# Distribution and Prediction of Incremental Cutter Flank Wear in High-Efficiency Milling
## 4 Characterization of Distribution of Instantaneous Contact Stiffness  
The surface roughness varies continuously and is affected by material of cutter and workpiece, cutting vibration, and matching degree of cutter and workpiece during the cutting process. Meanwhile, with the increase in the cutting stroke, the coating on the milling cutter teeth will gradually fall off and wear the milling cutter, thus affecting the processing quality. The structure of the milling cutter and the structure of the cutter teeth will affect the construction of the equation for the flank of the cutting edge and the milling cutter teeth, thus affecting the construction of a contact stiffness model of the cutter-workpiece contact surface and then, in turn, affecting the calculation of the posture of the flank friction and wear area elements and the establishment of the structure for processing the transition surface. In order to illustrate the dynamic properties of the instantaneous processing of the state of friction and wear area element transition surface on the cutter flank under vibration, the design process of the distribution profile of the instantaneous stiffness on the flank is shown in Figure 4.  
In Figure 4, \(O\)-\(XYZ\) is the co-ordinate system of the workpiece; \(o_{v}\)-\(x_{v}y_{v}z_{v}\) is the structural co-ordinate system of the milling cutter, point \(o_{v}\) is the intersection of the milling cutter axis and the plane where the lowest point of the cutter teeth is located; axis \(x_{v}\) is in the plane where the lowest point of the tooltip is located and perpendicular to the \(y_{v}\) axis; axis \(y_{v}\) is in the plane where the lowest point of the tooltip is located and the point at which the tool tip has the maximum diameter; \(o_{v}\)-\(x_{v}^{\prime}y_{v}z_{v^{\prime}}\) is the structure co-ordinate system of the milling cutter under vibration; \(C_{1}\), \(C_{2}\), and \(C_{3}\) represent cutter tooth 1, cutter tooth 2, cutter tooth 3, respectively. \(\varphi\) is the instantaneous rotation angle of the cutter tooth; \(\varphi_{e}\) is the effective cutting angle of the cutter tooth, \(\varphi_{e}=90^{\circ};\theta_{c}\) is the included angle between two cutter teeth; \(N_{i}\) is an arbitrary point on the flank face without vibration; \(N_{i}^{\prime}\) is an arbitrary point on flank face of a cutter tooth when \(N_{i}\) is vibrating; \(l_{a}\) is the vibration displacement of \(N_{i}\); \(N_{i}^{\text{in}}\) is the co-ordinate point when an arbitrary point on the cutting edge cutting into the workpiece; \(N_{i}^{\text{in}}\) is the co-ordinate point where an arbitrary point on the cutting edge finishes effectively cutting; \(r_{Ni}\) is the gyration radius of an arbitrary point on the cutting edge. After using MATLAB (2021a) software to calculate the instantaneous contact stiffness, the Origin (2022b) software was used to draw the distribution state of the instantaneous contact stiffness of the flank. The distribution of the instantaneous contact stiffness on the flank over six cycles of the high-feed milling cutter cutting a workpiece is given in Figures 5-7. Six instantaneous moments with a milling cutter rotation angle of \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\) were selected to study the distribution properties of the instantaneous contact stiffness of the cutter flank at different times under different cycles. From Figures 5-7, it is observed that in the axial direction of the flank, the instantaneous contact stiffness is mainly concentrated near the cutting edge. With the increase in milling cutter rotation angle, the instantaneous contact stiffness area first increases and then decreases. Similarly, with the increase in milling cutter rotation angle, the instantaneous contact stiffness value also shows a trend of increasing first and then decreasing.