This paper investigates the linear stability and nonlinear dynamics of drilling with non-uniformly distributed blades in a drill-bit. The analysis is based on a lumped parameter model considering both axial and torsional drill-string deformation, where regenerative cutting and frictional effects in bit-rock interactions are sources of drilling instability. Given flexibility of angles’ selection introduced by the non-uniform blade distribution, eigenvalue analysis reveals that introducing an extra blade can enlarge the stable region for stationary drilling. The perturbation analysis finds both subcritical and supercritical types of instability on the stability boundaries, where the subcritical Hopf bifurcation introduces large-amplitude oscillations, which deteriorates the global drilling stability in the regions close to the up-left and up-right areas of the stable regions. Moreover, the numerical bifurcation analysis of drilling with 3 non-uniformly distributed blades unveils various complex nonlinear effects including bit-bounce, stick-slip motion and loss of contact.
Yan, Y., & Wiercigroch, M. (2019). Dynamics of rotary drilling with non-uniformly distributed blades. International Journal of Mechanical Sciences, 160, 270–281. https://doi.org/10.1016/j.ijmecsci.2019.05.016