Establishment of a multi-clearance coupled 3D floating nonlinear model and vibration analysis for a coaxial reverse closed differential herringbone gear transmission system

Closed differential gear transmission systems are widely used in applications such as wind turbines and aviation equipment, yet the highly complex 3D nonlinear dynamics of these systems, particularly with floating herringbone gears, have not been adequately explored. Nevertheless, there is an urgent need for a specialized analytical model for the 3D floating of herringbone gears in space, which is crucial for studying the nonlinear dynamic behavior of gear systems. This article introduces a novel 3D floating analysis method that accounts for dynamic meshing parameters, coupled dynamic backlash with multiple clearances, and Time-Varying Meshing Stiffness (TVMS) of floating gears. Building on this approach, the study develops a 134-degree-of-freedom Bending Torsion Axial Pendular (BTAP) nonlinear dynamic model for the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS). The model investigates the system’s bifurcation characteristics and vibration behavior under varying radial, axial, and pendular floating conditions and is validated through bench vibration experiments. This model significantly enhances the accuracy of predicting the nonlinear dynamics of multi-degree-of-freedom systems operating under multiple clearance couplings, outperforming traditional models. The findings indicate that maintaining the radial floating value of gears within 0-20 μm ensures relatively stable dynamic behavior, avoiding multi-periodic and chaotic motion. Axial floating introduces diverse bifurcation characteristics, with values exceeding 0.28 μm leading to instability. Additionally, a gear end-face deviation angle around the X and Y axes greater than 0.007° results in complex bifurcation patterns and an increased risk of chaotic motion. This work establishes a theoretical foundation for 3D floating nonlinear vibration analysis in planetary gear transmission systems.