Abstract
The article formulates the condition for the simultaneous operation of all elements of the roller freewheel clutches. Based on this condition, a functional dependence of the profiling involute line of the sprocket working surface was obtained, ensuring the constancy of the angle of roller jamming, regardless of their size. The algebra of n-dimensional hypercomplex numbers is used to describe the isometry of the profiling involute line in space. This mathematical tool is used to simplify the translation of the involute surface equation into program blocks of numerically controlled machine. The formulas are given to determine the optimal values of the tolerances for the dimensions of the clutch parts. Requirements for the accuracy of manufacturing clutch parts have been developed. An express method for calculating the operational reliability of freewheeling clutches is proposed. The results of calculations by the proposed method are in qualitative agreement with the results of observations of the clutch operation and experimental data.
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