# Vibration Damage Analysis of Bottom Hole Assembly Under Axial Impact Based on Dynamic Analysis
## 3 Results and Discussion
### Effect of Different Impact Frequencies  
Under actual operating conditions, the hydraulic impactor uses drilling fluid as the power medium. It converts high-pressure fluid energy and dynamic water hammer energy into continuous impact loads, functioning as a bottom hole dynamic tool. According to the impact frequency control equation, the impact frequency \(f\) increases with the flow rate. To simplify the simulation process, each impact is assumed to apply the same magnitude of force, while only the angular frequency (corresponding to the impact period) in the input load control table is varied. The rotary speed is uniformly set to 60 r/mi. As shown in Figure 11, the axial force response of the drill string under different impact frequencies is analyzed. Within the 10-30 Hz range, the axial force of the drill string exhibits a periodic vibration pattern characterized by alternating stress peaks and troughs over time. During each peak, the axial load increases as the bit is pressed into the formation; subsequently, the cutting teeth fracture and penetrate the rock, resulting in a smaller peak in axial force. The duration of each peak corresponds to the phase in which the rock debris is gradually detached. Therefore, a higher frequency of axial stress peaks corresponds to a faster rate of penetration. This also indicates that the axial impactor increases the frequency of alternating stresses acting on the drill string, potentially accelerating fatigue damage and shortening the service life.  
Figure 10: Total energy curve under percussion drilling.  
Figure 9: Drill string torque curve with time: (**a**) axial stress; (**b**) radial stress (x); (**c**) radial stress (y).  
Figure 12 shows the torque variation curves of the drill string under different impact frequencies. It can be observed that at 20 Hz, the drill string experiences larger torque fluctuation amplitudes, whereas at higher frequencies, the fluctuations are comparatively smaller. Higher peaks in axial torque result in intensified torsional vibrations in the drill string. The maximum observed torque reaches 164.2 kN-m, which increases the risk of drill string collisions with the wellbore wall. Moreover, excessive torque can negatively affect the fatigue life of the drill string. This indicates that if the input impact frequency does not match the actual drilling conditions, it may aggravate fatigue damage and stress variation in the BHA.  
As shown in Figure 13, under the same impact force, the vibration amplitude at the borehole bottom is relatively small at lower impact frequencies. As the impact frequency increases, the amplitude variation increases proportionally. In the high-frequency range, the vibration becomes more intense, with sharper changes in the amplitude curve. This demonstrates that higher-frequency impacts result in more severe vibrations and greater energy dissipation.  
Figure 11: Stress curves of drill strings under different impact frequencies: (**a**) axial stress; (**b**) equivalent stress.  
Figure 12: Torque curve of extracted drill string under different impact frequencies.