Analytical method for time-varying meshing stiffness and dynamic responses of modified spur gears considering pitch deviation and geometric eccentricity

Abstract

Pitch deviation and geometric eccentricity are almost inevitable in gear transmission systems. Tooth profile modification (TPM) is a common method used to improve gear contact properties. However, the coupling interaction between the tooth profile deviation introduced by TPM and manufacturing errors is complex. There is a lack of an analytical model that can clarify the dynamic behaviors of the modified gear pair affected by multiple manufacturing errors, specifically pitch deviation and geometric eccentricity. To fill this gap, a comprehensive analytical gear mesh model is proposed considering TPM, pitch deviation, and geometric eccentricity. The calculation formulas for the time-varying meshing stiffness (TVMS) and load sharing factor (LSF) are derived considering the iterative change of gear pair meshing parameters with phase under the influence of multiple manufacturing errors. Then, the translation-torsion coupling dynamic model of the spur gear pair based on the lumped mass method is established to investigate the dynamic transmission error (DTE) and vibration characteristics. Results show that TPM is an effective method for improving the comprehensive stiffness of a gear pair within the meshing range containing pitch deviation, but it reduces the meshing phase that includes only geometric eccentricity. Compared with the unmodified gear pair, the suppression effect of changing the modification length on the maximum DTE and vibration acceleration is more significant than that of the modification amount. TPM increases the overall fluctuation threshold range of DTE for gear pairs with only geometric eccentricity. It is expected that the proposed method can provide a theoretical basis for exploring vibration suppression in gear pairs with geometric eccentricity and pitch deviation errors.