L. Rubio

A Note on the Use of Approximate Solutions for the Bending Vibrations of Simply Supported Cracked Beams

The main goal of this note is to discuss the applicability of approximate closed-form solutions to evaluate the natural frequencies for bending vibrations of simply supported Euler-Bernoulli cracked beams. From the well-known model, which considers the cracked beam as two beams connected by a rotational spring, different approximate solutions are revisited and compared with those found by a direct method, which has been chosen as reference.

Quasi-static numerical study of the breathing mechanism of an elliptical crack in an unbalanced rotating shaft

In this paper we present the numerical analysis of the quasi-static behavior of an unbalance cracked shaft with straight and elliptical cracks considering an eccentric mass. The rotation of the shaft has been simulated by considering different angular positions to complete one rotation. The influence of the mass eccentricity in the opening of the crack has been studied considering different angles of eccentricity. The study of the partially opening/closing of the crack in the rotation of the shaft under the influence of the eccentric mass is analyzed. The work allows us to know the influence of the unbalance in the crack breathing mechanism and will help to predict the influence of this behavior on the values of the Stress Intensity Factor and on the propagation of cracks.

Web-based application for descriptive geometry learning

In the education of basic matters of technical studies, as representation systems, it is necessary to introduce new technologies that allow individual learning to students. Learning can be traditional face to face or remotely by means of e‐learning. In this work, a web‐based computer specific application to study the Monge Projection is presented. The web site is design to have two different parts: the theoretical tutorials to remind the most important concepts of the subject, and some step by step solved exercises with indications, in order to fix the main ideas of the subject in the students mind. Likewise, and for a better comprehension, the students have the possibility, once finished the exercise, to visualize the three‐dimensional solution of the two‐dimensional problem. This application is initially thought to support the master classes, but it is also valid for distance learning, where students face alone the learning. This type of applications allows bringing basic matters closer to the students by the use of new technologies.

Identification of two cracks with different severity in beams and rods from minimal frequency data

It has been known for a long time that the problem of identifying two small cracks in a simply supported beam from the first three natural frequencies can be analytically formulated and solved if the two cracks have equal severity. In this paper we extend this result to the case of cracks with different severity. Each crack is simulated by a rotational elastic spring and the inverse problem is solved in terms of the damage-induced changes in the first four natural frequencies. Closed-form expressions of the damage parameters in terms of the measured frequencies are obtained. The results can be extended to the identification of two cracks in a longitudinally vibrating beam based on a suitable set of natural frequency and antiresonant frequency data. Numerical simulations support the theory, and show that if accurate input data are available and the cracks are not too close, then damage identification leads to satisfactory results.

Computer-aided tool for teaching mechanical clutch systems design

This paper describes an educational computer application—MecClutch—focused on teaching the design process of mechanical clutches and their operational conditions to Mechanical Engineering students. The software is divided into three sections: (1) multimedia files, pictures, and videos, produced in order to teach the working of the mechanism, (2) theoretical information related to mechanical clutches, and (3) interactive problems that allow to design a mechanical clutch and test changes in operational conditions when varying the value of critical design parameters. This software has become a very useful tool for undergraduate Mechanical Engineering students in compliment to theoretical classes or alone, as a self‐study tool.

Identification of an open crack in a beam with variable profile by two resonant frequencies

We consider the identification of a single open crack in a simply supported beam having nonuniform smooth profile and undergoing infinitesimal in-plane flexural vibration. The profile is assumed to be symmetric with respect to the mid-point of the beam axis. The crack is modeled by inserting a rotational linearly elastic spring at the damaged cross-section. We establish sufficient conditions for the unique identification of the crack by a suitable pair of natural frequency data, and we present a constructive algorithm for determining the damage parameters. The result is proved under a technical a priori assumption on the zeros of a suitable function determined in terms of the eigenfunctions of the problem. Extensions to beams under different sets of end conditions are also discussed. Theoretical results are confirmed by an extensive numerical investigation, both on simulated and experimental data.

Study of the Stress Intensity Factor of an Unbalanced Rotating Cracked Shaft

The components of machines very often present defects that can grow to fatigue cracks when they are submitted to the working solicitations. In the case of shaft,this is particularly important because the catastrophic failures can lead to personal injuries or economic problems. When a cracked shaft rotates, the breathing mechanism appears. The crack opens and closes passing from the open state to the close state with a transition that produces a partial opening. The shafts present additionally misalignments or/and unbalances that alter their normal function. In this paper, we present a Finite Element Method (FEM) study of the influence of the eccentricity in the breathing mechanism of a rotating cracked shaft. The classical Jeffcott rotor model has been chosen for this study. To simulate the rotation of the shaft, different angular positions have been considered. The Stress Intensity Factor (SIF) along the crack front during the rotation has been studied considering different angles of eccentricity. The work allows to know the influence of the unbalance of rotating shafts in the crack breathing mechanism, in the values of the Stress Intensity Factor and in the propagation of cracks.

Elliptical Crack Identification in a Nonrotating Shaft

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.

FEM Analysis of the SIF in Rotating Shafts Containing Breathing Elliptical Cracks

Failures due to the propagation of fatigue cracks in shafts are one of the most common problems in rotating machines as they can cause irreversible damage and put lives at risk. The main parameter for the study of crack propagation is the Stress Intensity Factor. When a cracked shaft rotates, the transverse crack contained in it presents the opening and closing mechanism (“breathing mechanism”). Although most of the studies on cracked shafts consider straight cracks, the real fatigue cracks have a semi-elliptical front. In this work, the numerical analysis of the Stress Intensity Factor along the entire front of a semi-elliptical crack during the rotation of the shaft has been developed taking into account the breathing mechanism.

Web-Application for Engineering Graphics - An Example of a Distance Learning Tool

The new global communication systems and their integration in all media communication, together with their potential interactivity, are changing our culture and are introducing new questions and challenges in the educative system. The teaching practices are strongly impacted by the development of the new technologies, not only because they influence the professional skills of the teachers, but also because of the roll they have assumed in the global university context.