## 4 Results and Discussion
### Measurement Results in Statistical Analysis  
The manufacturing drawings contain various types of information, both with respect to geometric deviations and, for example, the conditions for accepting the wheel from quality control. The authors verified the \(\Pi\) grade of the tested gears, bringing all the information on allowed errors to the DIN 3961 standard. Table 6 presents the drawing information with analysis in relation to the mentioned standard and the qualification of the wheel to the appropriate \(\Pi\) grade. It was needed, among other things, to determine the deviation of the base pitch, the value of which is reproduced as part of the research presented in this work. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Type of**} & \multirow{2}{*}{\(\varphi\)} & \multicolumn{5}{c}{**Module Range m [mm]**} \\ \cline{3-6} \multicolumn{2}{c}{**Error**} & & **do 0.6** & **od 0.6 do 1.6** & **od 1.6 do 4** & **od 4 do 10** \\ \hline \(\Delta\varepsilon\,\Delta t_{\mu}\,\Delta\omega\) & 1.4/1.6 & & & \(3+0.3m+0.2\sqrt{d}\) & & (19) \\ \(\Delta\varepsilon\,\Delta t_{\mu}\) & 1.4/1.6 & & & \(2.5+0.25m+0.15\sqrt{d}\) & & (20) \\ \(\Sigma\Delta t_{0}\) & 1.4/1.6 & & & \(10+m+0.8\sqrt{d}\) & & (21) \\ \(\Delta g\) & 1.4 & \(1.4+1.85\sqrt{m}+2.06\sqrt[d]{\zeta}\) (22) & \(1.4+1.85\sqrt{m}+2.18\sqrt[d]{\zeta}\) (23) & \(1.4+1.85\sqrt{m}+2.30\sqrt[d]{\zeta}\) (24) & \(1.4+1.85\sqrt{m}+2.48\sqrt[d]{\zeta}\) (25) \\ \(\Delta\tau\) & 1.4 & \(2+2.57\sqrt{m}+2.89\sqrt[d]{\zeta}\) (26) & \(2+2.57\sqrt{m}+3.07\sqrt[d]{\zeta}\) (27) & \(2+2.57\sqrt{m}+3.25\sqrt[d]{\zeta}\) (28) & \(2+2.57\sqrt{m}+3.45\sqrt[d]{\zeta}\) (29) \\ \(\Delta M\) & 1.4 & \(1.32+1.7\sqrt{m}+1.95\sqrt[d]{\zeta}\) (30) & \(1.32+1.7\sqrt{m}+2.06\sqrt[d]{\zeta}\) (31) & \(1.32+1.7\sqrt{m}+2.18\sqrt[d]{\zeta}\) (32) & \(1.32+1.7\sqrt{m}+2.3\sqrt[d]{\zeta}\) (33) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A list of formulas [25] to calculate the permissible error deviations of individual tooth elements, according to DIN 3961-1953 for \(\Pi\) grade 5 [26]. Values in [mm]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Type of Error**} & \multicolumn{5}{c}{**IT Grade**} \\ \cline{2-7}  & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(\Delta\varepsilon\,\Delta t_{\mu}\,\Delta\omega\) & 1 & 1.4 & 1.96 & 2.74 & 3.84 & 6.15 \\ \(\Delta t_{0}\,\Delta\tau_{z}\,\Sigma\Delta t_{0}\) & \(\Delta g\,\Delta\tau\,\Delta M\) & 1 & 1.4 & 1.96 & 2.74 & 3.84 & 5.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Conversion factors for the deviations of various toothing and engagement errors, according to DIN (TGL), depending on the \(\Pi\) grade. Only grades 5 to 10 are shown. In the case of Gear No. 1 Mark 16, a calculator [27] was used to check the correctness of the drawing and, indeed, for the seventh grade \(\Delta g=0.03\) mm. Gear No. 4 Mark 2 is the same wheel as Gear No. 3 Mark 2; however, it has significant signs of use, including large oil stains. In the drawing of Gear No. 5 Mark 3, the deviation of the base pitch is given directly. In the drawing of Gear No. 7 Mark 11, the standard number is not provided, but the DIN letter is. In the case of Gear No. 8 Mark 6, the measurement value deviation of 0.054 mm is close to the value of 0.047 mm, which corresponds to grade 9. The deviation of tooth thickness of 0.06 mm is as close to the value of 0.050 mm (grade 9) as to the value of 0.070 mm (grade 10). In both cases, the difference is 0.01 mm. However, due to the fact that the deviation of the measured value at the level of 0.054 mm on the right side is close to the normalized value of 0.047 for grade 9 and is far from the value of 0.089 mm for grade 10, the tested wheel should be classified as grade 9 according to DIN 3961. Figures 6-13 show blocks of double graphs created on the basis of measurement data and statistical calculations.