Strength model for bending and pitting calculations of internal spur gears

Abstract

An enhanced model for strength calculations of internal spur gear pairs is presented. The load sharing among couples of teeth in simultaneous contact is determined from the meshing stiffness, whose value has been calculated at any point of the path of contact, considering bending, compressive, shear and Hertzian deflections. This curve of variation of the meshing stiffness has been expressed by means of an approximate accurate equation, as a function of the effective contact ratio exclusively, allowing to express the load at each couple of teeth in a closed form. The values of the bending and pitting stresses along the path of contact have been accordingly computed, as well as their nominal values and their corresponding determinant load conditions. An adapted formulation of the meshing stiffness curve for non-standard tooth dimensions–including reduced tooth height, frequently required to avoid secondary interference–has been also developed. Calculation methods for the nominal stresses for these non-standard internal gears have been presented as well.