Experimentally validated reduced-order modeling of gear-rotor-bearing systems with three-dimensional shaft compliance and gyroscopic mapping

Abstract

Traditional one-dimensional beam models cannot adequately represent the three-dimensional local compliance of stepped transmission shafts, whereas full solid models are inefficient for system-level nonlinear simulations. This study proposes a high-fidelity reduced-order model for gear-rotor-bearing systems by combining Craig-Bampton condensation of solid shaft models with equivalent gyroscopic mapping. Continuously distributed coupling reference points are assigned at shaft shoulders, bearing locations, and gear mounting positions to retain local softening and non-planar warping. Speed-dependent gyroscopic terms are formulated using rotating Timoshenko beam elements and lumped-disk contributions, and embedded into the condensed coordinate space through coordinate transformation, degree-of-freedom alignment, and subspace mapping. The model is validated by input-shaft modal testing and gearbox vibration experiments. Compared with the one-dimensional Timoshenko beam model, the proposed model improves modal-frequency prediction and captures the dominant periodic and mesh-order vibration features. Neglecting local shaft compliance shifts modal frequencies, critical speeds, dynamic transmission error, and nonlinear transition boundaries. The method provides a physically consistent basis for modal prediction, critical-speed evaluation, vibration analysis, and nonlinear stability assessment of high-speed gear-rotor-bearing systems.