Enrico Bertocchi

Normalization of the stress concentrations at the rounded edges of a shaft–hub interference fit

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.

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

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.

On the loosening mechanism of a bush press-fitted in the small end of a connecting rod

The loosening mechanism is explored of a bush press-fitted into the small end bore of a con-rod. A modelling of the bush loosening mechanism is proposed. Numerical and analytical forecasts of the tensile inertial force responsible for the bush loosening are presented for a purely elastic model. Proper design charts are compiled that allow (a) the initial interference precluding any bush loosening to be determined within the respect of an imposed safety factor and (b) the maximum elastic stress within the small end to be computed for a general inertial load.

Normalization of the stress concentrations at the rounded edges of an interference fit between a solid shaft subjected to bending and a hub

ABSTRACT 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 Youngs 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.

Analytical evaluation of the peak contact pressure in a rectangular elastomeric seal with rounded edges

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.

Achievement of a uniform contact pressure in a shaft–hub press-fit

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.

Maximum equivalent stress in a pin-loaded lug in the presence of initial clearance:

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.

Contact stresses within a split ring inserted into a circular housing

The contact problem between a split ring and a circular housing is mechanically examined. This contact is revisited in terms of receding contact, the zones along which the ring beds over the housing are investigated, and normalizing design parameters are evidenced. The split ring is modelled in terms of a straight, purely flexural beam as well as of a curved, shear-elastic beam; for both models, analytical solutions are obtained. Various easy accessible design diagrams, useful for estimating the maximum elastic stresses within the split ring and the axial insertion force, have been prepared with the aid of these two beam models and using finite elements. The mechanical response of the split ring when its angular width is appreciably lower than π is clarified.

Formulation of the tangential velocity slip problem in terms of variational inequalities

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.

Composite Materials in Automotive: Improving Safety by Refining FEA Correlation

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 numerical-experimental correlation.Copyright