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The present work is aimed at predicting the static and dynamic behavior of geared transmissions comprising flexible components. The proposed model adopts a hybrid approach, combining classical beam elements, elastic foundations for the simulation of tooth contacts, and substructures derived from three-dimensional (3D) finite element grids for thin-rimmed gears and their supporting shafts. The pinion shaft and body are modeled via beam elements which simulate bending, torsion and traction. Tooth contact deflections are described using time-varying elastic foundations (Pasternak foundations) connected by independent contact stiffness. In order to account for thin-rimmed gears, a 3D finite element model of the gear (excluding teeth) is set up and a pseudo-modal reduction technique is used prior to solving the equations of motion. Depending on the gear structure, the results reveal a potentially significant influence of thin rims on both quasi-static and dynamic tooth loading.
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Bettaieb et al. (2006) studied this question.
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