Elliptical Crack Identification in a Nonrotating Shaft

Abstract

It is known that fatigue cracks are one of the most important problems of the mechanical components, since their propagation can cause severe loss, both personal and economic. So, it is essential to know deeply the behavior of the cracked element to have tools that allow predicting the breakage before it happens. The shafts are elements that are specially affected by the described problem, because they are subjected to alternative compression and tension stresses. This work presents, firstly, an analytical expression that allows determining the first four natural frequencies of bending vibration of a nonrotating cracked shaft, assumed as an Euler–Bernoulli beam, with circular cross section under pinned-pinned conditions, taking into account the elliptical shape of the crack. Second, once the direct problem is known, the inverse problem is approached. Genetic Algorithm technique has been used to estimate the crack parameters assuming known the natural frequencies of the cracked shaft.

Identification of cracks in low-speed rotating slender cracked beams using frequencies and artificial rabbit algorithm

“…Different methods and tools have been applied to address this problem. Of all of them, neural networks (Mohammed et al 2014;Muñoz-Abella et al 2020;Bilotta et al 2023) currently occupy a prominent place in comparison with conventional optimisation techniques (Suh et al 2000;Shekar 2004;Rubio 2009), or those based on constructive algorithms based on vibration problems (Fernández-Sáez et al 2017;Rubio et al 2018) or on genetic algorithms or other optimization methods (Maity and Tripathy 2005;Muñoz-Abella et al 2018;Ramezani and Bahar 2021;Muñoz-Abella et al 2022a, Gordan et al 2017, Jahangiri et al 2016, Marques et al 2018. However, there are some methods whose use is currently gaining more strength with the development of AI.…”

Dynamic Behavior Analysis of a Rotating Shaft with an Elliptical Breathing Surface Crack

“…Then, in Ref. [44] they introduced an analytical expression to evaluate the first four bending natural frequencies of a nonrotating pinned-pinned Euler-Bernoulli shaft. And as an inverse problem, they proposed a genetic algorithm technique to identify elliptical crack using these known natural frequencies.…”

Closed-Form Solution for the Natural Frequencies of Low-Speed Cracked Euler–Bernoulli Rotating Beams

“…On crack modeling, most authors model the cracked beam as two beams connected by one or more springs, located in the section that contains the crack, and whose stiffness represents the increase in local flexibility as a result of its presence. In most of the works, the stiffness of the spring is obtained from the application of Fracture Mechanics concepts such as the Stress Intensity Factor (SIF) or the integral J, such as in [27,28]. When addressing the problem of studying the behavior of the blade with a defect, the appearance of a crack implies the modification of the movement equations, requiring the introduction of terms that take into account the effect of damage.…”