# Simulation of Surface Topography Considering Cut-in Impact and Tool Flank Wear
## 1 Introduction
The above surface morphology model does not take into account the tool vibration with time-varying characteristics, and can not correlate it with the dynamic response of the milling process. Cutting vibration and tool wear have a significant influence on the surface quality in cutting process, which has attracted the wide attention of researchers. [PERSON] et al. [16] and [PERSON] et al. [17] used eddy current displacement sensors to obtain tool vibration displacement during milling. Then, the equation of cutting edges trajectory was modified based on the vibration displacement data, and the prediction model of surface topography considering tool vibration was established. [PERSON] et al. [18] used a laser displacement sensor to obtain tool vibration displacement in the cutting process, and established the milling morphology prediction model considering the tilting tool orientation and the tool vibration. Whether an eddy current displacement sensor or a laser displacement sensor, the accuracy of data acquisition is affected by spindle speed. Therefore, this method is not suitable for high-speed and ultra-high-speed machining. Based on the tool-tip trajectory equation, [PERSON] et al. [19] established a micro-ball-end milling morphology prediction model considering the tilting tool orientation, vibration, eccentricity and deformation. However, the vibration of the cutter in the axial direction was only considered in the surface topography model, while the vibration in the radial direction was ignored. Since the tool stiffness in the axial direction is much greater than that in the radial direction, the vibration amplitude in the radial direction is larger. If the radial vibration is neglected, the simulation precision of the surface morphology will be reduced. [PERSON] et al. [20] established a surface morphology prediction model for micro-milling considering kinematics, tool eccentricity and dynamic regeneration. [PERSON] et al. [21] established a surface morphology prediction model for micro-milling considering scale effect, multiple regenerative effect and tool deformation. [PERSON] et al. [22] investigated the influences of milling vibrations on the machined surface topography. [PERSON] et al. [23; 24] proposed a simulation model of surface topography in multi-axis ball-end milling considering tool wear. The effects of feed rate and the tilting tool orientation on surface topography were studied, but the effects of different tool wear on surface topography were not clearly revealed, which need to be further explored. [PERSON] et al. [25] established a mathematical model that can predict cutting force and surface morphology at the same time. The effects of tool eccentricity,tool deformation, system dynamics, flank wear and the tilting tool orientation on surface quality were studied. The simulation result was in good agreement with the experimental result, which verified the accuracy of the simulation mathematical model. Milling is a kind of interrupted cutting. Cutting impact vibration and cutting vibration caused by a nonlinear change of chip thickness exist in the process of cutting tool material removal. Meanwhile, tool wear will occur gradually on a flank face with the cutting progress. The morphological characteristics of machined surfaces are controlled by the dynamic characteristics of the cutting system and the tool flank wear of time variation. The influence of dynamic characteristics of cutting system and tool wear on surface morphology has not been taken into account in the morphology prediction model established in the existing literature. In the present study, the machined surface topography considering the dynamic characteristics of cutting system and tool flank wear is established. The research results have important guiding significance for the reasonable selection of processing parameters in actual production.