INTRODUCTION

This document includes the formulation for the geometrical dimensions of the worm and worm wheel, and that for the determination of gear mesh geometry (path of contact, zone and lines of contact) with the details to determine the non-dimensional parameters used to apply load capacity calculations (radius of curvature, sliding velocities). Thread forms of the worms of worm gear pairs are commonly related to the following machining processes:

— the type of machining process (turning, milling, grinding, metal forming);

— the shapes of edges or surfaces of the cutting tools used;

— the tool position relative to an axial plane of the worm;

— where relevant, the diameters of disc type tools (grinding wheel diameter).

The calculations developed in this document are relatively complex as they involved primary and secondary derivatives of mathematical expression. In order to facilitate the writing of equations, the numerators in the left part of formulae are often omitted; this is why several formulae have special symbols and are not written in a mathematical way:

Example in Formula (B.12): (d / dy_G )(alpha_G)(y_G) is written as (d) (alpha_G) (y_G)

Example in Formula (B.14): (d ² / dy_G² )(alpha_G)(y_G) is written as (d) 2(alpha_G) (y_G)

In this document, the figures show a generic representation of worm profile types A, I, N, K, C. For the influence of different worm profile types, see Annex E.

This document introduces all the aspects concerning the gear mesh geometry to define conjugate worm wheel, path of contact, lines of contact and other associated geometrical characteristics.

SCOPE