Error-sensitivity analysis of hourglass worm gearing with spherical meshing elements

• The errors and the variations are quantified.
• The error-variation equation is developed.
• The error-sensitivity formulas are deduced.
• The influence levels of different errors are analyzed.

This paper aims to study the influence of tooth errors and shaft misalignments on the tooth contact in hourglass worm gearing with spherical meshing elements. The geometries of the worm and worm-gear tooth surfaces are described, and the distribution characteristic of contact lines is explored. Based on the common moving frame of conjugate tooth surfaces, the errors and the variations are quantified, and the error-variation equation is developed; in order to evaluate the influence levels of different errors, the error-sensitivity formulas are deduced and illustrated by a numerical example. The results provide a theoretical basis for the manufacture and the tooth contact analysis of hourglass worm pair with spherical meshing elements.