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Bending Load on Internal Gears of Planetary Gear Sets
As compared to external toothings, the design fundamentals and standards for proving the load-carrying capacity of internal toothings have been little developed. Mostly only insufficiently considered is the influence of stress in the toothed gear rim, which is essential in almost all cases. Also for the theoretical borderline case of the infinitely thick toothed gear rim some design data are too inaccurate, since they are not based on the actual tooth fillet and on precise notch-stress calculations. Even larger are the deviations in elastically designed toothed gear rims. This paper is to present results of investigations for the more precise determination of stress in the tooth root or the toothed gear rim of internal toothings specifically for their use in planetary gearings. Proposals for the practical calculation are included. The results of calculation are confirmed by tests. At first, the considerations concern borderline cases of load in an infinitely thick toothed gear rim, whose mounting in the casing has no influence on the stresses examined here (very elastic connecting elements). On this basis, the case of the inner toothed gear rim with a cylindrical connection contour is treated (the internal toothing is positioned only on a part of the hollow cylinder). The influence of the connection contours on the stress as compared with the version with a ground contour was successfully taken into account by approximation relations. The assumptions and results of calculation were well determined by measurements done on a planetary gearing. The stress calculations are carried out by a locus-dependent superposition of the stress components resulting from the radial force and the tangential force. Proceeding from the moment curve and longitudinal-force curve determined in the tooth gear rim, the local stress in the tooth gullet is determined with the aid of the boundary element method. The practical application of the findings is facilitated by generalized stress concentration factors, which are newly calculated for internal toothings. To sum up, it can be stated that the contribution gives an insight into general connections and proposes a refined method for practical use.
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