Planetary gearboxes are becoming more popular due to their high-power density and potentially high efficiency. When the planet bearings are internally mounted, the body of the planet gear has to be hollow. The demand for large outer diameters due to high-load requirements might result in a small planet rim thickness. Depending on the rim thickness, its rigidity may become very low. Due to the low stiffness and the special load conditions caused by the double meshing, the deformation of the planet and its bearings are unique. In this paper, the influence of rim thickness on bearing load and lifetime is examined. The analysis is performed with a finite element method (FEM) model of a planet rim with a built-in cylindrical roller bearing. With the resulting planet deformation from the FEM calculation, the load distribution on the rolling elements in the bearing and the bearing lifetime according to ISO/TS 16281:2008 has been evaluated.
For the development of high power density gearboxes the knowledge of the gear mesh behavior is important. Especially, the tooth deflection influences flank load distribution and is the basis for the design of flank modifications. Analytical and numerical approaches are suitable to evaluate the behavior. Since numerical methods are complex, elaborate and time-consuming, fast and accurate analytical methods are still important and are worth to be further developed and assessed.An analytical method for calculating tooth deformation for gears goes back to Weber and Banaschek from 1953. In the initial work the final equations are given without many intermediate steps in the plane strain assumption for materials with Poisson’s ratio ν = 0.3. This paper derives the tooth deflection equations in a more detailed and general manner for any linear material. The final equations are valid for the plane stress and plane strain state in one new closed representation and are therefore suitable for an efficient implementation. While the plane strain state is typical for gears, the plane stress state is significant for a thin slice model or special gearings. The presented method captures the shear influence with a more detailed calculation of the shear correction factor.A calculation study validates the results from the derived analytical tooth deflection calculation method with a plane Finite Element Model. In the study the point of application of force and the gear body are varied to cover the influence of different variants (size and mesh position). Finally limits of the analytical modeling and the validation are discussed.
Planetary gearboxes are becoming more popular due to their high power density and potentially high efficiency. When the planet bearings are internally mounted, the body of the planet gear has to be hollow. The demand for large outer diameters due to high load requirements might result in a small planet rim thickness. Depending on the rim thickness, its rigidity may become very low. Due to the low stiffness and the special load conditions caused by the double meshing, the deformation of the planet and its bearings are unique. In this paper, the influence of rim thickness on bearing load and lifetime are examined. The analysis is performed with an FEM model of a planet rim with a built-in cylindrical roller bearing. With the resulting planet deformation from the FEM calculation, the load distribution on the rolling elements in the bearing and the bearing lifetime according to ISO/TS 16281:2008 have been evaluated.
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