Non-linear Dynamic Modelling and Analysis of Split-Torque Face-Gear Drive Systems

A nonlinear dynamic model of a multi-mesh involute spur pinion-driven face-gear split-torque drive system is developed. The lumped mass model consists of five pinions and two face-gears with seven rotational degrees-of-freedom. Model includes two inputs, two outputs, and three idler gears meshing with two identical face gears at the bottom and top of the assembly. Face-gear tooth form and corresponding spur gear teeth are established by differential geometry and the theory of gearing. Face-gear drive system mesh stiffnesses are established by utilizing Finite Strip Method for the first time in the literature. The mesh stiffness and damping are time-variant. The model includes clearance type nonlinearity. The Harmonic Balance Method (HBM) is utilized to solve the nonlinear differential equations of motion. The results are compared with the time simulation results. The stability is checked with Floquet Theory and bifurcation diagrams from Poincare Sections. The model is fully capable of generating the tooth geometries, mesh stiffnesses, and gear train dynamics without reliance on any package programs. Hence, the model provides flexibility and fast computation for parametric studies compared to existing literature. The effect of the pinions' orientation angle patterns on the face-gear are investigated to evaluate the mesh phasing effects among system dynamic response. The effect of subharmonic motion on the dynamic response of the split-torque face-gear system is also demonstrated for the first time in the literature. The case studies demonstrate that subharmonic resonance peaks are avoided.