# Numerical Analysis of the Kinematic Accuracy of the Hermetic Harmonic Drive in Space Vehicles
###### Abstract
Hence, it is essential to have knowledge of the accuracy of harmonic drives in terms of the applied type of generator. Depending on the available execution options, the type of wave generator affects the kinematic accuracy of the wave gear available under given conditions. In harmonic drives, it is essential to ensure the hermetic is possible by application flexspline about a specific construction. The flexspline is a long gear with the shape of a thin-walled sleeve with a toothed rim in the middle. On one side, it is finished with a flange for fastening to the partition and, on the other, with a bottom that separates the hermetic space from the ambient space (Figure 2). The flexspline construction results in many complex loads and deformations during work. It is the most loaded element of hermetic harmonic drive, and it is especially exposed to different kinds of damage through its thin-walled construction. As a result of the influence of the wave generator and torsional stresses derived from the torque, the flexspline bending stresses occur. In the existing literature on construction and technological solutions and the research on harmonic drives, there are very few works that present their hermetic type. Existing publications presented only general attributes of these harmonic drives and did not solve the important problems in terms of strength and durability [14; 15; 16; 17]. The largest number of publications on hermetic wave gears comes from the second half of the previous century due to the dynamic development of the space industry, research flights, and the landing and exploration of Earth's moon at that time. The studies on harmonic drives published at this time were published by many Russian researchers [18; 19; 20] and their competitors cooperating with NASA [8; 21]. In view of the results and conclusions from the calculations included in these works, these publications were not satisfied with the present expectations of and perspectives on the use of hermetic harmonic drives. Additional contemporary studies [22; 23; 24] discussed the geometry but did not raise the strength and kinematic problems of these gears. The most extensive discussion of the hermetic type of harmonic drives was included in the monograph [25], which describes their application to precise vacuum mechanisms. All the mentioned publications show the flexspline as a thin-walled sleeve of different shapes in the longitudinal section, starting from completely cylindrical through conical to curvilinear with large rounding radii. There are also propositions to combine two sleeves of different diameters to shorten the overall length of the flexspline. None of the constructions of the hermetic harmonic drive presented in the above-mentioned  
Figure 2: View of main component elements of hermetic harmonic drive: 1—circular spline, 2—flexspline, 3—wave generator. publications has been subjected to detailed strength and durability analysis. The most probable result is that such complicated calculations exceeded the technical possibilities of computers of the time. The computational works in this area were done only by the authors that rejected most of the proposed flexspline shapes as inadvisable due to the risk of cracking [26; 27; 28]. In view of the complicated shape of the flexible sleeves, the authors also performed the analysis of the flexspline with a welded bottom, which can make it easier to make it out of steel. Due to the perspective of the use of harmonics drives and their production by incremental methods in outer space, the authors also carried out research in this area [29; 30]. In addition to the work of the authors [29; 31], there are no studies considering the kinematic accuracy of hermetic harmonic drives. High kinematic accuracy is required especially in vehicles and devices working in outer space, where even the smaller setting error adversely affects changes in flying trajectory or settings of communication antennas. In view of the vacuum in space, the desired feature of devices that work is also their hermetic.