Analysis of a Dual Gearbox/Shaft System with Nonlinear Dynamic Mesh Phase Interactions

Abstract

It is well known that time-varying mesh stiffness fluctuations and backlash effects are a significant source of vibration and instability in geared rotor systems. This paper studies the nonlinear interactions between two gearboxes coupled by a torsionally flexible shaft. Such configurations are common in rotorcraft propulsion systems including tailrotor and cross-shafting drivelines. Shaft flexibility induces dynamic phasing between two coupled gearboxes. This dynamic phasing together with the kinematic dependence of the gear tooth mesh stiffness on the gear rotation induces a nonlinear dynamic interaction not explored in previous single-stage or rigid-shaft gear system investigations. The nonlinear time-varying equations-of-motion of a dual-spur gearbox/flexible shaft system are derived via an assumed mode technique. Steady-state harmonic and sub-harmonic solutions are obtained via a harmonic balance and arc-length continuation strategy. Under zero backlash conditions, the dynamic mesh phase produces a softening type nonlinearity in the resonance curves. Furthermore, under chattering conditions, increasing the shaft compliance tends to destabilize the single and double sided contact response amplitudes. The equations and analysis presented for the dual-gearbox shaft system demonstrate the importance of including nonlinear mesh phase interactions in multi-gearbox drive systems.