Neural approach to estimate the stress intensity factor of semi‐elliptical cracks in rotating cracked shafts in bending

In the last decades, neural network approach has often been used to study various and complex engineering problems, such as optimization or prediction. In this paper, a methodology founded on artificial neural networks (ANNs) was used to calculate the stress intensity factor (SIF) in different points of the front of a semi‐elliptical crack present in a rotating shaft, taking into account the shape and depth of the crack, the angle of rotation, and the location of the point in the front. In the event of rotating machines, such as shafts, it is crucial to know the SIF along the crack front because this parameter, according to the Paris Law, is related to the performance of the crack during its propagation. Previously, it was necessary to achieve the data for the ANN training, for this a quasi‐static numerical model was made, which simulates a rotating cracked shaft with a semi‐elliptical crack. The numerical solutions cover a wide range of crack depths and shapes, and rotation angles. The values of the SIF estimated by the ANNs were contrasted with other solutions available in the literature finding a good agreement between them. The proposed neural network methodology is an alternative that offers a very good option for the SIF estimation, because it is efficient and easy to use, does not require high computational costs, and can be used to analyse the propagation of cracks contained in rotating shafts by means of the Paris Law taking into account the nonlinear behaviour of the shaft.The authors would like to thank the Spanish Ministerio de Economía y Competitividad for the support for this work through the projects DPI2009-13264 and DPI2013-45406-

A closed expression for the stress intensity factor of concave fatigue cracks in rotating shafts

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.The authors would like to thank the Spanish Ministerio de Economía y Competitividad for the support for this work through the projects DPI2009-13264 and DPI2013-45406-

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., 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.The authors would like to thank the Spanish Ministerio de Economía y Competitividad for the support for this work through the project DPI2013-45406-P

Role of age and comorbidities in mortality of patients with infective endocarditis

[Purpose]: The aim of this study was to analyse the characteristics of patients with IE in three groups of age and to assess the ability of age and the Charlson Comorbidity Index (CCI) to predict mortality. [Methods]: Prospective cohort study of all patients with IE included in the GAMES Spanish database between 2008 and 2015.Patients were stratified into three age groups:<65 years,65 to 80 years,and ≥ 80 years.The area under the receiver-operating characteristic (AUROC) curve was calculated to quantify the diagnostic accuracy of the CCI to predict mortality risk. [Results]: A total of 3120 patients with IE (1327 < 65 years;1291 65-80 years;502 ≥ 80 years) were enrolled.Fever and heart failure were the most common presentations of IE, with no differences among age groups.Patients ≥80 years who underwent surgery were significantly lower compared with other age groups (14.3%,65 years; 20.5%,65-79 years; 31.3%,≥80 years). In-hospital mortality was lower in the <65-year group (20.3%,<65 years;30.1%,65-79 years;34.7%,≥80 years;p < 0.001) as well as 1-year mortality (3.2%, <65 years; 5.5%, 65-80 years;7.6%,≥80 years; p = 0.003).Independent predictors of mortality were age ≥ 80 years (hazard ratio [HR]:2.78;95% confidence interval [CI]:2.32–3.34), CCI ≥ 3 (HR:1.62; 95% CI:1.39–1.88),and non-performed surgery (HR:1.64;95% CI:11.16–1.58).When the three age groups were compared,the AUROC curve for CCI was significantly larger for patients aged <65 years(p < 0.001) for both in-hospital and 1-year mortality. [Conclusion]: There were no differences in the clinical presentation of IE between the groups. Age ≥ 80 years, high comorbidity (measured by CCI),and non-performance of surgery were independent predictors of mortality in patients with IE.CCI could help to identify those patients with IE and surgical indication who present a lower risk of in-hospital and 1-year mortality after surgery, especially in the <65-year group

Stress Intensity Factor and propagation of an open sickle shaped crack in a shaft under bending

Surface cracks commonly propagate in rotating machines due to cyclic loads. The propagation of these cracks in shafts is an important problem that can lead to catastrophic failure and put lives at risk. Although the majority of the works on cracked shafts consider that the shape of the front of the surface cracks is straight or almond, also sickle-shaped cracks can appear in shafts. In this study, we propose an expression that provides the value of the Stress Intensity Factor (SIF) of an open crack with sickle shape, located at the central section of a shaft, as a function of the relative depth of the crack, the shape factor and the relative position on the crack front. To this end, the SIF along the crack front has been determined through a 3D numerical analysis considering different elliptical geometries of the crack. To validate the expression, we have compared the obtained results with other solutions obtained by numerical approaches of the literature. It has been found that they are in good agreement. Finally, the sickle crack propagation has been analyzed using the expression for sickle cracks proposed and a developed algorithm based on the Paris Law.The authors would like to thank the Spanish Ministerio de Economía y Competitividad for the support for this work through the project DPI2013 45406 P

Closed-form solution for the natural frequencies of low-speed cracked Euler-Bernoulli rotating beams

This article belongs to the Section Engineering MathematicsIn 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.This work was supported by the "Agencia Estatal de Investigacion" (AEI) of the Government of Spain through the project PID2019-104799GB-I00/AEI/10.13039/501100011033 and by the "Comunidad de Madrid" (Spain) through the project EPUC3M20

Study of the propagation of concave semi-elliptical shaped breathing cracks in rotating shaft

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.The authors would like to thank the Spanish Ministerio de Economía y Competitividad for the support for this work through the project DPI2013-45406-P

Determination of the critical speed of a cracked shaft from experimental data

This article belongs to the Section Fault Diagnosis & Sensors.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.This research was funded by the Ministerio de Ciencia e Innovación under the projects DPI2006-09906 and DPI2009-13264

Contemporary use of cefazolin for MSSA infective endocarditis: analysis of a national prospective cohort

Objectives: This study aimed to assess the real use of cefazolin for methicillin-susceptible Staphylococcus aureus (MSSA) infective endocarditis (IE) in the Spanish National Endocarditis Database (GAMES) and to compare it with antistaphylococcal penicillin (ASP). Methods: Prospective cohort study with retrospective analysis of a cohort of MSSA IE treated with cloxacillin and/or cefazolin. Outcomes assessed were relapse; intra-hospital, overall, and endocarditis-related mortality; and adverse events. Risk of renal toxicity with each treatment was evaluated separately. Results: We included 631 IE episodes caused by MSSA treated with cloxacillin and/or cefazolin. Antibiotic treatment was cloxacillin, cefazolin, or both in 537 (85%), 57 (9%), and 37 (6%) episodes, respectively. Patients treated with cefazolin had significantly higher rates of comorbidities (median Charlson Index 7, P <0.01) and previous renal failure (57.9%, P <0.01). Patients treated with cloxacillin presented higher rates of septic shock (25%, P = 0.033) and new-onset or worsening renal failure (47.3%, P = 0.024) with significantly higher rates of in-hospital mortality (38.5%, P = 0.017). One-year IE-related mortality and rate of relapses were similar between treatment groups. None of the treatments were identified as risk or protective factors. Conclusion: Our results suggest that cefazolin is a valuable option for the treatment of MSSA IE, without differences in 1-year mortality or relapses compared with cloxacillin, and might be considered equally effective