Dynamics Modeling and Load-Sharing Performance Optimization of Concentric Face Gear Split-Torque Transmission Systems

The concentric face gear split-torque transmission system (CFGSTTS) has the advantages of a large reduction ratio and high power density. The CFGSTTS has considerable potential to be applied in helicopter main reducers. As such, in this study, we analyzed the load distribution characteristics of a dual input-dual output concentric face gear split-torque transmission system. A load-dependent time-varying meshing stiffness surrogate model was designed based on a feedforward neural network. The difference in the meshing stiffness between the pinion driving and face gear driving was analyzed. The coupled lumped parameter dynamic model of the bending-torsion-axis-pendulum was developed through Newton's second law, and the influences of the time-varying meshing stiffness, backlash, comprehensive transmission error, support stiffness, and damping were considered. Finally, the impact of the support stiffness on the load-sharing coefficient was analyzed. An optimization model was constructed with the objective function of minimizing the sum of the load-sharing coefficients and was solved by the marine predator algorithm. In addition, the validity of the optimization results was verified with a finite element model. The results indicate that (1) smaller support stiffnesses of input gears benefit the corresponding load balance; (2) the support stiffnesses of the face gears have different laws of influence on the load-sharing coefficient at the input gear and idler, and the support stiffnesses of the other gears need to be comprehensively considered; (3) the larger supporting stiffnesses of the idler gears and tail gear are beneficial for decreasing the load-sharing coefficient at the input gear; and (4) the optimized load-sharing coefficients at Input Gears 1 and 2 and the idler gear decrease by 23.7%, 24.2%, and 4.6%, respectively.