SIST ISO 10300-3:2015
Calculation of load capacity of bevel gears - Part 3: Calculation of tooth root strength
Calculation of load capacity of bevel gears - Part 3: Calculation of tooth root strength
ISO 10300-3:2014 specifies the fundamental formulae for use in the tooth root stress calculation of straight and helical (skew), Zerol and spiral bevel gears including hypoid gears, with a minimum rim thickness under the root of 3,5 mmn. All load influences on tooth root stress are included, insofar as they are the result of load transmitted by the gearing and able to be evaluated quantitatively. Stresses, such as those caused by the shrink fitting of gear rims, which are superposed on stresses due to tooth loading, are intended to be considered in the calculation of the tooth root stress, σF, or the permissible tooth root stress σFP. ISO 10300-3:2014 is not applicable in the assessment of the so-called flank breakage, a tooth internal fatigue fracture (TIFF).
The formulae in ISO 10300-3:2014 are based on virtual cylindrical gears and restricted to bevel gears whose virtual cylindrical gears have transverse contact ratios of Ɛvα
Calcul de la capacité de charge des engrenages coniques - Partie 3: Calcul de la résistance du pied de dent
Izračun nosilnosti stožčastih zobnikov - 3. del: Izračun nosilnosti zobnega korena
Ta del standarda ISO 10300 določa osnovne formule, ki se uporabljajo pri izračunu obremenitve zobnega korena ravnih, valjastih (poševnih) Zerol in spiralnih stožčastih zobnikov, vključno s hipoidnimi zobniki, z minimalno debelino venca pod korenom 3,5 mmn. Vključeni so vsi vplivi obremenitve na obremenitev zobnega korena, če so posledica obremenitve, prenesene z gonilom, in se lahko količinsko ocenijo. Obremenitve, kot so tiste, ki jih povzroči tolerančno vpenjanje zobatih vencev, superponiranih pri obremenitvah, povezanih z obremenitvijo zob, je treba upoštevati pri izračunu obremenitev zobnega korena, σF, ali dovoljene obremenitve zobnega korena σFP. Ta del standarda ISO 10300 se ne uporablja za oceno tako imenovane lomljivosti zobnih bokov oziroma lomljivosti notranje utrujenosti zoba (TIFF).
Formule v tem delu standarda ISO 10300 temeljijo na umišljenih valjastih zobnikih in so omejene na stožčaste zobnike z umišljenimi valjastimi zobniki s profilno stopnjo prekrivanja εvα < 2. Rezultati so veljavni znotraj obsega uporabljenih faktorjev iz standarda ISO 10300-1 (glej tudi ISO 6336-3[1]). Poleg tega se navedena razmerja uporabljajo za stožčaste zobnike, pri katerih je vsota koeficientov profilnega premika zobatega kolesca in kolesa nič (glej ISO 23509).
Ta del standarda ISO 10300 se ne uporablja za stopnje odpornosti, ki presegajo stopnje, dovoljene za 103 cikle, ker bi lahko obremenitve v tem obsegu presegle elastično omejitev zobnikovih zob. Opozorilo – Uporabnika opozarjamo, da naj bi se pri uporabi formul za velike povprečne srednje spiralne kote (βm1 + βm2)/2 > 45°, za kote efektivnega tlaka αe > 30° in/ali za veliko širino zoba b > 13 mmn izračunan rezultat ISO 10300 (vsi deli) potrdil z izkušnjami.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-marec-2015
1DGRPHãþD
SIST ISO 10300-3:2008
,]UDþXQQRVLOQRVWLVWRåþDVWLK]REQLNRYGHO ,]UDþXQQRVLOQRVWL]REQHJDNRUHQD
Calculation of load capacity of bevel gears - Part 3: Calculation of tooth root strength
Calcul de la capacité de charge des engrenages coniques - Partie 3: Calcul de la
résistance du pied de dent
Ta slovenski standard je istoveten z: ISO 10300-3:2014
ICS:
21.200 Gonila Gears
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 10300-3
Second edition
2014-04-01
Calculation of load capacity of bevel
gears —
Part 3:
Calculation of tooth root strength
Calcul de la capacité de charge des engrenages coniques —
Partie 3: Calcul de la résistance du pied de dent
Reference number
©
ISO 2014
© ISO 2014
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2014 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, units and abbreviated terms . 2
5 General rating procedure . 2
6 Gear tooth rating formulae — Method B1 . 3
6.1 Tooth root stress formula . 3
6.2 Permissible tooth root stress . 4
6.3 Calculated safety factor . 5
6.4 Tooth root stress factors . 5
6.5 Permissible tooth root stress factors .13
7 Gear tooth rating formulae — Method B2 .17
7.1 Tooth root stress formula .17
7.2 Permissible tooth root stress .17
7.3 Calculated safety factor .18
7.4 Tooth root stress factors .18
7.5 Permissible tooth root stress factors .36
8 Factors for permissible tooth root stress common for method B1 and method B2 .36
8.1 Size factor, Y .36
X
8.2 Life factor, Y .38
NT
Bibliography .41
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
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 documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2. www.iso.org/directives
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any
patent rights identified during the development of the document will be in the Introduction and/or on
the ISO list of patent declarations received. www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity
calculation.
This second edition cancels and replaces the first edition (ISO 10300-3:2001), which has been technically
revised.
ISO 10300 consists of the following parts, under the general title Calculation of load capacity of bevel
gears:
— Part 1: Introduction and general influence factors
— Part 2: Calculation of surface durability (pitting)
— Part 3: Calculation of tooth root strength
iv © ISO 2014 – All rights reserved
Introduction
When ISO 10300:2001 (all parts, withdrawn) became due for (its first) revision, the opportunity was
taken to include hypoid gears, since previously the series only allowed for calculating the load capacity
of bevel gears without offset axes. The former structure is retained, i.e. three parts of the ISO 10300
series, together with ISO 6336-5, and it is intended to establish general principles and procedures for
rating of bevel gears. Moreover, ISO 10300 (all parts) is designed to facilitate the application of future
knowledge and developments, as well as the exchange of information gained from experience.
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, it was agreed to include a
separate clause: “Gear tooth rating formulae — Method B2” in this part of ISO 10300, while the former
methods B and B1 were combined into one method, i.e. method B1. So, it became necessary to present
a new, clearer structure of the three parts, which is illustrated in ISO 10300-1:2014, Figure 1. Note,
ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when method B2.
Failure of gear teeth by breakage can be brought about in many ways; severe instantaneous overloads,
excessive pitting, case crushing and bending fatigue are a few. The strength ratings determined by the
formulae in this part of ISO 10300 are based on cantilever projection theory modified to consider the
following:
— compressive stress at the tooth roots caused by the radial component of the tooth load;
— non-uniform moment distribution of the load, resulting from the inclined contact lines on the teeth
of spiral bevel gears;
— stress concentration at the tooth root fillet;
— load sharing between adjacent contacting teeth;
— lack of smoothness due to a low contact ratio.
The formulae are used to determine a load rating, which prevents tooth root fracture during the design
life of the bevel gear. Nevertheless, if there is insufficient material under the teeth (in the rim), a fracture
can occur from the root through the rim of the gear blank or to the bore (a type of failure not covered
by this part of ISO 10300). Moreover, it is possible that special applications require additional blank
material to support the load.
Surface distress (pitting or wear) can limit the strength rating, either due to stress concentration
around large sharp cornered pits, or due to wear steps on the tooth surface. Neither of these effects is
considered in this part of ISO 10300.
In most cases, the maximum tensile stress at the tooth root (arising from bending at the root when the
load is applied to the tooth flank) can be used as a determinant criterion for the assessment of the tooth
root strength. If the permissible stress number is exceeded, the teeth can break.
When calculating the tooth root stresses of straight bevel gears, this part of ISO 10300 starts from the
assumption that the load is applied at the tooth tip of the virtual cylindrical gear. The load is subsequently
converted to the outer point of single tooth contact. The procedure thus corresponds to method C for the
[1]
tooth root stress of cylindrical gears (see ISO 6336-3 ).
For spiral bevel and hypoid gears with a high face contact ratio of ε > 1 (method B1) or with a modified
vβ
contact ratio of ε > 2 (method B2), the midpoint in the zone of action is regarded as the critical point
vγ
of load application.
The breakage of a tooth generally means the end of a gear’s life. It is often the case that all gear teeth are
destroyed as a consequence of the breakage of a single tooth. A safety factor, S , against tooth breakage
F
higher than the safety factor against damage due to pitting is, therefore, generally to be preferred
(see ISO 10300-1).
INTERNATIONAL STANDARD ISO 10300-3:2014(E)
Calculation of load capacity of bevel gears —
Part 3:
Calculation of tooth root strength
1 Scope
This part of ISO 10300 specifies the fundamental formulae for use in the tooth root stress calculation
of straight and helical (skew), Zerol and spiral bevel gears including hypoid gears, with a minimum rim
thickness under the root of 3,5 m . All load influences on tooth root stress are included, insofar as
mn
they are the result of load transmitted by the gearing and able to be evaluated quantitatively. Stresses,
such as those caused by the shrink fitting of gear rims, which are superposed on stresses due to tooth
loading, are intended to be considered in the calculation of the tooth root stress, σ , or the permissible
F
tooth root stress σ . This part of ISO 10300 is not applicable in the assessment of the so-called flank
FP
breakage, a tooth internal fatigue fracture (TIFF).
The formulae in this part of ISO 10300 are based on virtual cylindrical gears and restricted to bevel
gears whose virtual cylindrical gears have transverse contact ratios of ε < 2. The results are valid
vα
[1]
within the range of the applied factors as specified in ISO 10300-1 (see also ISO 6336-3 ). Additionally,
the given relationships are valid for bevel gears, of which the sum of profile shift coefficients of pinion
and wheel is zero (see ISO 23509).
This part of ISO 10300 does not apply to stress levels above those permitted for 10 cycles, as stresses
in that range could exceed the elastic limit of the gear tooth.
Warning — The user is cautioned that when the formulae are used for large average mean spiral
angles (β + β )/2 > 45°, for effective pressure angles α > 30° and/or for large face widths
m1 m2 e
b > 13 m , the calculated results of ISO 10300 (all parts) should be confirmed by experience.
mn
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable to its applica
...
INTERNATIONAL ISO
STANDARD 10300-3
Second edition
2014-04-01
Calculation of load capacity of bevel
gears —
Part 3:
Calculation of tooth root strength
Calcul de la capacité de charge des engrenages coniques —
Partie 3: Calcul de la résistance du pied de dent
Reference number
©
ISO 2014
© ISO 2014
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2014 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, units and abbreviated terms . 2
5 General rating procedure . 2
6 Gear tooth rating formulae — Method B1 . 3
6.1 Tooth root stress formula . 3
6.2 Permissible tooth root stress . 4
6.3 Calculated safety factor . 5
6.4 Tooth root stress factors . 5
6.5 Permissible tooth root stress factors .13
7 Gear tooth rating formulae — Method B2 .17
7.1 Tooth root stress formula .17
7.2 Permissible tooth root stress .17
7.3 Calculated safety factor .18
7.4 Tooth root stress factors .18
7.5 Permissible tooth root stress factors .36
8 Factors for permissible tooth root stress common for method B1 and method B2 .36
8.1 Size factor, Y .36
X
8.2 Life factor, Y .38
NT
Bibliography .41
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
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 documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2. www.iso.org/directives
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any
patent rights identified during the development of the document will be in the Introduction and/or on
the ISO list of patent declarations received. www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity
calculation.
This second edition cancels and replaces the first edition (ISO 10300-3:2001), which has been technically
revised.
ISO 10300 consists of the following parts, under the general title Calculation of load capacity of bevel
gears:
— Part 1: Introduction and general influence factors
— Part 2: Calculation of surface durability (pitting)
— Part 3: Calculation of tooth root strength
iv © ISO 2014 – All rights reserved
Introduction
When ISO 10300:2001 (all parts, withdrawn) became due for (its first) revision, the opportunity was
taken to include hypoid gears, since previously the series only allowed for calculating the load capacity
of bevel gears without offset axes. The former structure is retained, i.e. three parts of the ISO 10300
series, together with ISO 6336-5, and it is intended to establish general principles and procedures for
rating of bevel gears. Moreover, ISO 10300 (all parts) is designed to facilitate the application of future
knowledge and developments, as well as the exchange of information gained from experience.
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, it was agreed to include a
separate clause: “Gear tooth rating formulae — Method B2” in this part of ISO 10300, while the former
methods B and B1 were combined into one method, i.e. method B1. So, it became necessary to present
a new, clearer structure of the three parts, which is illustrated in ISO 10300-1:2014, Figure 1. Note,
ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when method B2.
Failure of gear teeth by breakage can be brought about in many ways; severe instantaneous overloads,
excessive pitting, case crushing and bending fatigue are a few. The strength ratings determined by the
formulae in this part of ISO 10300 are based on cantilever projection theory modified to consider the
following:
— compressive stress at the tooth roots caused by the radial component of the tooth load;
— non-uniform moment distribution of the load, resulting from the inclined contact lines on the teeth
of spiral bevel gears;
— stress concentration at the tooth root fillet;
— load sharing between adjacent contacting teeth;
— lack of smoothness due to a low contact ratio.
The formulae are used to determine a load rating, which prevents tooth root fracture during the design
life of the bevel gear. Nevertheless, if there is insufficient material under the teeth (in the rim), a fracture
can occur from the root through the rim of the gear blank or to the bore (a type of failure not covered
by this part of ISO 10300). Moreover, it is possible that special applications require additional blank
material to support the load.
Surface distress (pitting or wear) can limit the strength rating, either due to stress concentration
around large sharp cornered pits, or due to wear steps on the tooth surface. Neither of these effects is
considered in this part of ISO 10300.
In most cases, the maximum tensile stress at the tooth root (arising from bending at the root when the
load is applied to the tooth flank) can be used as a determinant criterion for the assessment of the tooth
root strength. If the permissible stress number is exceeded, the teeth can break.
When calculating the tooth root stresses of straight bevel gears, this part of ISO 10300 starts from the
assumption that the load is applied at the tooth tip of the virtual cylindrical gear. The load is subsequently
converted to the outer point of single tooth contact. The procedure thus corresponds to method C for the
[1]
tooth root stress of cylindrical gears (see ISO 6336-3 ).
For spiral bevel and hypoid gears with a high face contact ratio of ε > 1 (method B1) or with a modified
vβ
contact ratio of ε > 2 (method B2), the midpoint in the zone of action is regarded as the critical point
vγ
of load application.
The breakage of a tooth generally means the end of a gear’s life. It is often the case that all gear teeth are
destroyed as a consequence of the breakage of a single tooth. A safety factor, S , against tooth breakage
F
higher than the safety factor against damage due to pitting is, therefore, generally to be preferred
(see ISO 10300-1).
INTERNATIONAL STANDARD ISO 10300-3:2014(E)
Calculation of load capacity of bevel gears —
Part 3:
Calculation of tooth root strength
1 Scope
This part of ISO 10300 specifies the fundamental formulae for use in the tooth root stress calculation
of straight and helical (skew), Zerol and spiral bevel gears including hypoid gears, with a minimum rim
thickness under the root of 3,5 m . All load influences on tooth root stress are included, insofar as
mn
they are the result of load transmitted by the gearing and able to be evaluated quantitatively. Stresses,
such as those caused by the shrink fitting of gear rims, which are superposed on stresses due to tooth
loading, are intended to be considered in the calculation of the tooth root stress, σ , or the permissible
F
tooth root stress σ . This part of ISO 10300 is not applicable in the assessment of the so-called flank
FP
breakage, a tooth internal fatigue fracture (TIFF).
The formulae in this part of ISO 10300 are based on virtual cylindrical gears and restricted to bevel
gears whose virtual cylindrical gears have transverse contact ratios of ε < 2. The results are valid
vα
[1]
within the range of the applied factors as specified in ISO 10300-1 (see also ISO 6336-3 ). Additionally,
the given relationships are valid for bevel gears, of which the sum of profile shift coefficients of pinion
and wheel is zero (see ISO 23509).
This part of ISO 10300 does not apply to stress levels above those permitted for 10 cycles, as stresses
in that range could exceed the elastic limit of the gear tooth.
Warning — The user is cautioned that when the formulae are used for large average mean spiral
angles (β + β )/2 > 45°, for effective pressure angles α > 30° and/or for large face widths
m1 m2 e
b > 13 m , the calculated results of ISO 10300 (all parts) should be confirmed by experience.
mn
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable to its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials
ISO 10300-1:2014, Calculation of load capacity of bevel gears — Part 1: Introduction and general influence
factors
ISO 10300-2:2014, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability
(pitting)
ISO 23509:2006, Bevel and hypoid gear geometry
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1122-1 and ISO 23509
(geometrical gear terms) and the following apply.
3.1
tooth root breakage
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.