Strength Calculation of Planar Double-Enveloping Hourglass Worm Gears

In order to simplify the calculation method for bearing capacity of planar double enveloping hourglass worm gears, a contact stress analytic formula for the worm drive was proposed through regression analysis and interpolation method based on the Hertz theory. The bending strength calculation formula was improved by taking into consideration the load distribution coefficient among the meshing teeth. According to the contact finite element model of the worm-gears, three-dimensional stress distribution of the gears was obtained. The results show that the contact stress (or bending strength) obtained by the analysis formula is 6%—16% larger than that by the finite element method, and the analysis formula can meet the requirements for engineering use. The contact stress distribution is in a declining L shape along the contact line. As the load of the worm gear increased from 1 N·m to the rated value, the maximal load distribution coefficient among 5 pairs of meshing gears decreased from 32.4% to 27.5%.