Delayed feedback control and parameter continuation of multistability in a nonsmooth hydraulic rock drill model
Siyuan Chang1, Wei Ma2, Min Ye1
1Key Laboratory of Road Construction Technology and Equipment of MOE, Chang 'an University, Xi'an, Shaanxi 710064, China.
Chaos (Woodbury, N.Y.)
|June 17, 2025
Summary
This study models hydraulic rock drill multistability using dry friction theory. Delayed feedback control successfully unifies complex attractors, enhancing drilling efficiency and stability in experiments.
Area of Science:
- Mechanical Engineering
- Nonlinear Dynamics
- Rock Mechanics
Background:
- Hydraulic rock drills exhibit complex multistable behavior during operation.
- Understanding and controlling this multistability is crucial for improving drilling efficiency and stability.
- Existing models may not fully capture the nonlinear dynamics involved.
Purpose of the Study:
- To establish a physical model for hydraulic rock drill multistability.
- To investigate the use of delayed feedback control for managing multistability.
- To analyze parameter domains and bifurcation phenomena influencing system behavior.
Main Methods:
- Developed a four-degree-of-freedom physical model based on dry friction rock mechanics.
- Classified motion trajectories into non-viscous, impact viscous, and buffer viscous states.
- Applied delayed feedback control, approximating delay differential equations with ordinary differential equations.
- Utilized pseudo-arclength continuation and Floquet theory for parameter analysis.
- Conducted rock drilling experiments to validate the model and findings.
Main Results:
- Identified multistable attractors (p0q1, p1q2) using impact frequency as a bifurcation parameter.
- Successfully converted dual attractors into a single attractor (p0q1) using delayed feedback control (K=9, τd=0.35).
- Determined parameter domains (K, τd) divided by period-doubling bifurcation points (PD1, PD2).
- Demonstrated that smaller delay times (τd) increase system collisions and periodic motions.
- Experimental results confirmed model validity and the increased likelihood of multistability in hard, brittle rocks.
Conclusions:
- The established model accurately represents hydraulic rock drill multistability.
- Delayed feedback control is an effective strategy for managing multistability, enhancing drilling performance.
- Parameter tuning, particularly delay time, offers a method to control system dynamics and improve efficiency and stability.
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