Abstract: The structure of the hydraulic drifter is introduced. The process of drilling into rocks with a hydraulic drifter is established as a physical model of three degrees of freedom dry friction rock. The study investigates the stick and non-stick modes, explaining the differences between these two types of motion. By using Poincaré mapping and direct numerical integration methods, the angular frequency and amplitude of the hydraulic force are taken as control parameters, revealing period-doubling bifurcation and torus one. The data acquisition system for drilling rocks with the hydraulic drifter is introduced, comparing the displacement and velocity of the piston obtained from the model and experiments. The analysis results indicate that: to make the drifter work on “non-stick penetration” and period-1 trajectory, the range of angular frequency should be selected as 2.66 < ω < 5.28, and when ω = 3, the model achieves the maximum ROP. The range of the amplitude should be selected as 0.13 < a < 3. There is a strong correlation between the experiments and the model, and compared to the experiments, the model experiences deceleration before the collision between the piston and the drill string, adding an impact deceleration stroke.