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Planetary gearboxes in highly sophisticated applications such as turbofan engines are required to have a high power-to-weight ratio and excellent reliability. Hence, thin-rimmed gear units need to be designed as compact as possible which, however, is usually limited by the tooth root load capacity. In order to come up with the best design, a tooth root shape optimization process is developed for thin-rimmed planet gears.
Zhe paper introduces ideas from shape optimization to multibody system dynamics. A disk rolling down a given slope is taken as a simple example, for which it is the goal of the optimization to shape the rolling contour of the disk such that it takes a minimum time to cover a certain distance. The shape of the sontour is described by its radius of curvature. The governing equations of motion result from the kinematics of relative motion and the Nowton-Euler formalism. Three different kinds of spirals are defined and optimized.