Continuation analysis and experiment in a drifter‑rock model

The principle of the hydraulic drifter is introduced， and the process of drilling into rocks by the drifter is established as a physical model of rock with three-degree-of-freedom dry friction. The concept of rate of penetration （ROP） is introduced. The stick and non-stick modes are studied， explaining the differences between these two types of motion. The periodic trajectories of the nonlinear piecewise smooth dynamical system mathematical model are segmented. By using the pseudo-arclength continuation method and Floquet theory， the angular frequency and amplitude of the hydraulic force are taken as control parameters to obtain stable periodic trajectories and the point of maximum ROP. Bifurcations such as period-doubling bifurcation， saddle-node bifurcation， and torus bifurcation are discovered. The data acquisition system for drilling rocks with a hydraulic drifter is introduced， and the displacement and velocity of the piston obtained from the model and experiments are compared. The results indicate that to make the drifter work on the period-1 trajectory， the range of angular frequency should be ω<6.814， and the range of amplitude should be 0.03<a<3.051. There is a strong correlation between the experiments and the model， and compared with the experiment， the piston in the model undergoes deceleration before colliding with the drill tool， adding an impact deceleration stroke.