PSI - Issue 8

Francesca Curà et al. / Procedia Structural Integrity 8 (2018) 204–211 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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and fatigue working conditions, useful micro geometries have been investigated and corresponding influence parameters have been defined. As a matter of fact, the first engineering variable involved in this kind of damage is the contact pressure between teeth, related to the hertzian theory, that is very sensitive to the local geometry of the

Fig. 1. Basic rock profile according to DIN 5480-1.

two bodies in contact. To design an isodamage specimen, beyond the maximum pressure entity and the contact area size, also two other particular aspects have to be taken into account, the shape of the area (ratio between the half axis of the contact ellipse) and its position related to both tooth involute profile and length width. On the basis of these considerations, some micro corrections of the tooth geometry have been chosen as an attempt, related firstly to the crowning radius and then in terms of local variation of the involute profile. In particular, for as concerns the shaft (identified by the subscript 1),the crowning radius is related to the minimum curvature ρ 1min and the involute radius is related to the maximum one ρ 1max .For as concerns the hub (identified by the subscript 2), no crowning radius has been considered (maximum curvature ρ 2max is zero) and the involute radius corresponds to minimum curvature ρ 2min . All calculations have been made considering different values of applied torque, maximum and minimum curvatures of the shaft. In particular, 2 torque levels have been applied, 500 Nm and 700 Nm; four values of ρ 1max have been used, 1/11.3, 1/10.9, 1/10.5 and 11/10.7 mm -1 ; three values of ρ 1min have been chosen: 1/5000, 1/4000and 1/3000 mm -1 ; ρ 2min has been set as -1/14,05 mm -1 for all cases. For each possible combination of these three parameters, maximum contact pressure p max , mean contact pressure p mean , contact area and ratio a/b between half-axis of the contact ellipse (respectively maximum and minimum) have been calculated. In total, 24 possible combinations have been considered. A set of FE simulations have been run in order to calculate both contact pressures and teeth slidings in each specimen model. All numerical simulations have been made using Abaqus Software. An example of FE model is shown in Figure 2. First-order tetrahedral solid elements have been used throughout. The mesh size in the contact area is very fine (about 0.2 mm) to better fit the geometry and to obtain good results in terms of relative slips. In order to define the contact behaviour between the teeth, contact surfaces in each tooth have been created (as it can be seen in Figure 2). A kind of interaction named “contact pair” has b een chosen, characterized by a coefficient of friction equal to 0.11. Material has been defined using Young modulus E=210 GPa and Poisson coefficient  =0.3. Torque about shaft axis has been applied on the extremity of the shaft, while displacements related to all directions have been blocked on the opposite extremity of the hub. 2.2 Numerical simulations