# Numerical Analysis of the Kinematic Accuracy of the Hermetic Harmonic Drive in Space Vehicles
## 4 Results  
The calculations for all four variants were without errors and obtained a lot of result data, allowing us to conduct a thorough analysis of many aspects of the work of the hermetic harmonic drive. The basic results obtained in the Abaqus postprocessor are displayed as stress distribution on the surface of the analyzed model. The preliminary comparison of them has revealed that discrepancies occur with different types of generators. The distribution of areas with significantly higher values on the flexspline model in the next variant of calculations was also different. Figures 10 and 11 show the results obtained for the harmonic hermetic drive with a flexspline deformed double-roller generator without torque. Figure 10: Stress distribution on the model of harmonic hermetic drive with the double-roller generator. Areas of increased stress in all calculation variants occurred in areas of the major (D) and minor (M) axis of the generator because the deformation of the flexspline is the highest. However, in none of the computational models were the allowable stresses exceeded. However, a more detailed stress analysis was not performed because the main purpose of the analysis was to determine the kinematic accuracy of the harmonic drive. The first point of analysis was to compare the angle \(\delta\) of rotation of the circular spline of the harmonic drive depending on the angle \(\varphi\) of rotation of the generator. In these calculations, rotation of the generator model to angle 1 radian was forced, firstly in the positive destination and then in the negative from the major axis of the generator. The rotation of the wave generator caused the proper rotation of the circular spline, which is the result of the meshing pairs of teeth on both gears. Because the harmonic drive ratio tested was large (i = 95), observation of the models on the computer screen was not allowed for capturing the differences between individual results. For each of the models, there were prepared graphs of the angle of rotating the flexspline, depending on from angle of the rotating generator. In each of them, the nominal value of the angle of rotation of the flexspline has been drawn with a thin grey line. This theoretical value was determined from formulas only on gear ratio. None of the wave generators' values of the actual angle of rotation of the circular spline do not converge with the nominal values. In the case of both roller generators, in the first phase of cooperation, the rotation of the circular spline is delayed relative to the theoretical value. After rotation about the angle 1 radian, the equalization of the angle value of rotation of the circular spline was obtained in the results of the simulation with the nominal value. Therefore, at this value, the wave generator was stopped and forced to rotate in the opposite direction to a value of \(-1\) radian from the main axis. During the return movement, an even greater delay of the circular spline in relation to the theoretical value was noticed in the analyzed model. The delays occur in the first phase of moving the generator, and then the values of the angle of rotation of the flexspline are approaching theoretically. This shows the high kinematic inertia of the harmonic drive with roller generators. For the other two generators, the course of the graph of the angle of rotation of the circular spline obtained as a result of numerical calculations was much closer to the nominal one. It resulted from the construction of these generators, which allows for the control of form deformation of flexspline much better than roller generators. Of all the computational models, the most favorable course of the graph was obtained for the cam generator, which is in contact with the inner diameter of the flexspline along its entire circumference.