## 3 Results  
Table 3 shows the summary of the test results performed on the fine-module gears.  
Being the results of the testing campaign in the order RO-RO-RO-RO-F-F, the value of \(k=~{}3.56\) leads to a permissible force \(F_{FP_{STBF50\%}}=4006\) N. This value (4006 N) represents the fatigue limit for a probability of 50% of failure. Therefore, the result was decreased by 2.33-\(s\), where \(s\) represents the variance that, according to the Up-and-Down Method for Small Samples with Two Specimens \"in Series\" according to [PERSON], is equal to the force interval \(\Delta F\). This leads to a fatigue limit with a failure probability of 1% \(F_{FP_{STBF1\%}}=3773\) N.  
The result was multiplied by a factor 0.9 to consider the fact that the tests were performed on a pulsator without meshing [38; 39].  
This force can be converted into a permissible stress \(\sigma_{FP}\), equal to the actual one \(\sigma_{F}\), using the abovementioned formulas (ISO 6336). For the specific geometry, the form factor \(Y_{F}\) and the stress correction factor \(Y_{S}\) result, respectively, in 2.0298 and 1.9011. The values of \(h_{Fe}\) (3.3159 mm) and \(s_{Fe}\) (4.2999 mm) for the calculation of \(Y_{F}\) were graphically extracted (Figure 3).  
Figure 3: Determination of the most critical section.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test ID** & \(F_{max}\) [N] & \(F_{min}\) [N] & \(N\) [\(-\)] & **Status** \\ \hline
1 & \(-\)365 & \(-\)3650 & \(5.00\times 10^{6}\) & RO \\
2 & \(-\)375 & \(-\)3750 & \(5.00\times 10^{6}\) & RO \\
3 & \(-\)385 & \(-\)3850 & \(5.00\times 10^{6}\) & RO \\
4 & \(-\)395 & \(-\)3950 & \(5.00\times 10^{6}\) & RO \\
5 & \(-\)405 & \(-\)4050 & \(4.17\times 10^{5}\) & F \\
6 & \(-\)395 & \(-\)3950 & \(3.33\times 10^{6}\) & F \\ \hline \hline \end{tabular}
\end{table}
Table 3: Test results relative to the 2 mm-module gear.  
The value of the permissible stress \(\sigma_{FB_{2 mm}}\) results 570.34 MPa.  
According to literature [11], the nominal stress for 39 NiCMMo3 is \(\sigma_{Film}=280.92\) MPa. This value was obtained with standard 5 mm module gears for which the factors \(Y_{NT}\), \(Y_{grDFT}\), \(Y_{RefT}\) as well as the size factor \(Y_{X}\) result equal to one. \(Y_{ST}\) is instead equal to 2. Therefore, the corresponding permissible stress \(\sigma_{FP_{5 mm}}\) results 561.84 MPa.  
For the actual gear having normal module equal to 2 mm, \(Y_{NT}\) is also equal to one. \(Y_{RefT}\) is the relative surface factor. It is function of the roughness \(R_{Z}\). For the tested gears, the roughness \(R_{a}\) of the fillet was measured to be 6.3 \(\upmu\)m. This value was converted into \(R_{Z}\) using the DIN 4778 [40] resulting in 38.3 \(\upmu\)m. For this value of roughness, the ISO 6336 proposes a relative surface factor \(Y_{RetT}=0.9458\). \(Y_{grDFT}\) is the notch sensitivity factor (Equation (9)).  
\[Y_{RefT}=\frac{1+\sqrt{\rho^{\prime}X^{*}}}{1+\sqrt{\rho^{\prime}X^{*}_{T}}} \tag{9}\]  
where \(\rho^{\prime}\) is the slip player thickness, that for the present material is equal to 0.083, \(\chi^{*}\) is the relative stress gradient of the actual gear and \(\chi^{*}_{T}\) is the corresponding value for reference gears where the notch parameter \(q_{sT}=1.0\). For the 2 mm module gear, the notch parameter \(q_{s}\) according to Equation (10)  
\[q_{s}=\frac{s_{Fn}}{2\cdot\rho_{F}} \tag{10}\]  
results in \(q_{s}=2.6659\). \(Y_{RefT}=0.9458\).  
The direct comparison of the two values of permissible stress leads to the estimation of the size factor for the 2 mm normal module gear. It results \(Y_{X}=1.1327\). This value aligned with the findings of [PERSON] et al. (\(-3.9\%\) as shown in Figure 4) and significantly above the value proposed by the ISO 6336 and the DIN 3990 standards (\(+13.3\%\)).