## 4 Discussion  
The result of the testing campaign on the 2 mm-module gears has confirmed what highlighted by [PERSON] et al., that for normal modules below 5 mm the ISO 6336 approach underestimate the load carrying capacity of gears. To have a further confirmation of this phenomenon, already published data by the research group of the author were elaborated. Specifically, tests on 8 mm-module gears according to [PERSON] et al. [32] and on 4 mm-module gears according to [PERSON] et al. [41] were used. In both cases, the tests were  
Figure 4: Gear size factor vs. module. performed in order to compare different materials or investigate the effect of heat- or mechanical-treatments. In both cases the results were compared to a reference case and only the relative load carrying capacity increment was considered. For the materials tested by [PERSON] et al. and by [PERSON] et al. results in terms of tooth root bending resistance obtained on standard 5 mm-module gears are also available in literature [11]. A direct comparison of the fatigue limits obtained by [PERSON] et al. and by [PERSON] et al. with their counterparts from literature, allow the calibration of the gear size coefficient \(Y_{X}\) also for these configurations characterized by different modules and materials. Additional Data for the Calibration of a New Formulation for \(Y_{x}\): 8 mm Module Gears According to [PERSON] et al. To better calibrate a new formulation for \(Y_{X}\), valid not only for modules below 5 mm but in the whole range, additional data obtained by the author in a previous research were considered. The tests were performed in the framework of the project XL-Gear funded by Regione Lomabardia [32]. While the aim was to identify innovative solutions capable to improve large gears manufacturing as well as durability and strength, a standard case hardening steel (18 NiCrMo5) with a standard manufacturing cycle has been adopted as a base-line. The geometrical parameters of the gear are shown in Table 4. The surface roughness was Ra = 1.6 \(\upmu\)m.  
Tests were performed on a 60 kN electromechanical Schenk pulsator similarly to the tests performed on the small gear. Tests were performed with the short staircase method and post processed with the Dixon [37] approach. The stress that leads to a 50% failure probability results \(\sigma_{FP_{STBF50\%}}=1007\) MPa. This value was converted into the 1% failure probability \(\sigma_{FP_{STBF1\%}}=\sigma_{FP_{STBF50\%}}-2.33\cdot s=~{}916\) N, where \(s\) is the variance (39.6 MPa). This value was then multiplied by the a 0.9 factor to consider the fact that the tests were performed on a pulsator without meshing [38; 39], resulting in \(\sigma_{FP_{90\%}}=824\) MPa.. According to literature [11], the nominal stress for 18 NiCrMo5 is \(\sigma_{Film}=430\) MPa. This value was obtained with standard 5 mm module gears for which the factors \(Y_{NT}\), \(Y_{RefT}\), \(Y_{RefT}\), as well as the size factor \(Y_{X}\) result equal to one. \(Y_{ST}\) is instead equal to 2. Therefore, the corresponding permissible stress \(\sigma_{FP_{55\text{mm}}}\) results 860 MPa. For the 8 mm gear, \(Y_{NT}\) is equal to one. \(Y_{RefT}\), the relative surface factor results \(Y_{RefT}=0.9964\) while the notch sensitivity factor \(Y_{RefT}=0.9449\). Therefore, the size factor \(Y_{X}\) results \(Y_{X}=0.9027\). This results highlight that also for modules bigger than 5 mm, the ISO 6336 and the DIN 3990 standards (considering the Eh curve for case hardening steels) did not well predict the experimental evidences, and overestimate the value of the size factor by +10.4%. Additional Data for the Calibration of a New Formulation for \(Y_{x}\): 4 mm Module Gears According to [PERSON] et al. Additional data were extracted from the publication of [PERSON] et al. [41] performed on the same electromechanical 65 kN Schenk pulsator used by [PERSON] et al. [32]. The tested gears have a normal module \(m_{n}=4\) mm. The other geometrical parameters are shown in Table 5. The surface roughness was Ra = 3.2 \(\upmu\)m.