## 3 Results  
### Results of the Geometric Parameters Calculation of Alternative PS Variants  
The analysis of the results obtained (according to Table 2) showed that an engine with a housing diameter of 55 mm is not advisable for consideration in further calculations, since the PS dimensions exceed the permissible dimensions for installing the engine into the whipstock of the Perfobore technical system when drilling with a radius of curvature of less than 8 m.  
The results of calculating the geometric parameters of the PS of small-sized PDMs of various diameters, obtained under the assumption of a constancy in their working volume, make it possible to determine the degree of influence of a change in the diametric size in the required axial dimension of the PS or, in other words, the conditional \"transfer function\". This characterizes how much the length of a stator line PS with a certain kinematic ratio will change when the diameter changes by 1 mm.  
\[f_{tr}(i)=\frac{\Delta L}{\Delta D},\]  
The numerical values of function \(f_{tr}\) (_i_) are presented in Table 4 below.  
Thus, in this case, with an increase in the lobe configuration of the PS, the effect of the diametric size on the required axial dimension of the motor decreases and the difference in the stator lengths, when changing the housing diameter, will be minimal (for example, for pairs with i = 9:10, the required length when changing diameters from 43 to 48 mm changes to 120 mm).  
The changes in the required lengths of the stator lines for helical pairs for the different kinematic ratios are shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Kinematic Ratio**} \\ \cline{2-4}  & **5:6** & **7:8** & **9:10** \\ \hline \(f_{tr}\) (_i_), mm/mm & 31.4 & 25.2 & 24.0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Numerical values of function \(f_{tr}\) (_i_).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Kinetictic/-1} & \multicolumn{3}{c}{**Kinetic/-1} \\ \cline{3-6} \multicolumn{1}{c}{\(\mathbf{N}\)**} & **Parameters** & & **5:6** & **7:8** & **9:10** \\ \hline
18 & Number of contact lines & \(\Lambda\) & 4 & 5 & 6 \\
19 & Inter-turn pressure drop, MPa & \(\mathrm{P_{c}}\) & 1.0 & 0.8 & 0.67 \\
20 & Coefficient of unevenness of the diametrical & \(\mathrm{k_{d}}\) & 0.33 & 0.24 & 0.19 \\  & dimensions of the profile & \(\mathrm{\SIUnitSymbolMicro}\) & 1.5 & 1.5 & 1.5 \\
21 & Rotary mass (length L), kg & m & 1.5 & 1.5 & 1.5 \\
22 & Output speed, RPM & n & 203 & 211 & 209 \\
23 & Radial hydraulic force, kN & \(\mathrm{F_{h}}\) & 7.1 & 6.9 & 6.8 \\
24 & Inertial force, kN & \(\mathrm{F_{in}}\) & 0.03 & 0.05 & 0.07 \\
25 & Skewing moment, N-m & \(\mathrm{M_{sc}}\) & 665 & 565 & 550 \\
26 & Axial force, kN & \(\mathrm{F_{ax}}\) & 4.1 & 4.6 & 5.0 \\
27 & Loading frequency of the stator lining, Hz & F & 16.9 & 24.6 & 31.4 \\
28 & Sliding speed, m/s & \(\mathrm{v_{sl}}\) & 0.45 & 0.49 & 0.50 \\
29 & Axial velocity of the fluid, m/s & w & 6.40 & 7.88 & 9.38 \\
30 & Parameter of the curvature of the profile & \(\mathrm{\rho_{pr}/e}\) & 0.72 & 0.72 & 0.72 \\
31 & Hydraulic losses, MPa & \(\mathrm{P_{h}}\) & 0.009 & 0.014 & 0.024 \\
32 & Minimum contact stress, MPa & K & 2.24 & 1.31 & 0.78 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(Cont.\)