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<p>This study investigates nonlinear power flow characteristics in torsional vibration of helical gear systems, employing time-averaged input power (TAIP) to quantitatively evaluate the influence mechanisms of nonlinear factors such as backlash and time-varying meshing stiffness on system dynamic behaviors. The research focuses on the energy transfer properties of typical nonlinear phenomena, including impact effects, super/subharmonic resonances, multi-stable response coexistence, and bifurcation/chaotic responses. First-order approximate solutions under impact conditions are derived using the harmonic balance method (HBM). Higher-precision steady-state responses of period-<i>δ</i> motions are obtained by integrating HBM with discrete Fourier Transform (DFT). Results are numerically validated via the Runge–Kutta method (RKM). Stability criteria for periodic solutions are established based on the Floquet theory. Key findings reveal that bilateral impact responses induce significant power flow amplification, with discontinuous jumps observed in the primary resonance region. Through reduced dynamic excitation amplitudes, increased preloads, and enhanced damping coefficients, parametric optimization effectively suppresses bilateral impacts and mitigates nonlinear power flow effects. Notably, although increased damping suppresses nonlinear phenomena, it elevates overall power flow levels across the frequency domain. Moreover, the study also demonstrates that TAIP exhibits marked discontinuous jumps due to underlying soft/hardening spring characteristics in super/subharmonic resonances, while multi-stable coexistence enables switching between distinct power flow levels. The TAIP approximation model established via HBM effectively predicts power flow evolution patterns during bifurcation processes, with bifurcation diagrams revealing the complex impact mechanisms of the nonlinear dynamic behaviors. By clarifying nonlinear interaction mechanisms from energy input/dissipation perspectives, this work provides a practical TAIP evaluation methodology for dynamic optimization of gear transmission systems, offering critical insights for engineering applications.</p>

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Vibration power flow of nonlinear periodic dynamic response in helical gears based on harmonic balance method

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Yeping Yuan,
  • Wen Zhang,
  • Junguo Wang

摘要

This study investigates nonlinear power flow characteristics in torsional vibration of helical gear systems, employing time-averaged input power (TAIP) to quantitatively evaluate the influence mechanisms of nonlinear factors such as backlash and time-varying meshing stiffness on system dynamic behaviors. The research focuses on the energy transfer properties of typical nonlinear phenomena, including impact effects, super/subharmonic resonances, multi-stable response coexistence, and bifurcation/chaotic responses. First-order approximate solutions under impact conditions are derived using the harmonic balance method (HBM). Higher-precision steady-state responses of period-δ motions are obtained by integrating HBM with discrete Fourier Transform (DFT). Results are numerically validated via the Runge–Kutta method (RKM). Stability criteria for periodic solutions are established based on the Floquet theory. Key findings reveal that bilateral impact responses induce significant power flow amplification, with discontinuous jumps observed in the primary resonance region. Through reduced dynamic excitation amplitudes, increased preloads, and enhanced damping coefficients, parametric optimization effectively suppresses bilateral impacts and mitigates nonlinear power flow effects. Notably, although increased damping suppresses nonlinear phenomena, it elevates overall power flow levels across the frequency domain. Moreover, the study also demonstrates that TAIP exhibits marked discontinuous jumps due to underlying soft/hardening spring characteristics in super/subharmonic resonances, while multi-stable coexistence enables switching between distinct power flow levels. The TAIP approximation model established via HBM effectively predicts power flow evolution patterns during bifurcation processes, with bifurcation diagrams revealing the complex impact mechanisms of the nonlinear dynamic behaviors. By clarifying nonlinear interaction mechanisms from energy input/dissipation perspectives, this work provides a practical TAIP evaluation methodology for dynamic optimization of gear transmission systems, offering critical insights for engineering applications.