Novel Modelling and Full Spectrum Analysis for Robust Fault Identification in an Unbalanced and Cracked Rotor System Supported by Viscoelastic Foil Bearings

High-speed rotor systems are highly susceptible to resonance-induced vibrations, with coupled fault conditions such as unbalance and transverse cracks posing serious risks to reliability. This research article proposes a robust identification framework for simultaneous fault detection and support parameter estimation in a rigid rotor supported by viscoelastic foil bearings. A system model with an offset disc is developed, incorporating unbalance excitation, gyroscopic effects, and a switching crack mechanism to capture fault interactions. The viscoelastic foil bearing is modelled with stiffness and damping parameters, offering enhanced energy dissipation compared to conventional bump-type supports. Fault identification is performed using full spectrum analysis, wherein time-domain vibration responses are transformed into the frequency domain to extract characteristic signatures. Both clean and noise-contaminated signals are analyzed, with modelling errors deliberately introduced to evaluate robustness. Results show that unbalance effects dominate at higher rotational speeds, while crack-induced harmonics are more pronounced at lower speeds, producing complex vibration patterns. The viscoelastic layer effectively suppresses transient vibrations during startup and shutdown, improving stability under high-speed operation. Frequency-domain analysis reveals crack signatures through response modulation and distinctive eight-shaped orbital motions, even under noisy conditions. Parameter estimation of foil bearing stiffness and viscoelastic support damping remains consistent despite signal contamination, confirming the effectiveness of the identification strategy. The novelty of this work lies in integrating crack modelling in a rigid shaft with viscoelastic foil bearing dynamics, coupled with robust parameter identification via full spectrum analysis. The proposed approach enhances fault tolerance and reliability for advanced turbomachinery applications.