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Bifurcation and chaos analysis of gear-bearing system with fractal mesh stiffness and fractal friction excitation.

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Title: Bifurcation and chaos analysis of gear-bearing system with fractal mesh stiffness and fractal friction excitation.
Authors: Liu, Wei1,2, Cui, Ying1, Wang, Qiang1 wangqiang@hljit.edu.cn
Source: Sound & Vibration. 2026, Vol. 60 Issue 3, p1-24. 24p.
Subjects: Sliding friction, Bifurcation theory, Chaos theory, Nonlinear mechanics, Friction, Lyapunov exponents
Abstract: Studying tooth surface topography and sliding friction in gear-bearing system is crucial for enhancing its reliability and minimizing vibration and noise. Inspired by preliminary research on sliding friction, this study addresses a novel gear-bearing model, in which the fractal meshing stiffness and fractal friction excitation are emphasized simultaneously. Initially, the formula of time-varying meshing stiffness (TVMS) due to fractal characterization is developed by employing the W-M function. The influence of fractal dimension on TVMS is investigated. Subsequently, the sliding friction excitation corresponding to fractal dimension is derived and introduced into the proposed gear-bearing model. On this basis, the bifurcation and chaos of the gear-bearing system with and without fractal dimension are compared. The maximum Lyapunov exponent forecasting methodology is carried out to validate the dynamic characteristics. In order to clearly exhibit the influence of the fractal dimension, the nonlinear dynamic behaviors of the gear-bearing system are investigated by reference to its time-domain chart, phase diagram, frequency spectrum, and Poincare section. Ultimately, contributions of sliding friction on dynamic behaviors of gear-bearing system are also examined. This work is extremely significant for improving the gear dynamic performance through guiding gear surface design and manufacture. [ABSTRACT FROM AUTHOR]
Copyright of Sound & Vibration is the property of Academic Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Bifurcation and chaos analysis of gear-bearing system with fractal mesh stiffness and fractal friction excitation.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Wei%22">Liu, Wei</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Cui%2C+Ying%22">Cui, Ying</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Wang%2C+Qiang%22">Wang, Qiang</searchLink><relatesTo>1</relatesTo><i> wangqiang@hljit.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Sound+%26+Vibration%22">Sound & Vibration</searchLink>. 2026, Vol. 60 Issue 3, p1-24. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Sliding+friction%22">Sliding friction</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+mechanics%22">Nonlinear mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Friction%22">Friction</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Studying tooth surface topography and sliding friction in gear-bearing system is crucial for enhancing its reliability and minimizing vibration and noise. Inspired by preliminary research on sliding friction, this study addresses a novel gear-bearing model, in which the fractal meshing stiffness and fractal friction excitation are emphasized simultaneously. Initially, the formula of time-varying meshing stiffness (TVMS) due to fractal characterization is developed by employing the W-M function. The influence of fractal dimension on TVMS is investigated. Subsequently, the sliding friction excitation corresponding to fractal dimension is derived and introduced into the proposed gear-bearing model. On this basis, the bifurcation and chaos of the gear-bearing system with and without fractal dimension are compared. The maximum Lyapunov exponent forecasting methodology is carried out to validate the dynamic characteristics. In order to clearly exhibit the influence of the fractal dimension, the nonlinear dynamic behaviors of the gear-bearing system are investigated by reference to its time-domain chart, phase diagram, frequency spectrum, and Poincare section. Ultimately, contributions of sliding friction on dynamic behaviors of gear-bearing system are also examined. This work is extremely significant for improving the gear dynamic performance through guiding gear surface design and manufacture. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Sound & Vibration is the property of Academic Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.59400/sv4136
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      – Code: eng
        Text: English
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        PageCount: 24
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    Subjects:
      – SubjectFull: Sliding friction
        Type: general
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Chaos theory
        Type: general
      – SubjectFull: Nonlinear mechanics
        Type: general
      – SubjectFull: Friction
        Type: general
      – SubjectFull: Lyapunov exponents
        Type: general
    Titles:
      – TitleFull: Bifurcation and chaos analysis of gear-bearing system with fractal mesh stiffness and fractal friction excitation.
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            NameFull: Liu, Wei
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            NameFull: Cui, Ying
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            NameFull: Wang, Qiang
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          Dates:
            – D: 01
              M: 05
              Text: 2026
              Type: published
              Y: 2026
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              Value: 60
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            – TitleFull: Sound & Vibration
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