Analytical method for calculating the nominal tooth root stress in worm gear shafts

According to the state of the art, worm gears are designed due to the softer bronze-material of the worm wheel primarily against damage of the wheel because of wear, pitting or breakage of the teeth. The aim of research in the last decades is to optimize the load capacity on the worm wheel by using higher-strength bronze alloys, cast iron or steel to increase the transmission capacity of worm gears. This development may lead to an increased number of damage cases on the worm shaft. In literature, documented cases of tooth segment fractures of the worm shaft can already be found. Since the worm is only designed against deflection according to the state of the art, there is a need for a method to calculate the material stress in worm shafts. This paper presents an analytical method based on the nominal stress approach for calculating bending, compression, and shear stresses in the tooth root of worm shafts to close this gap. The stresses resulting from different load distributions in the tooth contact due to assembly deviations are calculated with the presented method and compared with results from the Finite Element Method.