ISO 21771-1:2024
(Main)Cylindrical involute gears and gear pairs — Part 1: Concepts and geometry
Cylindrical involute gears and gear pairs — Part 1: Concepts and geometry
This document specifies the geometric concepts and parameters for cylindrical gears with involute helicoid tooth flanks. Flank modifications are included. The formulae in this document apply to all pressure angles. It also covers the concepts and parameters for involute cylindrical gear pairs with parallel or crossed axes, and a constant gear ratio. Gear and mating gear in these gear pairs have the same basic rack tooth profile.
Roues et engrenages cylindriques en développante de cercle — Partie 1: Concepts et géométrie
General Information
Relations
Standards Content (Sample)
International
Standard
ISO 21771-1
First edition
Cylindrical involute gears and
2024-10
gear pairs —
Part 1:
Concepts and geometry
Roues et engrenages cylindriques en développante de cercle —
Partie 1: Concepts et géométrie
Reference number
© ISO 2024
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Contents Page
Foreword .vii
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols, subscripts and units . 1
3.1 Terms and definitions .1
3.2 Symbols .2
3.3 Subscripts .9
3.4 Units and conventions .10
3.4.1 Units .10
3.4.2 Conventions .10
4 Individual cylindrical gears . 10
4.1 General .10
4.2 Concepts for an individual gear .11
4.2.1 Gear, cylindrical gear, external gear and internal gear .11
4.2.2 Tooth system, external teeth and internal teeth .11
4.2.3 Tooth and tooth space .11
4.2.4 Tooth system parameters .11
4.2.5 Number of teeth and sign of number of teeth.11
4.2.6 Tooth number . 12
4.2.7 Top land and bottom land . 12
4.2.8 Tooth flanks and flank sections . 12
4.3 Reference surfaces, datum lines and reference quantities . 13
4.3.1 Reference surface and datum face . 13
4.3.2 Reference rack . 13
4.3.3 Basic rack tooth profile for involute gear teeth .14
4.3.4 Reference cylinder, reference circle and reference diameter . 15
4.3.5 Gear axis . 15
4.3.6 Sections through a cylindrical gear . 15
4.3.7 Module .16
4.3.8 Diametral pitch .16
4.3.9 Facewidth . .16
4.3.10 Profile shift, profile shift coefficient and sign of profile shift .17
4.4 Involute helicoids .18
4.4.1 Generator of involute helicoids .18
4.4.2 Base cylinder, base circle and base diameter .19
4.4.3 Transverse pressure angle at a point and transverse pressure angle .19
4.4.4 Normal pressure angle at a point and normal pressure angle . 20
4.4.5 Involute function . 20
4.4.6 Lead .21
4.4.7 Helix angle and lead angle.21
4.4.8 Hand of helix . 22
4.4.9 Roll angle of the involute . 23
4.4.10 Radius of curvature of the involute and length of roll . 23
4.4.11 Length of involute profile, L . 23
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4.5 Angular pitch and pitches . 23
4.5.1 Angular pitch . 23
4.5.2 Pitches on the reference cylinder . 23
4.5.3 Pitches on any cylinder .24
4.5.4 Axial pitch . 25
4.5.5 Base pitch . 25
4.6 Diameters of gear teeth . 25
4.6.1 General . 25
4.6.2 V-cylinder and V-circle diameter . 26
4.6.3 y-cylinder and y-circle diameter . 26
iii
4.6.4 Tip alteration coefficient . 26
4.6.5 Tip cylinder, tip circle and tip diameter . 26
4.6.6 Profile control diameter, d . 26
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4.6.7 Root cylinder, root circle and root diameter . 26
4.7 Gear tooth depth .27
4.7.1 Tooth depth .27
4.7.2 Addendum, working addendum, dedendum and working dedendum .27
4.8 Tooth thickness and space width .27
4.8.1 General .27
4.8.2 Transverse tooth thickness .27
4.8.3 Transverse tooth thickness half angle . 28
4.8.4 Transverse space width . 29
4.8.5 Transverse space width half angle . 29
4.8.6 Normal tooth thickness . 29
4.8.7 Normal space width . . 29
4.9 Radii of curvature of the tooth flanks in different planes . 30
4.10 Tilt angle of contact line .31
5 Parallel axis cylindrical gear pairs .32
5.1 General .32
5.2 Concepts for a gear pair .
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