PSI - Issue 75

Luca Corsaro et al. / Procedia Structural Integrity 75 (2025) 140–149 Luca Corsaro , Francesca Curà, Raffaella Sesana / Structural Integrity Procedia (2025)

142

3

and the studies proposed by Conrado et al. (2017), Concli (2018) and Bonaiti et al. (2019) are given as examples. However, it is important to note that the execution of a comprehensive analysis typically necessitates the application of statistical tools (Staircase or Dixon methodologies), which also impact the testing conditions and the number of gears necessary for the analysis. The field of Passive Thermography is a growing area of interest for researchers due to the possibility of performing analyses with numerous advantages, including non-contact, full-field measurements and reduced inspection time. The feasibility of these detectors for temperature analysis related to fatigue phenomena was initiated around the 1970s by Attermo and Östberg (1971). Then, the topic of fatigue limit estimation attracted considerable interest. The Thermographic Method was first documented as the One Curve Method (OCM) for estimating fatigue limits using PT (f.i. Curti et al. (1986) and Curti et al. (1989)). These works identified an empirical linear relationship between stabilisation temperatures and applied stress amplitudes, which allowed for the estimation of the fatigue limit. Subsequently, various papers were published with the aim of improving the OCM methodology, f.i. La Rosa et al. (2000) and Fargione et al. (2002). A further analysis was proposed by Curà et al. (2005) and Curà et al. (2012), where the fatigue limit was identified using the intersection of two linear curves approximating the surface temperature increment, defining the Two Curves Method (TCM). In a recent article, Faria et al. (2022) proposed the Thermographic Method for the analysis of mechanical components, instead of classical samples, and the results were in good agreement with those obtained from consolidated approaches (Staircase Method). So, the Thermographic Method offers a rapid and economical alternative to conventional methods such as Staircase analysis for fatigue life evaluation, although its primary application remains the analysis of classic samples. In the present study, the possibility of using the Thermographic Method for rapid fatigue limit estimation on a mechanical component such as a gear was investigated for the first time. The thermal emissions produced at the tooth root during different bending fatigue tests were acquired by means of a thermal camera. Subsequently, the thermal profiles were processed with the objective of estimating the fatigue limit in terms of endurable pulsating force by applying the TCM. In this work, two different gears were studied in terms of geometry and material. Then, the obtained results were compared with those evaluated using consolidated approaches such as the Staircase Method and with the indications available in the Standards ISO 6336-3 (2019) and ISO 6336-5 (2019). 2. Thermographic Methodology and gears calculation 2.1. The Thermographic Method The Thermographic Method used to estimate the tooth root bending fatigue strength is the TCM (proposed by Curà et al. (2005), Gallinatti (2009) and Curà et al. (2012)). In particular, the method was appropriately adapted for this work in order to estimate the endurable pulsating force (F pn ∾ ) of the tested gear instead of stress amplitude, which is the case in classical samples. The Thermographic Method is described in Fig. 1. The thermal evolution recorded by a thermal camera (Fig. 1(a)) was characterised by an initial heating phase, followed by a stabilised trend. However, if the load value applied during the fatigue test was higher than the corresponding endurance limit, an abrupt thermal increment was observed just before the material failure (solid red line). On the other hand, for a load value below the fatigue limit, the thermal profile remained stabilised (dashed red line). In order to estimate the fatigue limit from thermal emissions produced during the fatigue tests, the temperature increment (thermal increment, ∆T*) or the area subtended to the temperature profile (thermal area, A*) can be considered as thermal parameters for a given time (the number of cycles, N*). In the specific application of tooth root bending fatigue strength estimation, as presented in this work, the area obtained from an integration of the temperature profile was considered for each specific loading condition. The fatigue limit is estimated as shown in Fig. 1(b). In this method, a series of loading conditions were examined, starting with a low loading level and then increasing each load during the tests. Each loading condition was applied until a specified number of cycles (as well described in Section 4) was reached. At the end of each test, the sample had to be cooled up to environmental temperature in order to guarantee a proper starting condition for the next testing load. The process was completed when an abrupt thermal parameter increment (represented by the blue circles in Fig. 1(b)) was detected for a certain number of load levels. This way, a flat trend was obtained for low load values and, from a certain level, a variation in the evolution of the thermal parameters was observed.