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Giuseppe Carbone - Research Interests
Dr. Carbone’s main research interest is focused on contact mechanics, tribology, bio-mimetics, linear and non linear dynamics, and mechanical transmissions. Below a brief description of research activity follows.

Dry contact mechanics of rough surfaces with or without adhesion

The research activity in this field has been mainly concerned with the investigation of the influence of roughness and surface energies on the contact behaviour of elastic bodies and on the frictional behaviour of soft viscoelastic materials. The activity has been carried out both at theoretical and experimental levels. At theoretical level an ad hoc boundary element method has been conceived, implemented and employed to analyze the adhesive contact between an elastic layer and a isotropic or anisotropic rough rigid substrate. The methodology is based on Green's function approach and solve the problem (which belongs to the class of free boundary problems) by requiring that the total energy of the system (sum of the elastic energy and surface energy) is minimized while satisfying the constraint of impenetrability of the contacting bodies. In particular the developed methodology results in a strong reduction of computational cost both in terms of memory storage and computation time since only contact domains are discretized with an adaptive non-uniform mesh. This approach shows its strong potential especially when the contact occurs between rough surfaces since in this case a very large number of length scales, spanning several order of magnitudes, is involved in the problem. Our BEM methodology is indeed able to capture the multiscale character of the problem and for this reason never lose resolution even at the smallest length scales (often of order nanometers). This methodology has been employed to study the adhesive contact between different types of rough rigid surfaces (comprising self-affine fractal surfaces) and different elastic slabs of different thicknesses. In all cases periodic conditions have been considered and the Green function of the elastic response has been determined by means different methodologies which have comprised the solution of dual-series equations or by solving the elasto-static problem of the body loaded with a periodic array of unit concentrate load (e.g. a periodic array of Dirac deltas). Interestingly the Green function of elastic slab has been always determined analytically sometimes in closed form and other times in the form of a Fourier series. In particular moving from the Fourier series it has been always possible to obtain in closed form the expression of the Fourier transform of Green function also for the case of a non-periodic contact and as a function of the thickness of the slab. This results is very important when the numerical methodology to solve the contact problem relies on spectral method which makes use of the FFT technique to easily move from the real space to the frequency space. The research has allowed us to better understand the effect of roughness and adhesive forces on the real contact area and test some fully-analytical approaches as those based on multiasperity contact theories or the one recently presented by Persson. We have found that the predictions of multiasperity contact models mainly in terms of load vs. penetration strongly deviate from numerical calculations, whereas and Persson's theory agrees much better in this respect. In all cases both multiasperity contact models and Persson's theory show strong deviation from numerical calculations when the focus is determination of the size of the true contact area. We have carried out also experiments to clarify these points. These experiments have confirmed the main conclusions of the numerical investigations. The numerical methodology we have developed has also suggested that the hysteresis of adhesion may significantly contribute to sliding friction, as the sliding process can be regarded as the propagation of cracks at the interfaces. Because of adhesion hysteresis (caused by local viscoelastic energy dissipation) propagating cracks have different values of the energy release rates at the advancing and trailing edges, and therefore require an external source of energy to propagate. Moreover this increase of energy release rate at the trailing edge of each single contact area determines, for small sliding speed, an increase of the contact area (instead of a reduction, as one can expect), as the sliding is increased. This somehow counterintuitive result has been very recently confirmed experimentally by other. An important consequence of the investigation has consisted in clarifying what is the influence of the thickness of the adhesive layer on the strength of adhesion. In particular we have shown that, in the case of structural adhesives, decreasing the thickness of the adhesive film increases the adhesive strength of junction. More precisely it has been shown that decreasing the thickness of the adhesive reduces the effective energy of adhesion at the interface between the layer and the substrate (i.e. the work needed to separate the surface), but nevertheless it increases the adherence force, i.e. the tractive stress at which the elastic slab jumps out of contact. However, decreasing the layer thickness also increases the degree of confinement of the elastic materials and, as a consequence, increases the hydrostatic pressure in the layer. Thus, when the negative hydrostatic pressure is sufficiently large, cavitation may occur: new interfacial voids may be formed and grow. When this happens the interfacial crack propagation is inhibited and the strength of the adhesive joint is controlled by cavitation. The analysis allows also to estimate the critical slab thickness below which cavitation occurs and therefore to identify the optimal thickness of the adhesive layer which maximizes the strength of the adhesive joint.

Bio-inspired adhesive systems

Dr. Carbone's research activity has been also dealing with the investigation of bio-inspired micro-structured adhesives. In this field a lot of experimental research has been carried out but still there is not a complete understanding of the physical mechanism behind the superior performance of bio-adhesive. As an example Geckos are able to climb almost any surface thank to the van der Waals forces. Nowadays it has been well clarified that one of the key point to increase adhesion is to split the contact in a very large number of very small contacts. However there are other peculiarities of biological attachment system which may have a key-role in improving adhesion as, for example the presence of hierarchical structures, and shape of terminal ends. One of the purposes of our research was to explain why, e.g. in the case of Geckos, flies or rather beetles and other insects, a very thin terminal plate is very often present at the end of the attachment system. To try to answer the question we have considered the contact between the a very thin plate and fractal type roughness with fractal dimension variable between 2.2 and 2.6. Our theoretical investigation shows that one of the causes of the amazing climbing ability these insect is related the extremely high compliance of their attachment structure. Very thin leaf-like plates deform very easy and store a very small amount of elastic (repulsive energy) at the interface. This, in turn, determines and increases of the area of real contact and, hence, of the total adhesive force. Therefore beside contact splitting one needs very compliant terminal attachment ends to increase adhesion. But, actually, there is a third point. Indeed the shape of the terminal ends may have a very fundamental role in enhancing adhesion. Indeed very recently mushroom-shaped adhesive microstructures, inspired by the attachment system of the males of some species of beetles, have drawn the interest of scientists and engineers because experiments have proved their superiority compared to other micro- and nano-structures made of cylindrically shaped pillars. Our research shows that the presence of a axial-symmetric plate in this mushroom shaped microstructure modifies the debonding mechanism of the pillars by preventing crack propagation from the out perimeter towards the inner part of the pillar. This results in a strong enhancement of pull-off force and explain the origin of the superior adhesion of such microstructured surfaces. Our achievements can streamline optimisation of adhesive microstructures for industrial applications.

Crack propagation in viscoelastic solids

The amount of energy required to propagate the crack has been calculated by means of theoretical investigation which have led to a model of crack propagation in viscoelastic solids, which takes into account the influence of viscoelastic energy dissipation, non-uniform temperature distribution, surface geometry and load conditions. The theory also explains why in some cases it is observed that the energy per unit time required to move the crack may increase up to three or even more order of magnitude at high velocities, and also shows that because of the very high increase of temperature in a region very close to the crack tip (here the temperature increase is of 600-800 K as confirmed by some experiments) an instable behaviour may take place at certain crack velocities. The crack may show a stick-slip motion or e catastrophic propagation. This has been confirmed by recent experiments and the importance of such effect is fundamental in many application as for the design of tires. Beside theory recently also experiments have been carried out to test theory. We have carried out a campaign of experimental test to determine the relation between the energy release rate at the crack tip G and the crack propagation speed v and compare this measurements with theoretical prediction. The experimental set-up consists of a custom-made traction system, a step-motor to move the mobile cross beam, a couple of load cells to measure the applied load on the specimen, a couple of LPDS sensors to control the displacement, a high-speed camera to record the crack motion, a thermo-camera to measure the increase of temperature at the crack tip, and a data acquisition system. The samples used during the tests are made of Styrene Butadiene Rubber (SBR) which has a relatively linear viscoelastic response. To viscoelastic modulus of the material has been measured by a private company through the use of the instruments EPLEXOR® by GABO. To carry out the crack propagation experiment we control the initial displacement of the sample. Then we generate a small crack in the rubber sheet with a surgical type blade. The crack then propagates spontaneously driven by the elastic energy stored into the sample. The time evolution of the crack tip position and crack shape has been recorded by means of the high-speed camera to determine the crack propagation velocity. By changing the initial displacement we modify the elastic energy stored in the rubber sheet and then change the crack tip propagation speed.

 Contact mechanics and friction of viscoelastic solids

We have seen that one of the contribution to sliding or rolling friction comes from the local viscoelastic energy dissipation which occur close to the tip of propagating cracks. However, this is not the sole contribution to friction in viscoelastic materials, there is another contribution coming from the bulk deformation rate which occurs when a viscoelastic solid slides or rolls against a rough substrate. We have developed ad hoc BEM numerical method to solve the contact problem of a viscoelastic half-space in sliding or rolling contact with a rigid randomly rough surface. Differently from all other viscoelastic contact models in literature, our approach allow to treat general linear viscoelastic solids, i.e. viscoelastic solids with a very large number (in the limit case a continuous distribution) of relaxation times. This is not a trivial results since many attempts have been made in the past without success to develop numerical approach able to deal with very general viscoelastic materials. We also stress that our viscoelastic BEM retains all the advantages of our previous BEM model developed for the case of linear viscoelastic materials. Hence, it do not requires very high computational resources both in terms of memory space and computation time. In particular it also makes use of the same adaptive non-uniform grid on the contact areas and exploit a corrected version (to take into account the effect of relaxation times) of Love's elastic solution to solve the problem. In addition to this we have also extended Persson's analytical approach for calculating friction to the general case of anisotropic surfaces thus overcoming one limit of Persson's theory which was actually able to deal only with isotropic surfaces. Both numerical and analytical approaches have allowed us to calculate the dependence friction as a function of the rolling or sliding speed and how it depends on the statistical properties of the rough surfaces. In the case of rolling contact, we have also shown how friction is related to applied load. Our results suggest also a possible new experimental methodology for the determination of the complex modulus of viscoelastic materials. Experimental investigations have been and are still being carried out on the same topic. To this end an custom-made sliding device has been developed to measure sliding friction between a viscoelastic block and a much stiffer randomly rough surface. On the other end we are still carrying out experiment of rolling friction on modified pin-on-disk tribometer.

Contact mechanics of rough surfaces in presence of liquid at the interface

Part of the research activity has been also dedicated to the contact in presence ofliquid at the interface. In particular the research activity in this field hasbeen mainly concerned with: (i) roughness induced super-hydro-repellence ofmicro- and nano- structured surfaces, (ii) calculation of fluid leakage inseals, (iii) development of mean-field/homogenization techniques to investigate the soft and hard lubricatedin all lubrication regimes: boundary, mixed, EHL and HL contacts.

- Roughness induced hydrophobicity –Superhydrorepellence has attracted much interest from both fundamentalresearch, because of its potential applications to the high-tech field ofmicrofluidics, and industry for the "self-cleaning" ability of suchsurfaces (e.g. superhydrophobic paints, car windscreens). This phenomenon wasobserved for the first time in 1997 by the biologist Barthlott on the Lotusleaves. Since then an increasing number of researchers has been carrying outinvestigations in this field to find a way to replicate/mimic the properties ofthe lotus lead. However only a few theoretical studies have been presented whichattempt to explain the physical background of the Lotus-Effect®. In this filedwe have also carried out theoretical research to analyze the wetting/non-wetting properties ofa liquid drop in contact with a chemically hydrophobic rough surface is addressed.We show that, as it was expected, roughening the substrate may produce asuper-hydrophobic surface. The conditions under which a Cassie state isobtained and preserved are clearly identified. In particular theoreticallypredict the critical value of the drop pressure at which the compositeinterface configuration becomes unstable and a transition to the Wenzel statetakes place. This results has been observed in some recent experiments onsuper-hydrophobic man-made nanostructured surfaces. However, in manyapplications, e.g. car windscreens, this transition to the Wenzel state has tobe avoided, and an ad hoc substrate roughness designing procedure has to bedeveloped for this scope. A simple criterion has been then proposed tocalculate, once given the maximum drop pressure, the geometry of themicrostructured surface to preserve the super-hydrophobic properties of thesurface.

- Seals – The research has been focused also on theestimation of leakages in seals. A novel approach has been presented which isbased on the analogy between the seal-substrate interface and a porous medium.It is assumed that the interface is constituted of a random distribution ofnon-contact patches (the pores) and small but numerous contact spots (islands).Leakage may occur only through the pores, of which the lateral size and heightare distributed according to a probability density function, that is calculatedon the basis of a recent theory of contact mechanics. The theoretical approachis based on the critical path analysis (CPA) and percolation theory and allowsto calculate the conductance of the micro-channels carrying the liquid flow. Weshow that the conductivity of the seals is strictly related to the distancebetween two adjacent channels and to the distance between adjacent smallestconstrictions along the same channel. Some authors argued that the twoquantities are equal. In this case we obtain that the seal conductivity is justequal to the conductance of the smallest constriction encountered along the flowcarrying channel, which is formed at the non-contact area percolationthreshold. In this case, our calculated value of the seal conductivitycoincides with the one calculated with different approaches. However we alsoargued that the two relevant lengths may be very different. In this case theprobability distribution of local conductances takes a critical role indetermined the conductivity of the seal. Our investigation is stimulatingadditional research in the field of contact mechanics in wet/lubricatedconditions.

- EHL and mixed lubrication – The focus of this research has been to investigate theinfluence of roughness on lubricated contacts. A novel(mean-field/homogenization) model to describe the interfacial fluid-asperityand asperity-asperity contribution to total pressure has been developed tostudy the transition from the hydrodynamic lubrication to the boundarylubrication regime occurring in squeeze or the sliding contacts. In particular,we are able to estimate the flow factors and shear stress factors, which turnout to be affected by elastic deformation (e.g. interfacial separation) and thefluid pressure gradient that must be determined as a part of the solution ofthe homogenized system of equations. We have described how the fluid-induced asperitiesflattening, as well as local percolation effects and roughness anisotropicdeformation determine the average fluid flow at the interface. Finally, we havediscussed on the macroscopic friction laws (the so called Stribeck curves) interm of local average shear stresses. We show that interaction between fluidand the elastic solid determines a strong modification of the surface roughnessstatistical properties, e.g. isotropic surface may become anisotropic and viceversa, thus leading to direction-dependent flow and stress factors which arethen take the form of tensors. In particular the theory explain why, inpresence of anisotropic surface, the Stribeck curve may change radically withthe formation of a hump in the mid-velocity range. The theory has been alsoexploited to analyze the highly loaded strongly non-stationary squeeze processof an oil film sandwiched between an elastic spherical ball and a rigid roughsubstrate. We show that the coupling between the elastic properties of thecontacting solids, the oil rheology, the surface roughness and the applied loaddetermines a wide range of lubrication conditions from fullyelasto-hydrodynamic to mixed and even boundary lubrication. In particular wefind that increasing (decreasing) the surface roughness (the applied normalload) speeds up the squeeze process, anticipates and shrinks the time intervalduring which the transition to mixed lubrication conditions occurs. On thecontrary, the initial separation between the approaching bodies only marginallyaffects the transition time. We also observe that, in mixed lubricationconditions, the highest asperity– asperity contact pressure occurs in theannular region where the separation between solids takes its minimum value invery good agreement with recent experiments. 

Mechanical transmissions

The area of interest in the field of mechanical transmissions focuses mainly on the Continuously Variable Transmission (CVT), which is a power transmission device able to continuously provide an infinite number of speed ratios between two finite limits. CVT transmissions can be mainly distinguished in pushing belt CVTs (Van Doorne type), chain belt CVTs, and Toroidal Traction Drives. Infinitely variable transmission (IVT) instead are simply obtained by coupling one of the above written CVTs with a planetary gear and a fixed ratio gear, thus allowing for a neutral or even reverse gear. CVT transmissions are potentially able, when properly controlled, to reduce the vehicle fuel consumption, the polluting emissions. These transmission enable indeed the IC engine to operate closer to its economy line almost in every working conditions. CVTs are also able to improve the ride comfort and drivability of cars.

Metal Pushing V-Belt and Chain Belt CVTs In order to achieve better fuel consumption and comfort, an accurate and fast control of the rate of change of the speed ratio in CVT transmissions is a fundamental prerequisite. Several researchers have been studying different solutions in order to optimize the control strategy of the transmission and its performances. But, this advanced control strategies need an accurate model of the CVT dynamics, which should be able to predict the actual clamping forces needed to obtain a certain shift speed and improve CVT mechanical efficiency. The research carried out by Dr. Carbone is concerned with the study of the shifting and traction performance of the variator. The influence of belt-pulley lubrication has been investigated, as well as the effect of clearance among the steel segments in the case of pushing belt. It has been shown that the main ingredient to understand the CVT behaviour is the pulley bending. The pulley bending significantly affects the relative motion between the belt and the pulley and, therefore, the actual direction and magnitude of the friction forces at the belt-pulley interface. The research activity has led Dr. Carbone to develop the so called CMM (Carbone, Mangialardi, Mantriota) model of CVT dynamics, which has been further improved in recent years by the research group coordinated by Dr. Carbone. The model has been extensively tested and validated either at The Eindhoven University of Technology, where Dr. Carbone has been responsible for the experimental research activity on the power loop test rig in the automotive Engineering Science laboratory, either at the Department of Mechanical Engineering – Technical University of Bari, where a test rig has been designed to measure traction and efficiency curves of the CVT. Recently the test bench has been further improved to include a data-logger system which allows to measure the chain link forces.

Toroidal traction drives – A research activity has been also carried out in relation to the mechanical efficiency and traction performances of two different typologies of toroidal traction drive, (i) the full-toroidal, and (ii) the half toroidal double cavity CVTs. The aim of the research has been that of determining which of the aforementioned drives offers the higher mechanical efficiency. A fully flooded isothermal contact model between disks and rollers, based on the results of EHL theory, has been used to evaluate the slip and spin losses. Because of the very severe fluid contact conditions, the Bair and Winer non-Newtonian rheological model of the lubricant has been utilized, and the influence of pressure and on the limiting shear stress of lubricant has been taken into account as well. Moreover, according to Roelands model, the effects of pressure on fluid viscosity and on fluid density has been also considered. The results have shown that the half-toroidal traction drive offers a higher mechanical efficiency and a higher traction capability in comparison to the full toroidal traction drive. The reason of this important difference is related to the different spin losses which affect the two variators. The half toroidal variator, when compared to the full toroidal one, is much less affected by spin losses at the contact between the roller and the discs and, despite the torque losses in the support bearing, its mechanical efficiency is always about 4-5 % higher in comparison to the full-toroidal variator. Moreover the half-toroidal mechanical efficiency is almost constant, close to its maximum values (about 92%) and always over the threshold of 90% on most part of the torque range. Full toroidal CVT, instead, shows a different behavior, its efficiency varies within a wider range of values. The result obtained are also in good agreement with the experimental data found in the scientific literature. Recently a new typology of toroidal traction drive, very recently patented by M. J. Durack has been studied. This typology of variator is referred to as the Double roller  Full Toroidal traction drive. Our investigations have shown that this type of traction drive combines the advantages of classical full toroidal and half toroidal variators, resulting in an improvement of the mechanical efficiency over a wide range of transmission ratios, and in particular at the unit speed ratio, as in such conditions the DFTV allows for zero-spin thus strongly enhancing its traction capabilities.

IVT transmissions and vehicle fuel consumption – The IVT transmissions (infinitely variable transmission) if properly designed may allow to vary the speed ratio continuously from reverse to forward including a geared neutral state. These transmissions are made up by coupling a CVT, a planetary gear (PG) and a fixed ratio transmissions (FR). The research activity in this field has been concerned with the comparison of the fuel consumption of a mid class vehicle equipped with four different transmission's typologies: CVT, IVT, robotized discrete transmission (ROB) and manual transmission (MT). The comparison has been carried out in stationary conditions (i.e. at constant vehicle speed), in ECE15 urban cycle, and in EUDC extra-urban cycle. The chosen IVT design was the series-IVT with type I power flow, which has been shown to maximize the efficiency of transmission. The IVT mechanical efficiency has been calculated by taking into account the effect of the actual operative conditions on CVT and planetary gear efficiency. The optimization of fuel consumption has been achieved by choosing, in each condition, that particular value of the speed ratio able to maintain the engine operation point on the economy line. The results have shown that both CVT and IVT may have less fuel consumption than the traditional manual transmission, but, also that the robotized gearbox performs better than the others. However, the higher comfort of CVT and IVT could make this transmission preferable to robotized ones. The main cause of losses in the CVT and IVT system are related to the power losses in the hydraulic actuation system. Therefore a different actuation system, e.g. an electromechanical one, should result in much better performances.


AFM cantilever dynamics in liquids

Nowadays dynamic atomic force microscopes (dAFM) are being extensively investigated because of the so different and novel applications where dAFM are employed, e.g. to study biological targets as cells, proteins, DNA. In such cases the micro-cantilever tip often needs to operate in a liquid environment to extract the required information from the sample. However, tip dynamics is strongly affected by the presence of the liquid itself, so that understanding the actual microcantilever response in such conditions, has become one of the most challenging problems the researchers are trying to face. A deep knowledge of the degree of interaction between the cantilever dynamics and the fluid is extremely important to avoid misleading information. Because of the micro-scale size of the cantilever, thermal noise due to Brownian forcing of liquid particles cannot be neglected and therefore proper insights about this effect are required. This is why different numerical approaches have been presented in literature, which only approximatively describe the liquid - cantilever interaction. The research aims at providing a useful and relatively simple tool to describe the fluid-structure interaction. In particular an analytical heuristic formulation of the force the liquid exerts on the cantilever has been presented and utilized to successfully investigate the AFM cantilever dynamics under the action of both linear and non linear forces.



Giuseppe Carbone

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