THE BOUNDARY ELEMENT METHOD FOR CALCULATING THE BENDING STIFFNESSES OF THE ROTATING SHAFT WITH A TRANSVERSE CRACK

摘要

Transverse crack on a rotating shaft can increase its flexibilities (or decrease its stiffnesses) locally. With rotating shaft, the angle included between the direction of the opening and that of the resultant force on the cracked section varies with time. This causes the so-called "open or close" effect of the crack, with consequence of changing local flexibility near the crack. In this paper some skill of treatment for numerical calculation by the Boundary Element Method (BEM) are discussed, the flexibility of a cracked shaft segment under different open-close conditions is calculated, and a large computer software for 3-dimensional elasticity and fracture mechanics analysis of a cracked shaft segment is programmed. In the light of flexibility super-position principle for spring series connection, the corresponding stiffness of whole cracked shaft is obtained. By means of auxiliary softwares, a curve of stiffness increments Δk vs. carack direction with its first five harmonic components is established. The analytical result is of value to theoretical study of dynamic characteristics for cracked rotor-bearing systems and to further diagnosing a crack on the shaft through vibration monitoring.