ABSTRACT

The Geometry Factor for Bending Strength, J, also known as AGMA J-factor, is used to assess the tooth-root stress of spur and helical gear teeth. The Information Sheet AGMA 908-B89 presents a calculation method for the AGMA J-factor based on the Lewis’ parabola and computes the stress concentration factor from the minimum curvature radius of the fillet trochoid. Although the presented basic gear geometry is valid for external and internal gears, it was stated that the method for the analytical determination of the AGMA J-factor was not appropriate for internal gears and it was beyond the scope of the Standard. 

By using the Lewis’ method, the tooth section with maximum bending stress is calculated and the tooth-root stress determined. However, the modern definition of tooth-root stress considers other influences than pure bending, and therefore the Information Sheet AGMA 911-B21 suggests considering the highest total stress, including the compressive stress and the stress concentration at the considered section. In addition, the root-fillet trochoid is approximated to a circumference arc and the influence of the number of teeth and shift coefficient of the shaper is neglected.

In this paper, the AGMA J-factor is calculated in four different ways by considering: (i) the maximum total stress and minimum curvature radius of the trochoid fillet, (ii) the maximum total stress and curvature radius at the corresponding tooth section, (iii) the maximum total stress and circular fillet, and (iv) the maximum total stress obtained from FEM analyses. Based on the comparison of the results of the mentioned four approaches, guidelines for the preparation of a proposal for the calculation of the AGMA J-factor for internal gears are provided. It has been demonstrated that for internal gears generated by a shaper, the number of teeth and the profile shift coefficient of the shaper influences the values of the J factor.

Author(s): Alfonso Fuentes-Aznar, José I. Pedrero

ISBN: 978-1-64353-164-9