A novel stochastic model for perturbations in the axial-torsional bit-rock interaction of drill string dynamics

Abstract The main contribution of this paper is the development of a stochastic model that considers random perturbations in the torque and axial force that are applied at the bit of drill strings. The proposed formulation describes these perturbations as additive and non-stationary, whose variance increases as the bit angular speed increases. A lumped 5 DOF drill string nonlinear model with axial-torsional coupling is considered to test the new probabilistic strategy. A second contribution is the evaluation of multiaxial fatigue under this uncertain environment, where the Findley fatigue criterion is adopted. The results show that the proposed stochastic model can significantly affect the dynamic response of the system and may lead to non-negligible variations in fatigue indices, especially under operating conditions with higher bit-rotation rates. Comparisons between deterministic and stochastic scenarios highlight the importance of explicitly modeling uncertainty in the bit-rock loads when assessing drill string reliability.