Vibrations prediction and measurement of multi-stage bladed disks with non linear behavior due to friction contacts

The architecture of current aircraft turbofan engines consists of multi-stage assemblies resulting from the coupling of bladed disks by means of bolted flange joints. The efficiency of such systems in real working condition is strictly related to the dynamic properties of blades and disks constituting them. According to the current design practices, blades and disks are designed so that their weights are reduced and their slenderness increased. Therefore, latest generation turbofan engine thus result much more sensible to mechanical vibrations that may cause failure by high cycle fatigue phenomena. For these reasons robust computational techniques and innovative measurement systems have become necessary tools for the design and validation of multi-stage bladed disks assemblies, in order to preserve their structural integrity while operating in real working conditions. The topics developed in this Ph.D. thesis concern aspects of linear and non-linear dynamics in the turbomachinery field and give a series of important guidelines for the study of multi-stage bladed disks systems from both a numerical and experimental point of view. The research activity has been mainly focused on the following two topics: 1. Development of reduced order model techniques for the prediction of forced response of multi-stage bladed disk assemblies. The main challenge associated with modeling multi-stage assemblies is strictly related to the possible different cyclic symmetry characterizing the coupled stages. In such case a sector representative of the whole multi-stage system does not exist in general and typical dynamic calculations based on cyclic constraints can not be performed as in the case of single bladed disks. Therefore, two novel reduced order model techniques for multi-stage systems have been developed in order to overcome the mentioned drawback while guaranteeing high fidelity in modeling the system dynamics. Furthermore, for the first time the bolted flange joint coupling two bladed disks is considered as a possible source of damping due to friction phenomena. Understanding the effects of such non-linearities in damping blade vibrations could be crucial in design of bolted flange joint. The proposed reduction techniques then also allow the prediction of the forced response of a multi-stage system when friction contacts are present at the flange joint interface while maintaining low computational costs. 2. Validation of the Blade Tip-Timing measurement technique, for the identification of the modal properties of two laboratory dummy disks. In this frame an experimental procedure to validate the Blade Tip-Timing system against the strain gauges measurement has been proposed. Furthermore, a novel methodology for the identification of the operative deflection shape of a vibrating bladed disks in presence of small mistuning has been developed

Stress recovery algorithm for reduced order models of mechanical systems in nonlinear dynamic operative conditions

Nonlinear forced response analyses of mechanical systems in the presence of contact interfaces are usually performed in built-in numerical codes on reduced order models (ROM). Most of the cases these derive from complex finite element (FE) models, resulting from the high accuracy the designers require in modeling and meshing the components in commercial FE software. In the technical literature several numerical methods are proposed for the identification of the nonlinear forced response in terms of a kinematic quantity (i.e. displacement, velocity and acceleration) associated either to the master degrees-of-freedom retained in the ROM, or to the slave ones after having expanded the reduced response through the reduction matrix. In fact, the displacement is the quantity usually adopted to monitor the nonlinear response, and to evaluate the effectiveness of a partially loose friction interface in damping vibrations, with respect to a linear case where no friction interfaces exist and no energy dissipation can take place. However, when a ROM is used the engineering quantities directly involved in the mechanical design, i.e. the strains and stresses, cannot be retrieved without a further data processing. Moreover, in the case of a strong nonlinear behavior of the mechanical joints, the distributions of the nonlinear strains and stresses over the structure is likely different than the one obtained as a superposition of linear mode shapes whose definition require a-priori assumptions on the boundary conditions at the contact interface. This means that the mentioned approximation cannot be used to predict the safety margins of a structure working in real (nonlinear) operative conditions. This paper addresses this topic and presents a novel stress recovery algorithm for the identification of the strains and stresses resulting from a nonlinear forced response analysis on a ROM. The algorithm is applied to a bladed disk with friction contacts at the shroud joint, which make the behavior of the blades nonlinear and non-predictable by means of standard linear analyses in commercial FE software

Synchronous vibration parameters identification by tip timing measurements

The Blade Tip Timing (BTT) measurement system is a technique to measure vibration parameters of a rotating bladed disk. In particular for synchronous vibrations the BTT provides signals versus the rotation speed of the disk starting from the measurement of the time of arrival (TOA) of each blade under the tip timing probes. The signals must be post processed in order to obtain the interesting parameters of each blade vibration. The paper presents a method to extract the main parameters (amplitude and frequency) in resonance condition from the tip timing measurements. The proposed method is a revision of the already existing well known Two-Parameter Plot (2PP) method which requires a minimum of two probes. Improvements to the existing 2PP method are here suggested mainly in the part of engine order identification. The proposed method is then applied to the BTT measured signals coming from a rotating bladed disk excited at different engine orders. At the same time on the disk the vibration of one blade was detected by strain gauges. The strain gauges were calibrated and they provide the reference values of the vibration parameters. The vibration parameters derived by the proposed method are in agreement with those obtained by the strain gages methodolog

Synchronous vibration parameters identification by tip timing measurements

The Blade Tip Timing (BTT) measurement system is a technique to measure vibration parameters of a rotating bladed disk. In particular for synchronous vibrations the BTT provides signals versus the rotation speed of the disk starting from the measurement of the time of arrival (TOA) of each blade under the tip timing probes. The signals must be post processed in order to obtain the interesting parameters of each blade vibration. The paper presents a method to extract the main parameters (amplitude and frequency) in resonance condition from the tip timing measurements. The proposed method is a revision of the already existing well known Two-Parameter Plot (2PP) method which requires a minimum of two probes. Improvements to the existing 2PP method are here suggested mainly in the part of engine order identification. The proposed method is then applied to the BTT measured signals coming from a rotating bladed disk excited at different engine orders. At the same time on the disk the vibration of one blade was detected by strain gauges. The strain gauges were calibrated and they provide the reference values of the vibration parameters. The vibration parameters derived by the proposed method are in agreement with those obtained by the strain gages methodolog

Forced response of rotating bladed disks: Blade Tip-Timing measurements

The Blade Tip-Timing is a well-known non-contact measurement technique currently employed for the identification of the dynamic behaviours of rotating bladed disks. Although the measurement system has become a typical industry equipment for bladed disks vibration surveys, the type of sensors, the positioning of the sensors around the bladed disk and the used algorithm for data post-processing are still not standard techniques, and their reliability has to be proved for different operation conditions by the comparison with other well-established measurement techniques used as reference like strain gauges. This paper aims at evaluating the accuracy of a latest generation Tip-Timing system on two dummy blisks characterized by different geometrical, structural and dynamical properties. Both disks are tested into a spin-rig where a fixed number of permanent magnets excite synchronous vibrations with respect to the rotor speed. A new positioning for the Blade Tip-Timing optical sensors is tested in the case of a shrouded bladed disk. Due to the presence of shrouds, the sensors cannot be positioned at the outer radius of the disk pointing radially toward the rotation axis as in the most common applications, since the displacements at the tips are very small and cannot be detected. For this reason a particular placement of optical laser sensors is studied in order to point at the leading and trailing edges' locations where the blades experience the largest vibration amplitudes with the aim of not interfering with the flow path. Besides the typical Blade Tip-Timing application aimed at identifying the dynamical properties of each blade, an original method is here proposed to identify the operative deflection shape of a bladed disk through the experimental determination of the nodal diameters. The method is applicable when a small mistuning pattern perturbs the ideal cyclic symmetry of the bladed disk

A BENCHMARK FOR TIP TIMING MEASUREMENT OF FORCED RESPONSE IN ROTATING BLADED DISKS

The Blade Tip-Timing is a well known non-contact measurement technique for the identification of the dynamic properties of rotating bladed disks. Even if it is an industrystandard technique its reliability has to be proved for the different operation conditions by comparison with other well stablished measurement techniques. Typically a strain gauges system in conjunction with radio telemetry is used as reference. This paper aims at evaluating the accuracy of a last generation Tip-Timing system on two bladed dummy disks characterized by different geometrical, structural and dynamical properties. Both the disks were tested into a spinning rig where a fixed number of permanent magnets, equally spaced around the casing, excites a synchronous resonance vibration with respect to the rotor speed. The so called beam shutter method was adopted for the Tip-Timing system. Due to the presence of shrouds a particularly set up of the probes was chosen in order to avoid that the probes look radially inward at the blade tips as in the most common configurations. he probes are optical laser sensors pointing at leading and trailing edges locations where the blade experiences the greatest magnitude of displacement. The Blade Tip-Timing measured data are post-processed by two different methods, the Single Degree of Freedom Fit (SDOF) and the Circumferential Fourier Fit (CFF). The amplitude and frequency values at resonance obtained by the Tip-Timing system are compared with those obtained by the strain gauge measurements

Forced response of rotating bladed disks: Blade Tip-Timing measurements

The Blade Tip-Timing is a well-known non-contact measurement technique currently employed for the identification of the dynamic behaviours of rotating bladed disks. Although the measurement system has become a typical industry equipment for bladed disks vibration surveys, the type of sensors, the positioning of the sensors around the bladed disk and the used algorithm for data post-processing are still not standard techniques, and their reliability has to be proved for different operation conditions by the comparison with other well-established measurement techniques used as reference like strain gauges. This paper aims at evaluating the accuracy of a latest generation Tip-Timing system on two dummy blisks characterized by different geometrical, structural and dynamical properties. Both disks are tested into a spin-rig where a fixed number of permanent magnets excite synchronous vibrations with respect to the rotor speed. A new positioning for the Blade Tip-Timing optical sensors is tested in the case of a shrouded bladed disk. Due to the presence of shrouds, the sensors cannot be positioned at the outer radius of the disk pointing radially toward the rotation axis as in the most common applications, since the displacements at the tips are very small and cannot be detected. For this reason a particular placement of optical laser sensors is studied in order to point at the leading and trailing edges' locations where the blades experience the largest vibration amplitudes with the aim of not interfering with the flow path. Besides the typical Blade Tip-Timing application aimed at identifying the dynamical properties of each blade, an original method is here proposed to identify the operative deflection shape of a bladed disk through the experimental determination of the nodal diameters. The method is applicable when a small mistuning pattern perturbs the ideal cyclic symmetry of the bladed disk

Red-Eyes Removal through Cluster-Based Boosting on Gray Codes

Since the large diffusion of digital camera and mobile devices with embedded camera and flashgun, the redeyes artifacts have de facto become a critical problem. The technique herein described makes use of three main steps to identify and remove red eyes. First, red-eye candidates are extracted from the input image by using an image filtering pipeline. A set of classifiers is then learned on gray code features extracted in the clustered patches space and hence employed to distinguish between eyes and non-eyes patches. Specifically, for each cluster the gray code of the red-eyes candidate is computed and some discriminative gray code bits are selected employing a boosting approach. The selected gray code bits are used during the classification to discriminate between eye versus non-eye patches. Once red-eyes are detected, artifacts are removed through desaturation and brightness reduction. Experimental results on a large dataset of images demonstrate the effectiveness of the proposed pipeline that outperforms other existing solutions in terms of hit rates maximization, false positives reduction, and quality measure

La Regina di Saba. Un mito fra Oriente e Occidente. Atti del Seminario diretto da Riccardo Contini, Napoli, Università “L’Orientale” 19 novembre 2009 - 14 gennaio 2010

[Italiano]:Il volume raccoglie i contributi presentati all’Università di Napoli “L’Orientale” nel corso di un seminario svoltosi nell’autunno/inverno 2009-2010 sulle molteplici forme che il mito della regina di Saba ha assunto nelle letterature antiche e moderne, orientali come occidentali, nonché in una prospettiva archeologica e storico-artistica, dando spazio, oltre alle relazioni di studiosi già affermati, ai contributi di giovani ricercatori che hanno perfezionato la loro formazione nei diversi Dottorati di ricerca dell’Ateneo. Per conferire al quadro una maggiore completezza, sono stati qui aggiunti alcuni interventi di studiosi non intervenuti al seminario, che si sono concentrati tanto su temi ormai canonici nello studio della fortuna della regina ‒ quali il suo impatto sull’immaginario letterario francese e soprattutto il suo ruolo identitario nella tradizione etiopica ‒ quanto su aspetti finora mai toccati, come la rilettura del personaggio nella cultura nordamericana e nella letteratura araba egiziana per l’infanzia. ./[English]:This volume collects the contributions presented at the University of Naples “L’Orientale” during a seminar held in the autumn/winter 2009-2010, on the multiple forms that the myth of the Queen of Sheba has taken on in ancient and modern oriental and western literatures, as well as in an archaeological and historical-artistic perspective; giving space, in addition to the reports of already established scholars, to the contributions of young researchers who have accomplished their training in the various PhD programmes of the University. To give the picture greater completeness, some interventions by scholars who did not attend the seminar have been added here, focusing both on canonical themes in the study of the Queen of Sheba’s fortune ‒ such as its impact on the French literary imagination, and above all its role of identity in the Ethiopian tradition ‒ as far as aspects never hitherto touched on, such as the reinterpretation of the character in North American culture and in Egyptian Arabic literature for children