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

Abstract

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.

Vibrations of Misaligned Rotor System with Hysteretic Friction Arising from Driveshaft–Stator Contact under Dispersed Viscous Fluid Influences

“…The orbital trajectories of the centre of the rotors in a steady state with some regular and intermittent loops are orbitally stable (Figure 7a,b). The operating point of the driven shaft is close to the limit of stability compared to the previous study on the balanced twin-rotor system in [2]. The frequency analysis (Figure 7c) is confirmed in both shafts, the presence of the main rotational frequency from 0 to 50 Hz and the frequency multiple of the rotation frequency of the drive shaft.…”

“…where µ is a small perturbation parameter that depends on θ 1 . The kinematic relationship between the output motion θ 2 and input θ 1 is given by Seherr-Thoss et al, [15] tan θ 2 = cos β tan θ 1 (2) where β is the angle of inclination of the secondary shaft. Combining Equations ( 1) and (2), yields…”

“…Furthermore, a crack-induced excitation was identified in a two-axis model for a propeller shaft. The identification considered the torsional and elasticity of an unbalanced and misaligned shaft system using numerical and experimental techniques [2]. Study of the nonlinear dynamic response of a rotor system with multi-faults including unbalance, asymmetric shaft and angular misalignments were numerically investigated by Didier et al, and the influences of the stochastic fault parameters were analysed using a polynomial chaos expansion method for different kinds and levels of uncertainties.…”

“…the velocity vectors of unbalance masses m u1 and m u2 , respectively, rotating with the moment of inertia of disc 1 and disc 2[2]. After manipulation and calculation, the vectors .…”

A Comprehensive Study of Cardon Shaft Using Modal Analysis

“…Numerous theoretical and numerical works that emphasize nonlinear parameters and show various nonlinear phenomena and parametric excitation have been published [12][13][14]. Cardan shaft dynamic analysis, however, heavily relies on nonlinear effects, such as breathing cracks on connected shafts caused by a Hooke's joint, which have been examined in [15,16]. These effects were mostly caused by the time-varying stiffness' nonlinear properties, the fluctuating Hooke's joint's disturbance, and the mass imbalance of the rotor system.…”