A reduced-order flexible multibody framework for nonlinear spur gear dynamics

This work presents a solver-independent reduced-order flexible multibody framework for the nonlinear dynamic analysis of spur gear transmission systems. Classical lumped or rigid multibody models often neglect tooth-level elasticity, while full finite-element approaches are computationally prohibitive for nonlinear simulations. The proposed method bridges this gap by combining multibody kinematics with a reduced modal description of gear flexibility. Each gear is modeled as a rigid web coupled with flexible teeth, whose deformation is described using a floating frame of reference and a truncated set of fixed-interface normal modes. A consistent tooth–web coupling strategy is introduced, and the selected modal basis is validated to capture the dominant deformation mechanisms during meshing. Contact is modeled using a Hertzian-based penalty formulation, while damping accounts for modal, contact, and numerical contributions, ensuring a consistent energy dissipation. The framework is validated against benchmark experimental and numerical data, showing good agreement in terms of static and dynamic transmission error. The model captures key nonlinear phenomena, including resonance, stiffness variation, and jump behavior.