# Simulation of Surface Topography Considering Cut-in Impact and Tool Flank Wear
## 1 Introduction  
The operational performance of parts (fatigue performance, wear resistance, corrosion resistance) is controlled by surface integrity [1; 2]. The formation mechanism of machined surface topography is an important part of surface integrity research. Ball end milling cutter is widely used in the complex surface finishing of important parts in aerospace, die and automobile industry because of its strong adaptability. Due to the high surface quality requirements of these products, extensive research work has been carried out around this milling process [3; 4]. The cutting edges geometry of the ball-end milling cutter is complex, and the contact point between the cutting edges and the workpiece is constantly changing during milling. In addition, the dynamic characteristics of the milling process are complex [5]. It is difficult to study the surface quality of the machine by traditional experimental methods. Therefore, it is necessary to simulate the surface topography. [PERSON] et al. [6; 7] established a theoretical model for predicting the surface topography during milling. The effects of the shape of cutting edge, the tilting tool orientation, the tool eccentricity and the interference area of tool flank face on the surface topography were studied. However, the simulation results of surface topography considering the shape of cutting edge, the tilting tool orientation and the tool eccentricity were not verified by experiments. [PERSON] et al. [8] developed a simulation algorithm considering milling kinematics to determine the shape of the undeformed chip, cutting force, tool deformation and surface topography. The effects of different milling methods, the tiltingtool orientation, feed rate and radial cutting width on surface morphology were investigated. Based on the assumption that the envelope of the cutting edge of the ball-end milling cutter is approximated, a hemisphere when the spindle speed is much larger than the feed speed, [PERSON] et al. [9; 10] defined three types of ridges to represent the scallop-height of surface, and proposed a ridge model to predict the surface morphology and roughness. The surface morphology characteristics of one-way feeding and reciprocating feeding are studied. It was found that one-way feeding can obtain smaller surface roughness than reciprocating feeding. Based on a Z-map model, [PERSON] et al. [11] developed a comprehensive simulation system for predicting surface topography and roughness characteristics during finishing milling. The influence of tool eccentricity and wear on surface morphology and roughness was studied by modifying tool center movement and the shape of cutting edge. It was found that tool wear and tool eccentricity have little effect on surface morphology and roughness, but the prediction model of surface quality considering tool wear and tool eccentricity is closer to the experimental value. [PERSON] et al. [12] established a mathematical model for predicting the surface topography and roughness by constructing surface topography into a functional relationship between cutting parameters and tool geometry parameters. [PERSON] et al. [13] proposed an improved surface topography simulation algorithm based on a Z-map model. The effects of cutting feed rate, cutting width, the tilting tool orientation and tool runout on surface quality were studied. By solving the cycloidal equation of cutting edge and the feed plane equation, the intersection points of all feed planes and the cycloidal trajectory of cutting edge are determined. Then, the surface morphology of five-axis milling process is obtained by an intersection points matrix [14]. The effects of the tilting tool orientation, tool lead angle and tool eccentricity on surface morphology were studied. However, the proposed model had lower accuracy. [PERSON] et al. [15] established a five-axis milling surface topography analysis model considering positioning error, spindle error, machine tool geometry error and tool deformation.