On the modeling of rotors with rolling element bearings using bond graph

This paper describes the development of a generic rotordynamic model incorporating rolling element bearings. Aimed at examining model fidelity requirements for bearings, the work contributes to advancing knowledge on rotordynamic system models suitable for studying mechatronics- and controls-related applications, transient issues and fault conditions. The bond graph method is applied in a consistent manner, giving a clear model structure. Body-fixed equations of motion, derived from Lagrange's method, are contained in field elements. An alternative cage implementation and a flexible outer ring are introduced, providing a more complete basis for bearing modeling. The flexible outer ring is modeled using the modal approach with a solution for moving loads. The derivation of the equations of motion and the bond graph formulation are thoroughly presented. Following the display of versatility and connectivity in the modeling approach, a simulation example is presented to demonstrate the capability and usefulness of the model for transient analyses. A classic time-series analysis of a run-up of an unbalanced rotor, with and without a damaged bearing, directly yields interesting results; the complex interaction between model elements following the passing of the first critical speed leads to a stationary vibratory condition taking significantly long time to develop in the damaged bearing case and involves persistent slip.