Novel discrete flexible multibody model for ball bearings with deformable rings in harmonic drive applications

Deformable ball bearings play a critical role in harmonic drives, where the transmission principle relies on elastic deformation of thin-walled components. Classical models based on rigid rings or computationally expensive FEM approaches struggle to capture the dynamic behaviour required for accurate description and/or have too expensive simulation costs. This work presents a discrete flexible multibody modelling approach in which the inner ring, rolling elements, and a discretized outer ring are represented as interacting bodies connected by spring-damper systems, nonlinear Hertzian contacts, and beam-based homogenization and anchoring forces. The outer ring deformation is reconstructed dynamically by modelling each circumferential sector as a simply supported Euler-Bernoulli beam, enabling a computationally efficient yet physically consistent description of ring curvature, sector coupling, and preload effects. Dynamic analyses show the emergence of consistent and predictable deformation-induced interactions. The proposed formulation, exploiting the discrete flexible multibody approach, bridges the gap between simplified analytical models and full FEM, providing an efficient tool suitable for integration into complete harmonic drive simulations and offering improved capabilities for dynamic performance prediction, and health-monitoring applications.