Research on Load Distribution Methods for Planetary Gearboxes Based on Three-Dimensional Tolerance Analysis

Based on the Jacobian tensor and small displacement tensor theories, this paper establishes a three-dimensional tolerance chain analytical model for manufacturing and assembly errors in planetary gearboxes and proposes three methods for managing tolerance accumulation paths. Through tolerance analysis, the cumulative pitch error is quantified and incorporated into the nonlinear dynamic model of the planetary gearbox to determine the time-varying meshing force between the ring gear and planetary gear. This enables calculation of the theoretical load distribution coefficient while accounting for three-dimensional tolerance effects. To validate the model’s accuracy, a dedicated test bench was constructed, and dynamic stresses were measured using a root strain gauge array; the experimental load distribution coefficient was then derived. Comparison of simulation and experimental results shows that the deviation in the load distribution coefficient is only 7.4%, strongly confirming the reliability of the three-dimensional tolerance-dynamics coupled model. This study represents the first closed-loop verification from tolerance propagation to system-level load distribution, providing a theoretical foundation for tolerance design optimization and load distribution performance enhancement in high-precision planetary gearboxes.