Generalized Breathing Functions for Stiffness Model of Transversely Cracked Hollow Shaft

Abstract

The exact breathing mechanism of the transverse crack in the hollow shaft that appears due to the shaft weight is important to analyze correctly the dynamic behavior of the rotor system. We discuss a breathing phenomenon which appears only in the hollow shaft rotation and determine the exact time-varying area moments of inertia for the cracked element cross-section. Considering the variation behavior of the area moments of inertia, generalized breathing functions are suggested to formulate the finite-element stiffness matrix of the crack element. The harmonic balance method (HBM) is employed to solve the finite-element model of the rotor-bearing-disk system. We study the influence of ratio of the internal and external diameter of shaft, dimensionless crack depth, location of crack and angle between the crack and imbalance directions. Some significant behaviors of the system are compared with some previously published results, and they can be contributed to detecting the crack in hollow shaft early. Comparison shows the generalized breathing functions are accurate to model the stiffness variation of shaft due to the crack.