PSI - Issue 80

Francesco Manni et al. / Procedia Structural Integrity 80 (2026) 177–186 Francesco Manni/ Structural Integrity Procedia 00 (2019) 000–000

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Nitrided area

Non-nitrided area

Fig. 3. Detail of the mesh in a tooth section.

3.2. Boundary conditions To accurately simulate the residual stresses induced by the nitriding process, it has been necessary to introduce a thermal strain field within the FE model. Specifically, a thermal field has been applied to the nodes on the external profile of the gear tooth, causing the outermost layer of elements to expand and, in turn, dragging the internal layers along. However, the temperature value alone does not define the resulting expansion. In fact, the combination of the temperature variation and the thermal expansion coefficient, α, determines the actual deformation. Since the objective has been to replicate a specific residual stress profile, the temperature and expansion coefficient values used have not been based on real material properties. The temperature has normalized between 0 °C and 1 °C, while the thermal expansion coefficient α has been calibrated to reproduce the residual stress distribution provided by the manufacturer, see Fig. 4 (Aubert & Duval, 2016). In detail, a simplified analytical model has been developed to tune α and, therefore, to predict the stress distribution resulting from surface expansion in a simple geometry and here omitted for the sake of brevity. Multiple simulations have then been conducted, adjusting α until the resulting stress curve closely matched the one provided by the material supplier. Fig. 5 shows the resulting residual stress distribution within the tooth. It is important to note, however, that applying residual stresses via thermal deformation inherently causes distortion of the component geometry. Therefore, a specific procedure has been developed to introduce the desired residual stress state while preserving the original geometry of the gear, including its micro-geometry. This further method involved several steps and it is resumed by. First, a FE simulation has been carried out applying the previously defined couple of thermal field and α. Next, the distance of each deformed node from the desired position has been calculated. Finally, these values have been used and reversed to define a counter-deformed geometry. This last profile, although slightly smaller and distorted compared to the original, served as the starting point for a second simulation. In this second FE forecast, the same thermal field has been applied to the counter-deformed geometry. As a result, the final shape of the component matched the original desired geometry very closely, preserving the intended micro-geometry while also incorporating the residual stresses generated by the nitriding process.