PSI - Issue 75

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

141

2

Nomenclature ∆ T

thermal increment ∆ Temp relative temperature A thermal area N number of cycles F pn pulsating force F pn ∾ endurable pulsating force F t nominal tangential load m n normal modulus z number of teeth α pressure angle b face width x shift profile Rz tooth root roughness HV tooth root hardness Y S stress correction factor Y F stress correction factor Y ST

stress correction factor relevant to the dimensions of the standard reference test gears

Y NT Y δrelT Y RrelT

life factor

relative notch sensitivity factor

relative surface factor

Y X

size factor

S F min

minimum required safety factor

σ F

tooth root stress

σ Flim

nominal stress numbers (bending)

σ FP permissible bending stress σ FP-ISO permissible bending stress from ISO Standard computations σ FP-SC permissible bending stress from the Staicase method computations σ FP-TCM permissible bending stress from the Thermographic method computations

1. Introduction In mechanical engineering, the assessment of material resistance is a key factor in preventing failures and ensuring the durability of components. In the specific case of gears, one of the most important mechanical resistance characterisations is the bending strength analysis. A series of research activities were proposed over the years, covering various topics and involving both numerical and experimental studies. As an example, a certain number of analyses examined the location of the most stressed point during the bending condition of the tooth by using photo elastic and Digital Image Correlation techniques, as reported by Raptis and Savaidis (2018) or Curà et al. (2024). Another topic of great interest is the bending resistance of gears in case of fatigue working conditions. These analyses are essential to avoid the generation of fatigue cracks at the tooth root, that are responsible for the failure of the gear. The result of a loading condition resulting in an applied stress close to the fatigue limit of the material was reported by Shanyavskiy et al. (2023). This led to an irreversible failure affecting not only the gear but the entire mechanical transmission. The literature on diagnostics and health monitoring proposed techniques for detecting the onset of gear failure on the basis of changes in mechanical properties due to crack growth. An example was presented by Egbert et al. (2024) in which the development of an image-based system for measuring the surface crack length and the cyclic crack growth during the last part of the crack was presented by the authors. In any case, the solution to prevent such failures due to bending fatigue requires a careful assessment of the mechanical strength of the gear in terms of bending fatigue limit. A significant number of works in the literature were presented on how to investigate this property for gears,