National foreword

This British Standard is the UK implementation of ISO 21771‑1:2024. It supersedes BS ISO 21771:2007, which is withdrawn.

The UK participation in its preparation was entrusted to Technical Committee MCE/5, Gears.

A list of organizations represented on this committee can be obtained on request to its committee manager.

Contractual and legal considerations

This publication has been prepared in good faith, however no representation, warranty, assurance or undertaking (express or implied) is or will be made, and no responsibility or liability is or will be accepted by BSI in relation to the adequacy, accuracy, completeness or reasonableness of this publication. All and any such responsibility and liability is expressly disclaimed to the full extent permitted by the law.

This publication is provided as is, and is to be used at the recipient’s own risk.

The recipient is advised to consider seeking professional guidance with respect to its use of this publication.

This publication is not intended to constitute a contract. Users are responsible for its correct application.

Compliance with a British Standard cannot confer immunity from legal obligations.

This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 October 2024.

Foreword

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The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of ISO document should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

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This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 1, Nomenclature and wormgearing.

This first edition of ISO 21771‑1 cancels and replaces ISO 21771:2007, which has been technically revised.

The main changes are as follows:

the sign convention for internal gears used in the ISO 6336 series^[⁸^] has been adopted. The negative value for the number of teeth of an internal gear is applied to the diameters and centre distance, so these dimensions of internal gears have negative values;
flank direction has been renamed as hand of helix and sign (+/-) of helix angle is used;
a definition of normal surface has been added and this is used rather than normal plane;
the annex on tooth thickness was removed because it is now addressed in ISO 21771‑2.

Additional material has been added to cover:

calculation of form diameters for tooth tip corner radius and tooth root fillet radius in the transverse plane for an involute cylindrical gear (Clauses 10, 11 and Annex B);
calculation of the tooth tip corner radius for a specified form diameter and tip diameter of an involute cylindrical gear;
calculation of a radius tangent to the involutes of adjacent teeth at root or tip diameter (Annex A);
generated tooth root fillet shape for individual involute cylindrical gears (Annex B);
concepts and parameters for involute cylindrical gear pairs with crossed axes (Clause 6 and Annex C);
geometry of surfaces in contact (Annex D);
projection of a transverse plane profile of a tooth onto another plane (Annex E);
interface to ISO 10828 for involute worm gear geometry (Annex F).

A list of all parts in the ISO 21771 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

1 Scope

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.

2 Normative references

3 Terms, definitions, symbols, subscripts and units

3.1 Terms and definitions

3.2 Symbols

3.3 Subscripts

3.4 Units and conventions

4 Individual cylindrical gears

4.1 General

4.2 Concepts for an individual gear

4.3 Reference surfaces, datum lines and reference quantities

4.4 Involute helicoids

4.5 Angular pitch and pitches

4.6 Diameters of gear teeth

4.7 Gear tooth depth

4.8 Tooth thickness and space width

4.9 Radii of curvature of the tooth flanks in different planes

4.10 Tilt angle of contact line

5 Parallel axis cylindrical gear pairs

5.1 General

5.2 Concepts for a gear pair

5.3 Mating quantities

5.4 Calculation of the sum of the profile shift coefficients

5.5 Tooth engagement

5.6 Backlash

5.7 Velocities and sliding conditions at the tooth flanks

6 Crossed axis cylindrical gear pairs

6.1 General

6.2 Concepts for a gear pair

6.3 Mating quantities

6.4 Tooth engagement

6.5 Backlash

6.6 Sliding conditions at the tooth flanks

7 Principal radii of curvature of the tooth flanks

7.1 General

7.2 Angle between the principal radius of curvature at point of contact

7.3 Particularities for crossed axis helical involute gear

7.4 Equivalent radii of curvature at point of contact

8 Tooth flank modifications

8.1 General

8.2 Tooth modifications which restrict the usable flank

8.3 Transverse profile modifications

8.4 Flank line (helix) modifications

8.5 Flank face modifications

8.6 Descriptions of modifications by functions

9 Geometrical limits

9.1 General

9.2 Counterpart rack tooth profile and rack tool profile

9.3 Machining allowance

9.4 Limits of normal tooth thickness

9.5 Generating profile shift, generating profile shift coefficient

9.6 Generated root diameter

9.7 Usable area of the tooth flank, tip and root form diameter

9.8 Undercut

9.9 Overcut

9.10 Minimum tooth thickness at the tip circle of a gear

10 Start of involute for hob or rack type cutters

10.1 Formulae of involute and trochoid

10.2 Undercut conditions

10.3 Determination of start of involute

10.4 Determination of radius of curvature of trochoid

11 Start of involute calculation in case of pinion-type cutter

11.1 Geometry of pinion-type cutter

11.2 Undercut condition

11.3 Determination of start of involute when no undercut exists

11.4 Start of involute when there is undercut

Bibliography

BS ISO 21771-1:2024

Cylindrical involute gears and gear pairs - Concepts and geometry

Current, Under Review

Published:

31 Oct 2024