Theoretical Analysis of the Deflection along Line of Action of Planet Gear with Thin Rim

A planet gear with a thin rim, which has a small radial clearance between the rim and a planet gear shaft, is chosen as the subject of study. Both the fillet stress and the stiffness along the line of action of the planet gear which have been little clarified until now have to be estimated for designing the bending strength of planet gear. A theoretical method of obtaining nominal stresses in the rim was shown to estimate the fillet stress by using an equivalent ring whose bending stiffness was equal to that of the planet gear after a theoretical method of determining the magnitude of a region where the rim is in contact with the gear shaft was shown in the previous report. In this report, a theoretical method of obtaining the radial, circumferential and angular displacements at an arbitrary position in the equivalent ring of the planet gear is shown considering the condition of contact between the rim and the gear shaft. Further, a method of translating the displacements of the equivalent ring to those along the line of action in order to obtain the total deflection of the planet gear along the line of action which is composed of both the deflection of tooth and that of rim.