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<p>To comprehensively investigate the nonlinear dynamic behaviors and the effects of critical parameters in herringbone gear transmission systems, a dynamic model with 16 degrees of freedom was developed. This model incorporates various nonlinear elements, including time-varying mesh stiffness, backlash, bearing clearance, transmission errors, and input/output excitations. A numerical co-simulation method using two-parameters was employed to identify the types and regions of periodic motions on a parameter plane defined by key excitation frequencies and backlash values. This methodology uncovered the transition patterns between non-impact and impact vibrations, as well as the relationships between adjacent fundamental periodic motions. The findings reveal that the shift from non-impact to tooth surface impact vibrations is primarily driven by grazing bifurcation. In contrast, transitions between adjacent tooth surface impact motions are influenced by both grazing and period-doubling bifurcations. Within a certain range, variations in backlash values do not alter the types or regions of periodic motion patterns; these variations solely affect the displacement of meshing pairs. Moreover, an increase in transmission error alters the transition dynamics between non-impact and tooth surface impact vibrations, decreasing the areas of non-impact motion while enlarging the impact motion regions within the two-parameter framework. Additionally, the regions for quasi-periodic and chaotic motions expand significantly, fragmenting the areas of periodic motion. This research offers a theoretical foundation and guidance for analyzing the dynamic characteristics and optimizing the design of herringbone gear transmission systems.</p>

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Nonlinear dynamics analysis of herringbone gear transmission systems in two-parameter plane

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Jun Liu,
  • Yanxia Zhang,
  • Junwang Hu,
  • Fenxia Liu,
  • Yinjing Yao,
  • Jiaye Mo

摘要

To comprehensively investigate the nonlinear dynamic behaviors and the effects of critical parameters in herringbone gear transmission systems, a dynamic model with 16 degrees of freedom was developed. This model incorporates various nonlinear elements, including time-varying mesh stiffness, backlash, bearing clearance, transmission errors, and input/output excitations. A numerical co-simulation method using two-parameters was employed to identify the types and regions of periodic motions on a parameter plane defined by key excitation frequencies and backlash values. This methodology uncovered the transition patterns between non-impact and impact vibrations, as well as the relationships between adjacent fundamental periodic motions. The findings reveal that the shift from non-impact to tooth surface impact vibrations is primarily driven by grazing bifurcation. In contrast, transitions between adjacent tooth surface impact motions are influenced by both grazing and period-doubling bifurcations. Within a certain range, variations in backlash values do not alter the types or regions of periodic motion patterns; these variations solely affect the displacement of meshing pairs. Moreover, an increase in transmission error alters the transition dynamics between non-impact and tooth surface impact vibrations, decreasing the areas of non-impact motion while enlarging the impact motion regions within the two-parameter framework. Additionally, the regions for quasi-periodic and chaotic motions expand significantly, fragmenting the areas of periodic motion. This research offers a theoretical foundation and guidance for analyzing the dynamic characteristics and optimizing the design of herringbone gear transmission systems.