# Influence of Rake Angles of Multi-Position Tool on Cutting Characteristics
## 3 Discussion  
### The Impact of Different Cutting Depths on Cutting Characteristics  
Different tool rake angles in cutting characteristics can obviously affect the cutting force. When the cutting rake angle and cutting depth is too big, the cutting force also increases relatively, as shown in Figure 7a-c. The main reason for this is that when the rake angle is big, the contact area of the flank is increased, which causes an increase of the cutting force. In this experiment, the direction of the X axis is the feed-rate cutting direction, thereby the cutting force in the direction of the X axis is  
Figure 6: (**a**) Experiment equipment and method of measurement; (**b**) Experiment flow chart.  
big. With different cutting depths, the bigger the cutting depth is, the smaller the stress the Z axis is, which is mainly affected by the size effect. Therefore, the tangential shear effect and the tangential plough effect will be discussed.  
Generally, \(K_{\text{fs}}\) is the tangential shear constant, and its unit is MPa or N/mm\({}^{2}\). In the physical sense, it means the energy consumption when removing work-piece material per unit volume, in the unit of (J/mm\({}^{3}\)). It can be divided into shear effect and plough effect in general cutting. In shear effect, \(K_{\text{fs}}\) is the cutting constant of tangential shear force, which can stand for the tangential cutting power of removing the non-deformable chip sectional area per unit, or the power of removing material per unit volume. This includes the chip deformation energy of the main shear area and the energy consumption caused by abrasion of the second shear area and tool rake angle. This parameter can be  
Figure 7: **(a)** The impact of different cutting depths of 0.1 mm on the cutting force; (b) The impact of different cutting depths of 0.2 mm on the cutting force; (c) The impact of different cutting depths of 0.3 mm on the cutting force.  
used to estimate the difficulty level of removing the material. In the plough effect, \(K_{ts}\) is the cutting constant of the ploughing force, which can stand for the abrasion of the contact width between the unit tool and work-piece and the plough effect. Therefore, the cutting constant of the tangential plough force has much to do with the abrasion of the flank.  
The cutting force constant will be increased as the cutting depth becomes smaller. This is mainly because of the size effect during cutting processing. [PERSON] [14] illustrates this with the dislocation theory, as a big shear force must be given to the cutting material with a small shear area to cause plastic deformation. Figure 8 shows that the smaller the feed per tooth \(tc\) is, the bigger the tangential shear cutting constant \(K_{ts}\) is. As shown in Figure 8, the smaller the cutting chip thickness is, the bigger the driving force that is needed in processing [15]. Correspondingly, the shear cutting constant is bigger, and the average cutting force is also obviously improved. The precipitation of material by hardening, and the size effect are main reasons for this [16; 17; 18; 19; 20; 21; 22].  
The ploughing force mainly shows the relationship between the contact length of the flank and the work-piece [8], as shown in Figure 9. When the cutting rake angle is increased, the contact length of the flank and the work-piece is also increased, which causes the increase of the ploughing force. Thereby, the cutting rake angle increases relative to increases in the cutting force, which is mainly because the increase in the contact length of the flank and work-piece causes the increase of the tangential plough constant. Therefore, the tool clearance angle will be increased relatively when the cutting rake angle increases.