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Professore Associato presso: Dipartimento di Ingegneria "Enzo Ferrari"

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2019 - A paradox in curved beams [Articolo su rivista]
Strozzi, Antonio; Bertocchi, Enrico; Mantovani, Sara

It is sometimes possible to relieve the stresses in a mechanical component by removing material, where relief grooves are the commonest expedient approach. Within the rectilinear beam realm, rare situations are known in which, by removing material in the cross-sectional zones that are farthest from the neutral axis, a bending stress diminution is achieved. With regard to curved beams, selected examples are presented in which a bending stress diminution is achieved by laterally removing material from the zones close to the neutral axis. An approximate mathematical approach based on Gateaux linearization is developed that delimits the lateral zones of the beam cross-section in which material removal is accompanied by bending stress reduction. While the achievable stress diminution is generally marginal, the reduction of the beam’s cross-section is technically interesting.

2019 - On the strength weakening effect of stiffening ribs in the design of machine components [Capitolo/Saggio]
Strozzi, A.; Bertocchi, E.; Mangeruga, V.

The bending stress in beams may often be reduced by adding material to the cross section. In some paradoxical cases, however, the bending stress increases by adding material from zones far away, or close to, the neutral axis. Similarly, the bending stress of rectilinear or curved beams may often be reduced by adding ribs to the initial beam section. However, such ribs may sometimes cause a both undesired and unexpected stress increase, although they still produce a beneficial stiffening effect. The aim of this paper is twofold: A) to examine this unexpected result within the context of the paradoxical behaviour of some known beam sections, and especially of a recently noted paradox; b) to provide a preliminary rule of thumb for the mechanical design of ribs sometimes added to the outer surface of an eye, with particular regard to the small end of a connecting rod.

2018 - A repertoire of failures in gudgeon pins for internal combustion engines, and a critical assessment of the design formulae [Articolo su rivista]
Strozzi, A.; Baldini, A.; Giacopini, M.; Bertocchi, E.; Mantovani, S.

The geometries commonly employed in gudgeon pins for internal combustion engines are examined. In particular, various methods for reducing the pin weight are considered. The selection of the appropriate clearance is addressed. The most typical failure modes are classified and interpreted in the light of stress analysis. The available approximate design formulae are assessed versus selected Finite Element forecasts. The fatigue cycles of stress and displacement related parameters are examined. The effect of the initial clearance on the contact pressure and on the pin ovalization is explored for selected clearance values. A typical Y-shaped fatigue crack is interpreted with the aid of Mohr circle. An error in a classical design approach based upon the containment of the pin ovalization is hypothesized.

2018 - A simple method of analysis of partial slip in shrink-fitted shafts under torsion [Articolo su rivista]
Bertocchi, E.; Mantovani, S.; Ciavarella, Michele

A solution method is proposed for the partial slip problem of a shrink-fitted shaft under torsion, that relies on the superposition of axisymmetric, elastically uncoupled problems all solved with FE. First, a problem is solved for the contact pressure induced by the interference coupling alone. In the presence of remotely applied torque, antiplane slip occurs at the indenting edge contact extremity; shear actions at the slip portion of the contact interface may merely be derived by scaling the pressure profile through the friction coefficient. A semi-inverse solution approach is derived, based on the assumed extent for the near-edge slip zone; two linear elastic solutions are parametrically mated to cancel stress singularities at the stick-slip transition point, the first solution concerning the remote torque alone, and the second one addressing the interface slip actions alone. We finally discuss the results for a selection of geometrical ratios, and the viability of simplified approaches based on beam theory.

2018 - Analysis of a segmented locking ring for shell-bottom connection in pressure vessels [Articolo su rivista]
Strozzi, A.; Bertocchi, E.; Mantovani, S.

A simplified mechanical analysis is carried out for a specific closure system of a pressure vessel, consisting of a segmented locking ring, partially inserted into an annular slot; the ring portion protruding from the slot supports the vessel bottom; sealing is achieved by placing a copper gasket between the ring and the bottom. An approximate contact reaction is assumed, that is formed by a distributed constant linear force and by concentrated forces at the extremities of the ring-slot contact. Analytical expressions of the ring internal forces are provided. A numerical example is presented.

2018 - Appreciable cross section reduction upon moderate intrados bending stress increase in curved beams [Relazione in Atti di Convegno]
Strozzi, A.; Bertocchi, E.; Mantovani, S.

2018 - Shaft-hub press fit subjected to couples and radial forces: analytical evaluation of the shaft-hub detachment loading [Articolo su rivista]
Bertocchi, Enrico; Lanzoni, Luca; Mantovani, Sara; Radi, Enrico; Strozzi, Antonio

A shaft-hub press fit subjected to two non-axisymmetric loading conditions is examined and the situation of incipient detachment between the shaft and the hub is determined. The first condition consists of a central radial load P applied to the hub, balanced by two lateral forces P=2 applied to the shaft at a distance d from the hub lateral walls. In the second condition, a central couple C is applied to the hub, and it is balanced by two lateral opposite loads withstood by the shaft at a distance d from the hub lateral walls. The shaft-hub contact is modelled in terms of two elastic Timoshenko beams connected by distributed elastic springs (Winkler foundation), whose constant is analytically evaluated. Based upon this enhanced beam-like modelling, the loading inducing an undesired shaft-hub incipient detachment is theoretically determined in terms of the shaft-hub geometry, of the initial shaft-hub interference, and of the elastic constants. Finite element forecasts are presented to quantify the error of this beam-like approximate analytical approach.

Strozzi, Antonio; Bertocchi, Enrico; Mantovani, Sara

An approximate structural analysis is presented of a shell-bottom connection in which a locking ring, partially protruding from an annular slot machined in the vessel wall, supports the bottom loaded by the internal pressure. The ring is segmented into four parts, to permit assembling. The contact pressure between the ring and the slot lower face may be conveniently approximated. Simplified expressions of the internal forces within the ring are obtained.

2017 - On the contact stresses at the indenting edge of a shaft-hub interference fit subject to bending and shear forces [Relazione in Atti di Convegno]
Bertocchi, Enrico; Mantovani, Sara; Strozzi, Antonio

The contact stress field is addressed that is developed at the indenting edge of a keyless shaft-hub interference fit, in the case that both bending and shear forces are applied, and in the absence of friction. The combined effect of a set of elementary load cases is assessed for the sharp notch case in terms of a generalized stress intensity factor, with the aid of Finite Elements and for a class of shaft-hub geometries. In fact, linearity is preserved in the case of a sharp edged bore up to the incipient detachment condition; such event, which may occur as a result of e.g. excessive bending loads, may be forecast based on the proposed framework. Contact stresses in the case of rounded edge may be subsequently predicted by scaling an appropriate local solution; fatigue analysis may then be performed in the case of rotating or fluctuating loads. An exhaustive design table is finally compiled to assist the designer in dimensioning an interference fit in the presence of an arbitrary combination of time varying bending and shear forces.

2017 - On the evaluation of the peak contact stresses in a press-fitted shaft-hub coupling subject to bending [Relazione in Atti di Convegno]
Bertocchi, Enrico; Mantovani, Sara; Baldini, Andrea; Strozzi, Antonio

The peak contact stresses are addressed that are developed from the frictionless press fit of a shaft subjected to bending into an elastically similar hub with bore rounded edges. The non-linear behavior of this progressive contact is addressed by scaling a local solution available from the literature, with the aid of intermediate, auxiliary problems extracted from the fracture mechanics realm. The title problem being linear on the global domain with both the bending couple and the interference, this problem is solved by combining the FE forecasts obtained for two separate load cases, i.e. a) the interference alone and, b) the bending couple alone. Such results are expressed in terms of a) stress intensity factors for the auxiliary FM problems, and b) hoop strain component, as sampled in the proximity of the indenting edge for both the mating members. Design formulae for the contact stresses are proposed, that account for various normalized geometrical parameters, such as the outer to inner hub radii ratio, the radius of the hub bore fillet, and the contact length. Comprehensive coefficient tables are provided as well. Finally, an error analysis for the proposed method is presented.

2017 - Shaft-hub press fit subjected to bending couples: Analytical evaluation of the shaft-hub detachment couple [Articolo su rivista]
Radi, Enrico; Lanzoni, Luca; Strozzi, Antonio; Bertocchi, Enrico

A mathematical modelling of a shaft-hub press-fit subjected to bending couples applied to the shaft extremities is developed, and the value of the bending couple inducing an un- desired shaft-hub incipient detachment is analytically determined. The shaft-hub contact is modelled in terms of two elastic Timoshenko beams connected by a distributed elastic spring, whose stiffness is analytically evaluated. Two models of the distributed spring are considered. The first model expresses the combined deformability of both the shaft and the hub cross sections. The second model accounts for the stiffening effect exerted by the shaft portion protruding from the hub on the adjacent shaft part that is in contact with the hub, and, consequently, it assumes only a rigid body motion of the shaft cross section, thus neglecting its deformability. Based upon this beam-like model, the bending couple producing the incipient detach- ment between the shaft and the hub is theoretically determined in term of the shaft-hub geometry, of the initial shaft-hub interference, and of the elastic constants. Comparisons with selected Finite Element (FE) forecasts indicate that the first modelling produces an incipient detachment couple that appreciably overrates the FE forecasts, whereas the sec- ond modelling lowers the error down to technically acceptable predictions.

2016 - A New Volumetric Parameter for a Comparative Finite-Element Analysis of a Six- or Four-Implant Mandibular Total-Arch Rehabilitation [Articolo su rivista]
Natali, Alfredo; Bertocchi, Enrico; Baldini, Andrea; Mulas, Giuseppe Antonio; Martinolli, Matteo; Bortolini, Sergio

In a full-arch implant rehabilitation ad modum Branemark, the distribution of stress and strain in mandibular bone is influenced by the type, number and position of implants used. In particular, the biomechanical behaviour of the bone structure after complete osseointegration depends on the load transferred to the bone by each fixture. In this study, a finite-element analysis of two models was performed. Models of an all-on-four configuration and a six-implant configuration were com- pared in a worst-case scenario. A new V parameter is presented to aid the quantitative and com- parative analysis of the all-on-four and six-implant configurations. The influence of orthotropy was also investigated, and a geometric change in the all-on-four configuration is presented.

2016 - A complete 3-D description of the elastic behavior of a piston ring and its influence on the tribological behavior of the piston ring-cylinder liner interface [Relazione in Atti di Convegno]
Mastrandrea, LUCA NICOLO'; Giacopini, Matteo; Bertocchi, Enrico; Strozzi, Antonio; Dini, D.

Advances in modern engine development are becoming more and more challenging. The intense increase of thermal and mechanical loads as a result of higher power density requires perfecting the function of all engine components especially with regard to emission and friction reduction. In particular, piston rings pack represent one of the most important cause of mechanical friction loss in internal combustion engine [1], and inadequate ring-liner lubrication leads to high fuel/oil consumption and increased engine emissions with dramatic impact over the entire system efficiency. A desirable piston ring-pack set has to provide efficient sealing performance with both the cylinder wall in a radial direction and the top or bottom sides of the piston ring housing in an axial direction, leading to minimal gas blow-by, oil consumption and friction loss. Moreover piston ring other requirement are low friction, low wear and good resistance against mechanical/thermal fatigue. This is a challenging task due to the nature of the phenomena and interactions associated with piston rings. For example, increasing the installed ring tension, which is a method to control oil consumption, also tends to increase ring friction. Hence, any attempt to optimize ring-pack performance output parameters requires a good understanding of the dynamics of all the involved components. Different key elements have to be considered: the ring shape in its free state (namely free shape), the ring crossing-section geometry and the contact surface profile, which play important roles in determining the ring behavior. In order to achieve sealing, the piston rings are first held against the cylinder liner in its front face by their tension after being installed into the cylinder bore. The contact pressure on the cylinder wall is achieved by the inherent spring force of the ring in conjunction with the gas pressure behind the ring. During different engine operating conditions, the piston rings experience dynamically changing forces and axial as well as radial movements of the rings can occur. The contact on the side of the piston housing is achieved by the axial forces acting on the ring. The axial forces are composed of the gas pressure above and under the ring, the mass forces (inertia), and the friction forces. These forces change their direction during the cycle, and, as a result, the piston ring moves from one side of the groove to the other during the engine cycle. This is known as ring fluttering when the axial movement becomes excessive. This behavior open an additional gas flow path: gas can flow around the inner diameter of the ring which results in very high engine blow-by loss. In addition the ring pack design should also consider other factors, including gas blowback and, as said before, ring pack friction. The blowback is the reverse process of blowby and is highly related to engine emission and oil consumption while ring friction can cause severe ring and cylinder wall wear, which results in the ring losing its sealing capability. These factors are related to the ring circumferential pressure distribution, which is defined by the ring free shape and the ring cross section geometry. The understanding of the piston ring behavior is an hard challenge for automotive engineer. Firstly, in 1936 Castleman [2] investigated and proposed the concept of hydrodynamic lubrication for the piston ring. Thereafter, more and more research has been done in this field. Dowson et al. [3] predicted the behavior of a piston ring using the EHL theory. Sun [4] conducted his study for ring-bore conformability, in which the ring was modeled as a curved beam under in-plane loads. Liu and Tian [5, 6] developed an FEA tool for piston ring design. Ejakov et al. [7] modeled ring twist behavior predicting ring axial, radial displacements, bending and twisting angles along the ring periphery over an engine cycle. In this contributions a complete 3D model of the piston ring is propose

2016 - A repertoire of failures in connecting rods for internal combustion engines, and indications on traditional and advanced design methods [Articolo su rivista]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Mantovani, Sara

Several typical and uncommon failure modes in con-rods for internal combustion engines are commented from the stress level viewpoint. The interpretation of the fractures is supported with traditional calculations, with more advanced analytical models, and with Finite Element (FE) predictions. The repertoire of failures in a con-rod is presented by separately addressing the parts composing the con-rod itself, namely the shank, and the small and big ends.

2016 - Analytical evaluation of the peak contact pressure in a rectangular elastomeric seal with rounded edges [Articolo su rivista]
Strozzi, Antonio; Bertocchi, Enrico; Mantovani, Sara; Giacopini, Matteo; Baldini, Andrea

The contact pressure is considered for an elastomeric rectangular seal with rounded edges. An asymptotic matching is performed between an available analytical expression of the contact pressure that neglects the finiteness of the seal dimensions and a fracture mechanics solution describing a periodically laterally cracked strip of finite width. This matching provides a corrected formula for the peak contact pressure that accounts for the finiteness of the seal dimensions. The analytical expression for the peak contact pressure is validated versus finite element predictions for a large family of seal geometries and, in particular, for a seal reference shape extracted from the pertinent literature. An appraisal of the finite deformation effect has been carried out numerically.

2016 - Normalization of the stress concentrations at the rounded edges of an interference fit between a solid shaft subjected to bending and a hub [Articolo su rivista]
Strozzi, Antonio; Bertocchi, Enrico; Baldini, Andrea; Mantovani, Sara

The elastic stress concentrations are addressed that are developed from the keyless frictionless press fit of a shaft subjected to bending into a hub with rounded bore edges. Derived from a formal modeling of the title problem in terms of an integral equation, a set of normalized parameters is proposed that accounts for the combined effects on the hub stress concentration of the fillet radius, the shaft radius, the hub outer radius, the hub axial length, the interference, the Young's modulus, and the bending couple. A numerical validation of the normalized parameters is presented. With the aid of Finite Elements, various design charts are compiled that (a) forecast the bending couple initiating the detachment between the shaft and the hub, and (b) report the elastic stress concentrations within the hub versus the proposed normalized parameters in the absence of shaft–hub detachment. Such charts assist the designer in dimensioning an interference fit in the presence of a bending couple.

2015 - A Note on the Legendre Series Solution of the Laplace Equation for Cylindrical Problems [Articolo su rivista]
Strozzi, Antonio; Bertocchi, Enrico

The mechanical modelling of cylindrical problems is addressed. A series solution is considered of the Laplace equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.

2015 - Aluminum structures in automotive: Experimental and numerical investigation for advanced crashworthiness [Relazione in Atti di Convegno]
Miscia, Giuseppe; Rotondella, Vincenzo; Baldini, Andrea; Bertocchi, Enrico; D'Agostino, Luca

Ductility of aluminum alloys is highly used in automotive applications where crashworthiness becomes relevant. Due to its physical and mechanical properties, aluminum allows structures to be designed with good capacity to absorb energy, without increasing the overall weight of cars. In particular, high elongation allows for the conversion of a great amount of kinetic energy related to crash events in plastic deformation. If this was not the case, the energy involved during an accident could interest also the occupants, causing serious injuries. During large deformation of structures, chassis components may be subjected to failure, limiting the capacity of energy absorption. Therefore, the capability to predict the behavior of structures under crash loads becomes very important during the cars design process. Under these circumstances, finite element analysis is useful to simulate the response and to validate a project. In the last few years, prediction of materials behavior has become relevant in order to simulate in the best possible way the reaction of structures under dynamic loads. Contrary to what was expected, aluminum alloy might show anisotropic behavior after manufacturing processes. Extrusion, lamination and forging processes can modify crystallography, grains shape, precipitates and dislocations structures, affecting considerably the plastic properties. Furthermore, the failure limit strictly depends on the stress-strain state in the material during the crash event. Tensile state, shear state, compressive state and mixing states generally return different failure limits. Hence, it is indispensable to arrange a huge experimental campaign to define a thorough characterization of an aluminum alloy. Finite element (FE) codes give the possibility to include all these aspects, but several parameters need to be finely tuned. By limiting the number of tests, the present work aims at obtaining the numerical-experimental correlation of some crash absorbers during an impact. Tensile and shear specimens have been cut from the extruded parts of the chassis in 0°, 45° and 90° with respect to the extrusion direction. It is possible to define a fracture locus curve that identifies the equivalent strain limit of the aluminum alloys studied. For instance, Johnson-Cook and Bao-Wierzbicki criteria for aluminum alloys have been defined starting from a complete experimental campaign. They also give approximated analytical functions to define the entire fracture locus curve depending on the stress state. Uniaxial tensile and shear failure limits are the only ones taken into account in this work. Different hypothesis have been considered to define the rest of the fracture locus. Tuning the function parameters of the chosen criteria, a failure curve for compression, shear, tensile and mixing states have been set according to the experimental tests performed. The material card obtained has been further refined during the numerical-experimental correlation of both the samples and the crash absorbers: mesh size effects have been taken into account to assess the approximations of stress and strain into shell elements. In this work, fine mesh is only used during the initial correlation of specimens. This allows for considerably reducing the computational time of FE models studied. Acceleration signals and failures have been monitored in the crash absorbers. A high correlation between the experimental and numerical tests have validated the current methodology. Because of the few experimental tests performed on samples, it is not possible to study the exact mesh scaling effects at the beginning. Further refining is needed during the correlation of the whole component to get the right failures. In any case, the error given by the experimental dispersion could compromise the correlation and this is the reason why accuracy is not always necessary during the first phases of the correlation settings.

2015 - Analytical evaluation of the peak contact pressure in a rectangular elastomeric seal with rounded edges [Abstract in Atti di Convegno]
Baldini, Andrea; Bertocchi, Enrico; Giacopini, Matteo; Mantovani, Sara; Strozzi, Antonio

Rectangular seals constitute an alternative design to O-rings. Rectangular seals are employed in demanding applications such as aircraft actuators, e.g. ref. [1]. The seal edges are generally rounded, ref. [2]. As a consequence of the presence of filleted edges, the contact pressure exhibits Hertzian-type local bumps in its lateral zones; it remains almost flat in the central zone of the contact. The lateral bumps and the central flattish zone confer to the contact pressure distribution a camel-backed profile, see ref. [2], and ref. [3] for a similar axisymmetric problem. It is difficult to derive a rigorous, analytical expression of the contact pressure curve for the title problem. In fact, the analytical solution available for a rectangular punch with rounded edges indenting a half plane, e.g. ref. [4] and related bibliography, is exact only in the situation of a rigid punch indenting a deformable half plane, ref. [5], whereas in the title problem the punch (i.e., the seal) is flexible and the half plane (i.e., the counterface) is rigid. It has recently been shown in refs [5-7] that the unrealities of the above analytical solution may be corrected by combining the analytical solution with Fracture Mechanics (FM) results dealing with the stress singularities at the tip of a transverse crack in a strip of finite width. In this paper, an extension of formula (20) of ref. [5] is developed, that accounts for the combined effects of a) the presence of a filleted edge, and b) a finite seal width and height.

2015 - Elastohydrodynamic analysis of the conrod small-end of a high performance motorbike engine via a mass conserving cavitation algorithm [Relazione in Atti di Convegno]
Mastrandrea, Luca Nicolo'; Giacopini, Matteo; Dini, Daniele; Bertocchi, Enrico

In this contribution a complementarity formulation for the solution of EHL problem in presence of cavitation is employed in order to investigate the tribological behavior of the conrod small-end of a high performance motorbike engine. The influence of different physical and geometrical parameters is discussed. In particular, the clearance between the conrod small-end and the piston pin, the lubricant physical properties, the surface roughness and the stiffness of the piston pin are investigated, thus providing preliminary guidelines for the correct design of the coupling. Due to the negligible influence of the transversal forces acting on the conrod small-end and of the relative sliding speed between the mating surfaces, a two symmetrical model of the assembly is prepared and results are compared with those obtained adopting a simply symmetrical model.

2015 - On the applicability of the Boussinesq influence function in modelling the frictionless elastic contact between a rectangular indenter with rounded edges and a half-plane [Articolo su rivista]
Strozzi, Antonio; Bertocchi, Enrico; Baldini, Andrea; Giacopini, Matteo

The applicability of the Boussinesq influence function in modelling the frictionless elastic contact between a rectangular indenter with rounded edges and a half-plane is numerically explored. The potential of the asymptotic matching method combined with classical fracture mechanics results is investigated. Manageable design formulae for evaluating the maximum equivalent stress are analytically derived with the aid of the asymptotic matching method.

2015 - Preliminary investigation of the cavitation damage in the conrod big end bearing of a high performance engine via a mass-conserving complementarity algorithm [Abstract in Atti di Convegno]
Giacopini, Matteo; Bertocchi, Enrico; Baldini, Andrea; Strozzi, Antonio

The conrod big end bearing is one of the most critical components of internal combustion engines; it is usually subjected to high dynamic loads and high sliding velocities between contacting surfaces are often involved. Therefore, the tribological behaviour of the conrod big end bearing is often one of the key elements to engine reliability, and it has been investigated both theoretically and experimentally in several contributions in the pertinent literature [1]. With the ever-increasing quest to improve engine performance, and the consequent increase of the rotational speed and combustion/inertial loads, the cavitation of the lubricant used in conrod big end bearings may play a crucial role in the assessment of bearing durability. To overcome problems related to film cavitation, palliatives such as the reduction of the clearance between the components, the increase of the oil supply pressure and/or the use of harder coating materials have been commonly adopted. However, such simple adjustments do not always represent a valid solution; further investigations are required in order to avoid cavitation damage occurrence. The cavitation damage has been studied for more than a century both theoretically [2-5] and experimentally [6,7], and many attempts have been made to predict or measure the pressure spikes developing in the cavitated areas due to bubble collapse. Although a universally accepted theory seems not to exist, it is clear that the cavitation damage occurs due to the rapid and violent collapse of the vapour bubbles in the proximity of a solid boundary. The aim of the present work is the preliminary evaluation of the damaging effect of the cavitation in a conrod big end bearing via elasto-hydrodinamic numerical analyses.

2015 - The influence of textured surfaces on the tribological behaviour of hip replacements employing a mass conserving complementarity algorithm [Relazione in Atti di Convegno]
Dini, Daniele; Giacopini, Matteo; Giuseppe, Mulas Antonio; Bertocchi, Enrico

The tribological behaviour of Metal-on-Metal (MoM) hip prostheses is a key factor for their success. In particular, wear is recognized to have a crucial role in the failure of a prosthesis and can have severe consequences on the patient’s health, e.g. pseudo-tumors in MoM implants, [1,2]. The lubrication of the coupling between the prosthetic head and the acetabular cup can affect both the contact behaviour and the wear of the prosthesis [3]. Different contributions exist in the pertinent literature addressing the elastohydrodynamic analysis of the head-acetabulum coupling, but rarely these analysis are performed taking into account the possible fluid cavitation in the contact area between the mating surfaces [4]. In order to improve the tribological performance of hip implants, the use of textured surfaces has been proposed in recent studies [5]. The present contribution focuses on the possible improvement that textured surfaces could give to the hip joint replacement tribological behaviour. Textured surfaces are widely used in mechanics in order to increase the carrying capacity of various kind of joints working in elastohydrodynamic condition [6-8]. Textured surfaces typically show a path of cavitated zones due to the presence of dimples in the contact surfaces. The effect of these cavitated zones can result in a global decreasing of friction and wear [9]. This preliminary contribution aims at studying, by means of preliminary simplified one-dimensional models, the influence of the geometrical parameters of the textures on the tribological behavior of a hip joint coupling. The analysis have been carried out employing a linear complementarity mass-conserving algorithm originally proposed in [10], capable of properly capturing the phenomenon of cavitation.

Mulas, Giuseppe Antonio; Giacopini, Matteo; Strozzi, Antonio; Baldini, Andrea; Bertocchi, Enrico

Il comportamento tribologico e in particolare l’usura gioca un ruolo cruciale nel fallimento di una protesi d’anca. La lubrificazione dell’accoppiamento tra testa protesica e coppa acetabolare può influenzare sia la dinamica del contatto sia l’usura della protesi. Il regime di lubrificazione che governa l’accoppiamento testa-acetabolo è elastoidrodinamico. Nei diversi studi presenti nella bibliografia pertinente, raramente le analisi sono effettuate considerando la possibile cavitazione del fluido nella zona di contatto, o al più applicando una modellistica di cavitazione che si è dimostrata imperfetta in termini di conservazione della massa. Al fine di incrementare le prestazioni tribologiche di protesi d’anca, recenti studi hanno proposto l’impiego di superfici texturizzate. Attraverso l’utilizzo di un preliminare modello semplificato, viene studiata l’influenza, sul comportamento dell’accoppiamento, dei parametri geometrici che descrivono le texture. Si è utilizzato un recente algoritmo di complementarietà lineare capace di simulare il fenomeno della cavitazione conservando la massa di fluido.

2014 - Formulation of the tangential velocity slip problem in terms of variational inequalities [Articolo su rivista]
Strozzi, Antonio; Giacopini, Matteo; Bertocchi, Enrico; Dini, D.

This contribution deals with a modelling of the tangential velocity slip problem in terms of variational inequalities. In particular, various technical situations for which the slippage problem appears to play an important role are first reviewed. Then, a mathematical formulation in terms of variational inequalities is developed where the critical shear stress criterion is considered. The theoretical conditions under which a unique solution exists are also discussed and an algebraic description based upon a complementarity approach is presented. Preliminary numerical results end the paper and a validation versus an analytical solution is proposed.

2014 - Frequency embedded box beam crash absorbers under oblique impacts [Articolo su rivista]
Qureshi, OMER MASOOD; Bertocchi, Enrico; Qaiser, Zeeshan; Aslam Awan, Khalil

Among recent developments in automotive crash absorbers, box-section thin-walled beams with embedded sinusoidal patterns on wall surfaces have been proposed in literature and have shown promising results under axial impacts. To cater for real-life accident situations, an efficient automotive frontal crash absorber must be able to absorb high amounts of impact energy not only in the axial direction, but also during misaligned and oblique impacts. The purpose of this paper is to study and analyse the performance of beams with embedded sinusoidal patterns subjected to oblique impact loads which exert both an axial force and a bending moment. Two types of triggering mechanisms for these beams which have been recently proposed in literature, i.e. conventional notch triggers and progressive frequency triggers have been numerically studied under oblique impacts in this paper. The results obtained are compared with a plain reference specimen using the critical angle criterion. It is observed that patterned beams with notch triggers are only marginally better in oblique impacts as compared to plain beams with the same triggers. Progressive frequency triggers on the other hand, greatly improve the beam's performance under inclined tests.

2014 - Numerical investigation of the cavitation damage in a high performance engine conrod big end bearing via a mass-conserving complementarity algorithm [Relazione in Atti di Convegno]
Dini, Daniele; Mastrandrea, LUCA NICOLO'; Giacopini, Matteo; Bertocchi, Enrico

The object of the study is the conrod big end bearing of an high performance motorbike engine. Comparative analyses involving different geometrical configurations of the crankpin/conrod assemblies, and in particular of different shapes of the inner profile of the bearing, are presented. The influence of the properties of the lubricant is also discussed. A preliminary cavitation damage index is proposed based on the variation in time of the void fraction at a certain location. The results obtained show a strong influence of the geometry of the bearing on the cavitation phenomenon. Experimental evidence qualitatively agrees with numerical forecasts, thus corroborating the use of both the methodology and the cavitation damage index proposed in this contribution.

2013 - A Complementarity Formulation of the Tangential Velocity Slip Problem in Lubricant Films [Relazione in Atti di Convegno]
Strozzi, Antonio; Giacopini, Matteo; Bertocchi, Enrico; Daniele, Dini

This contribution deals with a modelling of the tangential velocity slip problem in terms of variational inequalities. In particular, the critical shear stress criterion is considered. The theoretical conditions under which a unique solution exists are discussed and an algebraic description based upon a complementarity approach is presented, similar to the one adopted in [7]. Finally, preliminary numerical results are presented and discussed.

2013 - Achievement of a uniform contact pressure in a shaft–hub press-fit [Articolo su rivista]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Bertocchi, Luca

In this article, the achievement of a uniform elastic contact pressure in a frictionless, keyless, shaft-hub interference fit obtained by properly shaping the mating profiles is examined. The peculiarity of the hub mechanical response according to which, under the effect of a uniform pressure applied to the hub bore, the bore axial profile moves radially without any distortion, is exploited to simplify the determination of the mating profiles that return a uniform pressure. In particular, the hub radial deflection may be computed with a simple plane model, whereas only the shaft radial deflection requires a more complex analysis in cylindrical coordinates. Explicit approximate expressions are reported for the shapes to be conferred to the mating profiles to achieve a uniform pressure. Selected examples are presented to clarify the proposed design procedure and to preliminarily explore the effect on the pressure profile of simple shape errors.

2013 - Composite materials in automotive: Improving safety by refining FEA correlation [Relazione in Atti di Convegno]
Miscia, Giuseppe; Bertocchi, Enrico; D'Agostino, Luca; Baldini, Andrea; Dolcini, Enrico; Narducci, Angelo

In the last few years, the restrictive safety standards and the need for weight reduction have brought the crashworthiness research to focus on composite materials because of their high energy absortion-to-mass ratio. On the other hand, the possibility of obtaining predictive dynamic FEA models for these new materials is still an open issue: The present work aims at developing a methodology for the characterization of composite materials with particular interest for the head impact simulation. Composite materials behavior, defined through the mathematical models implemented in FEA codes, is very complex and requires a large amount of physical and numerical setting parameters. The majority of these parameters can be obtained by an experimental campaign that involves several kind of different tests. The presented methodology allows to obtain a good numerical-experimental correlation simply performing few tests which emulate the behavior of the component during the head impact event. A software tool based on a genetic optimization technique has been developed in order to determinate automatically the material properties values that guarantee the best numericalexperimental correlation. Copyright copy; 2013 by ASME.

2013 - Crash performance of notch triggers and variable frequency progressive-triggers on patterned box beams during axial impacts [Articolo su rivista]
Qureshi, OMER MASOOD; Bertocchi, Enrico

Embedding complex sinusoidal patterns on the wall surfaces of box beam impact absorbers has been recently proposed in literature and demonstrated to significantly improve energy absorption capability of box beams during axial impacts. However, no suitable trigger has yet been devised for these absorbers. This paper evaluates the viability of using conventional notch triggers on patterned beams. A progressive triggering mechanism on box beams with embedded patterns is also proposed by a novel idea of using a variable pattern throughout the length of the beam. In the proposed progressively triggered beams, the reaction force slightly increases with each progressive collapse buckle formation throughout the collapse. An extensive FEM study is performed using the commercial pre-processor HyperCrash™ and the commercial explicit FEM solver RADIOSS™. It is found that, as opposed to point triggers, progressive triggering through variable pattern formulation effectively triggers and initiates a more stable collapse. More importantly, progressive triggers cause less stray deformations elsewhere along the beam and are consequently much more robust against global bending.

2012 - A contribution to the Legendre series solution of the mechanical analysis of cylindrical problems [Relazione in Atti di Convegno]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Campioni, Eleonora; Mantovani, Sara

A series solution in terms of Legendre polynomials of the stress function suitable for modelling the mechanical response of a cylindrical component is revisited, and some contributions to the definition of the series terms are given. In particular, the correction to be imparted to a logarithmically singular series solution is considered, and a recursive approach for its determination is developed. A preliminary example dealing with an elastic, deformable cylindrical hub forced onto a rigid shaft is presented.

2012 - Crash behavior of thin-Walled box beams with complex sinusoidal relief patterns [Articolo su rivista]
Qureshi, OMER MASOOD; Bertocchi, Enrico

This paper proposes a new automotive box-beam crash absorber design with sinusoidal patterns embedded on the beam surfaces. Six different types of surface patterns were initially proposed and a total of 43 samples were simulated using the commercial pre-processor HyperCrash™ and the commercial explicit FEM solver RADIOSS™. The aim of the study is to improve energy absorption properties of the beams by controlling the wavelength of progressive buckle formations and obtaining denser collapse formations. It was found that the relief patterns could be used effectively to change the buckling modes and reduce the buckle wavelength. A maximum of 42 percent increase in the amount of total energy absorbed and an increase in the energy efficiency factor from 1.08 to 1.54 was observed moving from the reference model to the best design so far. This research may possibly pave new avenues in crash absorber design.

2012 - Stress Concentrations at the Rounded Edges of a Shaft-Hub Interference Fit Expressed in Terms of a Coefficient Normalizing the Coupling Geometry and the Young’s Modulus Effects [Relazione in Atti di Convegno]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Bertocchi, Luca

The elastic stress concentrations developed from the keyless, frictionless, static press-fit of a solid shaft into a hub with bore rounded edges are addressed. Derived from an analytical approach, a normalising parameter Φ is employed that accounts for the combined effects on the hub stress concentration of the fillet radius of the hub bore, the shaft radius, the interference, and the Young’s modulus. Compiled with the aid of Finite Elements, several design charts are presented that report the elastic stress concentrations within the hub versus the normalising parameter Φ. Each curve is valid for prescribed ratios of a) the hub inner radius to the outer radius, and b) the fillet radius to the shaft radius. An approximating expression of ample validity is also presented for a prompt evaluation of the hub stress concentration factor.

2011 - High performance automotive chassis design: a topology optimization based approach [Articolo su rivista]
Cavazzuti, Marco; Baldini, Andrea; Bertocchi, Enrico; Costi, Dario; Torricelli, Enrico; P., Moruzzi

Automotive chassis design in view of car weight reduction is a challenging task due to the many performance targets that must be satisfied, in particular in terms of vehicle safety. In this paper a methodology for automotive chassis design in involving optimization techniques is presented. In particular, topology, topometry and size optimizations are coupled with fem analyses and adopted in cascade for reaching an optimum chassis configuration. The methodology is applied to the design process of a rear-central engine high performance vehicle chassis. The objective of the optimization process is the chassis weight reduction, yet in fulfilment of structural performance constraints as required by Ferrari standards. The results demonstrate the general applicability of the methodology presented for obtaining the general trusses layout and thicknesses distribution of the structure. The numerical model at this stage shows a significant weight reduction when compared to the chassis of the Ferrari F458 Italia.

2011 - Maximum equivalent stress in a pin-loaded lug in the presence of initial clearance [Articolo su rivista]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Bertocchi, Luca

Various design charts of ample validity and prompt access are presented, which permit the contact stresses within the lug of a pinned connection to be forecast in the presence of an initial clearance between the pin periphery and the lug bore. To cover the range of the practically encountered geometries and loadings, round-ended lugs of various widths and with a variously tapered shank are considered, and several inclinations of the applied load are addressed. The charts are compiled with the aid of finite elements. The employment of the recently proposed load factor Φ allows the combined effects on the peak contact stresses of the load intensity and of the initial clearance to be predicted.

2011 - Normalization of the stress concentrations at the rounded edges of a shaft–hub interference fit [Articolo su rivista]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Bertocchi, Luca

The elastic stress concentrations developed from the keyless frictionless static press-fit of a shaft into a hub are addressed. Two configurations are examined, namely (a) an infinitely long solid shaft press-fitted into a hollow hub with bore rounded edges, and (b) a shaft with filleted extremity, partially inserted into a hub. Derived from an analytical approach, a normalizing parameter is proposed that accounts for the combined effects on the stress concentrations of the fillet radius, the shaft radius, the interference, and Young’s modulus. With the aid of finite elements, various design charts are compiled that report the elastic stress concentrations within the hub versus the proposed normalizing parameter. Each curve is valid for a fixed ratio of inner to outer hub radii.

2011 - Torque Transmission by Friction in a Keyed Shaft-Hub Press-Fits [Relazione in Atti di Convegno]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Bertocchi, Enrico; Bertocchi, Luca; Campioni, Eleonora; Mantovani, Sara; O., Quareshi

Interference fits are widely employed to semi-permanently connect gears, pulleys, flanges, wheels, disks, rotors, and similar mechanical components, to a shaft. The stress state along the hub central portion may be thoroughly predicted by modelling the press-fit problem as plane and by employing the Lamé equations for thick-walled cylinders, and the transmissible torque may be confidently estimated by relying on the Lamé predictions, since they are valid along most of the contact axial length. Often a key is added to the press-fit, to secure the torque transmission and to prevent any relative rotation between the shaft and the hub. Both parallel and tapered keys are employed in practical applications. With respect to their tapered counterparts, parallel keys possess the advantage that they do not cause any eccentricity. This study considers parallel keys only. The presence of the keyseat increases the compliance of the hub and the shaft, thus producing a diminution of the contact pressure between the hub and the shaft, which results in a similar diminution of the transmissible torque. In this paper, a preliminary Finite Element analysis is carried out to quantify the above diminution of the contact pressure in the assumption of frictionless contact. The analysis is carried out for a solid shaft and for a practically relevant selection of ratios between the hub inner and outer radii. A preliminary development is presented of an analytical approach based upon the classical Michell polar solution, which is particularly suitable to mimic rings. The diminution of the transmissible torque with respect to a keyless shaft-hub press-fit is quantified, and the results are presented in a design diagram.

Natali, Alfredo; C., Pirondi; Bortolini, Sergio; E., Campioni; Bertocchi, Enrico; Baldini, Andrea; Consolo, Ugo


2010 - Advanced high performance vehicle frame design by means of topology optimization [Relazione in Atti di Convegno]
Cavazzuti, Marco; A., Merulla; Bertocchi, Enrico; Strozzi, Antonio; M., Pettazzoni

Automotive chassis design, often based on the company know-how and the designer experience, usually leads to consolidated solutions that are poorly innovative and not necessarily altogether efficient. Optimization techniques are powerful means for systematic design that can make it possible to avoid this drawback. The present study proposes a methodology for automotive chassis design based on topology, topometry and size optimizations coupled with fem analyses. In particular, the methodology is applied to the design of a chassis suitable for a rear-central engine high performance car. A massive 3d fem model is conceived, in order to respect the geometrical requirements yet leaving maximum freedom to the topology optimization algorithm. Shell mod- els are employed for the subsequent topometry and size optimizations. The objective is the minimization of the chassis mass in fulfillment of a given set of structural performance constraints. The results demonstrate the general applicability of the method proposed.

2010 - Automazione e Verifica del Processo di Incollaggio in Linee Produttive di Telai per Vetture d’Alta Gamma [Abstract in Atti di Convegno]
Andrisano, Angelo Oreste; Baldini, Andrea; Bertocchi, Enrico; Giacopini, Matteo; Leali, Francesco; Mantovani, Sara; Pellicciari, Marcello; Pini, Fabio; Strozzi, Antonio; Vergnano, Alberto

Sommario. La produzione industriale dei telai auto ha registrato, nel tempo, una grande evoluzione progettuale e tecnologica, spinta dalla necessità di garantire alte prestazioni e comfort elevato, nel rispetto della sicurezza dei passeggeri e della sostenibilità ambientale. Le linee produttive di assemblaggio sono, soprattutto in segmenti di fascia alta, progettate per l‟esecuzione, su telai diversi, di articolati processi ibridi di giunzione, basati, cioè, sull‟adozione di tecnologie di saldatura, rivettatura ed incollaggio. I sistemi che ne derivano sono, dunque, caratterizzati da elevata complessità e richiedono lo sviluppo di dispositivi automatici dedicati e l‟impiego simultaneo di robot industriali e risorse umane. La soluzione di tali problematiche richiede l‟intervento sinergico di vari settori dell‟Ingegneria Meccanica poiché coinvolge competenze metallurgiche, progettuali e tecnologiche. A queste si aggiungono le competenze necessarie alla progettazione di sistemi produttivi ad alta flessibilità che, secondo la visione proposta dagli autori, siano caratterizzati da elevata modularità strutturale ed operativa, parametricità e standardizzazione delle soluzioni progettuali e dei componenti, autonomia esecutiva, e che assicurino una rapida ed efficace riconfigurazione, garantendo, parallelamente, l‟alto livello qualitativo dei prodotti ed il completo controllo dei processi realizzati. Il presente articolo tratta lo sviluppo e la progettazione integrata del modulo robotizzato di incollaggio per linee di assemblaggio ibride di telai in alluminio, svolta in collaborazione con il gruppo ALCOA e con SIR SpA. Successivamente vengono presentati i risultati sperimentali ottenuti dalla verifica strutturale a lap shear e peeling di alcuni provini ricavati da assemblati del tunnel, effettuata secondo normative interne Ferrari SpA. Abstract. In the last years, industrial production of automotive chassis has gained a great evolution in design and technology, spurred by the need to achieve high performance and comfort, while ensuring both the safety of passengers and the environmental sustainability. State-of-the-art assembly lines, especially in top class segments, are designed to employ hybrid junctions on different chassis. Such complex process is based on the simultaneous adoption of welding, riveting and adhesive bonding technologies. The production systems design engages the development of specific automated devices and the cooperation of industrial robots and human resources. The solution of these issues involves the synergic action of various sectors of mechanical engineering, as metallurgy, design, and mechanical technology. Design of high flexibility production systems is another important issue: according to the viewpoint proposed by the authors, such systems are characterized by high structural and operational modularity, by parametric and standard design of solutions and components, by executive autonomy and rapid reconfiguration capability, thus simultaneously ensuring high quality of products and the complete control of processes. The present paper deals with the development and integrated design of the robotic adhesive bonding module in hybrid assembly lines for aluminum chassis, carried out in collaboration with the ALCOA group and SIR SpA. Experimental results are also presented, that refer to lap shear and peeling tests, carried out on specimens extracted from the chassis tunnel, according to Ferrari SpA internal standards.

Natali, Alfredo; C., Pirondi; Bortolini, Sergio; E., Campioni; Baldini, Andrea; Bertocchi, Enrico; Consolo, Ugo

Purpose: A recent procedure called “All-on-four " provides the rehabilitation of atrophic edentulous jaws by means of a fixed prosthesis supported by 4 implants. Purpose of this work is the comparative evaluation between the biomechanical features of the All on Four versus traditional therapyMethods: it was created a 3D model (SolidWorks - Dessault Systems SolidWorks Corp - Concord, MA, USA) of a clinical case with 6 mandibular implants and a screwed framework. The FEM analysis was performed by varying the number and position of the implants and the superstructure material. 9 different models were analyzed. The load was 300 N on the distal part of the framework.Results: Implants closest to the application of the force are the more loaded. In the superstructure there was a stress peak that exceeds the plasticization value of one material (titanium), although the area is very limited. In the bone, maximum stress occurs in the cortical component, while the medullary component is less interested. The distal implant (closer to the force) has a compressive load, while the mesial one has a tractive stress.Conclusion: The strategic distribution of implants appears to be the key factor that governs the distribution of loads. A limited number of implants, strategically placed, can be an effective alternative rehabilitation in selected cases. This suggests a possible effectiveness of the fixed implant prosthesis on 4 implants, accompanying the reduction of, costs, post-operative morbidity and the difficulty of the prosthesis than other procedures.

2010 - Sport car space-frame chassis design in view of weight reduction [Relazione in Atti di Convegno]
Torricelli, Enrico; Costi, Dario; Baldini, Andrea; Bertocchi, Enrico; P., Moruzzi

Road vehicle homologation has become more and more challenging due to the introduction of stringent regulations regarding pollutant emissions. In order to fulfil these requirements, the focus in automotive industry mainly settled on the improvement of the engine performance in terms of fuel consumption. Another design approach aims at the vehicle lightening, yet in the respect of the safety standards. In the present work a methodology for preliminary space-frame chassis design for rear-central engine sport cars is proposed. The purpose is to design a chassis able to attain given performance goals in view of weight reduction. The design problem is faced using finite element analysis. The chassis numerical model is made of shell elements and is split into three sub-models: front, central, and rear. This allows the parallelization of the work among different teams. The sub-models undergo topometry and size optimizations in order to asses the optimal shell thickness distribution.

2009 - Contact stresses within a split ring inserted into acircular housing [Articolo su rivista]
Strozzi, Antonio; Baldini, Andrea; Giacopini, Matteo; Rosi, Roberto; Bertocchi, Enrico

The contact problem between a split ring and a circular housing is mechanicallyexamined. This contact is revisited in terms of receding contact, the zones along which the ringbeds over the housing are investigated, and normalizing design parameters are evidenced. Thesplit ring is modelled in terms of a straight, purely flexural beam as well as of a curved, shearelasticbeam; for both models, analytical solutions are obtained. Various easy accessible designdiagrams, useful for estimating the maximum elastic stresses within the split ring and the axialinsertion force, have been prepared with the aid of these two beam models and using finiteelements. The mechanical response of the split ring when its angular width is appreciably lowerthan p is clarified.

Baldini, Andrea; Bertocchi, Enrico; Giacopini, Matteo; Margini, Stefano; Rivasi, Stefano; Rosi, Roberto; Strozzi, Antonio

In the paper, the authors discuss possible causes of conrod torsional vibrations. Several simplified models are laid out for prediction, evaluation and future research. Some critical remarks about these prospective models are presented. Comparisons with a limited number of experimental cases is finally provided.

2008 - Shakedown of coupled two-dimensional discrete frictional systems [Articolo su rivista]
Ahn, Y. J.; Bertocchi, Enrico; Barber, Jr

Recent results have established that Melan's theorem can be applied to discrete elastic systems governed by the Coulomb friction law only when the normal contact reactions are uncoupled from the tangential (slip) displacements. For coupled systems, periodic loading scenarios can be devised which lead to either shakedown or cyclic slip depending on the initial condition. Here we explore this issue in the simplest coupled system involving two contact nodes. The evolution of the system ‘memory’ is conveniently represented graphically by tracking the instantaneous condition in slip-displacement space. The frictional inequalities define directional straight line constraints in this space that tend to ‘sweep’ the operating point towards the safe shakedown condition if one exists. However, if the safe shakedown region is defined by a triangle in which two adjacent sides correspond to the extremal positions of the two frictional constraints for the same node, initial conditions can be found leading to cyclic slip. The critical value of a loading parameter at which this occurs can be determined by requiring that three of the four constraint lines intersect in a point. Below this value, shakedown occurs for all initial conditions. Similar concepts can be extended to multi-node systems.