## 3 Results
### Results of the Operational Parameters Calculation of Alternative PS Variants
Thus, the root diameters (d\({}_{\rm r}\)) of the rotor profile for pairs 7:8 and 9:10 are obtained as 20.2 and 21.4 mm, respectively. This is sufficient if the creep strength (\(\tau_{\rm cs}\)) of the rotor material is 500 MPa and the safety coefficient is 2.5. In this case, the shaft diameter required from the condition of torsional strength for M = 75 Nm is 12 mm. Based on this, both of the selected variants, in terms of the totality of the indicators discussed above, can, in principle, be used as power sections of a PDM for the given operating parameters of the TS Perfobore. However, provided that the dominant selection criterion is the minimum axial dimension of the power section, a screw pair with a kinematic ratio of 9:10 should be recommended as the basic variant. This would provide additional and essential advantages, such as reduced eccentricity (1.1 versus 1.35 mm), minimal contact stress (0.78 versus 1.31 MPa) and a more uniform profile contour (19% versus 24%). It would also favorably affect the operability of the hinge joint, the durability of the PS and the deformation of the stator lining  
Similar conclusions can be reached when choosing the optimal variant for other diametres of the PS; the geometric parameters of which are given in Table 2. The recommended variants of PS (i = 9:10) for all considered sizes are as follows:  
D\({}_{\rm b}\) = 43 mm; D\({}_{\rm c}\) = 28 mm; e = 1,1 mm; T = 300 mm; L = 450 mm  
D\({}_{\rm b}\) = 45 mm; D\({}_{\rm c}\) = 30 mm; e = 1,2 mm; T = 260 mm; L = 390 mm  
D\({}_{\rm b}\) = 48 mm; D\({}_{\rm c}\) = 33 mm; e = 1,3 mm; T = 220 mm; L = 330 mm  
Thus, for the given design conditions (V = 0.235 l; k = 1.5), the transition to the next diametric size of engine PS with a kinematic ratio of 9:10 and a negative profile \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Technical Indicator**} & \multicolumn{3}{c}{**Variant of the PS**} \\ \cline{2-3}  & **7:8** & **9:10** \\ \hline \multirow{4}{*}{Geometric indicator} & \multirow{4}{*}{-} & \multicolumn{2}{c}{Preferable to eccentricity, axial} \\  & & & dimension, the number of contact \\ \cline{1-1}  & & - & lines, turn-to-turn pressure drop \\ \cline{1-1}  & & & and the coefficient of irregularity of \\ \hline \multirow{2}{*}{Hydraulic indicator} & \multirow{2}{*}{\begin{tabular}{c} Preferable to axial fluid velocity \\ and hydraulic losses. 1 \\ \end{tabular} } \\  & & & \\ \hline \multirow{2}{*}{Tribological indicator} & \multirow{2}{*}{\
\begin{tabular}{c} Preferable to the loading \\ frequency of the stator line. \\ \end{tabular} } \\  & & & \\ \hline \multirow{2}{*}{Power indicator} & \multirow{2}{*}{
\begin{tabular}{c} Preferable to in terms of \\ inertial force. \\ \end{tabular} } \\  & & Axial force in PS; radial hydraulic force and skewing moment both \\ \cline{1-1}  & pairs under consideration are at approximately the same level. 2 \\ \hline \end{tabular}  
* At the same time, the calculated value of hydraulic losses in the internal channels at the rate of drilling mud (Q = 1 L/s) is insignificant (with Re \(>\) 10:10\({}^{-}\)), which provides motivation to further use pairs with increased lobe configurations, for example 11:12; 2 however, it is necessary to note a sufficiently high level of force factors, which should be taken into account when designing joint hinges and axial bearing of the downhole assembly.  
\end{table} 
Table 5: Estimative comparative analysis of the technical indicators of PSs. displacement leads to a change in the engagement eccentricity of 0.1 mm, and in the required axial dimensions of 60 mm. If necessary, an upgraded variant with the shortest length of power section, corresponding to 1.2 stages, can be considered. Such a design is undesirable from the point of view of the general theory of single-screw hydraulic machines [24] which will reduce the active length of the stator line (in particular, for D\({}_{\text{b}}\) = 43 mm by 90 mm to a length of L = 360 mm, and for D\({}_{\text{b}}\) = 48 mm by 66 mm to a very small axial dimension of the lining of L = 264 mm).