A rayleigh-ritz approach to modeling bending and shear deflections of gear teeth

Abstract The Rayleigh-Ritz energy method was used to study the shear effect of an involute gear tooth. The gear tooth was simulated by a tapered plate model subjected to a concentrated load. The plate deflections, including shear deformation, were determined and compared with the theoretical values and experimental data. The comparisons indicate that the deflections of the shear plate model are higher than those computed from the thin plate models which neglects the shear effects. On the other hand, the experimental results are higher than those of the shear plate model due to the base flexibilities of the experimental models. The shear model deflections are also shown to be in excellent agreement with finite element results. The shear plate model could replace the finite element model since it is more computationally efficient and its results are accurate enough for most engineering purposes.

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