Abstract: This paper introduces the structure of a hydraulic drifter. Integrated with a nonlinear rock model, the process of drilling the rock is established as a four-degree-of-freedom mechanical model and a mathematical model. Both stick and non-stick modes are studied, explaining the differences between these two types of motion. Taking the angular frequency, amplitude and vertical offset of the hydraulic force as control parameters, the single-parameter continuation analysis is carried out, and the period-doubling bifurcation, saddle-node bifurcation and torus bifurcation are found. A comparison is made between the piston displacement and velocity data obtained from the model and experimental results. The results indicate that to make the drifter work on the period-1 trajectory, the range of angular frequency should be 2.09 < ω < 5.327. The range of amplitude should be 0.012 < a < 0.746, 0.005 < a < 1. The range of vertical offset should be 0.093 < b < 0.25. The hydraulic forces of the experiment and the model have the same performance trend, and the piston displacement and velocity of the model are roughly within the range of "experimental mean ±standard deviation", which indicates that the model well simulates the experimental results.

Key words: hydraulic drifter, nonlinear rock model, continuation, stick, bifurcation