Calculation of load capacity of spur and helical gears —
Part 3:
Calculation of tooth bending strength

SCOPE: This document specifies the fundamental formulae for use in tooth bending stress calculations for involute external or internal spur and helical gears with a rim thickness sR > 0,5 ht for external gears and sR > 1,75 mn for internal gears. In service, internal gears can experience failure modes other than tooth bending fatigue, i.e. fractures starting at the root diameter and progressing radially outward. This document does not provide adequate safety against failure modes other than tooth bending fatigue. All load influences on the tooth root stress are included in so far as they are the result of loads transmitted by the gears and in so far as they can be evaluated quantitatively.

This document includes procedures based on testing and theoretical studies such as those of Hirt[11], Strasser[14] and Brossmann[10]. The results are in good agreement with other methods (References [5], [6], [7] and [12]). The given formulae are valid for spur and helical gears with tooth profiles in accordance with the basic rack standardized in ISO 53. They can also be used for teeth conjugate to other basic racks if the virtual contact ratio εαn is less than 2,5.

The load capacity determined on the basis of permissible bending stress is termed “tooth bending strength”. The results are in good agreement with other methods for the range, as indicated in the scope of ISO 6336-1.

If this scope does not apply, refer to ISO 6336-1:2019, Clause 4.

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This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity calculation.

This third edition cancels and replaces the second edition (ISO 6336-3:2006), which has been technically revised. It also incorporates the Technical Corrigendum ISO 6336-3:2006/Cor.1:2008.

The main changes compared to the previous edition are as follows:

• modification of the Yβ factor in Clause 8 "Helix angle factor, Yβ";
• modification of the YF factor in 6.2 “Calculation of the form factor, YF: Method B”;
• integration of 6.2.4 "Tooth root normal chord, sFn, radius of root fillet, ρF, bending moment arm, hFe, for external gears generated with a shaper cutter";
• integration of 6.2.5 "Tooth root normal chord, sFn, radius of root fillet, ρF, bending moment arm, hFe, for internal gears generated with a shaper cutter";
• integration of a new Annex C.

A list of all parts in the ISO 6336 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.

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