MODAL ANALYSIS AND DYNAMIC RESPONSES OF A HYSTERETICALLY DAMPED AXLE SHAFT WITH A TRANSVERSE CRACK

摘要

An axle shaft supports rotating elements, and is fitted to the housing by means of bearings. It mostly does not transmit torque, with exceptions such as in train axles. Non-rotating axles are subjected to bending moments due to dynamic transverse loads. Axles such as in automobiles are marked with occasional failures due to fatigue cracks, which can prove serious, if the cracks are not detected early. Vibration based condition monitoring is the field concerned with crack detection based on the dynamic responses of the system. In this light, the present paper discusses the vibration analysis of a cracked axle. The cracked shaft is modelled using finite element method, for transverse vibration conditions. The shaft is modelled based on Euler-Bernoulli theory for bending, while the crack is modelled based on fracture mechanics approach. After modelling, modal analysis of the system is carried out, with the consideration of proportional hysteretic damping. The Eigen value problem provides the natural frequencies and mode shapes. The Frequency Response Functions (FRF's) magnitude and phase plots are obtained, from which the natural frequencies and structural damping loss factors can be calculated. Further, the free vibration and forced vibration system time responses are obtained, using numerical integration methods. The corresponding responses in frequency domain are obtained using Fast Fourier Transformation (FFT). The FRF's and dynamic responses of the shaft without and with crack are comparatively studied. The study provides the platform for condition monitoring of shaft cracks.