## 3 Results and Discussions
### Tongue and Temperature  
Four examples of time histories of the torque, workpiece temperature, and the hole depth obtained are demonstrated in Figure 8, where two values of axial force (6 kgf and 12 kgf) were applied.  
Figure 8 shows that cutting torque and temperature increased along with the drilling depth. Higher torque and temperature appeared at greater depths of the hole. However, their growth rates in CD were substantially higher than those in UAD.  
It is clear that in the cases of CD (Figure 8a,c), just after the torque and then temperature jumped up, the drill bit became unable to penetrate the workpiece. This can be explained by the fact that, at this instant, chips started flocking in the flutes, resulting in increased friction along the hole wall. The drilling chips jammed the flutes, leading to increased pressure of the chips on flutes and hole walls. The increased friction caused a rise in the cutting torque and also caused a temperature increase. At high temperature and pressure, adhesion of the chips onto flute walls occurred, preventing evacuation of chips from the flutes. This could accelerate further chip packing as well as adhesion of the chips onto the cutting edges; thus, the tool would quickly lose its cutting ability, as mentioned in Section 3.1 and shown in Figure 6.  
Figure 7: (**a**) Material removal rate (MRR) and (**b**) MRR ratios at different axial force levels. A higher ratio means a higher MRR of UAD compared with that of CD.  
However, the phenomena above were not appeared in both cases of UAD as shown in Figure 8b,d. In these cases, ultrasonic addition would minimize the friction and thus help the chips exit through drill flutes easier; in some UAD tests, chips were in continuous form. This would be one of the most important benefits of UAD and needs to be further investigated.  
In order to have a quantity comparison, the maximum values of torque and workpiece temperature during drill progress were taken. Ratios of torque between CD tests and UAD tests at the same hole number were then calculated. Ratios of temperature were found in the same way. Figure 9 presents the torque and temperature ratios with respect to the drilled hole numbers.  
Figure 9 shows that almost all values of the investigated ratios were bigger than 1. This means that torque and temperature in CD were higher than those in UAD under the same drilling condition. There were some cases at the axial force of 9 kgf where both torque and temperature ratios were smaller than 1. For the investigated level of axial forces, the force of 9 kgf was the worst case, compared with the levels of 6 kgf and 12 kgf.  
As shown in Figure 9a, the torque induced in CD was 2 times (at 6 kgf, hole 5) to 6 times (at 6 kgf, hole 4) higher than that in UAD. Figure 9b indicates that using UAD can reduce the temperature up to 5 times compared with using CD (at hole 2). In addition, the effectiveness of UAD over CD has been found to be increased when drilling a greater number of holes. For example, under the axial force of 6 kgf, the temperature difference at hole 5 is 3.5 times whereas it is only 1.5 times when drilling the first hole. The results indicate the outstanding effectiveness of UAD for reducing torque as well as temperature when compared with CD in deep drilling.  
Figure 8: Time histories of cutting torque, temperature, and drilling depth with respect to time in CD (**a**,**c**) and UAD (**b**,**d**) with conditions of axial force of 6 kgf, hole 4 (**a**,**b**) and 12 kgf, hole 5 (**c**,**d**).