Analytical calculation method for meshing contact characteristics of face gear pairs
LU Chengzhi
CHEN Shuhan
LIU Jie
XIAO Zeliang
Abstract：[Objective]The loaded transmission error and the maximum contact stress represent two pivotal indices for identifying the operational smoothness and load-carrying capacity of face gear drives.To eliminate the intensive time consumption and low computational efficiency inherent in conventional finite element simulations,a highly efficient and accurate analytical calculation methodology was explored to determine the meshing contact characteristics of face gear pairs.[Methods]Firstly,based on the configuration outputs of tooth contact analysis,a global structure deformation matrix was developed by dividing the single tooth into discrete slices and treating each slice as an analytical variable-cross-section cantilever beam.Secondly,the localized non-Hertzian elastic contact deflection and high-fidelity stress distributions across the complex tooth flanks were resolved via the conjugate gradient-fast Fourier transform technique.Thirdly,by incorporating a rigorous multi-tooth contact path evaluation scheme,the initial spatial gaps and load sharing trajectories were iteratively updated under multi-level load sweeps.Finally,numerical sweeps were subsequently executed on a pair of profile-modified face gears,and the analytical predictions were compared against a refined five-tooth finite element mesh model for verification.[Results]Comparative results indicate that the loaded transmission error and maximum contact stress curves obtained from the proposed analytical method possess identical meshing cycles and evolutionary characteristics with those from finite element simulations.Under external torques of 100,160,and 800 N·m,the maximum relative deviations are tightly bounded within 8.29%for the loaded transmission error and 10.3%for the peak contact stress.Furthermore,the analytical method consistently yields slightly larger peak contact stress values than the finite element analysis,thereby guaranteeing conservative and robust safety margins for tooth strength checkups while substantially minimizing recursive optimization time.
Keywords：Face gearContact stressLoaded transmission errorAnalytical calculation
Publication Date：2026-07-15
Online Publishing Date：2026-09-12(First online date of this platform, not the publication date of the document)
Pages：8( 118-125 )