Adaptive modeling of vibrations and structural fatigue for analyzing crack propagation in a rotating system

Abstract

This study is concerned with adaptive modeling of vibrations and structural fatigue in a rotating system with a propagating crack. The system consists of a Jeffcott rotor with a transverse surface crack at mid-span. It undergoes low and high cycle loadings due to an unbalance force. The high cycle loading (HCL) and the consequent high cycle fatigue (HCF) can accelerate crack growth, structural degradation and occurrence of mechanical failure. Therefore, accurate modeling is critical for lifetime prediction and prognostics requirements. There is a significant difference between the time constants of the rotor’s dynamic behavior and that of crack growth. Hence, in most of the prior studies, it has been assumed that the crack depth is constant, which implies that the system undergoes low cycle loading (LCL). In some studies that do focus on HCL, the loading scenario is assumed to be a summation of LCL steps with constant length. This study shows that assuming constant and pre-defined length for these steps can significantly affect the accuracy of the model leading to inaccurate lifetime prediction and poor prognostics in general. Hence, in this study, a novel approach is proposed in which the LCL step length is variable and adaptive. Considering different relationships proposed for modeling the fatigue crack growth, fluctuation of stress intensity factor (SIF) is the most important factor for driving the crack growth. Hence, an index is defined based on the rate of SIF fluctuation. Critical thresholds of this index are set at rapid and slow crack growth conditions. The level of proximity to these thresholds determines each LCL step length, which is hence determined adaptively. The equations governing the rotor motion and crack growth are formulated using Newton’s second law of motion and Paris–Erdogan’s fatigue crack growth law, respectively. The equations are solved numerically using the Runge–Kutta method. It is shown that this novel adaptive approach makes the modeling process realistic and computationally efficient while providing high accuracy. The results of this study could be of significance in decision making processes that would require lifetime prediction and prognostics of crack growth.