Sara Mantovani

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.

Dynamic Modal Correlation of an Automotive Rear Subframe, with Particular Reference to the Modelling of Welded Joints

This paper presents a comparison between the experimental investigation and the Finite Element (FE) modal analysis of an automotive rear subframe. A modal correlation between the experimental data and the forecasts is performed. The present numerical model constitutes a predictive methodology able to forecast the experimental dynamic behaviour of the structure. The actual structure is excited with impact hammers and the modal response of the subframe is collected and evaluated by the PolyMAX algorithm. Both the FE model and the structural performance of the subframe are defined according to the Ferrari S.p.A. internal regulations. In addition, a novel modelling technique for welded joints is proposed that represents an extension of ACM2 approach, formulated for spot weld joints in dynamic analysis. Therefore, the Modal Assurance Criterion (MAC) is considered the optimal comparison index for the numerical-experimental correlation. In conclusion, a good numerical-experimental agreement from 50 Hz up to 500 Hz has been achieved by monitoring various dynamic parameters such as the natural frequencies, the mode shapes, and frequency response functions (FRFs) of the structure that represent a validation of this FE model for structural dynamic applications.

A paradox in curved beams

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.

Design Methodology for Gear Design of a Formula One Racing Car: A Modelling Procedure Based on Finite Element

FIA regulations for the 2015 Formula One World Championship introduced an upper limit to the number of transmission assemblies employed during the season; a new approach to reliability has been forced on the designers, along with a reconsideration of the calculation procedures. Whereas mechanical transmission reliability calculations are well coded within the commercial transportations field, the peculiar aspects of the motorsport branch - namely a) the quest for an extreme lightweight design, b) the harsh dynamic transitions in speed and torque at gear shifts with a seamless shift transmission and wheel-road chattering, c) the circumscribed consequences of a breakage due to the controlled nature of the racing track environment, and d) the frenzied design procedures pace - urged for the development of specific validation procedures, that have to be rapidly redefined with the 2015 regulation adjustment. The present contribution rethinks those reliability assessment procedures - mostly based on nonlinear, dynamic Finite Element (FE) calculations - for a Formula One gearbox. In particular, the required model complexity is discussed with respect to the inclusion of shafts, bearings and carter compliance, chassis load induced deformation, significant load case selection, misuse robustness. The finalized validation procedure is shown to be predictive with respect to the augmented reliability requirements, while remaining feasible within the motorsport timescale environment.

On the Contact Stresses at the Indenting Edge of a Shaft-Hub Interference Fit Subject to Bending and Shear Forces

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.

Optimization Methodology for an Automotive Cross-Member in Composite Material

Optimization methods are useful and effective techniques for the design and development of components from the weight reduction point of view. This paper presents an optimization methodology applied to the front cross-member of a Maserati chassis for metal replacement application with the objective of the minimization of the mass of the structure using composite materials. Firstly, a topological optimization of the front side of the vehicle is performed, and the available design space is considered to determine the optimal load path of the design volume and, consequently, to assess a preliminary geometry of the component under scrutiny. Secondly, free-size optimization of the preliminary cross-member design is developed, initially neglecting and subsequently considering the manufacturing constraints. In addition, a linear analysis of the cross-member, modeled as a rigid component, is carried out to evaluate the maximum contribution of this component on the structural performance of the front side of the vehicle. Finally, size and shuffle optimizations are carried out on the new design concept to determine the number and the thickness of the composite plies, and the optimal stacking sequence, respectively, in order to fulfill the structural requirements. A comparison between the new composite structure and the aluminium Maserati cross-member is presented.

Mechanical Analysis of a Hexagonal Joint

A hexagonal joint is mechanically analysed. A cross section of the receding contact between the male and female components is modelled as a plane strain problem. Particular attention is paid to the effect of the presence of fillets in the hexagonal male. Finite Element (FE) results show that, for each side of the hexagonal contact, the contact zone constitutes a small portion of the length of the hexagonal side, and separation occurs elsewhere. The normalized peak contact pressure and the contact length along the male sides are numerically evaluated.