<p>This investigation explores the nonlinear dynamics and multistable behavior of hydraulic rock drill systems through a nonlinear rock contact model. By treating angular frequency, amplitude, and vertical offset as primary control parameters, comprehensive one-parameter bifurcation and continuation analyses along with two-parameter domain studies are conducted. The results of research show that, in angular frequency bifurcation analysis, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$p_2q_3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> <msub> <mi>q</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> trajectory demonstrates superior global stability relative to both <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$p_1q_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> and quasi-periodic solutions. Amplitude variations induce distinctive basin stability patterns <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$p_1q_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>-1 exhibits non-monotonic behavior culminating in extinction, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$p_1q_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>-2 progressively emerges, while <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$p_2q_3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> <msub> <mi>q</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> undergoes continuous attenuation. Continuation analysis identifies torus (TR) and saddle-node (SN) bifurcations. Two-parameter investigations confirm coexisting periodic, quasi-periodic, and chaotic attractors, validating bifurcation diagram multistability. This study proves that the model of rock drills drilling nonlinear rocks has multiple stabilities, providing a theoretical basis for the next step of controlling and eliminating the multistability.</p>

Multistable analysis of discontinuous nonlinear dynamics for rock drilling by hydraulic rock drills

期刊论文
发表日期：

2026年7月6日

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Wei Ma,
Yuansheng Zhang,
Rong Guo,
Fei Ma,
Joseph Páez Chávez

摘要

This investigation explores the nonlinear dynamics and multistable behavior of hydraulic rock drill systems through a nonlinear rock contact model. By treating angular frequency, amplitude, and vertical offset as primary control parameters, comprehensive one-parameter bifurcation and continuation analyses along with two-parameter domain studies are conducted. The results of research show that, in angular frequency bifurcation analysis, the $p_2q_3$ $p_{2} q_{3}$ trajectory demonstrates superior global stability relative to both $p_1q_1$ $p_{1} q_{1}$ and quasi-periodic solutions. Amplitude variations induce distinctive basin stability patterns $p_1q_1$ $p_{1} q_{1}$ -1 exhibits non-monotonic behavior culminating in extinction, $p_1q_1$ $p_{1} q_{1}$ -2 progressively emerges, while $p_2q_3$ $p_{2} q_{3}$ undergoes continuous attenuation. Continuation analysis identifies torus (TR) and saddle-node (SN) bifurcations. Two-parameter investigations confirm coexisting periodic, quasi-periodic, and chaotic attractors, validating bifurcation diagram multistability. This study proves that the model of rock drills drilling nonlinear rocks has multiple stabilities, providing a theoretical basis for the next step of controlling and eliminating the multistability.