PSI - Issue 80

Simone Messina et al. / Procedia Structural Integrity 80 (2026) 232–243 Simone Messina/ Structural Integrity Procedia 00 (2019) 000–000 the only the last revised approach is here reported. 3 × load cases, where represents the load case duration, have been set up. The simulation has been carried out using quasi-static analyses. In the first step, the torque has been applied alone. Then, in the second step, the previous torque has been reduced of 90 % as a preparatory action to help the software to reach the convergence in the next phase. In the third step, the required rotation has been imposed on both gears, with the angle adjusted according to the simulated step. To select the best n number four distinct simulations have been conducted, each corresponding to different time step resolutions: 55, 110, 220, and 330. In each case, the analysis has been focused on the load history of the most critically stressed nodes. A key observation emerging from the full gear mesh analyses has been the variation in results across different time step resolutions. Fig. 7 and 8 illustrate the maximum principal stress at the most critically loaded node on the tooth surface subjected to full contact. Among the four simulations performed, the case with 55 time steps, represented by the blue curve, has exhibited the most significant variation in stress values. These deviations might be attributed to the unrealistic acceleration applied to Gear 1, resulting in an artificial and abrupt impact on Gear 2. Specifically, under this configuration, Gear 1 has undergone rapid acceleration when torque is applied, leading to an exaggerated collision with Gear 2. This phenomenon has explained the significant increase in stress levels observed in this scenario. The stress amplification has been particularly evident in the 55 steps simulation, where each step has corresponded to a 0.4° rotation. In contrast, the other three simulations have distributed the rotational motion more gradually 0.2° for 110 steps, green line, 0.1° for 220 steps, red line, and approximately 0.067° for 330 steps, black line, leading to more stable and realistic loading conditions. The simulation with 330 steps has demonstrated a behavior closely aligned with the 220-step case, however it entails a considerably longer computational time without yielding any appreciable gain in accuracy or predictive quality for fatigue life estimation. Therefore, it has been excluded from further consideration. Comparative analysis of the 110 and 220 step simulations have revealed similar load histories for Gear 1 as can be seen in Fig.7. Nevertheless, a more detailed examination of the maximum principle value of stress of the most stressed nodes of the teeth of Gear 2, visible in Fig.8, indicates that inertial effects remain significant in the 110-step case, introducing non-negligible deviations in the results. In conclusion, the simulation using 220 time steps has offered the best compromise between computational efficiency and result accuracy, and, thus, has been considered to be the most reliable among the four tested numerical set up. 239 4.1 Full gear mesh results

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Maximum principle value of stress

220 Maximum Principal Value of Stress Node 102341 330 Maximum Principal Value of Stress Node 102341 55 Maximum Principal Value of Stress Node 102341 110 Maximum Principal Value of Stress Node 102341

Fig. 7 Maximum principle value of stress in different time step simulations for Gear 1.