## 3 Results
### Results of the Operational Parameters Calculation of Alternative PS Variants  
A distinctive feature of all PS variants of small-sized high-torque PDMs, distinguishing them from the general range of serial motors for drilling and well servicing, are significantly increased values of the helical line rise angle (more than 74 degrees) and the surface shape coefficient lobes (more than 11), which, on the one hand, allows to increase the working volume to a given value, and, on the other hand, leads to an undesirable increase in axial dimensions. Analysis of the data in Table 3 shows that, for the given conditions, the use of PS with a kinematic ratio 5:6 is impractical, since this pair has a maximum axial dimension of L = 567 mm, which does not practically fit it into the given restrictions on the length of the section (Lmax = 650 mm). In doing so with a one-and-a-half-pitch length of PS, it has the smallest number of contact lines (\(\Lambda\) = 4) and the largest turn-to-turn pressure drop (1 MPa), which limits the load capacity. In addition, the 5:6 pair is characterized by the greatest contact stress in the engagement of screw pair lobes, which will affect the durability. At the same time, the advantages of such a pair are the minimum values of the inertial force (because of its quadratic dependence on the number of rotor entries), axial force, axial fluid velocity, and hydraulic losses in the internal channels of the PS. With an increase in the screw pair lobe ratio of the PS, a decrease in eccentricity, area and hydraulic section radius, and the shape factor of the helical surface are observed. In this case, there is an increase in the length and area of the projections of the contact lines, the axial (loading the joint hinges) and inertial force (causing the vibration of the PDM), the loading frequency of the stator line and the axial velocity of the fluid (which for a 9:10 pair reaches 9.4 m/s). As a result, the 9:10 pair is characterized by the greatest hydraulic losses because of the high axial velocity of the fluid and the small hydraulic radius of the section (4.6 mm), additionally, there is also an increased inertial force and the stator lining loading frequency (31.4 Hz). Compared to other pairs, the 9:10 variant, from an operational point of view, has a minimal contact stress and coefficient of unevenness of the diametrical dimensions of the profile (along the projections and depressions of their lobes). The sliding speed for all variants was at approximately the same level. In addition, the mass of the rotor and the parameter of curvature of the profile hardly change. The regularity of the change in the number of contact lines, which, all things being equal, determine the load capacity of the engine, is such that for one-and-a-half-pitch PSs, an increase in the number of entries by 2 leads to the appearance of another contact line;  
Figure 5: Histogram of the changes in the required lengths of the stator lines (in mm) for different diameters and kinematic ratios (k = 1.5). therefore, a 9:10 pair has two more contact lines than a 5:6 pair, which is essential in this project of the configuration of PDM. Thus, as a prototype PS of a high-torque small-sized PDM, taking pairs of medium i = 7:8 and high i = 9:10 lobe ratios with a standard engagement geometry and a negative profile displacement coefficient is recommended. In the final choice of the variant, their principal technical indicators (geometric, hydraulic, tribological, power) should be comprehensively considered. The results of such comparison are presented in Table 5.  
For the lower motor section of the assembly (with two shanks at the ends of the rotor), the root diameter of the rotor profile is essential, which determines the maximum possible diameter of the shank on which the connecting thread of the rotor is cut. In this respect, it is preferable to use PS with a maximum lobe configuration and minimum eccentricity.