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 / dyG )(alphaG)(yG) is written as (d) (alphaG) (yG)
Example in Formula (B.14): (d 2 / dyG2 )(alphaG)(yG) is written as (d) 2(alphaG) (yG)
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
This document describes the thread profiles of the five most common worm profile types and provides formulae of their axial profiles.
The five worm profile types covered in this document are designated by the letters A, C, I, K and N.
This document provides the formulae to calculate the path of contact, the conjugate profile of the worm wheel, the lines of contact, the radius of curvature and the velocities at points of contact. The application of those formulae to calculate parameters used in load capacity calculations are provided in 11.11.
NORMATIVE REFERENCES
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 701, International gear notation — Symbols for geometrical data
ISO 1122-2, Vocabulary of gear terms — Part 2: Definitions related to worm gear geometry
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