a dual compensational strategy based on a multi-model support vector regression [10]; [PERSON] et al. analyzed and modeled the milling cutter's wear and proposed a milling cutter wear monitoring system, which has an online measurement of the milling force and milling temperature [11]; [PERSON] the cutting force model and a wavelet analysis to develop a multilayer perceptron to estimate the milling tool's wear [12]. The above research results are of great significance in guiding the construction of the instantaneous wear volume model of the tool flank of the milling cutter. However, it is crucial to deeply establish a study on the effect of tooth error and milling vibration on the friction and wear process on the tooth flank, which is ignored.  
The formation and evolution process of wear on the tool flank of high-efficiency milling cutters is closely related to instantaneous friction energy consumption at tool-workpiece interface. [PERSON] used a cutting energy prediction model to reveal the work of the milling speed, the thickness of non-formed chips, and the tool angle of the cutting energy consumption [13; 14; 15]. [PERSON] et al. established a novel milling power-based energy consumption model for milling cutters and investigated the correlation between the machine tool energy consumption and milling cutter friction wear [16]; [PERSON] et al. used the relationship between the wear of the tooth flank and average tangential milling force coefficient to estimate the energy consumption for tool wear [17]. Some scholars proposed a prediction method for the SEC of machine tools considering tool wear evolution and established a prediction model by a support vector regression algorithm [18]. [PERSON] effectively reduced the cutting energy consumption by improving the friction behavior between the cutter-workpiece interface [19]; [PERSON] developed a grinding force model considering tool wear and an energy consumption estimation model for tool tooth flank wear and used a time series analysis method to achieve the prediction of the flank wear [20].  
This paper developed a model for solving the instantaneous wear volume and instantaneous friction characteristic variables on the flank of the cutter based on the study of the instantaneous position and instantaneous cutter contact relationships under the milling vibration and cutter tooth error. A method to identify the instantaneous friction and wear energy density distribution property of the cutter flank was proposed. The instantaneous friction and wear process of the milling cutter was exposed. The experimental verification and analysis of the loss response characteristics of the friction and wear of the cutter flank were carried out.