This paper presents a comprehensive numerical study of a higher order drifting oscillator that has been used to model vibro-impact drilling dynamics in previous publications by our research group. We focus on the study of the bit-rock interactions, for which both linear and nonlinear models of the drilled medium are considered.

Our investigation employed a numerical approach based on direct numerical integration via a newly developed MATLAB-based computational tool, ABESPOL (Chong et al., 2017), and based on path-following methods implemented via a software package for continuation and bifurcation analysis, COCO (Continuation Core) (Dankowicz and Schilder, 2013). The analysis considered the excitation frequency, amplitude of excitation and the static force as the main control parameters, while the rate of penetration (ROP) was chosen as the main system output so as to assess the performance of the system when linear and nonlinear bit-rock impact models are used.

Furthermore, our numerical investigation reveals a rich system dynamics, owing to the presence of codimension-one bifurcations of limit cycles that influence the system behaviour dramatically, as well as multistability phenomenon and chaotic motion.