## 2 Materials and Methods
### Calculation of Operational Parameters of Alternative PS Variants  
Calculation of the operational parameters of small-sized engines for the given operating conditions (M = 75 N-m; P = 4 MPa) and the selected alternative variants of the power sections (Table 2), using the example of a PDM with a body diameter of 43 mm for three kinematic ratios (5:6, 7:8 and 9:10), are presented in Table 3. When calculating the rotational speed of the output shaft, it is assumed that the volumetric efficiency (\(\eta_{\
u}\)) in the operating mode is 80%, and the working volume of the engine section and the displacement coefficient is refined based on the rounded-off values of the eccentricity and pitches of the PS.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Body Diameter, D\({}_{\text{b}}\),mm** & **43** & **45** & **48** & **55** \\ \hline \multicolumn{5}{c}{Stage of stator, mm} \\
4 & \(\text{T}_{\text{st}}\)\(\leqslant\)6 & 378 & 330 & 273 & 307 \\  & \(\text{T}_{\text{st}}\)\(\geqslant\)8 & 320 & 284 & 236 & 265 \\  & \(\text{T}_{\text{st}}\)\(\geqslant\)10 & 300 & 260 & 220 & 248 \\ \hline \multicolumn{5}{c}{Average diameter of the rotor, mm} \\
5 & \(\text{d}_{\text{av}}\)\(\geqslant\)6 & 21.0 & 22.6 & 24.8 & 27.9 \\  & \(\text{d}_{\text{av}}\)\(\geqslant\)8 & 22.6 & 24.2 & 26.6 & 29.9 \\  & \(\text{d}_{\text{av}}\)\(\geqslant\)10 & 23.6 & 25.2 & 27.8 & 31.2 \\ \hline \multicolumn{5}{c}{Surface shape coefficient} \\
6 & \(\text{c}_{\text{s}}\)\(\geqslant\)6 & 15.0 & 12.2 & 9.2 & 10.35 \\  & \(\text{c}_{\text{s}}\)\(\geqslant\)7.8 & 12.4 & 10.3 & 7.8 & 8.7 \\  & \(\text{c}_{\text{s}}\)\(\geqslant\)10 & 11.4 & 9.3 & 7.1 & 7.98 \\ \hline \multicolumn{5}{c}{Length of the stator line PS, mm} \\
7 & L 5:6 & 567 & 495 & 410 & 462 \\  & L 7:8 & 480 & 426 & 354 & 398 \\  & L 9:10 & 450 & 390 & 330 & 371 \\ \hline \multicolumn{5}{c}{Number of contact lines} \\
8 & \(\lambda\) 5:6 & & 4 & \\  & \(\lambda\) 7:8 & & 5 & \\  & \(\lambda\) 9:10 & & 6 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & **Variant of the PS** \\
**N** & **Parameters** & & **5:6** & **7:8** & **9:10** \\ \hline
1 & Eccentricity, mm & e & 1.75 & 1.35 & 1.1 \\
2 & Eccentricity factor & c\({}_{0}\) & 1.175 & 1.175 & 1.175 \\
3 & Tooth shape coefficient & c\({}_{\text{e}}\) & 2.175 & 2.175 & 2.175 \\
4 & Offset coefficient & \(\xi\) & \(-\)1.050 & \(-\)1.030 & \(-\)1.023 \\
5 & Surface shape coefficient & c\({}_{\text{s}}\) & 15.0 & 12.4 & 11.4 \\
6 & Helical line rise angle, grad & \(\Theta\) & 78.2 & 75.8 & 74.6 \\
7 & Average diameter of the rotor, mm & d\({}_{\text{av}}\) & 21.0 & 22.6 & 23.6 \\
8 & Root diameter of the rotor profile, mm & d\({}_{\text{r}}\) & 17.5 & 20.2 & 21.4 \\
9 & Stage of rotor, mm & T\({}_{\text{r}}\) & 315 & 280 & 270 \\
10 & Stage of stator, mm & T\({}_{\text{st}}\) & 378 & 320 & 300 \\
11 & Stator cover length, mm & L & 567 & 480 & 450 \\
12 & Area of flow section, cm\({}^{2}\) & S & 1.25 & 1.02 & 0.85 \\
13 & Wet perimeter, mm & \(\pi\) & 17.0 & 17.9 & 18.4 \\
14 & Area of contact line, cm\({}^{2}\) & S\({}_{\text{e}}\) & 4.1 & 4.5 & 4.8 \\
15 & Hydraulic radius, mm & R\({}_{\text{h}}\) & 7.4 & 5.7 & 4.6 \\
16 & Actual displacement volume, L & V & 0.236 & 0.227 & 0.230 \\
17 & Length of contact line, m & L\({}_{\text{e}}\) & 298 & 351 & 423 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Geometric and operational parameters of the power section of the PDM with the diametrical dimension of the sleeve being 43 mm (D\({}_{\text{c}}\) = 28 mm; V = 0.235 L; M = 75 N-m; P = 4 MPa; Q = 1 L/s; \(\eta_{\text{hm}}\) = 0.5; \(\eta_{\
u}\) = 0.8; k = 1.5).  
Based on the performed calculations, a comparative analysis of the principal technical indicators (comparison criteria) for each variant of the PS was performed.