Issue34

F. Curà et alii, Frattura ed Integrità Strutturale, 34 (2015) 447-455; DOI: 10.3221/IGF-ESIS.34.50 452 Eq. 1 is characterized by the presence of two coefficients, A and B, representing the contribution factors for the two stress tensors to the yield condition. In other words, when the only bending is present and creates yield condition, A is equal to one and B is equal to zero. The contrary occurs when only the centrifugal force is present. So a condition where both loads are active is represented by a combination of the two limit stress tensors and A and B represent the ratio to the limit conditions. Using that reasoning it is possible to study the interaction between the two loading conditions and all possible combinations can be easily studied. For analysing all possible conditions, the Von Mises formula has been applied on the computed stress tensors and solved with respect to A and B , by satisfying the following condition: tol yeld y x y x   2 2 2 3 (2) where tol is a tolerance value fixed on 10 MPa. The problem is obviously under-constrained, but solving it for all the possible combinations of A and B , the variation of maximum stress point can be highlighted. As a matter of fact, every time that the condition of eq. 2 is verified, it means that this load combination produced yield stress, so this couple of values is critical and the most stressed element may be detected. Fig. 6 shows all possible load combinations that have been determined. Figure 6 : Combination of A and B and the relative most stresses element. From Fig. 6 it is possible to observe that, for a defined A value, there are many B values that may produce critical stresses and so the most stressed element is different. Fig. 7 shows the limit curve where a defined A value corresponds to the first B value that produces yield stress and the corresponding element is highlighted. The curve of Fig. 7 is the envelope of all the possible conditions that produce yield in the tooth, so it could be used to understand the mutual effect of the two loading conditions and the possible location of the maximum stress. In that way, it is possible to relate the loading conditions to the crack nucleation point and hence give a forecast of the crack propagation behavior. Combining the geometrical features of the gear (backup and web ratii) with the curve of Fig. 7, it is possible to have a design indication for preventing catastrophic failures. Propagation Analysis Once highlighted the relationship between variation of loads and maximum stress points, the influence of centrifugal force with respect to the geometry has also been studied. In particular, the interaction between centrifugal load and geometrical parameters has been investigated considering the propagation effect.