# Vibration Damage Analysis of Bottom Hole Assembly Under Axial Impact Based on Dynamic Analysis
## 3 Results and Discussion  
### Effect of Different Impact Energies on BHA Vibration  
During percussive drilling, the torque and unidirectional axial impact are simultaneously applied at the bottom of the drill bit. The periodic impact load is fully converted into the initial drilling velocity of the bit acting on the rock. To analyze the vibration-induced damage of the drill string under impact drilling, numerical simulations are performed in which the rock elements, modeled using the D-P criterion, fail when the damage variable exceeds its maximum threshold during drilling. The impact parameters used in field operations are transformed into the bit's impact velocity based on the kinetic energy equation, and simulations are conducted to evaluate the percussive drilling process under different impact force levels.  
As shown in Figure 7, the rock fragmentation process after percussive drilling reveals that the damage of rock path elements varies periodically with the bit impacts. Due to the cyclic axial loading, the formation exhibits regular deep fracturing and damage patterns. When the bit contacts the rock, the cutting teeth penetrate the formation under the combined effect of weight on bit and the axial impact load. Subsequently, under the applied torque, the outermost rock layer begins to fracture, leading to a localized stress concentration. After the thin rock layer is broken, the bit rapidly retracts due to the drop in the impact load and then the bit repeats the rock-breaking process in the next impact cycle.  
As shown in Figure 8, the variation curve of the axial impact force on the drill string during a 10 Hz percussive drilling process indicates that when the periodic impact energy applied to the bit gradually increases, the axial stress in the drill string fluctuates intensely. The maximum axial stress reaches approximately 500 MPa. Under an impact force of 6 kN, the amplitude frequency of the drill string increases and the descent rate accelerates, indicating that increasing the impact energy significantly enhances the ROP. However, the axial vibration of the drill string also becomes more pronounced. This suggests that when the impact energy is excessively high and mismatched with the drilling parameters, the impact load acting on the bit decreases, while drill string vibrations intensely, leading to sudden peak stresses. Such conditions may adversely affect both the drilling efficiency and the service life of the drill string.  
Figure 9 shows the torque variation curve of the drill string under percussive drilling. During the 10 s simulation, the torque fluctuates within \(\pm\)30 kN\(\cdot\)m. Considering the enhanced ROP provided by the impactor, the drill string is subject to significant vibration disturbances. As the impact force increases, the torque on bit (TOB) also rises, indicating that a greater impact force leads to faster bit penetration. Consequently, the contact time and area between the bit and the formation increase, which raises the required torque and the energy consumed to overcome friction. This results in more severe torque fluctuations in the drill string, indicating that vibration and damage under percussive drilling are greater than those in conventional rotary drilling. Moreover, when the input impact force of the hydraulic impactor increases, both the amplitude and frequency of the drill string torque variations are intensified.  
Figure 8: Stress curve in all directions of the drill string: (**a**) axial stress; (**b**) radial stress (**x**); (**c**) radial stress (**y**).  
Figure 7: Rock breakage at the borehole base over time: (**a**) t = 0.764 s; (**b**) t = 1.153 s; (**c**) t = 3.234 s; and (**d**) t = 5.154 s.  
Figure 10 presents the energy consumption curves for conventional drilling and percussive drilling. It can be observed that increasing the impact force leads to greater energy consumption in the drill string system, with more pronounced fluctuations, further complicating the stress variations within the bottom hole assembly.