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

Wei Liu; Ying Cui; Qiang Wang

doi:10.59400/sv4136

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

Wei Liu
College of Automobile and Traffic Engineering, Heilongjiang Institute of Technology, Harbin 150050, China; College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
Ying Cui
College of Automobile and Traffic Engineering, Heilongjiang Institute of Technology, Harbin 150050, China
Qiang Wang
College of Automobile and Traffic Engineering, Heilongjiang Institute of Technology, Harbin 150050, China

Article ID: 4136

Keywords: gear dynamic; fractal dimension; bifurcation and chaos; TVMS (time varying meshing stiffness); sliding friction

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.

Published

2026-05-25

How to Cite

Liu, W., Cui, Y., & Wang, Q. (2026). Bifurcation and chaos analysis of gear-bearing system with fractal mesh stiffness and fractal friction excitation. Sound & Vibration, 60(3). https://doi.org/10.59400/sv4136

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Issue

Vol. 60 No. 3 (2026): In Progress

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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