The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system.

This paper aims at constructing a stochastic model for the hysteretic behaviour of the nonlinear bit-rock interaction of a drill string under torsional vibrations using field data. The proposed model takes into account the fluctuations of the stick-slip oscillations and the hysteretic effect due to the nonlinear bit-rock interaction observed during the drilling process. These fluctuations are modelled by introducing a stochastic process associated with the variations of the bit-rock interaction during the drilling. The parameters of the stochastic model are calibrated with field data. Finally, independent trajectories of the proposed stochastic model are generated and used to simulate the stochastic response of the drill string torsional dynamics in presence of random bit-rock interaction. The stochastic model is then used to estimate statistics on the stability of the drill string.