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Nonlinear dynamics and continuation analysis of a four degree-of-freedom drifter-rock model

Author

Listed:
  • Ma, Wei
  • Chang, Siyuan
  • Chávez, Joseph Páez
  • Wang, Songyuan
  • Wu, Wenzhang

Abstract

A rock contact model is introduced, and the rock drilling process of the hydraulic drifter is established as a four degree-of-freedom (DOF) mechanical model. The mechanical model is simplified using a nondimensionalization method, resulting in a compact form. The periodic trajectories of the mechanical model are segmented to establish a mathematical model. Non-stick period-1 trajectories are obtained. The angular frequency and vertical offset are used as control parameters for bifurcation and basins of attraction. One-parameter continuation and two-parameter domain are conducted. Results indicate that: When 0<ω≤2.34, the model exhibits stick behavior. For 2.35≤ω≤20, the model transitions to the non-stick mode. The fingered chaotic attractor emerges from stable periodic trajectories via period-doubling bifurcations. Period-doubling, saddle–node, and torus bifurcations are identified. To ensure operation on a period-1 trajectory, the angular frequency should be chosen within the range of 2.35<ω<6.611, and the vertical offset should be within 0.0467

Suggested Citation

  • Ma, Wei & Chang, Siyuan & Chávez, Joseph Páez & Wang, Songyuan & Wu, Wenzhang, 2025. "Nonlinear dynamics and continuation analysis of a four degree-of-freedom drifter-rock model," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004837
    DOI: 10.1016/j.chaos.2025.116470
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