# Vibration Damage Analysis of Bottom Hole Assembly Under Axial Impact Based on Dynamic Analysis
## 3 Results and Discussion
### Fatigue Life Analysis of Drill Strings  
#### 3.3.1 Equivalent Stress Analysis of Drill Strings  
During percussive drilling, the BHA is subjected not only to impact stresses caused by drill string-wellbore collisions, but also to axial vibrations and reverse torsional stresses generated during rock-breaking. These factors significantly increase the complexity of the mechanical loads acting on the BHA. To visualize the buckling behavior of the BHA during percussive drilling, the displacement of the drill string assembly and the formation reaction force under different impact energy levels are extracted, as shown in Figure 14.  
Figure 14: Combined displacement of the bottom drilling tool under different impact forces (2 times magnification factor): (**a**) conventional drilling; (**b**) 2 kN; (**c**) 6 kN; (**d**) 8 kN.  
Figure 13: Variation curve of bottom hole kinetic energy under different impact frequencies.  
As shown in Figure 15, under low impact forces, the bending of the drill string is not pronounced, with buckling primarily concentrated near the top of the drill rod. As the impact force increases, the curvature of the drill rod becomes more severe, causing a slight inclination at the bit. The main bending region remains concentrated along the drill rod, while the location of the maximum equivalent stress appears near the bottom hole assembly. This indicates that as the impact force increases, the more flexible parts of the drill string, such as the rods, tend to buckle first, initiating vibration in the BHA. Moreover, during the impact drilling of hard rock formations, the bit may experience bit bounce (jumping), but the vibration is gradually suppressed under stable drilling conditions. The extracted stress data will be used in the next chapter for the fatigue analysis of the drill string.  
The equivalent stress at the stress concentration points of the drill string assembly under different impact loads is extracted, as shown in Figure 16a. It can be observed that the equivalent stress in the drill string exhibits periodic variation, indicating that before each rock layer is fractured during percussive drilling, the equivalent stress gradually accumulates. As penetration progresses, this process is repeated. With the increasing impact load, the fluctuation trend becomes more pronounced. At an impact frequency of 100 Hz, the maximum stress experienced by the drill string significantly increases, with the peak equivalent stress reaching 109.5 MPa, representing a 55.3% increase compared to the condition at 40 Hz. This suggests that higher-frequency impacts result in an increased energy transfer to the drill string and intensified vibration.  
The post-processed axial stress variation curves under different impact loads are shown in Figure 16b. Compared with the influence of an increasing impact frequency, lower impact forces produce higher axial stress peaks in the drill string, suggesting that the impact load has a more direct effect than the frequency on stress levels. As the impact force  
Figure 16: Variation of equivalent stress in drill string under different control parameters: (**a**) impact frequency; (**b**) impact force.  
Figure 15: Analysis curves of formation reaction force and amplitude during drilling.  
increases, the trend of stress variation becomes more uniform, but the magnitude remains large. Under a 25 kN impact load, the maximum axial stress reaches 243.7 MPa, indicating a significant influence of the impact force on the fatigue life of the drill tool. At an impact load of 15 kN, regular fluctuations in stress peaks begin to emerge, implying that the drill bit gains sufficient kinetic energy at this level to penetrate the formation more effectively. In high-impact load operating ranges, the drill string's fatigue life is expected to decrease due to intensified cyclic stress amplitudes.