Matteo Giacopini

A Mass-Conserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation

A new mass-conserving formulation of the Reynolds equation is developed using the concept of complementarity. This new method overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. Validation against a number of analytical and semi-analytical formulations, for a variety of problems including textured bearings and squeeze film dampers, is performed. The current formulation is shown to be in very good agreement with existing analytical and numerical mass-conserving solutions.

A General Finite Volume Method for the Solution of the Reynolds Lubrication Equation with a Mass-Conserving Cavitation Model

This contribution presents the development of a general discretization scheme for the solution of Reynolds equation with a mass-conserving cavitation model and its application for the numerical simulation of lubricated contacts to be discretized using irregular grids. Such scheme is based on a hybrid-type formulation, here named as element-based finite volume method that combines the flexibility of the FEM to deal with unstructured grids, while preserving the local and global fluid-flow conservation aspect of the FVM throughout the discretized domain. The accuracy and robustness of the method are successfully tested using several benchmark cases proposed in the recent literature. Simulations of fully or partially textured sliding bearings are finally employed to show the advantages of being able to adopt irregular meshes both in terms of flexibility for the discretization of complex surface features and computational speed.

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.

Influence of the initial clearance on the peak stress in connecting-rod small ends

Abstract The stress increase that is caused by the presence of an initial clearance within the small end of connecting rods for motorbike and car engines is investigated. Plane analytical and numerical modellings of the dry contact between the small-end and piston pin are adopted. Based upon a recent analytical result, a normalizing parameter is introduced, which allows the stress concentration factor at the small-end bore sides to be expressed as a function of a proper combination of the initial clearance between the small end and gudgeon pin, the applied load, and Youngs modulus, for prescribed aspect ratios of the small end and hollow pin. Design diagrams summarizing the consequences of an initial clearance between the small-end bore and gudgeon pin on the eye peak stress are reported, which cover a wide range of geometries, clearances, and loadings. Selected comparisons between two-dimensional and three-dimensional models are carried out.

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 load and clearance effects in ball-in-socket-like replacements.

Abstract A normalizing loading parameter useful in summarising the mechanical response of plane pin-in-plate-like contacts is extended to axisymmetric ball-in-socket-like contacts. An example addressing a compliant layered artificial hip joint is presented, and the usefulness of the normalizing loading parameter is evidenced.

Influence of different temperature distributions on the fatigue life of a motorcycle piston

In this paper, finite element analyses are performed to evaluate the stresses and the strains in a motorcycle piston. Non-linear finite element models are employed to mimic the piston behaviour when subjected to different loading conditions. In particular, the gas forces, the inertial forces and the piston-to-cylinder contact forces are considered. Appropriate temperature distributions are applied to the model to include the thermal stresses and strains in the analyses. Two different thermal configurations are considered: the first has a standard design of the oil jet hitting the underside zone of the piston crown, while the second presents modified parameters able to increase the heat transfer coefficient appreciably. The different operating temperature distributions related to the two thermal configurations considered strongly influence the piston’s thermomechanical behaviour. This paper aims to perform high-cycle fatigue analyses to show how the fatigue life and fatigue-critical points of the component change when moving from the standard configuration to the modified configuration.

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.