Nonlinear Dynamic Analysis of Drill-String System Coupling Rock Surface Morphology Evolution and Dry Friction Effect

Stick–slip vibration, reversal, axial impact, and dynamic instability are major challenges in deep drilling operations and are closely associated with nonlinear bit–rock interaction. To investigate these phenomena, this study develops a nonlinear axial–torsional coupled dynamic model of a drill-string system by integrating rock surface morphology evolution with a Stribeck dry friction model. The drill string is discretized into a distributed lumped-parameter model with coupled axial and torsional degrees of freedom. A surface morphology matrix is introduced to simulate the rock-cutting process, while the Stribeck friction model is employed to characterise the nonlinear frictional behaviour at the bit–rock interface. Time-domain simulations, bifurcation analysis, and frequency spectrum analysis are performed to investigate the dynamic responses of the system. The results indicate that rock surface morphology evolution significantly influences the contact conditions and frictional behaviour at the bit–rock interface, and together with dry friction induces transitions among steady-state, multi-periodic, and chaotic motions. Stick–slip vibration is accompanied by axial impact, bit bounce, and a reduction in the dominant torsional vibration frequency. In addition, variations in both driving and frictional parameters can trigger dynamic instability and state transitions. The proposed model provides an effective framework for analysing nonlinear drilling dynamics and offers theoretical guidance for drill-string vibration suppression, drilling parameter optimisation, and efficient drilling in complex formations.