Finite Element Method Analysis of a Spur Gear with a Corrected Profile

The difference between the stress value calculated by a two-dimensional finite element model of spur gears and those obtained by the rules in ISO 6336 was evaluated. Hertz theory, which provides information on the extension of the contact area and the maximum value of the contact pressure, was used to choose the dimensions of the elements. The mesh was created using the stress analytical solution relative to a model consisting of two cylinders in contact. Analogous optimization was executed for the mesh of the teeth feet; a mesh of 15 elements was considered optimum, because it minimized the difference to 0.5 per cent in the bending stress calculation. Stress values, obtained using the finite element method (FEM), are generally lower than those obtained with the ISO rules. Hence, this approach yields a conservative determination of the effective material strength. In all the examined cases, the difference was less than 2.5 per cent. The set FEM technique gives a result accuracy of better than 1 per cent; the difference between the stress obtained by FEM and those obtained by ISO 6336 is less than 2.5 per cent, so that the FEM confirmed, consistent with the ISO rules, that correction of the profile results in significant benefits with respect to determination of the mechanical resistance of spur gears.