A numerical approach to the static analysis of an annular sector mindlin plate with applications to bevel gear design

Abstract A numerical procedure based on the Rayleigh-Ritz method is used to determine the flexural behavior of a cantilevered annular sector plate of variable rigidity, including the effects of shear deformation. The Ritz method used employs algebraic polynomial trial functions in two dimensions to obtain the deflections and stresses in the shear flexible sector plate. Convergence is investigated, with attention being given to the number of terms taken for each coordinate direction. The application of the mathematical model to predict the deflections and root stresses in a straight bevel gear is demonstrated. The compliance computations based on the sector plate model can be readily integrated into existing computer codes for bevel gear design to determine the load distribution and transmission error. Numerical results are compared with previously published results wherever available and finite element methods.

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