# Vibration Damage Analysis of Bottom Hole Assembly Under Axial Impact Based on Dynamic Analysis
## 1 Introduction  
Deep oil and gas reservoirs are predominantly characterized by low-permeability formations and an exceptionally high rock strength. The inherent complexities of drilling operations combined with harsh downhole conditions impose significant challenges to drill string reliability during drilling processes. During hydrocarbon exploration drilling, axial vibration impact drilling tools generate reciprocating impact loads under mud-driven actuation. The impact hammer transmits frequency-specific impact energy to the drill bit, achieving combined percussive-cutting rock fragmentation [1, 2, 3, 4, 5]. However, under high-speed rotary-percussive drilling operations, the Bottom Hole Assembly (BHA) experiences high-frequency cyclic impact loading--distinct from conventional rotary drilling. This induces periodic reciprocating vibrations in the drill string assembly, substantially amplifying the stress complexity in downhole configurations [6, 7]. To further elucidate the dynamic behavior of drilling assemblies during percussive drilling, researchers have conducted extensive investigations: [PERSON] [8] analyzed drill stringdisplacement and vibration under varying Weight on Bit (WOB) and rotary speeds using a BHA motion simulation experimental apparatus. [PERSON] et al. [9] modeled surface crack propagation in drill pipes during rotary drilling using 3D finite element analysis integrated with the Walker model, demonstrating the critical influence of axial forces on crack growth. [PERSON] et al. [10] evaluated frequency-dependent fatigue damage in integrated vertical drilling and multi-dimensional vibration reduction systems under continuous hydraulic impactor loading and formation reaction forces. [PERSON] et al. [11] developed a finite element model for drill pipe joint fatigue life, identifying the stress concentration, residual stresses, and surface quality as significant factors influencing the drill string fatigue life. [PERSON] et al. [12] established a composite drill string fatigue life model, demonstrating through case studies that non-buckled drill strings exhibit a shorter fatigue life than buckled drill strings. [PERSON] et al. [13] implemented fuzzy systems to model the dimensionless strength factors of drill pipes, predicting the fatigue life using fuzzy systems and cumulative damage theory. The analysis revealed that the drill string fatigue life is highly sensitive to initial crack size measurement accuracy. [PERSON] et al. [14] formulated a dynamic model for push-the-bit rotary steerable drilling BHAs using [PERSON]'s principle, calculating and analyzing dynamic characteristics including natural frequencies and dynamic stresses. The analysis indicated that peak stress correlates with the WOB and drilling rate. [PERSON] et al. developed a BHA fatigue life prediction model based on drill string dynamics theory using the FEM, incorporating the initial crack defects. The results demonstrated that transverse vibration exceeds longitudinal vibration, with transverse vibration being the primary cause of BHA fatigue failure. [PERSON] et al. [15] conducted experiments using a mechanical rock-breaking test system under a combined impact and WOB loading, performing a comparative analysis of the torsional impact versus static pressure impact fragmentation on sandstone samples. The findings indicate that simultaneous pulsed torque and WOB application during PDC bit-cutting and friction processes significantly mitigates the bit stick-slip effect. A comparative analysis of red/yellow sandstone demonstrated that the torsional impact achieves a superior rate of penetration (ROP) enhancement when drilling experimental rock samples to equivalent depths. The current research on the axial impact vibration characteristics of drill strings predominantly focuses on the influence of control parameters on the dynamic and static behavioral characteristics of drilling assemblies. In contrast, the relationship between the impact vibration characteristics and fatigue life requires further investigation.