# New Construction Solutions of Gear Using in Space Vehicle Control Systems
## 3 Results
However, also in this case, the flexspline with an outer flange has a more unfavourable stress distribution, so it is not recommended in constructions with high demands for durability and reliability. According to the initial assumption, an attempt was made to shorten the flexspline. Therefore, the construction in variant IX was modeled, where the length L was reduced by half. However, the stress distributions obtained for this model (shown in Figure 13) did not allow for this solution to be correct. The area of dangerously high stress values near the rim of the toothed wheel and the major axis of the generator makes a risk of damaging the flexspline during exploitation. Ultimately, a solution was decided in which the length of the flexspline was equal to L = 115 [mm]. Such a shortening allowed us to reduce the dimensions of the harmonic drive by about a quarter of its initial length. This final solution was marked as variant X, and, like the previous ones, it was subjected to FEM numerical analysis in the Abaqus program. The results of the calculations, in the form of the stress distribution on the surface of the flexspline, are shown in Figure 14. The maximum stress values observed near the toothed rim are equal to 340.78 [MPA], which do not exceed the limit values for the assumed wheel material (30 HGSA). Figure 11: The distribution of the stresses in the flexspline model—variant VII. In other areas of the flexspline, for example, at the bottom, the stress values are also on a safe level and are below 100 [MPa]. It can be assumed that the construction of the flexspline proposed in variant X is the right solution and can be the basis for future research. Stress values indicate that the structural safety factor of the analyzed flexspline is high and allows it to be used in devices requiring long-term and failure-free operation. Figure 15 shows a new shape of the flexspline, which was proposed based on the conclusions of the FEM analysis for many different construction variants. The recommended values of the geometric parameters for which a flexspline with a more compact structure and a strength comparable to that in classic constructions can be obtained are given in Table 2. The proposed elliptical shape of the flexspline body has the advantages of solutions requiring a long body and reduces the probability of breakage to the radius near the bottom. Figure 5:0 The distribution of the stresses in the flexspline model—variant VIII. Figure 5:1 The distribution of the stresses in the flexspline model—variant IX. Figure 5:2 The distribution of the stresses in the flexspline model—variant X.  
Figure 5:3 New shape of the flexspline of harmonic drives (variant X). To perform a quantitative analysis, the stresses \(\sigma_{\rm z}\) in the longitudinal sections were determined through the major axis of the generator for the ten construction variants of the flexspline. The compared diagrams will help to assess the impact of individual design solutions on the stress level in the analyzed models. Figure 16 shows the diagrams for selected variants of the flexspline with a standard length \(\rm L=150\) [mm], while Figure 17 shows solutions for a few characteristic models with reduced lengths. Both diagrams show the results for variant X, which was positively evaluated and recommended for future exploration. Most of the models of the flexspline made in long variants have a similar nature of stress diagrams in the plane passing through the major axis of the wave generator. For the proposed variant X, the maximum stress values near the tooth wheel were slightly higher than those of other solutions analyzed. However, they did not differ significantly from them; it is necessary to keep in mind that this is a solution with a reduced length. The base model (variant I) had the lowest stress values in the rim of the area of the tooth wheel rim. Therefore, if the external dimensions are not decisive for the wave gear, this proven solution should definitely be used.