# Cutting Force Estimation Using Milling Spindle Vibration-Based Machine Learning
## 2 Relationship Between Tool Wear and Cutting Force
### Effect of Tool Wear on Cutting Force  
After completing the machining process, the tool wear of the end mill was measured. As shown in Figure 3a, all four cutting edges (flutes) exhibited wear exceeding 238 \(\upmu\)m. Additionally, as observed in Figure 3b, the worn region was concentrated within the lower 2 mm of the free surface of the workpiece. To analyze the effect of tool wear on the machined surface, the surface profile was captured, and surface roughness was measured for each layer. As shown in Figure 4, regular cusp formations were observed in the initial machining layers. However, from the 11 th layer, the cusps gradually disappeared from the upper part of the surface. By the 17 th layer, burr formation began at the upper surface, and the previously regular cusp patterns were entirely eliminated. The occurrence of burrs increased as machining progressed, and as tool wear intensified, the surface profile became more irregular and rougher. Additionally, the average surface roughness (Ra) was analyzed for each layer, as shown in Figure 5. Initially, significant variations in Ra values were observed between layers, but these fluctuations gradually diminished. This trend is attributed to the effect of replacing the workpiece every seventh layer, causing variations due to material and tool positioning changes. However, from the 17 th layer of the third workpiece, Ra values began increasing again, followed by a reduction in fluctuation. This indicates that as tool wear progresses, surface roughness stabilizes, which serves as an important indicator of the tool wear stage. Figure 4: Surface morphology changes on the workpiece side. Figure 3: Tool wear condition and surface quality characteristics of the end mill: (**a**) Post-machining tool wear condition; (**b**) Positions affecting surface quality on the end mill. The variation in the average value of cutting force per pass as the number of passes increases is shown in Figure 6. The average cutting force in the machining direction (\(F_{x\_avg}\)) decreased from 490 N to 270 N, while the average cutting force in the lateral direction (\(F_{y\_avg}\)) gradually increased from approximately 630 N to 875 N. These changes in \(F_{x\_avg}\) and \(F_{y\_avg}\) suggest a close relationship with the change in machining angle due to tool wear. As tool wear progresses, the angle between the tool edge and the material gradually shifts towards a more perpendicular orientation. Accordingly, the formation and disappearance of cusps, as well as the occurrence of burrs, seem to be directly influenced by the wear of the cutting edge and changes in the cutting geometry. As shown in Figure 7, the correlation between x-axis force (\(F_{x}\)) and y-axis force (\(F_{y}\)) for each pass was analyzed, revealing a decreasing trend in the correlation coefficient as the number of passes increases. Additionally, as seen in Figure 8, the variation in the correlation coefficient across passes shows a sharp decline during the first 400 passes, after which the correlation coefficient remains relatively stable. However, the correlation coefficient between \(F_{x}\) and \(F_{y}\) significantly decreases after the 17 th layer (486-516 passes), which coincides with the point of reduced machining performance. Figure 5: Variation in surface roughness (Ra). Figure 6: Cutting force by pass. These findings clearly demonstrate that as tool wear progresses, the cutting edge undergoes wear, leading to a reduction in machining performance, which provides critical information for predicting the point at which tool replacement is necessary. In industrial settings, it is standard practice to replace tools when defects such as burrs appear in the product. Therefore, by analyzing the correlation between \(F_{x}\) and \(F_{y}\) based on cutting forces,  
Figure 8: Correlation coefficient, similarity of \(F_{x\_arg}/F_{y\_avg}\), and its variation with machined surface changes. Figure 7: Correlation between \(F_{x}\) and \(F_{y}\) by pass.