## 4 Results and Discussion
### Measurement Results in Statistical Analysis
3 Mark 2, only worn to a different extent and covered with oil stains) and, coincidentally, Gear No. 8 Mark 6 (which performed relatively well compared to the other wheels), all other cases for _Average_ range from 0.261 to 1.141. In the future, we should try to generate average values of the so-called \"straightening coefficients\". The idea is to reduce the shifted graph to a nominal field. This will be conducted analytically (by multiplying the center of the distribution by appropriate coefficients) or graphically (by using asymmetric distributions). The authors assessed the degree of filling of the estimated tolerance field inside the nominal field, i.e., the estimator ratio expressed in [%]. A point allocation matrix was proposed (Table 9). However, the above matrix does not directly explain important issues such as how a specific estimator relates to a given IT grade, how narrow the designed tolerance zone would have to be in relation to the nominal zone, and, consequently, how expensive it would be to produce a gear with a better IT grade. One important issue still remains, namely, what IT grade to choose for the reproduced gear. Although the research results generate a general view as to which estimator best approximates the nominal tolerance zone of the base pitch, it is still unknown within which IT grade this is achieved. The most effective estimator (Model X with S-F distribution and confidence level \(\alpha=60\%\)) was chosen, and this issue was subjected to a preliminary analysis. Table 10 presents the analysis report. These results do not take into account the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Gear Designation**} & \multirow{2}{*}{**Direction**} & \multicolumn{2}{c}{**Degree of Shift \(\Delta_{1}\) and \(\Delta_{2}\) [%]**} \\ \cline{3-4}  & & **Relative to** & **Relative to** \\  & & **Average** & **Median** \\ \hline No. 1 Mark 16 & \(\rightarrow\) & 1.028 & 1.254 \\ No. 2 Mark 13 & \(\rightarrow\) & 0.918 & 0.704 \\ No. 3 Mark 2 & \(\leftarrow\) & 0.595 & 0.722 \\ No. 4 Mark 2 & \(\leftarrow\) & 5.676 & 4.109 \\ No. 5 Mark 3 & \(\leftarrow\) & 0.261 & 0.181 \\ No. 6 Mark 5 & \(\rightarrow\) & 0.464 & 0.972 \\ No. 7 Mark 11 & \(\rightarrow\) & 1.141 & 1.141 \\ No. 8 Mark 6 & \(\rightarrow\) & 0.171 & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Direction and degree of shift of the graphs of the estimated tolerance zones. analysis of the IT grade of the tested wheel. For now, the authors are only preliminary checking what the applied estimator would cause in the context of the nominal IT grade. Some estimated IT grades are defined by a range (e.g., 7 to 8 for Gear No. 1 Mark 16), because the estimated deviation is as close to the values representing the given IT grades in the range. In general, the results are quite satisfactory from the point of view of the designer recreating the gear because the increase in the cost of producing a gear wheel using two higher IT grades occurred only in the case of one of the eight tested wheels. It would be very useful at this stage to explain how the value of the base pitch \(p_{b}\) changes and how the value of the span measurement \(M_{n}\) changes with a worn wheel. For this purpose, it would be necessary to know the number of load cycles, transmitted torque, and rotational speed of the gear wheel (or possibly the power on the machine shaft) and perform a dynamic simulation using the finite element method (e.g., in the ABAQUS system environment). Of course, the material the gear is made of and the type of heat and/or thermochemical treatment are also important. Gear wear may also have a different nature. Wear may be production-related (occurring during the production of the wheel) or may be one of the classic failure modes, such as pitting, breakage, or scoring [28].