Verein Deutscher Ingenieure

Calculation of the load capacity of the tooth root in internal toothings with influence of the gear rim
 N VDI 2737

Annotation

This standard applies to the calculation of safety against fatigue fracture and damage caused by crack initiation, permanent deformation and overload breakage of toothings with a basic rack profile according to DIN 867. For fractures it is assumed that they commence in the fillet curve or in the tooth bottom of the running gears, thus being caused by the notch stress.

Gear materials according to DIN 3990-5 are taken as a basis.

Helical toothings can be calculated as equivalent spur gears according to DIN 3990 up to a helix angle |?| ? 30°.

If the internal toothing is wider than the toothing of the mating gear (planet), this higher width may be substituted in the calculation of the load capacity of the tooth root, however limited to 1· mn at each tooth front edge.

At last, it is taken as a basis that for continuous loading the decisive (equivalent) load is known or has been determined with the aid of a suitable hypothesis of damage accumulation as well as that the maximum load is known or given as a prerequisite for the determination of deformation limit, crack strength or fracture limit.

This standard applies to an approximately uniform distribution of the planets on the periphery and a number of planets p ? 2. In the calculation method there is distinguished between a stiff gear rim and an elastically designed one, in accordance with the limits stated in Section 4.1 and Section 4.2. In planetary gearings with more than three planets and high loadings the longitudinal stresses are not insignificant due to the longitudinal forces in the gear rim. It is advisable to take these into account, too [6; 7].