Dynamics of rotary drilling with non-uniformly distributed blades

This paper investigates the linear stability and nonlinear dynamics of drilling with non-uniformly distributed blades in the drill-bit. The analysis is based on a lumped parameter model considering both axial and torsional drill-string deformation, with both regenerative cutting and frictional effects in bit-rock interaction considered as sources of drilling instability. Given the flexibility of angles’ selection introduced by the non-uniform blade distribution, eigenvalue analysis reveals that letting one angle occupy the majority of the angles summation and introducing an extra blade can enlarge the stable region for stationary drilling. Then perturbation analysis finds both subcritical and supercritical types of instability on the stability boundaries, where the subcritical Hopf bifurcation introduces large-amplitude oscillations to deteriorate the global drilling stability in the regions close to the up-left and up-right areas of the stable regions. Moreover, numerical bifurcation analysis of drilling with 3 non-uniformly distributed blades discovers various complex nonlinear dynamics including bit-bounce, stick-slip motion, loss of contact.