Theoretical and experimental analysis of an unbalanced and cracked cardan shaft in the vicinity of the critical speed

This paper presents a theoretical and experimental analysis of a coupled lateral and torsional vibrations of two identical rotors interconnected by a flexible Hooke’s joint and modelled as a multibody system with a small misalignment angle. Using energy principle and a Lagrangian transformation, the governing equation of the propeller shaft system is established by considering a nonlinear elastic shaft time-dependent perturbation. To study the sensitivity of the crack for a rotating shaft, the model is enriched by considering the periodical feature of the time-varying stiffness deriving from the crack breathing model. The nonstationary response of a cracked rotor system in the presence of unbalance has been evaluated using orbit patterns and Fast Fourier Transform. The highly oscillated feature of the rotors system is theoretically obtained and experimentally analysed. The analysis demonstrated that the crack parameters in the input shaft tend to inhibit the occurrence of unstable oscillations in lateral deflection, orbit and frequency spectrum of the secondary response. It is also found that the passage of the cracked primary shaft near to an integral multiple of the critical speed leads to the phenomenon of sup-harmonic resonance. Subsequently, the experimental analysis conducted equally indicated that the quantitative relation between the faults and the performance of the transmission is impacted by the time-varying stiffness and is the main cause of the frequency-modulated feature in the Cardan shaft system. Finally, the experimental results were informative for the transient response exploration and comparable to the theoretical findings for validating the proposed twin-rotor model.