## 6 Conclusions  
On the one hand, miniaturization is an actual trend and, therefore, new designs will adopt more and more small gears. On the other hand, the actual standards did not properly include the effect of the size of the gears on the allowable stresses for modules different from 5 mm. Therefore, there is the need for new extended factors. [PERSON] et al. proposed a new formulation for the size factor \(Y_{X}\) based on experiments performed on gear samples made of 16 MnCr5 and having modules between 0.45 and 20 mm. The experimental evidence shows that for small gears having a normal module below 5 mm, the allowable stresses results significantly above those for standard reference gear. The results of this work are aligned with the findings of [PERSON] et al., confirming the increased load carrying capacity of small gears.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & \(\sigma_{\mathbf{FP}_{\text{ST  
In this study the reference stress \(\sigma_{\text{F}_{\text{fin}}}\) for gears made by 39 NiCrMo3 having a normal module \(m_{n}=2\) mm was obtained via STBF tests. Tests were conducted using the short staircase approach and the results statistically postprocessed with the up-and-down method for small samples with two specimens \"in series\" according to [PERSON]. The ISO 6336 standard was applied to convert the applied forces into stresses. The obtained value of reference stress was compared with the one available in literature for 39 NiCrMo3. This comparison has led to the calibration of the size factor \(Y_{X}\) according to ISO 6336 for a normal module \(m_{n}=2\) mm resulting in \(Y_{X}=1.1327\). This value is significantly above the value suggested by the standard (\(Y_{X}=1\)) and aligned with the model proposed by [PERSON] et al.  
In addition to that, in order to have a more reliable data set, starting from data published by author's research group in the past and the comparison of those data with literature data available for the same materials and obtained on 5 mm-module gears, additional values for the gear size factor for 4 mm- and 8 mm-module gears were derived.  
Finally, based on the actual data, data on literature, results published by the author in the past, and other data from collaborators, an alternative formulation for the size factor \(Y_{X}\) was proposed. This formulation shows a slightly higher coefficient of determination \(R^{2}\) with respect to the model proposed by [PERSON] et al. and significantly higher than the one proposed by the ISO 6336 and DIN 3990 standards. However, while both the actual model and the one according to [PERSON] et al. show similar trends in the 2-20 mm module range, for higher values they differ significantly. In order to clarify which one is more suitable, additional tests are planned on big-module gears.  
[PERSON] followed the development of the rig, performed the tests, post-processed the results and wrote the paper. The author has read and agreed to the published version of the manuscript. This work was supported by the Open Access Publishing Fund of the Free University of Bozen-Bolzano.  
Not applicable.  
The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.  
The authors declare that they have no competing interests.