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MARCO BARBIERI

Professore Associato
Dipartimento di Ingegneria "Enzo Ferrari"

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Pubblicazioni

2023 - Influence of heat treatment on fatigue resistance of two NiTi endodontic files [Articolo su rivista]
Generali, Luigi; Veneri, Federica; Barbieri, Marco; Bolelli, Giovanni; Lusvraghi, Luca; Cavani, Francesco; Matteucci, Tommaso; Pedullà, Eugenio
abstract

OBJECTIVES To evaluate the cyclic, torsional fatigue resistance and phase transformation of two heat-treated and non-heat-treated nickel-titanium reciprocating instruments. MATERIALS AND METHODS Twenty non-heat-treated (Procodile, Komet, Brasseler GmbH & Co., Lemgo, Germany) and 20 heat-treated (Procodile Q, Komet, Brasseler GmbH & Co., Lemgo, Germany) files (25 mm length, #25 apical diameter and 0.6 taper) were subjected to fatigue resistance tests. The dynamic cyclic fatigue was tested at 35 & PLUSMN;1 & DEG;C, using a dedicated patented device, in an artificial stainless-steel canal with a 60 & DEG; angle of curvature, the plate containing the artificial canal performing a controlled axial upand-down movement at 8 mm/s speed. The instruments were operated with a specific reciprocating motion (Reflex Dynamic & REG;, Komet, Breasseler GmbH & Co., Lemgo, Germany). Time to fracture (TtF) was recorded and the length of the fractured tips was measured. The torsional fatigue resistance was tested at room temperature (21 & PLUSMN;1 & DEG;C) using a custom-made device manufactured according to ISO 3630-1. The instruments were fixed 3 mm from the tip and their shafts were rotated counterclockwise at a speed of 2 rpm until fracture. The maximum torque load (Ncm) and corresponding rotation angle at fracture were recorded. All the results were statistically analysed (p <0.05). Fractographic analysis was performed using a field emission gun scanning electron microscope (FEG-SEM) to disclose the fractured surface characteristics. To assess the temperature range for phase transformations, differential scanning calorimetry (DSC) was performed on small segments of & AP;20 mg mass subjected to 2 heating and 2 cooling thermal cycles at rates of 5 & DEG;C min-1 in flowing N2 atmosphere over a temperature range of-40 & DEG;C to +110 & DEG;C. RESULTS The heat-treated instruments showed a greater resistance to dynamic cyclic fatigue as compared to the non-heat-treated sample (TtF 303 & PLUSMN;18.5 s vs 220 & PLUSMN;18.4 s; p <0.05) and a higher resistance to torsional fracture, bearing a greater maximum torque load (1.67 & PLUSMN;0.16 vs 0.82 & PLUSMN;0.07 Ncm; p <0.05). No significant differences were detected between heat-treated and non-heat-treated samples in mean angular rotation to fracture (298 & PLUSMN;25 & DEG; i,�312 & PLUSMN;32 & DEG;; p >0.05) and in the mean length of the fractured fragments (p >0.05). All instruments showed both ductile and brittle fracture patterns. According to the DSC, the direct (cooling) and reverse (heating) transformations of the non-heat-treated files occurred at lower temperatures (<25 & DEG;C) than those of the heat-treated files (& AP;50 & DEG;C), the latter thus not being austenitic at room and body temperatures at which they are operated. Also, the different transformation enthalpies suggest a multi-step transformation, likely involving R-phase formation, for heat-treat-ed files, against a direct transition between austenitic and martensi-tic phase for non-heat-treated files. CONCLUSIONS According to these findings, heat treatment of the tested files pro-vides them with microstructural properties more suited to the clin-ical operating conditions and im-proved performances in terms of torsional and flexural strength. CLINICA L SIGNIFICANCE Heat-treated files might be the best choice, over the traditional non-heat-treated files, when fac-ing challenging clinical condi-tions, such as curved and con-stricted canals.

2021 - Efficiency and Durability of Spur Gears with Surface Coatings and Surface Texturing [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

Experimental results on mechanical efficiency and durability of spur gears are presented. Reducing the power losses and increasing the reliability of gears are fundamnetal aspects of the design of transmissions. In order to analyze the tribological performance of innovative coatings and laser texturing, three different types of spur gears were tested: standard carburized gears, WC/C-coated carburized gears, and carburized gears with laser texture pattern. Tests have been carried out through a power recirculating test rig equipped with a single-stage transmission; power losses were evaluated by analyzing the torque-meters signals; several pictures of the teeth were taken at scheduled times to monitor the wear progression. In conclusion, results are presented and discussed.

2021 - Resonances and nonlinear vibrations of circular cylindrical shells, effects of thermal gradients [Articolo su rivista]
Iarriccio, G.; Zippo, A.; Pellicano, F.; Barbieri, M.
abstract

In this paper, the results of an experimental campaign focused on the vibrations of shells are presented. More specifically, the goal is to investigate the effect of thermal gradients across the shell thickness on the nonlinear dynamics. The shell is made of polymeric material and an aluminum mass is clamped on one end of the shell; the other shell end is clamped to an electrodynamic shaker, which provides a base harmonic excitation. Tests are performed in a controlled environment where a thermal gradient on the shell thickness is generated by means of a climatic chamber and an internal cartridge heater. Different temperature gradients and base excitation levels have been considered. The nonlinear dynamic scenario is analyzed through amplitude–frequency diagrams, bifurcation diagrams, waterfall diagrams, time histories, Fourier spectra, phase portraits, and Poincaré maps. Results show a strong effect of the temperature on the dynamic response of the shell: subharmonic, quasi-periodic, and chaotic vibrations take place as well as large amplitude vibrations, high sound levels are detected.

2020 - Dynamic characterization of polymeric vibration dampers [Relazione in Atti di Convegno]
Barbieri, Marco; DE FELICE, Alessandro; Pellicano, Francesco; Sorrentino, Silvio; Zippo, Antonio
abstract

Polymeric dampers are used in many fields for vibration isolation. These devices are based upon a low stiffness and high damping connection between a vibrating support and the item to be fastened. Whenever the connection is assured by a polymeric element, it is mandatory to be aware that stiffness and damping change with the excitation frequency. The characterization of stiffness and damping of the polymeric element in terms of storage modulus and loss modulus is commonly carried out at low frequency by means of a Dynamic Mechanical Analysis (DMA), nonetheless this approach cannot be applied at higher frequency. In the present study, a novel experimental approach for estimating the frequency dependent storage modulus and loss modulus in a polymeric vibration damper is presented. The proposed method is based on a direct measurement of the energy loss in hysteretic cycles and it is suitable for simple implementation using common instruments for vibration measurement.

2020 - Efficiency and Durability of DLC-Coated Gears [Relazione in Atti di Convegno]
Barbieri, M.; Iarriccio, G.; Pellicano, F.; Strozzi, M.; Zippo, A.
abstract

This paper presents an experimental study on spur gears. Gears with and without tungsten-carbide coatings (WC/C) are compared in terms of efficiency, durability and vibration performance. In order to carry out the experiments, a test rig including two electric motors/brakes is described. Gears are designed for this specific experimental campaign, so that the number of teeth, the selected materials and thermochemical treatments are optimal to investigate gear efficiency and durability. The experimental procedure allows for a simultaneous evaluation of efficiency and dynamic transmission error by varying the rotational velocity of the gear pair. An additional investigation has been performed for varying load, so that a complete characterization of the effect of WC/C coating on gear performance is presented.

2020 - Experimental Study on Nonlinear Random Excitation [Relazione in Atti di Convegno]
Pellicano, F.; Zippo, A.; Iarriccio, G.; Barbieri, M.
abstract

Experimental design methods are instruments for directing useful, time-effective and efficient experiments and an accurate strategy in experimental activities lead to successful results. In the present paper is explained an experimental campaign focused on the random vibrations of circular cylindrical shells under thermal gradients across the shell thickness and broadband random loading to identify a particular phenomenon called synchronicity: the investigation is fully experimental. Nuclear, aerospace and automotive are some of the engineering fields involved in this subject, and in these real environments non-deterministic excitations can be coupled with a thermal load; extreme thermal conditions can cause differences of the temperature inside and outside the shell, e.g. thermal ex-changers. Due to the importance of the subject, the literature on shell vibration is extremely wide, it is not analyzed here for the sake of brevity; however, it is to note that the number of papers containing experimental results is not large. Under a random forcing, a system generally expects a random response, the statistical properties of the random response are correlated with the forcing through the transfer function in the case of linear systems, or more complicated relationships in the case of nonlinear systems. However, in some particular conditions (e.g. internal resonances, parametric resonances, ...) the presence of nonlinearity in the systems can give rise to a surprising phenomenon, said synchronicity or entrainment. In this work a shell subjected to a random base excitation is analyzed experimentally, the excitation is random (flat or limited frequency band), and takes advantage of previous setup and experimental techniques [3–5] developed by the present research team. The phenomenon of synchronicity is clearly observed for some particular thermal conditions: a strong transfer of energy from a broadband excitation signal to an almost harmonic response is experimentally observed, confirming the general findings of refs. [1, 2].

2020 - Experimental study on large amplitude vibrations of a circular cylindrical shell subjected to thermal gradients [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

In this paper, an experimental study on large amplitude vibrations of a thin-walled shell, subjected to thermal gradient across the thickness, is presented. The temperature gradient effects on the shell dynamic behavior are investigated. The vibration tests are performed on a polymeric cylindrical shell that carries a top mass. The structure is harmonically excited in the longitudinal direction by means of an electrodynamic shaker. The results of the experimental study are here reported and discussed.

2020 - Metodo e dispositivo per la prova di file endodontici [Brevetto]
Barbieri, Marco; Bolelli, Giovanni; Generali, Luigi; Lusvarghi, Luca; Puddu, Pietro
abstract

RIASSUNTO Sono descritti un metodo, ed un dispositivo per l’attuazione di detto metodo, per realizzare prove di fatica, su file endodontici (2) rotanti o 5 reciprocanti in leghe Ni-Ti a memoria di forma. Il metodo è del tipo che prevede l’inserimento di detto file (2) in canali artificiali (3), ed è caratterizzato dal fatto di effettuare: - prove di fatica statica, ponendo in rotazione 10 detto file (2) e obbligandolo a deformarsi ciclicamente ad ogni rotazione del file (2) stesso; - prove di fatica dinamica, mediante un inserimento del file (2) in profondità in un canale (3), detta placchetta (4) venendo allontanata e 15 riavvicinata di una corsa predefinita. Il dispositivo è del tipo che comprende uno o più canali artificiali (3), ed è caratterizzato dal fatto di comprendere: - primi mezzi (5) atti a posizionare il file (2) 20 rispetto a detti canali artificiali (3); - secondi mezzi (6) atti a fare in modo tale che il file (2) entri ed esca da detti canali (3), per effettuare una prova di fatica dinamica; - terzi mezzi (7) per imprimere al file (2) un moto 25 rotatorio, per effettuare una prova di fatica statica. 1

2020 - Nonlinear vibrations of circular cylindrical shells with thermal effects: an experimental study [Articolo su rivista]
Zippo, Antonio; Barbieri, Marco; Iarriccio, Giovanni; Pellicano, Francesco
abstract

The nonlinear dynamics of a polymeric cylindrical shell carrying a top mass under axial harmonic excitation are experimentally investigated; the tests have been carried out in a controlled environment under several conditions of homogeneous temperature and excitation amplitude. The thermal effects on shells dynamics have been studied. The purpose of this paper is to fill an important gap in the literature regarding the effect of the temperature on the complex dynamics of shells. The cylindrical shell is excited in the axial direction by means of a seismic excitation provided by an electrodynamic shaker. The analysis is focused on the range of frequencies of excitation close to the first axisymmetric mode resonance; the base motion induces a parametric excitation. A saturation phenomenon of the top mass vibration is observed; the vibrating energy directly transferred from the shaker to the first axisymmetric mode is transferred to radial motion of the shell. The experimental data are examined and discussed in detail; a complete dynamic scenario is analyzed by means of: amplitude–frequency curves, bifurcation diagrams, spectrograms, Poincaré maps, phase portraits, Fourier spectra and time histories. Results show that: (i) the temperature strongly affects the instability regions and the magnitude of the measured kinematic quantity, (ii) high environmental temperature leads to a more complex shell dynamics.

2020 - Vibrations of circular cylindrical shells under random excitation and thermal gradients [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Barbieri, M.
abstract

The present paper is focused on the random vibrations of circular cylindrical shells subjected to thermal gradients across the shell thickness; the investigation is fully experimental. The topic is of practical interest in many engineering fields such as: Aerospace, Automotive, Civil, Nuclear. Indeed, in real environments the excitations are likely non deterministic, moreover, extreme thermal conditions can cause differences of temperature inside and outside the shell, e.g. thermal exchangers. Due to the importance of the subject the literature on shell vibration is extremely wide, it is not analyzed here for the sake of brevity; however, it is to note that the number of papers containing experimental results is not large. When a system is excited with random forcing one generally expects a random response of the system, the statistical properties of the random response are correlated with the forcing through the transfer function in the case of linear systems, or more complicated relationships in the case of nonlinear systems. However, in some particular conditions (e.g. internal resonances, parametric resonances,…) the presence of a nonlinearity in the systems can give rise to a surprising phenomenon, said synchronicity or entrainment (see [1, 2]), which consists in a response made of a combination of random and harmonic signals. In this work a shell subjected to a random base excitation is analyzed experimentally, the excitation is random (flat or limited frequency band). The work take advantage from previous setup and experimental techniques [3–5] developed by the present research team. The phenomenon of synchronicity is clearly observed for some particular thermal conditions: a strong transfer of energy from a broad band excitation signal to an almost harmonic response is experimentally observed, confirming the general findings of refs. [1, 2].

2019 - Experimental durability test for condition monitoring of carburized spur gears [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

An experimental study on the durability of spur gears has been carried out. Tests have been performed through a power re-circulating test rig at a fixed speed and torque load. For condition monitoring purpose, vibrations have been measured through a triaxial accelerometer mounted on the shaft frame. Acquired data have been post-processed and preliminary results are shown. The aim of the present work is to analyze the changes in the vibrations signal in order to depict a clear view on the onset and progression of the wear and damages in gear transmissions.

2019 - Experimental investigation on spur gears with novel coatings and surface micro texturing [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Barbieri, M.
abstract

Gears fault diagnostic and prognostic techniques have been the significant subjects of the condition-based monitoring systems in recent time due to the potential advantages that could be gained from. The present work is part of a more extensive study regarding efficiency and durability of novel tungsten carbide coatings and surfaces laser micro-texturing applied on carburized and nitride gears for several industrial application. In this paper, the effect of the different gear coatings and texturing on the vibration level is investigated experimentally. The durability and the pitting arising have been examined. The test rig consists of two electric motors with an electric power recirculating layout and is equipped with a temperature monitoring of the oil-jet type lubrication system. Vibrations phenomena are measured through triaxial accelerometer mounted on the shaft frame, close to the bearings, in order to detect spectral characteristics of vibration signals due to gear fault. Tests have been conducted far from the resonances of the system at a fixed speed and torque load; Vibration measurements have been performed at planned intervals. Results are presented and discussed

2019 - Experimental study on the nonlinear vibrations of a circular cylindrical shells: Effects of thermal gradients [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

In this paper, an experimental study on the large amplitude vibrations of a thin polymeric cylindrical shell subjected to a thermal gradient across the thickness is presented. The effects of the temperature gradient on the shell dynamic behavior are investigated. The present study has the aim of providing a deeper contribution to the experimental literature on the shell structures. Test have been carried out in controlled environment condition thanks to a climatic chamber and a heater cartridge placed inside the shell. The shell carries a top mass and an electro-dynamic shaker has been used in order to excite, with a harmonic load, the test specimen in the longitudinal direction. The harmonic forcing load consists of a stepped-sine sweep with frequency band limits containing the resonance frequency of the first axisymmetric vibration mode. Four different excitation amplitude levels and two different thermal gradients have been considered. The experimental results are presented and discussed in detail by means of frequency response analysis and bifurcation analysis

2019 - Temperature gradient effect on dynamic properties of a polymeric circular cylindrical shell [Articolo su rivista]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

In this paper, an experimental study on the dynamic of cylindrical shells made of Polyethylene terephthalate (PET) is presented; a thermic gradient has been applied on a specimen of the present work to obtain a functionally gradient material (FGM) equivalent properties: the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79 °C. A complex setup has been specifically designed and built to characterise, with dynamic tests, the structural properties of the specimen on temperature change from −10 °C up to about 90 °C and under thermic gradient with different forcing load. Predicting the mechanical properties of shells, panels and plates is one of the main concerns of structural engineers; since shell elements present complicated stability behaviours, rich linear vibration spectra (high modal density), high sensitivity to perturbations and strong interactions with surrounding elements. The linear and dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2018 - Active isolation of structures under seismic vibrations [Relazione in Atti di Convegno]
Barbieri, M.; Ilanko, S.; Pellicano, F.
abstract

Seismic isolation of structures is very important to prevent serious damage in buildings due to earthquake, and to protect equipment during transportation. Several passive or semi-active devices exist for protecting structures from secondary seismic waves, but few solutions are present to avoid damage due to primary waves. Usually, primary waves are considered less dangerous than secondary waves, nonetheless they can produce serious damage close to the epicentre. In order to protect structures from vertical oscillations, in this paper an active vibration control system is proposed. In the present formulation, active vibration control is based upon varying foundation stiffness during the seismic movement. In the paper, it will be shown how such kind of vibration control is effective in suppressing vibrations for the case of a measured earthquake signal.

2018 - Active vibration control of seismic excitation [Articolo su rivista]
Barbieri, Marco; Ilanko, Sinniah; Pellicano, Francesco
abstract

Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include base isolators and tuned mass dampers. In the present paper, a time-varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: When the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable of filtering seismic excitation close to the natural frequency of the controlled system and reducing the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Moreover, control effectiveness has been proven for a measured seismic signal, showing its robustness in presence of noise.

2018 - Experimental identification of static and dynamic stiffness of polymeric vibration dampers [Relazione in Atti di Convegno]
Barbieri, Marco; DE FELICE, Alessandro; Pellicano, Francesco; Sorrentino, Silvio; Zippo, Antonio
abstract

Polymeric dampers are frequently used in the automotive field in order to filter engine produced vibrations and thus protecting electronic devices. An accurate knowledge of damper stiffness is therefore important for a proper design of such mechanical filters. Since viscoelastic materials exhibit a significant stiffness–frequency dependency, characterization of dynamic stiffness is required for automotive vibration dampers. In the present paper, a method for broadband identification of the dynamic complex stiffness is described; since the proposed method is reliable at medium and high frequency only (500–1500 Hz), an additional static measurement has been performed. Therefore, the resulting method is a combination of static and dynamic measurements and it does not require specific DMA equipment: all experiments have been carried out using typical vibration testing equipment.

2017 - A novel method for dynamic characterization of polymeric vibration dampers [Relazione in Atti di Convegno]
Barbieri, Marco; DE FELICE, Alessandro; Pellicano, Francesco; Sorrentino, Silvio; Zippo, Antonio
abstract

Polymeric vibration dampers are very important devices used in many fields for vibration isolation and damping. These devices are based upon a low stiffness and high damping connection between a vibrating support and the item to be fastened. Whenever the connection is assured by a polymeric element, it is mandatory to be aware that stiffness and damping change with the excitation frequency as well as with temperature. Characterization of stiffness and damping of the polymeric element in terms of storage modulus and loss modulus is commonly carried out at low frequency by means of a Dynamic Mechanical Analysis (DMA), nonetheless this approach cannot be applied at higher frequency. In the present paper, a novel experimental approach for estimating the frequency dependent storage modulus and loss modulus in a polymeric vibration damper is presented. The proposed method is based on a direct measurement of the energy loss in hysteretic cycles, and it is suitable for simple implementation using common instruments for vibration measurement.

2017 - Dynamic imbalance of high-speed planetary gears [Articolo su rivista]
Masoumi, Asma; Barbieri, M; Pellicano, F; Zippo, A; Strozzi, M
abstract

A non-linear 2D lumped mass model of a single-stage spur planetary gear system with time-varying mesh stiffness, bearing compliance and non-smooth non-linearity due to backlash is taken into account. The time-varying meshing stiffness is evaluated by means of a non-linear finite element model, through an accurate evaluation of global and local tooth deformation. The non-linear dynamic behaviour of the system is analysed over a reasonable range of rotation speed and torque. The possibility of occurrences of different dynamic phenomena and instability of the system with respect to the bearing compliance and operating parameters are also evaluated. The possibility of dynamic imbalance of equally-spaced planetary gears in the presence of chaotic regimes is discussed. Such imbalance may lead to unexpected high-level stresses on bearings and gears.The effect of tooth profile modification at the sun-planet and ring-planet meshes on the vibration behaviour of the planetary gear system is also investigated in this paper. In order to avoid modification on the ring gear, both tip and root reliefs are considered for sun and planet gears.

2017 - Effects of gear manufacturing errors on rack and pinion steering meshing [Relazione in Atti di Convegno]
Marano, D.; Piantoni, A.; Tabaglio, L.; Lucchi, M.; Barbieri, M.; Pellicano, F.
abstract

In the present paper the effects of rack manufacturing errors on the meshing of crossed helical rack and pinion are analyzed. The study is performed using multibody simulations that include the effects of the forces acting at the gear mesh to determine the influence of rack geometrical errors on operating center distance; results are in good agreement with a simplified analytical formulation.

2017 - Experimental analysis of pre-compressed circular cylindrical shell under axial harmonic load [Articolo su rivista]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

In this paper the nonlinear dynamics of circular cylindrical shells under axial static (compressive) and periodic resonant loads have been experimentally investigated, the goal is to study the dynamic scenario and to analyze nonlinear regimes. A special test rig has been developed for the experiment in order to apply a static axial load combined with a dynamic axial load. The setup allows for investigating the linear behavior under static preload by means of the usual modal testing techniques; moreover, it allows for analyzing the nonlinear response which occurs when the dynamic axial load is periodic and gives rise to complex resonances. The complex dynamics, arising when a periodic axial load excites the asymmetric (shell like) modes, are analyzed by means of amplitude frequency diagrams, waterfall spectrum diagrams, bifurcation diagrams of Poincaré maps; a deep analysis of time histories, spectra, phase portraits and Poincaré maps completes the study of the complex dynamic scenario.

2017 - Experimental identification of FGM shell properties (aimeta 2017) [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Barbieri, M.; Strozzi, M.; Masoumi, A.
abstract

Functionally gradient materials (FGMs) have attracted a growing interest as advanced structural materials because of their heat-resistance properties. In this paper, an experimental study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of Polyethylene terephthalate (PET) is presented: to obtain functional gradient proprieties the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79°C. The setting up of the experiment is explained and deeply described along with the thermal characterisation of the specimen. The linear and the nonlinear dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2017 - Modal localization in vibrating circular cylindrical shells [Relazione in Atti di Convegno]
Pellicano, F.; Zippo, A.; Barbieri, M.; Strozzi, M.
abstract

The goal of the present paper is the analysis of the effect of geometric imperfections in circular cylindrical shells. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wavelength in the circumferential direction. In presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. This study is carried out by means of a semi-analytical approach compared with standard finite element analyses.

2017 - Numerical simulation and experimental validation of normal strain distribution and pitting phenomenon in industrial gears [Relazione in Atti di Convegno]
Strozzi, M.; Barbieri, M.; Zippo, A.; Pellicano, F.
abstract

In this paper, the normal strain distribution and pitting phenomenon on gears are investigated by means of numerical finite element analyses and experimental activities. In the first part of the paper, results of experimental tests for the investigation of the pitting phenomenon on gears are reported. These durability tests are made at a specific nominal load and far from the resonance. The experimental data are collected periodically from two tri-axial accelerometers placed on the gear shafts. After a short time, a visible pitting phenomenon arises on the gear teeth, where the contact pattern is perfectly centered (due to the high lead crown imposed on the teeth) and the wear pattern is consistent with FE simulations. In the second part of the paper, numerical finite element studies on the normal strain distribution at the base of the gear teeth during the contact are reported. These analyses are made at the same nominal load of the previous pitting analyses and at very low rotational speed (static analyses). A peak of normal strain at the base of the contact tooth is found around the contact time, preceded and followed by a low constant value of normal strain. The numerical results are validated by comparisons with experimental tests carried out in the same operating conditions and placing strain gauges at the tooth base of the gears.

2017 - Numerical study on nonlinear vibrations, energy exchange and resonant interactions in single walled carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, M.; Barbieri, M.; Zippo, A.; Pellicano, F.
abstract

In this paper, the nonlinear vibrations, energy exchange and resonant interactions of singlewalled carbon nanotubes (SWNTs) are investigated. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The circumferential flexural modes (CFMs), radial breathing modes (RBMs) and beam-like modes (BLMs) are studied. A numerical model of the SWNT dynamics is proposed. The three displacement fields are expanded in the nonlinear field by using approximate linear eigenfunctions. An energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved using the implicit Runge-Kutta numerical method. The nonlinear energy exchange along the SWNT axis is analysed for different initial excitation amplitudes. The resonant interactions between CFMs, RBMs and BLMs are investigated. The transition from energy beating to energy localization in the nonlinear field is studied.

2017 - Optimization of planetary gear systems by means of genetic algorithm [Relazione in Atti di Convegno]
Masoumi, A.; Barbieri, M.; Pellicano, F.
abstract

Effect of tooth profile modifications on dynamic behaviour of the planetary gear systems is analysed in this study. A nonlinear 2D lumped mass model of planetary gear system with time varying mesh stiffness, bearing compliance and non-smooth nonlinearity due to the backlash is taken into account. Genetic Algorithm (GA) is used to find the optimum profile shape of each element of the planetary gear system and the goal is to optimize the total static transmission error of the gearbox. The comparison between vibrations of the optimized and pure involute gear sets is performed in order to evaluate the effectiveness of the proposed method for optimization of the planetary gear systems.

2017 - Optimization of planetary gearboxes [Relazione in Atti di Convegno]
Masoumi, A.; Barbieri, M.; Pellicano, F.
abstract

This study investigates the effect of tooth profile modification on the vibrations of a single stage spur planetary gearbox. A lumped mass nonlinear dynamic model of the gearbox is used [1] to study the effect of tooth profile modifications applied on the sun-planet and ring-planet meshes on vibration behavior. In order to avoid modification on ring gear, both tip and root reliefs are considered for sun and planet wheels. The static model for planetary gear system with tooth profile modification is validated through comparisons with a static finite element analysis of the whole system, performed using commercial software. In the present study, an optimization approach based on Genetic Algorithms (GA) is proposed to improve planetary gear dynamic performances toward vibration reduction. As proven by dynamic analyses, a genetic algorithm is an effective optimization tool to design reliable profile modifications for reducing the planetary gears vibration amplitude over a wide frequency range.

2017 - Vibration Localization of Imperfect Circular Cylindrical Shells [Relazione in Atti di Convegno]
Pellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo
abstract

2017 - Vibration of functionally graded cylindrical shells [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Barbieri, M.; Strozzi, M.
abstract

Functionally gradient materials (FGMs) have attracted a growing interest as advanced structural materials because of their heat-resistance properties. In this paper, an experimental study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of Polyethylene terephthalate (PET) is presented: to obtain functional gradient proprieties the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79°C. The setting up of the experiment is explained and deeply described along with the thermal characterisation of the specimen. The linear and the nonlinear dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2016 - A contact mechanics interpretation of the duplex theory of tactile texture perception [Articolo su rivista]
Fagiani, Ramona; Barbieri, Marco
abstract

The tactile perception of a surface texture originates from scanning a finger on the surface. This kind of sliding contact activates the mechanoreceptors located into the skin, allowing the brain to identify the object and to perceive information about the scanned surface. Perception is collected by mechanoreceptors either by sensing pressure or by sensing vibration: the first mechanism is typical of large spaced surface textures, while the second is necessary to perceive finer textures. These different behaviors are well known in the literature as the duplex perception mechanism. In the present paper a numerical model describing finger-surface scanning is introduced in order to investigate the relationship between contact induced vibrations and scanning conditions. The model has been validated by experimental comparisons in a previous work. The perception model is used to develop a parametric analysis of the vibration induced from the finger-surface scanning as a function of surface geometry, scanning speed and contact force. The proposed parametric analysis points out the minimum number of parameters needed to describe the tactile perception of a periodic texture, and it shows the tribological reasons for which duplex perception mechanism is an effective biological evolution towards optimal tactile perception.

2016 - Active vibration control of a composite plate [Relazione in Atti di Convegno]
Zippo, A.; Barbieri, M.; Pellicano, F.; Strozzi, M.
abstract

A new active vibration control methodology is proposed and experimentally tested. The technique is applied to a honeycomb panel having a carbon-fiber reinforced polymer (CFRP) outer skins and a polymer-paper core, subjected to an orthogonal disturbance, due to an electrodynamics exciter. The control is carried out by means of Macro Fibre Composite (MFC) actuators and sensors. MFC parches consist of rectangular piezoceramic rods sandwiched between layers of adhesive, electrodes and polyamide film. The MFC actuators and sensors are controlled by a programmable digital dSPACER controller board. The control algorithm proposed in this paper is based on the Positive Position Feedback (PPF) technique, Single Input - Single Output, MultiSISO and Multi Input Multi Output controls are applied in order to control the first four normal modes. The control appears to be robust and efficient in reducing vibration in linear (small am- plitude) and nonlinear (large amplitude) vibrations regimes, although the structure under investigation exhibits a relativity high modal density, i.e. four resonances in a range of about 100Hz. The control strategy allows to effectively control each resonance both individually or simultaneously.

2016 - Dynamic imbalance of high speed planetary gears [Relazione in Atti di Convegno]
Masoumi, A.; Barbieri, M.; Pellicano, F.; Zippo, A.; Strozzi, M.
abstract

A nonlinear 2D lumped mass model of planetary gear system with time varying mesh stiffness, bearing compliance and nonsmooth nonlinearity due to the backlash is taken into account. The time varying meshing stiffness is evaluated by means of a nonlinear finite element model, through an accurate evaluation of global and local tooth deformation. Nonlinear dynamic behaviour of the system is analyzed over a reasonable range of rotation speed and torque. Possibility of occurrences of different dynamic phenomena and instability of the system with respect to bearing compliance and operating parameters is evaluated as well. Bifurcation diagrams are extracted as well and for specific regimes, the nonlinear scenario of system is discussed using the spectra, phase portraits and Poincare maps. Periodic, quasiperiodic and chaotic regimes are found and discussed with respect to system parameters. The possibility of dynamic imbalance of equally spaced planetary gears in presence of chaotic regimes is discussed. Such imbalance may lead to unexpected high level stresses on bearings and gears.

2016 - Experimental investigation of dynamic behaviour of pre-compressed circular cylindrical shell [Relazione in Atti di Convegno]
Zippo, Antonio; Pellicano, Francesco; Barbieri, Marco; Strozzi, Matteo
abstract

Circular cylindrical shells are very efficient structures that have many applications and plays as key elements in several engineering fields. Shells usually exhibit a complicated dynamic behaviours because the curvature will effectively couple the flexural and in-plane deformations together as the three displacement fields simultaneously appear in each of the governing partial differential equations and boundary conditions. Therefore, it is understandable that the axial constraints can have direct effects on a predominantly radial modes. For instance, it has been shown that the natural frequencies for the circumferential modes of a simply supported shell can be noticeably modified by the constraints applied in the axial direction. In this paper the results of experimental tests on pre-compressed circular cylindrical shell will be presented: different combinations of preload and harmonic external axial load have been tested but for brevity only few results are shown.

2016 - Experiments on shells under base excitation [Articolo su rivista]
Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo
abstract

The aim of the present paper is a deep experimental investigation of the nonlinear dynamics of circular cylindrical shells. The specific problem regards the response of circular cylindrical shells subjected to base excitation. The shells are mounted on a shaking table that furnishes a vertical vibration parallel to the cylinder axis; a heavy rigid disk is mounted on the top of the shells. The base vibration induces a rigid body motion, which mainly causes huge inertia forces exerted by the top disk to the shell. In-plane stresses due to the aforementioned inertias give rise to impressively large vibration on the shell. An extremely violent dynamic phenomenon suddenly appears as the excitation frequency varies up and down close to the linear resonant frequency of the first axisymmetric mode. The dynamics are deeply investigated by varying excitation level and frequency. Moreover, in order to generalise the investigation, two different geometries are analysed. The paper furnishes a complete dynamic scenario by means of: (i) amplitude frequency diagrams, (ii) bifurcation diagrams, (iii) time histories and spectra, (iv) phase portraits and Poincaré maps. It is to be stressed that all the results presented here are experimental.

2016 - Linear vibrations of multi-walled carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio
abstract

In this paper, the linear vibrations of Multi-Walled Carbon Nanotubes (MWNTs) are analysed. A multiple elastic shell model is considered. The shell dynamics is studied in the framework of the Sanders-Koiter shell theory. The van der Waals (vdW) interaction between two layers of the MWNT is modelled by a radius-dependent function. The shell deformation is described in terms of longitudinal, circumferential and radial displacements. Simply supported, clamped and free boundary conditions are considered. The three displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. The present model is validated in linear field by means of data derived from the literature. This study is focused on determining the effect of the geometry and boundary conditions on the natural frequencies of the MWNTs.

2016 - Modelling and Testing Techniques for Gear- boxes Analysis and Optimization [Relazione in Atti di Convegno]
Andrisano, A. O.; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo
abstract

2016 - Nonlinear Dynamics of Pre-Compressed Circular Cylindrical Shell Under Axial Harmonic Load: Experiments [Relazione in Atti di Convegno]
Pellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo
abstract

2016 - Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes [Articolo su rivista]
Gelman, L; Harish Chandra, N.; Kurosz, R.; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio
abstract

In this paper, the novel wavelet spectral kurtosis (WSK) technique is applied for the early diagnosis of gear tooth faults. Two variants of the wavelet spectral kurtosis technique, called variable resolution WSK and constant resolution WSK, are considered for the diagnosis of pitting gear faults. The gear residual signal, obtained by filtering the gear mesh frequencies, is used as the input to the SK algorithm. The advantages of using the wavelet-based SK techniques when compared to classical Fourier transform (FT)-based SK is confirmed by estimating the toothwise Fisher's criterion of diagnostic features. The final diagnosis decision is made by a three-stage decision-making technique based on the weighted majority rule. The probability of the correct diagnosis is estimated for each SK technique for comparison. An experimental study is presented in detail to test the performance of the wavelet spectral kurtosis techniques and the decision-making technique.

2016 - Pitting and stress analysis of gears: A numerical and experimental study [Relazione in Atti di Convegno]
Strozzi, M.; Barbieri, M.; Pellicano, F.; Zippo, A.
abstract

In this paper, the pitting phenomenon and stress distribution of gears are investigated by means of experimental activities and numerical finite element analyses. In the first part, results of experimental accelerated endurance tests for the investigation of the pitting phenomenon of gears are reported. These durability tests are made at a specific nominal load and far from the resonance. After a short time, a visible pitting phenomenon arises. In the second part, finite element numerical analyses for the evaluation of gear stresses are listed. The numerical analyses start from stress-vibration correlations and dynamic factors obtained by a 2-dof dynamic model; these results are used in the dynamic FEM simulations in order to calculate the maximum normal stress and the contact pressure on the contact tooth of the pinion vs. vibration amplitude for different dynamic factors.

2015 - A model for vibration-mediated tactile perception [Relazione in Atti di Convegno]
Fagiani, Ramona; Barbieri, Marco
abstract

Tactile perception originates from scanning the fingertip on object surfaces: in this condition, pressure and/or interaction between fingertip and surface ridges induce stresses and vibrations in the mechanoreceptors located in the skin, allowing the brain to identify objects and to perceive information about the surfaces [1-3]. In addition, many experimental investigations have shown that low wavelength surface patterns (with the respect to the fingerprint spatial period) are perceived by pressure, while high wavelength patterns are sensed by means of vibrations (duplex perception mechanism). In the present work, a numerical model describing finger-surface scanning is introduced. The model takes into account finger and surface shapes, material properties, normal contact force, and scanning velocity. The proposed model describes the vibration induced by a sliding contact between two sinusoidal surfaces, and it is capable to explain the duplex perception mechanism on a mathematical basis. Validation has been fulfilled by comparison with experimental results present in the literature; a parametrical investigation is performed in non-dimensional formulation in order to clarify the role played by contact/scanning parameters on the induced vibration, and to investigate the influence of material and contact properties on tactile perception.

2015 - Active vibration control of a composite sandwich plate [Articolo su rivista]
Zippo, Antonio; Ferrari, Giovanni; Amabili, Marco; Barbieri, Marco; Pellicano, Francesco
abstract

Active vibration control of a free-edge rectangular sandwich plate is proposed and tested. The experimental setup consists of a honeycomb panel having a carbon-fiber reinforced polymer (CFRP) outer skins and a polymer-paper core, subjected to an orthogonal disturbance, due to an electrodynamics exciter and controlled by Macro Fibre Composite (MFC) actuators and sensors. MFC parches consist of rectangular piezoceramic rods sandwiched between layers of adhesive, electrodes and polyamide film. The MFC actuators and sensors are controlled by a programmable digital dSPACE (R) controller board. The control algorithm proposed in this paper is based on the Positive Position Feedback (PPF) technique and is successfully applied with different combinations of inputs/outputs (Single Input Single Output, MultiSISO, Multi Input Multi Output) in order to control the first four normal modes. The control appears to be robust and efficient in reducing vibration in linear (small amplitude) and nonlinear (large amplitude) vibrations regimes, although the structure under investigation exhibits a relativity high modal density, i.e., four resonances in a range of about 100 Hz. The control strategy allows to effectively control each resonance both individually or simultaneously.

2015 - Beating phenomenon and energy localization in Single-Walled Carbon Nanotubes [Abstract in Atti di Convegno]
Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio
abstract

In this paper, the low-frequency nonlinear oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied in the framework of the Sanders-Koiter nonlinear shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported, clamped and free boundary conditions are analysed. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double mixed series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion, which are then solved using the multiple scales analytical method. The natural frequencies of SWNTs obtained by considering the analytical and numerical approaches are compared for different boundary conditions. A convergence analysis in the nonlinear field is carried out for the numerical method in order to select the correct number of the axisymmetric and asymmetric modes providing the actual localization threshold. The effect of the aspect ratio on the analytical and numerical values of the localization threshold for SWNTs with different boundary conditions is investigated in the nonlinear field.

2015 - Dynamic modelling of gear pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo; Serafini, Lorenzo; Pellicano, Francesco; Bonori, Giorgio
abstract

A clear understanding of the dynamics of gear pairs is important for many reasons. First of all, gear vibration is a main source of noise in gearboxes and vehicle trasmissions, secondly the torsional elasticity of the gear trasmission can produce relevant amplification of the contact force, and thus of the gear stress. Furthermore, gear vibrations are a useful parameter for gear monitoring and prognostics. In the present work, an overview of the models used to describe the dynamic behaviour of gear pairs will be presented, along with a comparison between a dynamic finite element model and different lumped parameter approaches. A correlation between the vibration transmitted to the gearbox, and thus easily measurable in a real application, and the local stresses in the gear pair will be drawn. The proposed approach is suitable to describe the effect of localized defects on the gear pair, such as tooth root cracks and pitted profiles, on the signal measured on a gearbox.

2015 - Dynamics and Stability of Carbon Nanotubes [Abstract in Atti di Convegno]
Strozzi, Matteo; Barbieri, Marco; Zippo, Antonio; Pellicano, Francesco
abstract

The low-frequency oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are studied in the framework of the Sanders-Koiter shell theory. The circumferential flexure modes (CFMs) are analysed. Simply supported, clamped and free boundary conditions are considered. Two different approaches are proposed, based on numerical and analytical models. The numerical model uses in the linear analysis a double mixed series expansion for the displacement fields based on Chebyshev polynomials and harmonic functions. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations, which is solved by the Runge-Kutta numerical method. The analytical model considers a reduced version of the Sanders-Koiter shell theory obtained by assuming small circumferential and tangential shear deformations. These two assumptions allow to condense the longitudinal and circumferential displacement fields into the radial one. A nonlinear fourth-order partial differential equation for the radial displacement field is derived, which allows to calculate the natural frequencies and to estimate the nonlinearity effect. An analytical solution of this equation is obtained by the multiple scales method. The previous models are validated in linear field by means of comparisons with experiments, molecular dynamics simulations and finite element analyses retrieved from the literature. The concept of energy localization in SWNTs is introduced, which is a strongly nonlinear phenomenon. The low-frequency nonlinear oscillations of the SWNTs become localized ones if the intensity of the initial excitation exceeds some threshold which depends on the SWNTs length. This localization results from the resonant interaction of the zone-boundary and nearest nonlinear normal modes leading to the confinement of the vibration energy in one part of the system. The value of the initial excitation corresponding to this energy confinement is referred to as energy localization threshold. The effect of the aspect ratio on the analytical and numerical values of the energy localization threshold is investigated; different boundary conditions are considered.

2015 - EHL lubrication in spur and helical gear pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

Gear efficiency is highly relying on elasto-hydrodynamic lubrication (EHL), and gear lubrication is significantly dependent upon non stationary conditions in gear pairs. Furthermore, the presence of lubricant is the main responsible of the damping effect in gear pair vibration. For these reasons, gear vibration and gear lubrication are to be considered as coupled problems. In the present work, a dynamic model of gear pairs taking into account for EHL lubrication is presented. The multilevel technique is used to solve the EHD lubrication problem, together with the equation describing the relative motion of the mating gears. Gear lubrication conditions at different gear rotation speed are investigated, in order to point out the effect of coupling between a thin lubricant film and elastic deformations in contacting bodies; a comparison between a dry contact and a lubricated contact is drawn, in order to clarify the amount of damping introduced by the lubricant film.

2015 - Experimental and numerical study of MIMO active vibration control [Relazione in Atti di Convegno]
Zippo, Antonio; Pellicano, Francesco; Barbieri, Marco; Amabili, Marco
abstract

In this paper the finite element method is used for choosing the best position of nearby collocated pairs of actuator-sensor couples, an experimental investigation of active vibration control validates the theory; the application regards a rectangular sandwich laminated plate (carbon-epoxy outer skins and Nomex paper honeycomb core) with free boundary conditions. The piezoelectric unidirectional patches are used as strain sensors and strain actuators, respectively. The collocation of the patches is led by the results of a finite element modal analysis and allows the design of a modal control strategy, the efficiency of which is targeted to single vibration modes. The control configurations presented in this paper is a MIMO configuration in linear field. The identification activity and the extraction of stabilised transfer functions are performed by means of a dedicated Matlab algorithm. The stability and the robustness of the algorithm are briefly studied. A substantial reduction of the vibration amplitude is obtained both at specific frequencies and in a broadband random excitation-disturbance. It is also possible to control disturbances that would otherwise trigger geometrically nonlinear vibrations. The modal character of the resulting control is guaranteed by means of the MAC. An experimental setup has been developed, two to four Macro Fiber Composite (MFC) actuators and two MFC sensors are used in conjunction with a DSPACE controller system. The control appears robust and efficient in reducing vibration levels in linear and nonlinear field, even though the structure under investigation exhibits a high modal density, four resonances in a range of about 100Hz, and allows controlling each resonance separately or together.

2015 - Nonlinear oscillations of carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Manevitch, Leonid I.
abstract

In this paper, the low-frequency nonlinear oscillations and energy localizations of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied within the framework of the Sanders-Koiter thin shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported boundary conditions are investigated. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion which are solved using the multiple scales analytical method. The natural frequencies obtained by considering the two approaches are compared in linear field. The effect of the aspect ratio on the analytical and numerical values of the localization threshold is investigated in nonlinear field.

2015 - Symmetry breaking and chaos-induced imbalance in planetary gears [Articolo su rivista]
Masoumi, Asma; Pellicano, Francesco; Samani, Farhad S.; Barbieri, Marco
abstract

The goal of the present paper was a com- plete analysis of the dynamic scenario of planetary gears. A lumped mass two-dimensional model is adopted; the model takes into account: time-varying stiffness; nonsmooth nonlinearity due to the backlash, i.e., teeth contact loosing; and bearing compliance. The time-varying meshing stiffness is evaluated by means of a nonlinear finite element model, which allows an accurate evaluation of global and local teeth defor- mation. The dynamic model is validated by compar- isons with the most authoritative literature: linear nat- ural frequencies and nonlinear response. The dynamic scenario is analyzed over a reasonable engineering range in terms of rotation speed and torque. The clas- sical amplitude–frequency diagrams are accompanied by bifurcation diagrams, and for specific regimes, the spectral and topological properties of the response are discussed. Periodic, quasiperiodic and chaotic regimes are found; nonsmooth bifurcations lead period one to period two trajectories. It is found that the bearing com- pliance can influence the natural frequencies combina- tion magnifying the modal interactions due to internal resonances and greatly enlarging the chaotic regions. It is evidenced that the chaotic response indices a sym- metry breaking in the dynamical systems. The physical consequence is that the planetary gearbox under inves- tigation, which is perfectly balanced for each position, can suffer of a big dynamic imbalance when chaotic regimes take place; such imbalance gives rise to alter- nate and unexpected high-level stresses on bearings.

2014 - Adaptive grid-size finite element modeling of helical gear pairs [Articolo su rivista]
Barbieri, Marco; Zippo, Antonio; Pellicano, Francesco
abstract

A method for solving the contact problem for generic helical gear pairs (either external or inter- nal) is described. Gear profiles are obtained by means of numerical simulation of the cutting pro- cess and an accurate description is provided in terms of NURBS curves or surfaces. A new method for finding the enveloping profiles for a generic tool (e.g. from a measured topography) is pro- posed. The minimum number of parameters needed to describe the profile in the presence of tip and root reliefs, helix modification and crowning is discussed. A reference structured grid is de- fined on the tooth, then refinement criteria are applied in order to obtain accurate solutions in terms of tooth deflection, contact pressure and fillet stress. The method allows to automatically perform a Loaded Tooth Contact Analysis (LTCA) starting from the design data of a gear pair. Re- sults from the LTCA include contact pressure and contact pattern maps, as well as maximum fillet stress and fatigue strength. Combining several analyses within a mesh cycle, information about the Static Transmission Error (STE) and mesh stiffness is provided. The whole procedure has been implemented in a software called helical pair. A comparison with other approaches is given.

2014 - Complex dynamics of circular cylindrical shells [Articolo su rivista]
Pellicano, Francesco; Barbieri, Marco
abstract

Complex dynamics of circular cylindrical shells subjected to inertial axial loads are investigated. The shell is vertically mounted on a shaker, i.e. its base is clamped to the shaker fixture, which induces a vertical motion along the shell axis. On the top of the shell a rigid disk is mounted, the vertical motion induced by the shaker induces huge inertial forces due to the rigid body motion. A complicating effect is due to the base actuator, which is an electro-dynamic shaking table; the interaction between the shell and shaker dynamics changes dramatically the system behaviour. The non-linear Sanders–Koiter theory is considered for the structural dynamics: the resulting set of non-linear partial differential equations is coupled with the linear ordinary differential equations that govern the shaker dynamics. A deep analysis of the non-stationary response of the shell is carried out in order to clarify the transition from stationary to non-stationary response. The model is validated by means of experimental results.

2014 - Complex dynamics of planetary gear systems [Relazione in Atti di Convegno]
Masoumi, Asma; Pellicano, Francesco; Barbieri, Marco
abstract

A full 2D dynamic model of a single-stage planetary gear system with backlash and time varying stiffness is considered here. This dynamic model is time variant and non-smooth, due to the presence of time varying meshing stiffness and backlash for all sun- planets and ring-planets meshes; moreover, bearing compliance is accounted for. The linear averaged equations of motion are solved to obtain the natural frequencies; conversely, the fully nonlinear equations of motion are analyzed numerically to study the effect of time varying stiffness and backlash and to point out the nonlinear dynamics of the system. The complex dynamics is deeply investigated over the meaningful mesh frequency ranges. The dynamic scenario is obtained by means of bifurcation analysis and completed with time spectral and topological properties of the response.

2014 - Modelling of finger-surface contact dynamics [Articolo su rivista]
Fagiani, Ramona; Barbieri, Marco
abstract

The tactile perception of a surface texture originates from the scanning of a finger on the surface. This kind of sliding contact activates the mechanoreceptors located into the skin, allowing the brain to identify the object and to perceive information about the scanned surface. In this paper, a numerical model describing finger-surface scanning is introduced in order to investigate the relationship between contact induced vibrations and scanning conditions. The model takes into account finger and surface shapes, material properties, normal contact force, and scanning velocity. Model validation is provided by comparison with experimental tests. Afterwards, the model is applied to clarify the role played by contact/scanning parameters on the induced vibration. The proposed model is useful to develop a comprehensive parametrical analysis of the vibration induced in finger-surface scanning, and to investigate the influence of material and contact properties on tactile perception.

2014 - Non-smooth active control of seismic vibrations [Relazione in Atti di Convegno]
Barbieri, Marco; Ilanko, Sinniah; Pellicano, Francesco
abstract

In order to prevent seismic damage in civil buildings and mechanical equipment, e.g. during transport, passive isolators and dampers are commonly used. In the present work, a non-smooth strategy for active seismic isolation is presented. The method provides isolation from base excitation by dynamically switching the stiffness of the foundation. The controller works as follows: when the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable to filter seismic excitation close to the natural frequency of the controlled system, and to reduce the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Even though the controlled system is linear, the controller presents a non-smooth fluctuation of the stiffness, so that a limit cycle occurs within the system.

2014 - Nonlinear dynamics of axially loaded shells: experimental study [Relazione in Atti di Convegno]
Pellicano, Francesco; Zippo, Antonio; Barbieri, Marco
abstract

In this paper recent experiments on nonlinear dynamics of shells are described, such experiments were focused to circular cylindrical shells subjected to axial loads. Different types of axial loads were considered: inertial loads due to rigid bodies connected to the shell; static and dynamic loads induced by direct shell excitation. The latter type of loading allows to study the effect of pre-compression, which typically induces natural frequency variation and changing of the dynamic scenario. The experiments show an extremely complex dynamic scenario, which needs a deep analysis to be interpreted and explained. The goal of the present work is twice: describe experimental evidence of complex dynamics and furnish explanation when possible.

2013 - Active vibration control of seismic excitation [Relazione in Atti di Convegno]
Barbieri, Marco; Cinque, Fabio; Ilanko, Sinniah; Pellicano, Francesco
abstract

Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include Base Isolators (BI) and Tuned Mass Dampers (TMD). In the present paper, a time varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: when the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable to filter seismic excitation close to the natural frequency of the controlled system, and to reduce the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Even though the controlled system is linear, the controller presents a non-smooth fluctuation of the stiffness, so that a limit cycle occur within the system.

2013 - Behavior of lubricant fluid film in gears under dynamic conditions [Articolo su rivista]
Barbieri, Marco; Lubrecht Antonius, A.; Pellicano, Francesco
abstract

This paper presents a new method for modeling the fluid film lubrication in gears, considering the actual meshing conditions and gear dynamics. The model takes into account both the elastohydrodynamic lubrication (EHL) and the dynamic load between the mating tooth pair. The EHL film is described as a fully flooded elliptical contact. The present approach is validated by means of comparison with other methods found in the literature, in which dynamic effects were neglected. The effect of the gear dynamics on the fluid film is investigated. It is shown that pressure and film thickness are strongly modified by the dynamics of the gear pair. The dependence of the dynamic gear lubrication on dimensionless parameters is investigated: a new dimensionless inertia parameter is added to the standard Moes' parameters. These parameters are useful to describe the lubrication conditions in gear pairs.

2013 - Circular Cylindrical Shells under combined axial loads: an experimental study [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

Thin shells structures have an important role in engineering; several important examples can be found in Structural Engineering, Mechanical Engineering and Aerospace: water tanks, containment shells of nuclear power plants, concrete arch domes, piping systems, pressure vessels, aircrafts, missiles, rockets, ships. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number; in particular, rare experimental reports have been published about shells loaded with in-plane . In this paper the response of a circular cylindrical shells subjected to axial compressive and periodic loads has been experimentally investigated. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear shell behavior is investigated by means of a finite element model in order to enhance the comprehension of experimental results in the linear field. The main goal is to investigate the nonlinear phenomena associated with a combined effect of compressive static and a periodic axial loads, the investigation have been carried out for different combinations of loads. Several interesting nonlinear phenomena have been observed such as softening-type non-linearity and non stationary response when the periodic axial load is resonant with one of the shell modes.

2013 - Dynamic modelling of finger-surface contacts [Relazione in Atti di Convegno]
Fagiani, Ramona; Barbieri, Marco
abstract

The tactile perception, originated from the scanning of the fingertip on object surfaces, is related to the contact stresses and to the vibrations induced by the sliding contact that activate the mechanoreceptors located in the skin, allowing the brain to identify objects and to perceive information about their surfaces [1-3]. The relationship between the friction induced vibration and the tactile sensation is rarely investigated, while a clear understanding of the mechanisms of the tactile sense is basilar for manifold applications, like the development of artificial tactile sensors for intelligent prostheses or robotic assistants, and for the ergonomics. In this context, it is necessary to perform appropriate experiments to find out the frequency characteristics of the vibrations induced by the surface scanning. The aim is to analyze the induced vibrations highlighting their dependence on contact and scanning conditions. The study of a finger that moves on a surface involves different difficulties that are related to the material characteristics and to the measurements themselves. In fact, the goal is the measurement and the analysis of the vibrations induced by the scanning, which are very low in magnitude; thus, it is complicated to isolate them from the vibration noise coming out from the experimental set-up and to detect them without significant alteration. For these reasons, an experimental set-up named TRIBOTOUCH was developed to recover the contact forces and the induced vibrations [4]. While the experimental tests, describing how the spectra of the vibrations measured on finger nail can be related to surface characteristics, to scanning speed and to contact force, are presented in the previous works [5-6], in this paper a numerical model reproducing the finger-surface scanning is introduced. The model takes into account finger and surface geometries, their material properties, normal contact force and scanning speed.

2013 - Modelling lubrication in gear pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

The lubrication regime in gear pairs is usually elasto-hydrodynamic, i.e. solid deformations due to the fluid pressure are not negligible. It is well known that lubrication in gear pairs depends upon a number of kinematical parameters, so that it is a non stationary EHD problem. Moreover, it depends upon the dynamic response (i.e. the dynamic load) of the gear pair [1-5]. The problem of finding the dynamic response in gear systems, especially spur gears, has been studied by many research works. Most of them consider as the main source of vibration the time variation of the number of teeth pairs that are in contact at the same time. This fluctuation makes the transmission more stiff, when two pair of teeth are in contact, more deformable when only one pair is in contact. This behaviour can cause oscillations of the gears, and eventually detachment of the teeth in contact, with impacts and noise. The purpose of the present work is to investigate the effect of the varying rotational velocity of the gear pair on the film thickness and the contact pressure distribution. The lubrication regime in spur gear pairs is investigated using an EHL lubrication model. The solver described by Venner and Lubrecht [6] is adapted to the specific transient problem. Different test cases at different speeds are presented, in order to point out the role of the dynamic coupling on the lubricated contact.

2013 - Nonlinear vibrations and energy conservation of Single-Walled Carbon Nanotubes [Relazione in Atti di Convegno]
Zippo, Antonio; Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Barbieri, Marco
abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied in order to obtain approximate natural frequencies and mode shapes. Free boundary conditions are analysed. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions; an energy approach based on the Lagrange equations is considered in order to reduce the nonlinear partial differential equations to a set of nonlinear ordinary differential equations. Nondimensional parameters are considered. The total energy conservation of the system is verified by considering the combinations of different vibration modes. The effect of the companion mode participation on the nonlinear vibrations of the carbon nanotube is analysed.

2013 - Transient thermal diffusion in elliptic contacts [Relazione in Atti di Convegno]
Fava, Elisabetta; Barbieri, Marco
abstract

The paper deals with the transient thermal diffusion in localized contacts. Starting from Jaeger's solution for an instantaneous point heat source in a half space, a solver for generic bodies in contact under time varying load is proposed. As a benchmark, the steady state solution for elliptical contacts heated by Coulomb friction has been found. Such problem depends upon two dimensionless parameters, ellipticity and Peclet number. The grid size has been set so that the error is less than 1%.

2012 - Corrigendum to: Optimum profile modifications of spur gears by means of genetic algorithms [Articolo su rivista]
Barbieri, Marco; Bonori, Giorgio; Pellicano, Francesco
abstract

The purpose of the present work is to correct some inaccuracies of the paper "Bonori, G., Barbieri, M., Pellicano, F., 2008, Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms, Journal of Sound and Vibration, 313, pp. 603-616"; in that work, the aim was the reduction of vibrations in spur gears by means of profile modifications. This goal was achieved by using an ad hoc genetic algorithm, where the objective function was the peak to peak or the harmonic content of the Static Transmission Error (STE) computed by Finite Element calculations.The efficiency in terms of vibration reduction of the optimized profile reliefs was checked using a one degree of freedom dynamic model. This dynamic model considers time varying mesh stiffness, backlash, and profile error. In the original paper the effect of intentional profile modifications was considered as part of the mesh stiffness, thus overestimating their effect in vibration reduction.In the present corrigendum, the dynamic model is updated, keeping into account profile deviations by means of an error function. Finally, the optimal profile modifications found in the original paper are checked using the updated model.

2012 - Experimental Study on Prestressed Circular Cylindrical Shell [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo; Errede, Vito; Pellicano, Francesco
abstract

In this paper an experimental study on circular cylindrical shells subjected to axial compressive and periodic loads is presented. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear and the nonlinear dynamic behavior associated with a combined effect of compressive static and a periodic axial load have been investigated for different combinations of loads; moreover, a non stationary response of the structure has been observed close to one of the resonances. The linear shell behavior is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2012 - Fluid-structure interaction in EHD lubricated contacts close to the elastic resonance [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

Elasto-hydrodynamical lubrication is governed by a set of non-linear integro-differential equa- tions describing the coupling between fluid properties in a thin lubricant film and elastic defor- mations in contacting bodies. In the present paper, the non-stationary behavior of an elliptic lubricated contact in Elasto-hydrodynamical lubrication regime is investigated. Non-linear contacts in gear pairs are considered as a case study: a comparison between dry contact and lubricated contact is drawn. The lubrication conditions close to the main resonance of the linearized elastic system are pointed out. The multilevel technique is used to solve the EHD lubrication problem, together with the equation describing the relative motion of the mating gears.

2012 - Linear and nonlinear dynamics of a circular cylindrical shell under static and periodic axial load [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo; Errede, Vito; Pellicano, Francesco
abstract

In this paper an experimental study on circular cylindrical shells subjected to axial compres- sive and periodic loads is presented. The setting of the experiment is explained and deeply described along with a complete analysis of the results. The linear and the nonlinear dynamic behaviour associated with a combined effect of compressive static and a periodic axial load has been considered and a chaotic response of the structure has been observed close to the resonance. The linear shell behaviour is also investigated by means of a theoretical and finite element model, in order to enhance the comprehension of experimental results, i.e. the natural frequencies of the system and their ratios.

2011 - 3D Nonlinear Finite Element Modeling of Helical Gears [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

A method for carrying out the Loaded Tooth Contact Analysis (LTCA) of helical gear pairs is described in this paper. Gear profiles are obtained by means of numerical simulation of the cutting process and an accurate description is provided in terms of NURBS curves or surfaces.The minimum number of parameters needed to describe accurately the profile in presence of tip and root reliefs, helix modification and crowning is discussed. Some cases are presented and discussed.

2011 - Adaptive Grid-Size Modelling of Helical Gear Pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Zippo, Antonio; Pellicano, Francesco
abstract

Amethod for solving the contact problem in a generic helical gear pair (either external or internal) is described. Gear profiles are obtained by means of numerical simulation of the cutting process and an accurate description is provided in terms of NURBS curves or surfaces. The minimum number of parameters needed to describe accurately the profile in presence of tip and root reliefs, helix modification and crowning is discussed. A reference structured grid is defined on the tooth, then refinement criteria are discussed in order to obtain accurate solutions in terms of tooth deflection, contact pressure and fillet stress. A comparison with other approaches is given.

2011 - Energy dissipation in EHL Film in Gear Lubrication [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

A characterization of the energy dissipation of the lubricant film between mating teeth in gear pairs is proposed. The film fluid is modeled using the fully flooded elastohydrodynamical point contact and the solution is found by means of a numerical multilevel solver. Some comparison with other solutions proposed in the literature for the line contact problem are drawn to validate the proposed approach. In order to understand the effect of the lubricant film on the vibration of the gear pair, it is important to describe both the stiffness of the film and the viscous energy dissipation: in the present paper, some initial results about this problem are presented.

2010 - Coupling of two EHL-lubricated contacts in gear dynamics [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

In this paper, the effect of vibrations on the elastohydrodynamical lubrication in spur gear pairs will be described. The relevance of inertial effects on film fluid lubrication is clarified by means of comparisons with static formulations. The multilevel technique is used to solve the transient EHL problem for elliptical contacts. Coupling with load balance equation and with different equations of motion is studied. A new model describing the dynamic behavior of two coupled transient EHL elliptical contacts is developed and applied to characterize the dynamics of a spur gear pair.

2010 - Influence of dynamic effects on point EHL contacts in gear systems [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

In this paper, the effect of vibrations in elastohydrodynamical lubrication of spur gear pairs will be described. The relevance of inertial effects in the contacting bodies on film fluid lubrication will be clarified with comparisons to static formulations. A new model describing the dynamic behavior of two coupled transient EHL elliptical contacts will be presented and applied to characterize the dynamics of a spur gear pair.

2008 - Optimization Methods for Spur Gear Dynamics [Relazione in Atti di Convegno]
Barbieri, Marco; Scagliarini, Giorgio; Bonori, Giorgio; Pellicano, Francesco; Bertacchi, Gabriele
abstract

In the present paper two different approaches for spurgear noise reduction using micro-geometrical modifi-cations are compared. The two approaches are basedrespectively on the reduction of Static TransmissionError (STE) and Dynamic Transmission Error (DTE)fluctuations. The dynamic behaviour of the system iscomputed through a simple lumped parameter model.A genetic algorithm is proposed to find the best solu-tions inside the parameters space because the evalua-tion of the objective functions requires finite elementscalculations and numerical ODE integrations. A relia-bility analysis is afterwards performed to evaluate theeffect of manufacturing errors on the dynamic perfor-mance of the achieved optimum.

2008 - Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms [Articolo su rivista]
Bonori, Giorgio; Barbieri, Marco; Pellicano, Francesco
abstract

An original application of Genetic Algorithms (GAs) is developed in order to optimize spur gear pairs toward vibrationand noise reduction. The approach takes into account the most important parameters of micro-geometric modifications,namely tip and root relief, therefore the parameter space is eight dimensional. The objective function of the GA depends onthe static transmission error (STE) that is related to teeth flexibility. STE is estimated by means of a nonlinear finite elementapproach: either the amplitude of the STE fluctuation or its harmonic content are considered as objective functions.The effectiveness of the approach is checked on an actual test case: GAs are able to find the optimum after a reasonablenumber of steps; such optimum is obtained on static basis and gives a strong vibration reduction. The reliability test provesthat GAs lead to robust optima.

2006 - Vibration of gears: A global optimization approach [Relazione in Atti di Convegno]
Bonori, G.; Scagliarini, G.; Barbieri, M.; Pellicano, F.
abstract

The importance of studying dynamic aspects of gear transmissions has been well established since many years; however, recently a new interest on this topics grew up because of significant improvement in gear design technology. The literature can supply different approaches to evaluate the vibrations response of simple and complex gears system. Numerical and analytical methods can provide important information on resonances, non linear behaviours and combined dynamic interactions in existing systems. In particular the reduction of vibrations is strictly related to minimize the value of the peak to peak of the static transmission error in a mesh cycle, through modifications of the tooth profile. The present paper combines a numerical model to study spur gear pair dynamics, with a genetic optimization technique to define the best profile modification capable to reduce the vibration. The numerical model is able to take into account gear geometry, profile modifications and profile manufacturing errors. The genetic optimization routine can provide the best set of profile modification considering the peak to peak value of the static transmission error or a generic number of its harmonic components. In the last part of this work some testcases are investigated and the improvement in the dynamics is shown. © (2006) by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved.