Most helicopter transmissions utilize a planetary gear train as the final speed reduction stage. Due to weight constraints these transmissions have high power-to-weight ratios and relatively flexible structures. This investigation addresses the analysis of planetary gear trains with the ring gear mounted on a flexible support structure. The approach utilizes recent advances in automated contact methods for nonlinear finite element analysis. Rather than using a line of action spring to model gear pair mesh stiffness, finite element models of complete gears are developed, and the elastic gear members are engaged and rolled through mesh. The procedure includes detailed gear tooth geometry with profile modifications. A nonlinear approach is required due to large displacements associated with gear rotation and nonlinear boundary conditions associated with the gear tooth surface contact. The updated Lagrangian formulation and the MARC K-4.1 automated contact features are applied in the analysis. The ring gear support structure is modeled by an elastic foundation linking the ring gear to a rigid support. Calculation of gear pair deflections, stresses, transmission error, and mesh stiffness through the gear meshing cycle are demonstrated for external and internal spur gear pairs and a planetary gear train. Issues relating to the accuracy of the nonlinear finite element contact method, gear mesh stiffness, transmission error, and the planetary gear train elastic support structure are discussed.; vii
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