Meshing theory and error sensitivity of mismatched conical surface enveloping conical worm pair

Abstract

The point-contact meshing theory is well established for a mismatched conical surface enveloping conical worm pair. The contact equations with nine unknowns are established to ascertain the momentary contact points. In order to solve preceding equations expediently, the elimination artifice is adopted to transform it into its equivalent form with three unknowns. A datum point, where the drive ratio error of the worm pair equals zero, is also determined by solving a modified contact equation group. The angular position relationship between the two moving frames located at the contact point is made clear, and the relative principal curvatures are obtained correctly. The computing methods of the drive ratio error and the transmission error of the worm pair are elaborated systemically. The numerical results indicate that the mismatched worm pair has excellent meshing behavior and is insensitive to the assembly errors on the whole. Comparatively speaking, the worm pair is slightly more sensitive to the shaft angle error than to other types of errors. The error sensitivity of the worm wheel convex tooth surface is somewhat higher than its concave tooth surface.