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Purpose <p>Dynamic modeling is a crucial method for studying fault mechanisms, with the calculation of time-varying meshing stiffness (TVMS) being a key aspect. This study aims to introduce a novel method for calculating the TVMS of cracked gears and to investigate the dynamic responses of a planetary gearbox under different crack stages.</p> Methods <p>A new model based on an extended cantilever beam theory is proposed. This model accounts for the migration of the beam root at the gear root circle caused by crack propagation. The crack growth is divided into four stages, and the reduction in moment of inertia and load-bearing area at each stage is incorporated. Furthermore, a lumped-parameter dynamic model of a&#xa0;planetary gearbox is established to simulate its dynamic responses.</p> Results <p>The proposed model is validated by the comparison between the measured and simulated dynamic responses under both healthy and faulty conditions. The stiffness calculated using the extended cantilever beam model becomes lower than that derived from the traditional model and shows strong agreement with results obtained from a finite element method. The dynamic responses&#xa0;exhibit pronounced impact distortions and increased amplitudes, with distinct sidebands spaced by the number of planet gears emerging in the order spectrum.</p> Conclusion <p>The extended cantilever beam model provides a more accurate and computationally efficient method for TVMS evaluation in cracked gears, effectively capturing stiffness reduction under fault conditions. The dynamic model successfully characterizes crack-induced vibration signatures, demonstrating its value for fault diagnosis in planetary gearboxes. The consistency&#xa0;between simulation and experiment underscores the model’s reliability and practical applicability in condition monitoring and predictive maintenance.</p>

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Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Planetary Gearboxes for Tooth Crack Detection

  • 期刊论文

  • 发表日期：

    2025年9月10日

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  • Zongyao Liu,
  • Haibin Ma,
  • Jiahao Li,
  • Hao Ding,
  • Chengbao Li

摘要

Purpose

Dynamic modeling is a crucial method for studying fault mechanisms, with the calculation of time-varying meshing stiffness (TVMS) being a key aspect. This study aims to introduce a novel method for calculating the TVMS of cracked gears and to investigate the dynamic responses of a planetary gearbox under different crack stages.

Methods

A new model based on an extended cantilever beam theory is proposed. This model accounts for the migration of the beam root at the gear root circle caused by crack propagation. The crack growth is divided into four stages, and the reduction in moment of inertia and load-bearing area at each stage is incorporated. Furthermore, a lumped-parameter dynamic model of a planetary gearbox is established to simulate its dynamic responses.

Results

The proposed model is validated by the comparison between the measured and simulated dynamic responses under both healthy and faulty conditions. The stiffness calculated using the extended cantilever beam model becomes lower than that derived from the traditional model and shows strong agreement with results obtained from a finite element method. The dynamic responses exhibit pronounced impact distortions and increased amplitudes, with distinct sidebands spaced by the number of planet gears emerging in the order spectrum.

Conclusion

The extended cantilever beam model provides a more accurate and computationally efficient method for TVMS evaluation in cracked gears, effectively capturing stiffness reduction under fault conditions. The dynamic model successfully characterizes crack-induced vibration signatures, demonstrating its value for fault diagnosis in planetary gearboxes. The consistency between simulation and experiment underscores the model’s reliability and practical applicability in condition monitoring and predictive maintenance.