A deformable body dynamic analysis of planetary gears with thin rims

Planetary gear sets are used commonly by automotive and aerospace industries. Typical applications include jet propulsion systems, rotorcraft transmissions, passenger vehicle automatic transmissions and transfer cases and off-highway vehicle gearboxes. Their high-power-density design combined with their kinematic flexibility in achieving different speed ratios make planetary gears sets often preferable to counter-shaft gear reduction systems. As planetary gear sets possess unique kinematic and geometric properties, they require specialized design knowledge [1]. One type of the key parameters, the rim thickness of the gears, must be defined carefully by the designer in order to meet certain design objectives regarding power density, planet load sharing, noise and durability. From the power density point of view, the rim of the each gear forming the planetary gear set must be as thin as possible in order to minimize mass. Besides reducing mass, added gear flexibility through reduced rim thickness was shown to reduce the influence of a number of internal gear and carrier errors, and piloting inaccuracies [2]. In addition, it was also reported that a flexible internal gear helps improve the load sharing amongst the planets when a number of manufacturing and assembly related gear and carrier errors are present [3–6]. Many of these effects of flexible gear rims were quantified under quasi-static conditions in the absence of any dynamic effects. The effect of rim thickness on gear stresses attracted significant attention in the past. A number of theoretical studies [7–14] modelled mostly a segment of spur gear with a thin rim. In these studies, the gear segment was typically constrained using certain boundary conditions at the cut ends and a point load along the line of action was applied to a single tooth in order to simulate the forces imposed on a sun or an internal gear by the mating planet. This segment of the gear was modelled by using the conventional finite element (FE) method with the same boundary conditions applied in order to simulate the actual support conditions. These models do not

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