PSI - Issue 80

Simone Messina et al. / Procedia Structural Integrity 80 (2026) 232–243 Simone Messina/ Structural Integrity Procedia 00 (2019) 000–000

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2024). A crucial aspect of gearbox design is the accurate accounting of fatigue damage (Bonaiti et al., 2019), which directly influences performance, durability and operational safety. The present study aims at developing a numerical procedure adopting FE simulations tailored for the comprehensive analysis of a high-performance electric motor gearbox, focusing on developing a methodology for fatigue life prediction. In particular, a progressive modeling approach has been conceived to identify key parameters that can affect system stiffness, stress distribution, and overall mechanical performance. This paper provide a numerical approach that might guide the first step of the design process allowing an estimation of fatigue life and system durability. A state-of-the-art review has been conducted started from current international standards and regulations governing gearbox structural design. The analysis of gear stress and performance is governed by international standards, among which ISO 6336 is the most widely adopted for strength calculation and fatigue assessment (ISO 6336, 2006). In this standard, the tooth is considered as a simple cantilever beam subjected to the load generated by the gear meshing process. Several studies adopt this normative framework as a reference or validation benchmark for both numerical and experimental investigations. In particular, many works apply the ISO methodology to calibrate computational models or to validate analytical results. A number of publications employ FE simulations to analyze gear behavior in detail (Y.-C. Chen & Tsay, n.d.; Kawalec et al., 2006; Rajesh et al., 2022; Tesfahunegn et al., 2010) , incorporating the evolution of contact. However, they typically do not account for the progression of stress throughout the relative motion of the meshing gears. The present study addresses this limitation by proposing and discussing a methodology capable of describing the full gear meshing operation. In addition, the analysis is complemented by a fatigue assessment. While other studies often approach fatigue analytically based on the behavior of a single tooth, the fatigue analysis presented here is more comprehensive, as it considers multiple loading instances across varying relative positions of the mating gears. Indeed, when considering helical gears, identifying the position of maximum stress at the tooth root is not trivial, as it can be for spur gears. Therefore, it becomes necessary to simulate the complete meshing cycle in order to grasp the instants of highest mechanical stress experienced by the component. The paper is structured as follows. Section 2 is focused on the system description and the discretization process, a fundamental aspect of the study, as it critically affects the accuracy and reliability of FE simulations. The quality of the discretization significantly influences the reliability of the results, making it a key factor in the overall modeling approach. Section 3 involves a comparative static analysis of several simulation models, beginning with a simple gear pair and gradually increasing in complexity by adding elements such as discretized shafts, bearing compliance, and micro geometry details. Section 4 is focused on the full gear meshing simulation. Some details about the influence of time step selection on both simulation accuracy and computational efficiency are discussed in terms of numerical accuracy and computational effort. Section 5 presents an analysis of the fatigue behavior of tooth root is assessed adopting a multiaxial fatigue criterion. Section 6 includes a discussion that tend to highlight the reason to the application of a full gear meshing simulation. Finally, some conclusions end the paper. The analyzed mechanism, visible in Fig. 1, represents one half of a symmetric gearbox of an electric motor transmission. It consists of four gears: the pinion, small purple one in Fig. 1, which is directly connected to the motor via splined shaft and it has 25 teeth. The second gear, the yellow one in Fig. 1, has 99 teeth. Together with the first gear, it forms the first reduction stage of the transmission, with a transmission ratio of 3.96. The third gear, the brown one in Fig. 1, is mounted on the same shaft as the second gear and has 28 teeth. Along with the fourth gear, the large purple one in Fig. 1 with 75 teeth, it constitutes the second reduction stage, which has a transmission ratio of 2.6. Gears 2 and 3 have the same helical direction to reduce axial load on the shaft. All gears have a normal pressure angle of 17.5°, a normal module of 1.2, and a helix angle ( β) of 25°. In the first transmission stage, the torque to be transmitted is 141 Nm, and the contact ratio is approximately 4.8, with 2.4 from profile contact and 2.4 from flank contact. Table 1 collects these data. Fig. 2 depicts the computational domain, only the first reduction stage and in particular eleven teeth per gears have been discretized and therefore simulated. This choice has been made deliberately following a study aimed at minimizing simulation time. In fact, to ensure that at least one tooth experiences the complete loading history of a full meshing cycle, it is necessary to discretize a number of teeth equal to twice the maximum number of teeth in contact, plus one (Lisle et al., 2017). 2. System analysis and discretization method 2.1 System analysis