# Vibration Damage Analysis of Bottom Hole Assembly Under Axial Impact Based on Dynamic Analysis
## 3 Results and Discussion
### Fatigue Life Analysis of Drill Strings
#### 3.3.2 BHA Fatigue Life Analysis  
Based on the fatigue analysis module, a study was conducted on the fatigue damage of the BHA under impact-induced vibration. The equivalent stress amplitude and loading frequency obtained from previous simulations were used as input conditions for the fatigue analysis. A coupled finite element model of the system was established. Using the Static Structural module in the ANSYS Workbench, the stress, deformation, and other responses of the system under impact loading were computed, enabling a vibration fatigue life prediction of the drill string assembly. Combining the results from the dynamic response analysis, the critical stress points on the BHA were extracted. Based on the material S-N curve, a vibration fatigue life analysis of the drill string assembly was carried out. The impact load was applied at the reference sub-location in the form of a sinusoidal amplitude-time curve, defined as Step 1. The equivalent stress at the critical point was then applied as a cyclic load on the outer surface of the drill string, with the far-end cross-section set with elastic boundary conditions to simulate drill string connections. The formation reaction force was applied at the bottom surface of the bit, defined as Step 2. The resulting fatigue life distribution of the critical section is shown in Figure 17.  
The cyclic fatigue life curve of the drill string assembly under different impact forces is plotted in Figure 18. By comparing the minimum fatigue life of various components in the system, it is observed that the lower section of the drill string reaches the fatigue limit first and is most prone to fatigue failure under cyclic percussive vibrations. The minimum fatigue life of the drill string is approximately \(6.472\times 10^{4}\) cycles and there is nearly a fivefold difference in life between the lower drill pipe and the drill collar. Fatigue damage is mainly concentrated in the upper threads and the connection between the drill pipe and the bit. Therefore, special attention must be given to monitoring and reinforcing the structural integrity of these connection zones to prevent premature failure.  
Figure 17: Contour of fatigue life of drilling tool combination.  
Figure 19 illustrates the available cyclic fatigue life contour map of the BHA under typical impact forces and impact frequencies of axial impactors, reflecting actual field operating conditions. Based on the relationship among the impact energy, impact frequency, and drill string fatigue life, two envelope regions can be identified at both low and high frequencies. The fatigue life of the drill string generally decreases with the increasing impact frequency. After 30 Hz, the slope of the curve begins to level off, and beyond 60 Hz, the fatigue life curve gradually stabilizes. Interestingly, at high frequencies (above 100 Hz), the fatigue life increases again, indicating that at very high frequencies, the impact load has a relatively smaller effect on fatigue damage. Therefore, if the fatigue life is a primary consideration, it is recommended to operate within the 60-100 Hz impact frequency range. If high-stress amplitudes are needed, higher frequencies such as 100 Hz at the same impact force can generate larger peak stress values. At lower impact energies, the maximum available fatigue life of the drill tool is achieved, although the associated stress amplitude is relatively low. If deep formations are to be penetrated, impact energies above 200 J can be used to generate higher stress amplitudes. However, when the impact energy increases to 400 J, a noticeable inflection point appears in the fatigue life curve, indicating a sharp increase in damage. This suggests that high-energy impact drilling at this level is not suitable for long-term operation.  
Figure 18: The usable life of different parts of the drilling tool combination under different impact forces.