On the Bending Stress of a Spur Gear : 1 st Report, Stress at the Fillet Curve and Inner Stress at the Root of Gear Tooth

Abstract

The present study was carried out for the purpose of calculating the bending stress of a gear tooth theoretically and finding the bending strength of a spur gear. Using the two-dimensional elastic theory and the transform function, the authors introduced equations for the calculation of the stress at the fillet curve of a gear tooth. Investigating the stress calculated by these equations in various loading conditions, the authors reached the conclusion that it was reasonable to take the shearing force into consideration for the calculation of the bending stress of a gear tooth. Then they introduced equations for the calculation of the inner stress, and obtained the following result : the inner stress shows a smaller value than the stress at the fillet curve, so it is reasonable to determine the bending strength of a gear tooth by calculating the maximum stress at the fillet curve.