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  • Publication
    Elliptical Crack Identification in a Nonrotating Shaft
    (2018-10-24) Muñoz Abella, María Belén; Rubio Ruiz de Aguirre, María Lourdes; Rubio Herrero, Patricia; Montero García, Laura; Ministerio de Economía y Competitividad (España)
    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., is 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.
  • Publication
    Determination of the critical speed of a cracked shaft from experimental data
    (MDPI, 2022-12-02) Muñoz Abella, María Belén; Montero García, Laura; Rubio Herrero, Patricia; Rubio Ruiz de Aguirre, María Lourdes; Ministerio de Ciencia e Innovación (España)
    In this work, a procedure to obtain an accurate value of the critical speed of a cracked shaft is presented. The method is based on the transversal displacements of the cracked section when the shaft is rotating at submultiples of the critical speed. The SERR (Strain Energy Ralease Rate) theory and the CCL (Crack Closure Line) approach are used to analyse the proposed methodology for considering the behaviour of the crack. In order to obtain the best information and to define the procedure, the orbits and the frequency spectra at different subcritical rotational speed intervals are analyzed by means of the Fast Fourier Transform. The comparison of the maximum values of the FFT peaks within the intervals allows the subcritical speed to be determined, along with the value of the critical speed. When verified, the proposed procedure is applied to shafts with the same geometry and material and with cracks of increasing depth. The results show that the critical speed diminishes with the severity of the crack, as expected. A comparison is made between the critical speed obtained using the vertical and the horizontal displacements, finding no remarkable differences, meaning that in practical applications only one sensor for one of the displacements (in the vertical or horizontal direction) is needed to determine the critical speed. This is one of the main contributions of the paper, as it means that the orbits of the shaft are not needed. Finally, after this study we can conclude that the best results are achieved when the critical speed is obtained using data displacement in only one direction within the intervals around 1/2 or 1/3 of the critical speed.
  • Publication
    Closed-form solution for the natural frequencies of low-speed cracked Euler-Bernoulli rotating beams
    (MDPI, 2022-12-02) Muñoz Abella, María Belén; Rubio Ruiz de Aguirre, María Lourdes; Rubio Herrero, Patricia; Comunidad de Madrid; Ministerio de Ciencia e Innovación (España)
    In this study, two closed-form solutions for determining the first two natural frequencies of the flapwise bending vibration of a cracked Euler-Bernoulli beam at low rotational speed have been developed. To solve the governing differential equations of motion, the Frobenius method of solution in power series has been used. The crack has been modeled using two undamaged parts of the beam connected by a rotational spring. From the previous results, two novel polynomial expressions have been developed to obtain the first two natural frequencies as a function of angular velocity, slenderness ratio, cube radius and crack characteristics (depth and location). These expressions have been formulated using multiple regression techniques. To the knowledge of the authors, there is no similar expressions in the literature, which calculate, in a simple way, the first two natural frequencies based on beam features and crack parameters, without the need to know or solve the differential equations of motion governing the beam. In summary, the derived natural frequency expressions provide an extremely simple, practical, and accurate instrument for studying the dynamic behavior of rotating cracked Euler-Bernoulli beams at low angular speed, especially useful, in the future, to establish small-scale wind turbines' maintenance planes.
  • Publication
    Study of the propagation of concave semi-elliptical shaped breathing cracks in rotating shaft
    (Elsevier, 2019-12) Rubio Herrero, Patricia; Bernal Cuadrado, Javier; Rubio Ruiz de Aguirre, María Lourdes; Muñoz Abella, María Belén; Ministerio de Economía y Competitividad (España)
    When a cracked shaft rotates, the crack contained in it progressively opens and closes during a revolution. Accordingly, the behavior of the shaft becomes nonlinear. In this paper, the propagation of concave semi-elliptical shaped cracks contained in rotating shafts has been studied considering the nonlinear effect of the breathing crack. To study the propagation, we propose an integration algorithm based on the Paris-Erdogan Law which allows determining the crack shape evolution of concave breathing cracks in rotating shafts. The Stress Intensity Factor used by the algorithm to analyze the propagation has been computed using the four parametric expression for concave cracks proposed by the authors in a previous work. By now, it has not been found in the literature propagation studies of concave surface cracks in rotating shafts that consider the breathing mechanism of the crack.
  • Publication
    A closed expression for the stress intensity factor of concave fatigue cracks in rotating shafts
    (Elsevier Ltd., 2019-06-01) Rubio Herrero, Patricia; Bernal Cuadrado, Javier; Muñoz Abella, María Belén; Rubio Ruiz de Aguirre, María Lourdes; Ministerio de Economía y Competitividad (España)
    A new analytical model is developed that allows us to obtain the Stress Intensity Factor (SIF) in a point on a concave shaped crack contained in a rotating shaft as a function of the characteristics of the crack (depth and aspect), the point position on the crack front, and the rotation angle. The model can be used for all kinds of linear elastic materials. The Finite Element Method (FEM) has been used to make a tridimensional quasi-static model of a shaft that contains a concave shaped crack in its central section, subjected to rotary bending. Different rotation angles are taken into account in order to simulate the rotation of the shaft. The SIF is determined in every position of the front of the concave crack, for each crack geometry and for each rotation angle. Then an analytical model is developed using all the results of SIF obtained with the numerical model, and is verified comparing its results with solutions found in the literature. The proposed model may be very useful to study the dynamic behavior of shafts with concave shaped cracks, and can be employed to analyze the propagation of these types of cracks.
  • Publication
    Crack identification in non-uniform rods by two frequency data
    (Elsevier, 2015-12-01) Rubio Ruiz de Aguirre, María Lourdes; Fernández-Sáez, José; Morassi, Antonino
    We consider the inverse problem of identifying a single open crack in a longitudinally vibrating rod having non-uniform smooth profile. Without any a priori assumption on the smallness of the damage and assuming that the rod profile is symmetric with respect to the mid-point of the rod axis, we present a constructive diagnostic algorithm from minimal frequency data. We show that the crack can be uniquely identified, up to a symmetric position, from the first two positive natural frequencies of the rod under free-free end conditions. We also show that the non-uniqueness of the damage location can be removed by using as data the first positive resonant frequency of the free-free rod and the first antiresonant frequency of the driving-point frequency response evaluated at one end of the rod. The results of numerical simulations and of applications of the method to experimental data agree well with the theory. (C) 2015 Elsevier Ltd. All rights reserved.