Issue34

R. Citarella et alii, Frattura ed Integrità Strutturale, 34 (2015) 554-563; DOI: 10.3221/IGF-ESIS.34.61 555 Figure 1 : Polygonal profile with n = 3 lobes         2 2 m m D x e cos n cos n e sin n sin D y e cos n sin n e sin n cos                                     (1) In the preliminary stages of designing a new component, when many engineering solutions are considered, the use of FEM makes it difficult to quickly update a model subject to continuous shape optimisation. In these cases, it can be very advantageous to use BEM that performs the numerical study of a component by discretizing only the boundary, with the volume not being affected by the meshing operation and with a consequent reduction of “pre-processing” time. In addition, BEM, contrary to FEM, allows calculating traction and displacements at shaft-hub interface with the same accuracy (they are both primary variables ). For this reason, it is highly suitable when studying problems with high surface stress gradients, such as contact problems. In this paper a multi-objective optimization problem of a polygonal shaft-hub interference fit is analysed using the Taguchi method (robust design) [9-11], and the BEM commercial code BEASY [12]. BEM CONTACT STRESS ANALYSIS odelling of nonlinear contact [13] at shaft-hub interface takes place by means of special constraints (“normal gap”), defined between pair of nodes ( node to node contact ) belonging to overlapped elements at the interface area between the two zones (shaft and hub) in which the entire domain of the coupling is divided. Enforcing these constraints causes the code to consider the interface elements between the shaft and hub as separate, although initially coincident in modelling. Then a condition of interference or clearance is modelled, depending on the value, respectively negative or positive, attributed to the “normal gap”. The contact problems are nonlinear due to the variation of the contact area in dependence of the applied load. Therefore, the stress state at the interface depends on the friction coefficient, the load, the geometry as well as the material and extension of the contact area. The nonlinear behaviour of the coupling was studied by means of an incremental-iterative procedure, which is useful when following the evolution of the contact as a result of the gradual application of the load, even in the presence of friction, which can be modelled in both static and dynamic terms [14]. It is worth highlighting the convenience of using an adequate number of regularly distributed (without circumferential “grading”) linear elements rather than a smaller number of elements with higher polynomial order, on the interface area where the algorithm operates the contact. Such choice can improve the solution convergence and avoid “hot spots” occurrence (local irregularities at stress-deformational level in the numerical outcome). M