Modeling and analysis of internal excitation and vibration characteristics of gears with early-stage crack and 3D tooth surface error

Affected by the tooth surface errors, the vibration characteristics of early crack failures are usually various under different tooth surface precision level. Therefore, to reveal the influence of three-dimensional (3D) tooth surface error (TSE) on the internal excitation and vibration characteristics of gears with early-stage crack (ESC), a coupling internal excitation model of gears with ESC and 3D errors is proposed based on a double-layer iterative method. In this model, the influence of meshing phase between tooth pair and along tooth width direction (TWD) on the time-varying mesh stiffness (TVMS) are simultaneously considered, which overcomes the limitations of traditional models that are only suitable for characterizing the coupled excitation of the two-dimensional tooth profile errors and TVMS. Based on verifying the proposed model, the effects of TSE type, parameters, and load on the TVMS, loaded static transmission error (LSTE), load distributions, and torsional deformation of the cracked gear teeth are investigated, and the vibration characteristics of ESC failures under the effects of 3D TSE are also explored. The research results show that the distribution parameters of 3D TSE have a significant effect on the internal excitation and vibration characteristics of gears with ESC, and thus measuring and evaluating the distribution parameters of TSE can help improve the accuracy of gear fault identification and diagnosis methods.