In the last years new technologies and methodologies have been developed for increasing the reliability of fault diagnosis in mechanical equipment, mainly in rotating machinery. Global vibration indexes as RMS, Kurtosis, etc., are widespread known in industry and in addition, are recommended by international norms. Despite that, these parameters do not allow reaching reliable equipment condition diagnosis. They are attractive for their apparent simplicity of interpretation. This work presents a discussion about the diagnosis possibilities based on these traditional parameters. The database used comprises rolling bearings vibration signals taking into account different fault conditions, several shaft speeds and loading. The obtained results show that these global vibration parameters are limited regarding correct fault diagnosis, especially in initial faults condition. As an alternative method a new technique is proposed. This technique seeks to obtain a global parameter that makes better characterization of fault condition. This methodology, named Residual Energy, uses integration of the difference between the power spectrum density of the fault condition and the normal one. The results obtained with this technique are compared with the traditional RMS and Kurtosis.

Rui Gomes Teixeira de Almeida

Silmara Alexandra da Silva Vicente

Linilson Rodrigues Padovese

New Technique for Evaluation of Global Vibration Levels in Rolling Bearings

This article deals with the identification of elastic parameters (engineering constants) in sandwich honeycomb orthotropic rectangular plates. A non-destructive method is introduced to identify the elastic parameters through the experimental measurements of natural frequencies of a plate undergoing free vibrations. Four elastic constant are identified. The estimation of the elastic parameter problem is solved by minimizing the differences between the measured and the calculated natural frequencies. The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. The analysis of the results indicates the efficiency of the method.

Sergio Ferreira Bastos

Lavinia Borges

Fernando A. Rochinha

Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates

Even though there is a growing interest in active vibration isolation systems, passive approaches are still the best choice in many cases because they are inherently the simplest and of lowest cost. Moreover, better comprehension of the dynamics and specially of the damping behavior in passive systems is required for successful implementation of active schemes. In the vast literature of passive isolation systems, there are not many works that consider damping models more elaborated than the widely used complex modulus. In this work a passive isolation system composed of a base and two isolators, modelled as Timoshenko beams, and a vibration source, modelled as a rigid body, is considered. For the isolators, two different viscoelastic models are considered: the Anelastic Displacement Fields (ADF) and Fractional Calculus (FC), which will be compared with the complex modulus model. The results show that both ADF and FC models lead to better approximation of dissipated energy, since they account for frequency-dependence of the viscoelastic isolators. Analysis of the curve-fitting of material parameters, using ADF and FC models has shown that generally less parameters are needed by FC model, for the same fitting quality, although optimization results depends strongly on the initial guess for the solution.

Alberto Coronado

Marcelo A. Trindade

Rubens Sampaio

Frequency-Dependent Viscoelastic Models for Passive Vibration Isolation Systems

Fault identification in rotor systems has been studied by many authors, but the considered malfunction is one single fault only, generally an unbalance. Real machines can be affected by several different types of faults; moreover sometimes also two different faults may develop simultaneously. A model based method for identifying multiple faults acting simultaneously on a rotor system in the frequency domain is briefly described and its robustness with regards to measuring and modelling errors is evaluated, by means of numerical simulations performed on the models of two typical power plant machines: a steam turbogenerator and a gas turbogenerator.

Nicol&#xf2; Bachschmid

Paolo Pennacchi

Multiple Fault Identification Method in the Frequency Domain for Rotor Systems

This work compares the results of laboratory experiments with numerical modelling using the finite element method in order to assess the attenuation of hearing protectors under conditions of high amplitude impulse noise. Comparative data for the finite element simulation was provided from a series of experiments using a shock tube, acoustic test fixture, ear canal simulator and partial head form. The numerical model comprised a finite element mesh of fluid and porous materials in order to model the earmuff hearing protector coupled to the auditory canal. The results show that a simple 2-D finite element model is capable of making a reasonable prediction of the attenuation of an earmuff provided that headband force is also included in the model.

Felipe Vergara

Samir N. Gerges

Robert S. Birch

Numerical and Experimental Study of Impulsive Sound Attenuation of an Earmuff

A method for calculating the breathing behavior of transverse cracks of different types in rotating shafts is described. Thermal effects are included. Some results in terms of vibration excitation related to different shapes of cracks are presented.

Ezio Tanzi

Vibration Pattern Related to Transverse Cracks in Rotors

The Karhunen-Lo&#xe8;ve expansion is a powerful spectral technique for the analysis and synthesis of dynamical systems. It consists in decomposing a spatial correlation matrix, which can be obtained through numerical or physical experiments. The decomposition produces orthogonal eigenfunctions or proper orthogonal modes, and eigenvalues that provide a measurement of how much energy is contained in each mode. The relation between KL modes and mode shapes of linear vibrating systems has already been derived and demonstrated for two and three dofs mass-spring-damper systems. The purpose of this paper is to extend this investigation to more complex distributed-parameter linear systems. A plane truss and a simply supported plate subjected to impulsive forces, commonly used in modal analysis are studied. The resulting KL modes are compared to the analytical mode shapes. Damping and random noise effects in the procedure performance are evaluated. Two methods for indirectly obtaining natural frequencies are also presented.

Claudio Wolter

Obtaining Mode Shapes through the Karhunen-Lo&#xe8;ve Expansion for Distributed-Parameter Linear Systems

Unbalance and asynchronous forces acting on a flexible rotor are characterized by their positions, amplitudes, frequencies and phases, using its measured vibration responses. The rotary machine dynamic model is a neural network trained with measured vibration signals previously decomposed by wavelets. A typical compaction ratio of 2048:4 is achieved in this application, considering the stationary nature of the measured vibrations signals and the shape of the chosen wavelet function. The Matching Pursuit procedure, coupled to a modified Simulated Annealing optimization algorithm is used to decompose the vibration signals. The performance of several neural network with different input database sets is analyzed to define the best network architecture in the sense to achieve successful training, minimum identification error, with maximum probability to give the correct answers. The experiments are conducted on a vertical rotor with three rigid discs mounted on a flexible shaft supported by two flexible bearings. The vibration responses are measured at the bearings and at the discs. A methodology to balance flexible rotors based on the proposed identification methodology is also presented.

Francisco Paulo Lepore

Marcelo Braga Santos

Rafael Gon&#xe7;alves Barreto

Identification of Rotary Machines Excitation Forces Using Wavelet Transform and Neural Networks

This paper introduces a new type of Finite Element Method (FEM), called Composite Element Method (CEM). The CEM was developed by combining the versatility of the FEM and the high accuracy of closed form solutions from the classical analytical theory. Analytical solutions, which fulfil some special boundary conditions, are added to FEM shape functions forming a new group of shape functions. CEM results can be improved using two types of approach: h-version and c-version. The h-version, as in FEM, is the refinement of the element mesh. On the other hand, in the c-version there is an increase of degrees of freedom related to the classical theory (c-dof). The application of CEM in vibration analysis is thus investigated and a rod element is developed. Some samples which present frequencies and vibration mode shapes obtained by CEM are compared to those obtained by FEM and by the classical theory. The numerical results show that CEM is more accurate than FEM for the same number of total degrees of freedom employed. It is observed in the examples that the c-version of CEM leads to a super convergent solution.

Marcos Arndt

Roberto Dalledone Machado

Mildred Ballin Hecke

An Introduction to the Composite Element Method Applied to the Vibration Analysis of Trusses

The Electrodynamic Vibration Exciter (shakers) has been one of the most employed excitation sources in modal tests. The shaker is an electromechanical device that provides a mechanical motion due to the input signal sent to its coil. Despite being widely used, it is well known that the shaker interacts with the structure under test. In particular, when the structure passes through a given resonance, the force delivered by the shaker abruptly decreases, causing the so called drop off phenomenon. This paper aims to study this force drop off phenomenon in the single shaker modal testing. Analytical models are developed to help in understanding the physical principles involved in the interaction between the shaker and the structure under test. Experimental analyses are performed using different shakers as well as excitation signals, in order to evaluate the effects of the input signal, as well as the power amplifier operational modes, on the structure dynamics. Preliminary tests revealed that significant distortions might occur during vibration tests using shakers and these distortions significantly affect the determination of the structure response.

Paulo Sergio Varoto

Leopoldo Pisanelli Rodrigues de Oliveira

On the Force Drop Off Phenomenon in Shaker Testing in Experimental Modal Analysis

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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