ISO 6336-1:1996
(Main)Calculation of load capacity of spur and helical gears - Part 1: Basic principles, introduction and general influence factors
Calculation of load capacity of spur and helical gears - Part 1: Basic principles, introduction and general influence factors
Provides together with parts 2, 3 and 5 a method by which different gear designs can be compared. It is not intended to assure the performance of gear systems. Preferably intended for use by the experienced gear designer.
Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale — Partie 1: Principes de base, introduction et facteurs généraux d'influence
Izračun nosilnosti ravnozobih in poševnozobih zobnikov - 1. del: Osnove, uvajanje in koeficienti
General Information
Relations
Frequently Asked Questions
ISO 6336-1:1996 is a standard published by the International Organization for Standardization (ISO). Its full title is "Calculation of load capacity of spur and helical gears - Part 1: Basic principles, introduction and general influence factors". This standard covers: Provides together with parts 2, 3 and 5 a method by which different gear designs can be compared. It is not intended to assure the performance of gear systems. Preferably intended for use by the experienced gear designer.
Provides together with parts 2, 3 and 5 a method by which different gear designs can be compared. It is not intended to assure the performance of gear systems. Preferably intended for use by the experienced gear designer.
ISO 6336-1:1996 is classified under the following ICS (International Classification for Standards) categories: 21.200 - Gears. The ICS classification helps identify the subject area and facilitates finding related standards.
ISO 6336-1:1996 has the following relationships with other standards: It is inter standard links to ISO 6336-1:1996/Cor 2:1999, ISO 6336-1:1996/Cor 1:1998, ISO 6336-1:2006; is excused to SIST ISO 6336-1:2002/TC 1:2002, SIST ISO 6336-1:2002/TC 2:2002, ISO 6336-1:1996/Cor 1:1998, ISO 6336-1:1996/Cor 2:1999. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.
You can purchase ISO 6336-1:1996 directly from iTeh Standards. The document is available in PDF format and is delivered instantly after payment. Add the standard to your cart and complete the secure checkout process. iTeh Standards is an authorized distributor of ISO standards.
Standards Content (Sample)
INTERNATIONAL
IS0
STANDARD
6336-1
First edition
1996-05-15
Calculation of load capacity of spur and
helical gears -
Part 1:
Basic principles, introduction and general
influence factors
Calcul de la capacitg de charge des engrenages cylindriques ;i dentures
droite et h6licoi ’dale -
Partie I: Principes de base, introduction et facteurs g&W-aux d/influence
Reference number
IS0 6336-1:1996(E)
IS0 6336-l :I 996(E)
Contents
Page
................................. iv
Introduction
Scope .
.......................... 2
Normative references
..................... 3
Definitions symbols and units
.............................. 13
Basic principles
.......................... 19
Application factor KA
...................... 19
Internal dynamic factor Kv
................... 37
Face load factors K,+ and KFP
..............
Transverse load factors KHa and KFa
............... 77
Tooth stiffness parameters c’ and cr
Annexes
Guide values for crowning and end relief
A
of teeth of cylindrical gears . . . . . . . . . . . . . . . . . . . . . 85
Guide values for the application factor KA . . . . . . . . . s . 87
B
Derivations and explanatory notes . . . . . . . . . . . . . . . . 90
C
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
D
0 IS0 1996
All rights reserved. Unless otherwise specified, no part of this publication may be
reproduced or utilized in any form or by any means, electronic or mechanical, including
photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
ii
IS0 6336-l :I 996(E)
0 IS0
Foreword
IS0 (the International Organization for Standardization) is a
worldwide federation of national standards bodies (IS0 member
The work of preparing International Standards is
bodies).
normally carried out through IS0 technical committees. Each
member body interested in a subject for which a technical
committee has been established has the right to be represented
International organizations, governmental
on that committee.
and non-governmental, in liaison with ISO, also take part in the
work. IS0 collaborates closely with the International
Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
Draft International Standards adopted by the technical
committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at
least 75 % of the member bodies casting a vote.
International standard IS0 6336-l was prepared by Technical
Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear
capacity calculation.
IS0 6336 consists of the following parts, under the general title
Calculation of load capacity of spur and helical gears:
- Part 7: Basic principles, introduction and general influence
factors
- Part 2: Calculation of surface durability (pitting)
- Part 3: Calculation of tooth bending strength
Part 5: Strength and quality of materials
-
Annexes A to D of this part of IS0 6336 are for information only.
. . .
III
IS0 6336-l :1996(E)
0 IS0
Introduction
This part of IS0 6336 and parts 2, 3 and 5 provide the principles
for a coherent system of procedures for the calculation of the
load capacity of cylindrical involute gears with external or
internal teeth. IS0 6336 is designed to facilitate the application
of future knowledge and developments, also the exchange of
information gained from experience.
Design considerations to prevent fractures emanating from stress
raisers in the tooth flank, tip chipping and failures of the gear
blank through the web or hub should be analyzed by general
machine design methods.
Several methods for the calculation of load capacity, also for the
calculation of various factors are permitted (see 4.1.8). The
directions in IS0 6336 are thus complex, but also flexible. As
appropriate, the more detailed or simplified versions should be
chosen for inclusion in application standards derived from this
basic standard. Such application standards cover the following
fields:
- industrial gears (detailed and simplified method);
- high-speed gears and gears of similar requirements;
- marine gears;
- vehicle gears.
These application standards feature clear, and to some extent
simplified, rules for the calculations.
Included in the formulae are the major factors which are
presently known to affect gear tooth pitting and fractures at the
root fillet. The formulae are in a form that will permit the
addition of new factors to reflect knowledge gained in the future.
IV
IS0 6336-l :I 996(E)
INTERNATIONAL STANDARD 0 IS0
Calculation of load capacity of spur and helical gears
Part 1: Basic principles, introduction and general influence factors
.
1 Scope
11 l Intended use
This part of IS0 6336, together with parts 2, 3 and 5, provides a method by which different gear designs can
be compared. It is not intended to assure the performance of assembled drive gear systems. It is not intended
for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who
is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs
and awareness of the effects of the items discussed.
The formulae in IS0 6336 are intended to establish a uniformly acceptable method for calculating the pitting
resistance and bending strength capacity of cylindrical gears with straight or helical teeth.
IS0 6336 includes procedures based on testing and theoretical studies such as those of Hirt [l], Strasser [2],
and Brossman [3]. The results of rating calculations made by following this method are in good agreement with
previously accepted gear calculations methods (see references [4] through [8]), for normal working pressure
angles up to 25’ and reference helix angles up to 30 ”.
For larger pressure angles and larger helix angles the trends of products YF Ys YP and respectively Z,, Zc Zp
are not the same as those of some earlier methods. The user of IS0 6336 is cautioned that when the methods
in IS0 6336 are used for other helix angles and pressure angles, the calculated results should be confirmed by
experience.
12 . Exceptions
The formulae in IS0 6336 are not applicable when any of the following conditions exist:
- spur gears with transverse contact ratios less than 1 ,O;
- spur or helical gears with transverse contact ratios greater than 2,5;
- where interference exists between tooth tips and root fillets;
- when teeth are pointed;
- when backlash is zero.
The rating formulae in IS0 6336 are not applicable to other types of gear tooth deterioration such as plastic
yielding, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where
there may be an unpredictable profile breakdown The bending strength formulae are applicable to fractures
at the tooth fillet, but are not applicable to fractures on the tooth working surfaces, failure of the gear rim, or
failures of the gear blank through web and hub. IS0 6336 does not apply to teeth finished by forging or
sintering. It is not applicable to gears which have a poor contact pattern.
0 IS0
IS0 6336-l :1996(E)
based on pitting and tooth-root
The procedures in IS0 6336 provide for the calculation of load capacity,
breakage. At pitch line velocities below 1 m/s the gear load capacity is often limited by abrasive wear (see other
literature for information on the calculation for this).
1.2.1
Scuffing
Formulae for scuffing resistance on cylindrical gear teeth are not included in IS0 6336. At the present time,
there is insufficient agreement concerning the method for designing cylindrical gears to resist scuffing failure.
1.2.2 Wear
Very little attention and concern have been devoted to the study of gear tooth wear. This subject primarily
concerns gear teeth with low surface hardness or gears with improper lubrication. No attempt has been made
to cover the subject in IS0 6336.
1.2.3 Micropitting
IS0 6336 does not cover micropitting, which is an additional type of surface distress that may occur on gear
teeth.
1.2.4 Plastic yielding
IS0 6336 does not extend to stress levels greater than those permissible at IO3 cycles or less, since stresses
in this range may exceed the elastic limit of the gear tooth in bending or in surface compressive stress.
Depending on the material and the load imposed, a single stress cycle greater than the limit level at < 1 O3
cycles could result in plastic yielding of the gear tooth.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions of this part
of IS0 6336. At the time of publication, the editions indicated were valid. All standards are subject to revision,
and parties to agreements based on this part of IS0 6336 are encouraged to investigate the possibility of
applying the most recent edition of the standards indicated below. Members of IEC and IS0 maintain registers
of currently valid International Standards.
Cylindrical gears for general and heavy engineering - Basic rack.
IS0 53: 1974,
IS0 468: 1982, Surface roughness - Parameters, their values and general rules for specifying
requirements.
International gear notation
IS0 701: 1976, - Symbols for geometrical data.
IS0 1122-l : 1983, Glossary of gear terms - Part I : Geometrical definitions.
IS0 1328-1: 1995, Cylindrical gears - IS0 system of accuracy - Part I : Definitions and allowable values
of deviations relevant to corresponding flanks of gear teeth.
Calculation of load capacity of spur and helical gears - Part 2: Calculation of surface
IS0 6336-2: 1996,
durability (pitting).
IS0 6336-3: 1996, Calculation of load capacity of spur and helical gears - Part 3: Calculation of tooth
bending strength.
IS0 6336-5: 1996, Calculation of load capacity of spur and helical gears - Part 5: Strength and quality of
material.
ISO/TR 10495: 1996 Calculation of cylindrical gears
- Calculation of service life under variable load.
IS0 6336-l :I 996(E)
0 IS0
3 Definitions, symbols and units
For the purposes of IS0 6336, the definitions given in IS0 1122-I apply.
Symbols are based on and are extensions of the symbols given in IS0 701 and IS0 1328-I. Only symbols for
quantities used for the calculation of the particular factors treated in IS0 6336 are given, together with preferred
units. Table 1 list the symbols used in the calculations for all parts of IS0 6336.
Table 1 - Symbols and abbreviations used within IS0 63364, 2, 3 and 5
Description
Symbol Unit
Principal symbols and abbreviations
-11
center distance mm
facewidth mm
constant
d diameter (without subscript, reference diameter) mm
I
I
auxiliary quantity
deviation, tooth deformation
Pm
path of contact mm
tooth depth (without subscript, root circle to tip circle) mm
i transmission ratio
I
I -1
k addendum truncation factor
I I I
I ( bearing span mm
I I
m module,
mm
mass
kg
n
rotational speed s-’ or min-’
pitch, mm
P
number of planet gears
~~
auxiliary factor,
flexibility of pair of meshing teeth, see clause 9
(mm=pm)/N
material allowance for finish machining, see clause 5 of IS0 6336-3 mm
radius (without subscript, reference radius) mm
tooth thickness, distance between mid-plane of pinion and the middle of the bearing
mm
span
u gear ratio (z2 / z,) 2 1 ‘)
V tangential velocity (without subscript, at the reference circle M tangential velocity at
m/s
pitch circle)
W specific load (per unit facewidth, Ft / b) N/mm
X profile shift coefficient
running-in allowance (only with subscript a or p)
Y
Pm
I I I
~~ ~
Z number of teeth ’)
A, B, C, D, E points on path of contact (pinion root to pinion tip, regardless of whether pinion or
wheel drives, only for geometrical considerations)
total facewidth of double helical gear including gap width mm
I I -1
1) For external gearing a, z,, and z2 are positive; for internal gearing a and z2 have a negative sign, z, has a positive.
0 IS0
IS0 6336-l :I 996(E)
Description Unit
Symbol
constant, coefficient,
C
relief of tooth flank
Pm
mm
D diameter (design)
N/mm2
modulus of elasticity
E
material designation for case-hardening steel, case hardened
Eh
mm
case depth, see IS0 6336-5
Eht
F composite and cumulative deviations,
“N”
force or load
N/mm2
G shear modulus
material designation for grey cast iron
GG
material designation for cast iron (perlitic, bainitic, ferritic structure)
GGG
GTS material designation for black malleable cast iron (perlitic structure)
HB Brine11 hardness
HRC Rockwell hardness (C scale)
HR 30N Rockwell hardness (30 N scale), see IS0 6336-5
Vickers hardness
HV
HV 1 Vickers hardness at load F = 9,81 N, see IS0 6336-5
HV 10 Vickers hardness at load F = 98,lO N, see IS0 6336-5
IF material designation for steel and GGG, flame or induction hardened
Jominy hardenability, see IS0 6336-5
J
K constant, factors concerning tooth load
L lengths (design) mm
moment of a force Nm
M
MX
ME symbols identifying material and heat-treatment requirements, see IS0 6336-5
MQ
ML
N number, exponent, number of load cycles, resonance ratio
material designation for nitriding steel, nitrided
NT
NV material designation for through-hardening and case-hardening steel, nitrided (nitr.),
nitrocarburized (nitrocar.)
P transmitted power kW
S safety factor
St material designation for steel (Ok < 800 N/mm2)
T torque, Nm
tolerance
Pm
V
material designation for through-hardening steel, through-hardened (Ok 2
800 N/mm2)
W weighing factor
Y factor related to tooth-root stress
factor related to contact stress
z
0 IS0 IS0 6336-l :I 996(E)
ISymbol 1 Description Unit
a pressure angle (without subscript, at reference cylinder)
I I
helix angle (without subscript, at reference cylinder)
P
I I I
auxiliary angle,
Y
shear strain,
pinion offset factor, see equations in clause 7
6 deflection
Pm
I
& contact ratio, overlap ratio, relative eccentricity (see clause 7)
r I
effective dynamic viscosity of the oil wedge at the mean temperature of wedge
mPa s
rl
I I I
temperature
I I OC 1
coefficient of friction
P
I I I
V Poisson ’s ratio,
-2
kinematic viscosity of the oil mm /s
radius of curvature,
P
density (for steel, p = 7,83x10m6)
normal stress N/mm2
I I I
z shear stress N/mm2
I I
running-in factor
x
auxiliary angle,
w
relative bearing clearance (see clause 7)
1 angular velocity
radls
r
1 parameter on the line of action
I I
Y reduction of area on fracture
%
I
Subscripts to symbols
reference values (without subscript)
a addendum,
tooth tip
ann annulus gear
b base circle,
facewidth
be bearing
I --I
ca case
cal calculated
co contact pattern
I 1
dynamic
I --I
e outer limit of single pair tooth contact
I -1
effective value, real stress
eff
I I
tooth-root, dedendum
internal
k
tooth truncation,
values related to the notched test piece
lim value of reference strength
I
\ 5
IS0 6336-l :I 996(E)
Description Unit
Symbol
mean or average value (mean section)
m
ma manufacturing
max maximum value
minimum value
min
n normal *plane,
virtual spur gear of a helical gear,
number of revolutions
oil oil
pitch,
P
values related to the smooth polished test piece
parallel
Par
planet gear
Pla
r radial
red reduced
rel relative
S tooth thickness,
notch effect
sh shaft
stat static (load)
sun sun pinion, sun gear
t transverse plane
th theoretical
V velocity,
losses
W working (this subscript may replace the apostrophe)
running-in,
Y
any point on the tooth flank
A application,
external shock loads
pitch point,
C
profile and helix modification
D speed transformation,
reducing or increasing
E elasticity of material,
resonance
F tooth-root stress
G geometry
H Hertzian stress (contact stress)
L lubrication
M material
N number (a specific number may be inserted after the subscript N in the life factor)
IS0 6336-l :1996(E)
0 IS0
Description Unit
Symbol
P permissible value,
rack profile
R roughness,
rows
T
test gear,
values related to the standard reference test gear
W pairing of materials
X dimension (absolute)
Z sun
I I I
a transverse contact,
profile
total (total value)
Y
A rough specimen
1 contact ratio
I
I
0 basic value,
tool
1 pinion
I
I
2 wheel
1 .9
general numbering
I 1
end relief,
WI)
reference (nonreference) face
I
single-flank (subscript w possible) single-pair tooth contact
I I
If
double-flank contact (simultaneous contact between working and non-working flanks)
I
Combined symbols
length of journal bearing mm
bbe
I
I I
b calculated facewidth (figure 9) mm
cal I
I I
b length of tooth bearing pattern at no load (contact marking)
mm
co
I I I
reduced facewidth (facewidth minus end reliefs)
b mm
red
I -7
I
web thickness
bs -7 mm I
I I
1 facewidth of one helix on a double helical gear mm
I
I
length of end relief mm
bl(ll)
I T I
I bottom clearance between basic rack profile and mating profile
mm
cP I-
I
mean value of mesh stiffness per unit facewidth N/(mm=pm)
C’ maximum tooth stiffness per unit facewidth (single stiffness) of a tooth pair Nl(mm-pm)
theoretical single stiffness
---j-- N/mmYm) 1
“th
I
tip diameter mm
da
base diameter mm
db
diameter of circle through outer point of single pair tooth contact -7 mm 1
de
I
IS0 6336-l :I 996(E) 0 IS0
Description Unit
Symbol
root diameter mm
df
root diameter of internal gear mm
df2
mm
d external diameter of shaft, nominal for bending deflection
sh
internal diameter of a hollow shaft mm
d
shi
mm
pitch diameter
dw
ball diameter (ball bearing) mm
dB
mm
reference diameter of pinion (or wheel)
q2
component of equivalent misalignment2) due to bearing deformation
Pm
fbe
f component of equivalent misalignment2) due to case deformation
W-J
ca
profile form deviation (the value for the total profile deviation Fa may be used
IJm
ffa
alternatively for this, if tolerances complying with IS0 1328-I are used)
f mesh misalignment2) due to manufacturing deviations
Pm
ma
transverse single pitch deviation
Pm
fP
f non-parallelism of pinion and wheel axes (manufacturing deviation) 2,
Pm
Par
transverse base pitch deviation (the values of fpt may be used for calculations in
P-lm
fPb
accordance with IS0 6336, using tolerances complying with IS0 1328-l)
f component of equivalent misalignment2) due to deformations of pinion and wheel
Pm
sh
shafts
f component of misalignment due to shaft and pinion deformation measured at a
Pm
shT
partial load
f shaft deformation under specific load2) pm=mm/N
sh0
helix slope deviation (the value for the total helix deviation Fp may be used
Pm
fw
alternatively for this, if tolerances complying with IS0 1328-I are used)
tolerance on helix slope deviation for IS0 accuracy grade 6
Pm
fHp 6
length of path of contact mm
sol
h addendum of basic rack of cylindrical gears mm
aP
h tool addendum mm
a0
dedendum of basic rack of cylindrical gears mm
hfP
tool dedendum mm
hfo
dedendum of tooth of an internal gear
mm
hf2
h minimum lubricant film thickness mm
min
bending moment arm for tooth-root stress
mm
hF
bending moment arm relevant to load application at the tooth tip (defined by the mm
hFa
contact point of the 30” tangents)
bending moment relevant to load application at the outer point of single pair tooth mm
hF,
contact
effective length of roller (roller bearings) mm
‘a
m* relative individual gear mass per unit facewidth referenced to line of action
kg/mm
normal module mm
mn
The components in the plane of action are determinant.
2)
0 IS0 IS0 6336-l :I 996(E)
Symbol Description
Unit
I I I
reduced gear pair mass per unit facewidth referenced to the line of action
kg/mm
mred
I I
transverse module
mm
“t
I
I
rotation speed of pinion (or wheel)
min-’ or s-l
“I,2
resonance speed
min-’
“E
I
normal base pitch mm
Pbn
I I
transverse base pitch
mm
Pbt
I
I
minimum value for the flexibility of a pair of meshing teeth
(mmmpm)/N
9’
I I
protuberance of the tool, see figure 2 of IS0 6336-3
mm
4pr
I I
notch parameter, qs = sFn / 2@
9s
I I
notch parameter of the notched test piece
%k
I
notch parameter of the standard reference test gear, qsT = 2,5
%T
I
auxiliary factor
%t
I I
film thickness of marking compound used in contact pattern determination
sC Pm
I I
residual fillet undercut, s
mm
= 9pr-9
SPr Pr
tooth-root chord at the critical section
-17
‘Fn
I
rim thickness
mm
c
SR
maximum depth of grinding notch
mm
( mean specific load (per unit facewidth)
wm
tangential force per unit tooth width, including overload factors
N/mm
wt
rack shift coefficient for adjustment of tooth thickness
XE
addendum modification coefficient of pinion (or wheel)
x1 ,2
running-in allowance for a gear pair
Pm
ya
running-in allowance (equivalent misalignment)
Pm
yP
virtual number of teeth of a helical gear
‘n
I I
~~
number of teeth of pinion (or wheel) ‘), see page 3
=I ,2
I
B
constant, see equations in clause 7
I
tip relief
Pm
‘a
I
basic rack factor (same rack for pinion and wheel)
cB
basic rack factor (pinion), see 9.3.1.4
‘Bl
basic rack factor (wheel), see 9.3.1.4
‘B2
correction factor, see clause 9
cM
gear blank factor, see clause 9
cR
factors for determining lubricant film factors, see 11.2 of Part 2
‘ZL, ZR, Zv
crowning height
I
end relief
bearing bore diameter (plain bearings)
mm
Dbe
D
journal diameter (plain bearings)
mm
sh
radial force on bearing
N
Fbe r
0 IS0
IS0 6336-l :I 996(E)
F initial equivalent misalignment (before running-in)
Pm
Px
initial equivalent misalignment for the determination of the crowning height
F
Pm
px cv
(estimate)
equivalent misalignment measured under a partial load
Pm
FX
P T
F effective equivalent misalignment (after running-in)
Pm
PY
K constant for the pinion position in relation to the torqued end
dynamic factor
KV
application factor
KA
transverse load factor (root stress)
KFcl
face load factor (root stress)
KFP
transverse load factor (contact stress)
KHCt
face load factor (contact stress)
Kw
mesh load factor (takes into account the uneven distribution of the load between
KY
meshes for multiple transmission paths)
J” moment of inertia per unit facewidth kg=mm2/mm
number of balls (or rollers) per row
NB
exponent
NF
number of load cycles
NL
number of mesh contacts per revolution (normally 1, for idler 2)
NM
number of rows per bearing
NR
resonance ratio in the main resonance range
NS
number of webs
Nw
arithmetic mean roughness value, R, = l/6 Rz
P’
Ra
mean peak-to-valley roughness (as specified in IS0 468)
Pm
Rz
R mean peak-to-valley roughness of the notched, rough test piece
Pm
zk
R mean peak-to-valley roughness of the standard reference test gear, RzT = 10
Pm
zT
factor of safety from tooth breakage
SF
k
0 IS0 IS0 6336-l :I 996(E)
Description Unit
Symbol
factor of safety from pitting
sH
Sommerfeld number
so
nominal torque at the pinion (or wheel) Nom
T1,2
tooth form factor, for the influence on nominal tooth-root stress with load applied at
yF
the outer point of single pair tooth contact
form factor, for the influence on nominal tooth-root stress with load applied at the
‘Fa
tooth tip
tip factor, equal (Y Fa YSa), accounts for influences covered by YFa and Ysa
‘FS
life factor for tooth-root stress, relevant to the notched test piece
‘Nk
life factor for tooth-root stress, relevant to the plain polished test piece
yNP
life factor for tooth-root stress for reference test conditions
‘NT
tooth-root surface factor (relevant to the plain polished test piece)
yR
relative roughness factor, the quotient of the gear tooth-root surface factor of
‘R rel k
interest divided by the notch test piece factor, YR rel k = YR/YRk
relative surface factor, the quotient of the gear tooth-root surface factor of interest
‘R rel T
divided by the tooth-root surface factor of the reference test gear,
‘R rel T = ‘RIYRT
stress correction factor, for the conversion of the nominal bending stress,
yS
determined for application of load at the outer point of single pair tooth contact, to
the local tooth-root stress
stress correction factor, for the conversion of the nominal bending stress
‘Sa
determined for load application at the tooth tip, to the local tooth-root stress
stress correction factors for teeth with grinding notches
‘Sag? ‘Sg
stress correction factor, relevant to the notched test piece
‘Sk
stress correction factor, relevant to the dimensions of the reference test gears
‘ST
size factor (tooth-root)
yX
helix angle factor (tooth-root)
yP
notch sensitivity factor of the actual gear (relative to a polished test piece)
ys
sensitivity factor of a notched test piece, relative to a smooth polished test piece
‘Sk
sensitivity factor of the standard reference test gear, relative to the smooth polished
yST
test piece
test relative notch sensitivity factor, the quotient of the gear notch sensitivity factor
‘6 rel k
of interest divided by the notched test piece factor, Ys rel k = Ys /Y&
relative notch sensitivity factor, the quotient of the gear notch sensitivity factor of
‘8 rel T
interest divided by the standard test gear factor, Ys rel T = Ys /Y&T
contact ratio factor (tooth-root)
yE
velocity factor
=V
single pair tooth contact factors for the pinion, for the wheel
=B7 =D
elasticity factor
=E
Jiijiis
zone factor
=H
lubricant factor
=L
life factor for contact stress
=N
IS0 6336-l :I 996(E) 0 IS0
Symbol Description Unit
life factor for contact stress for reference test conditions
‘NT
roughness factor affecting surface durability
=R
work-hardening factor
=W
size factor (pitting)
=X
helix angle factor (pitting)
=I3
contact ratio factor (pitting)
=E
tip pressure angle of a virtual spur gear
aan
form-factor pressure angle, pressure angle at the outer point of single pair tooth
aen
contact of virtual spur gears
normal pressure angle
%
transverse pressure angle
cCt or aWt pressure angle at the pitch cylinder
tip load angle, angle relevant to direction of application of load at the tooth tip of
aFan
virtual spur gears
load direction angle, relevant to direction of application of load at the outer point of
aFen
single pair tooth contact of virtual spur gears
normal pressure angle of the basic rack for cylindrical gears
aPn
tip helix angle (at the tip surface of a gear)
P
a
base helix angle
Pb
form-factor helix angle, helix angle at the outer point of single tooth contact
P
e
deformation of bearing (1, 2) in direction of load
pm, mm
%,2
combined deflection of mating teeth assuming even load distribution over the
Pm
‘b th
facewidth
difference in feeler gauge thickness measurement of mesh misalignment fma
Pm
6g
elongation on fracture
%
%
transverse contact ratio
%
E virtual contact ratio, transverse contact ratio of a virtual spur gear
an
E overlap ratio
P
total contact ratio, lY = E, + 8P
%
addendum contact ratio of the pinion, cl = CE/Pbt
cl
addendum contact ratio of the wheel, ~~ = AC/Pbt
“2
tip radius of the tool
mm
Pa0
root fillet radius of the basic rack for cylindrical gears
mm
PfP
radius of grinding notch
mm
%
radius of relative curvature
mm
Prel
radius of relative curvature at the pitch surface
mm
PC
tooth-root radius at the critical section
mm
PF
slip-layer thickness
P’ mm
nominal notched-bar stress number (bending)
N/mm2
Ok lim
0 IS0 IS0 6336-l :I 996(E)
Description Description
Symbol Symbol Unit Unit
r--- I I I
pp-;;; 1 nominal nominal plain-bar plain-bar stress stress number number (bending) (bending) N/mm2 N/mm2
Op lim
I I
tensile tensile strength strength N/mm2 N/mm2 1
OB
I I
tooth-root tooth-root stress stress N/mmN/mm2 ’
““F F
I I I
nominal nominal stress stress number number (bending) (bending) N/mm2 N/mm2
OF OF iim iim
I I I I
allowable stress number (bending), CTFE = OF lim YsT N/mm2 N/mm2 I
allowable stress number (bending), CJFE = OF lim YsT
OFE OFE I I
tooth-root tooth-root stress stress limit limit N/mm2 N/mm2
OFG OFG
I I I
permissible permissible tooth-root tooth-root stress stress N/mm2 N/mm2
OFP OFP
r I I I
nominal nominal tooth-root tooth-root stress stress N/mmN/mm’ ’ I
OF0 OF0 I I
calculated contact stress N/mm2 N/mm2 I
calculated contact stress
OH I I
allowable allowable stress stress number number (contact) (contact) N/mm2 N/mm2 ~~~
OH OH lim lim
I I I I
modified modified allowable allowable stress stress number, number, GHG GHG = = 0f-t CYH fim fim SH SH N/mm2 N/mm2
OHG OHG
r--- I I ~~~~ 1
permissible permissible contact contact stress stress N/mm2 N/mm2
OHP OHP
I I
nominal nominal contact contact stress stress N/mm2 N/mm2 I
OH0 OH0
I I
yield yield stress stress N/mmN/mm2 ’
OS OS
N/mm2 N/mm2
proof proof stress stress (0,2 (0,2 % % permanent permanent set) set)
Oo,2 Oo,2
relative relative stress stress gradient gradient in in the the root root of of a a notch notch mm-mm-’ ’
x* x*
factor factor characterizing characterizing the the equivalent equivalent misalignment misalignment after after running-in running-in
xl3 xl3
I
relative relative stress stress gradient gradient in in a a smooth smooth polished polished test test piece piece mm-mm-’ ’
x*P x*P
angular angular velocity velocity of of pinion pinion (or (or wheel) wheel) radk radk
92 92
4 Basic principles
4.1 Application
Refer to 1 .I for intended use.
4.1 .I Particular categories
Pitting resistance and bending strength rating systems for a particular category of cylindrical gearing may be
established by selecting proper values for the factors used in these general formulae.
4.1.2 Specific applications
For the design of gears it is very important to recognize that requirements for different fields of application vary
considerably. Use of IS0 6336 procedures for specific applications demands a realistic and knowledgeable
appraisal of all applicable considerations, particularly of the:
allowable stress of the material and the number of load repetitions;
consequences of any percentage of failure (failure rate);
appropriate factor of safety.
The following three application fields exemplify the requirements of the above mentioned characteristics.
0 IS0
IS0 6336-l :1996(E)
4.1.2.1 Vehicle final drive gears, which are relatively low speed, coarse pitch teeth are chosen for adequate
strength. As a consequence, pinions have small numbers of teeth (z, of about 14), whereas a value zI of about
Thus, the tooth bending strength of
28 would be chosen for a comparatively high speed gear of similar size.
the former would be about twice that of the latter.
The computed reliability of vehicle gears can be as low as 80% to 90 % whereas that of high speed industrial
gears should be at least 99 %.
In general, the material used in high volume vehicle gear production may be of more uniform quality than that
used for gears produced in small numbers.
Comparison of applied gear designs has indicated that for about 10 000 cycles, the load transmitted by truck
final drive gears is about four times greater than that transmitted by aircraft or space vehicle gears, where the
material, the quality, the size and the design are the same.
For low speed vehicle gears which are intended to have short lives (less than 100 000 cycles), small amounts
Consequently, the levels of surface
of plastic deformation, pitting and abrasive wear can usually be tolerated.
stress which are permissible are substantially higher than would be permissible for long life, high speed gears.
4.1.2.2 Main drive for aircraft and space vehicles, which are found in helicopter rotor drives and the main
pump drives of space vehicle boosters, where gears of the highest quality material and accuracy are used. Such
gears are extensively tested. For example, 10 to 20 transmissions of the same production series may be tested
The tolerable wear rate is established on the basis of test
under operational conditions for the full design life.
results. Lubricant spray rate, position of injection points and direction of spray is optimized.
For these reasons, higher loading is permissible for a design life up to 100 times longer (in cycles of tooth
loading), and speeds about 10 times greater than those of a typical vehicle transmission. The probability of
damage in such cases shall not exceed O,l% to 1 %. Overall loading cannot be as high as for vehicle gears
since neither surface wear nor minor damage can be tolerated.
4.1.2.3 Industrial turbine gears, where the pitch line velocities exceed 50 m/s, the pinions are usually designed
with 30 or more teeth with the objective of minimizing the risk of scuffing and wear. A typical gear pair would
consist of a pinion with 45 teeth and a wheel with 248.
Industrial turbine gearing should be better than 99 % reliable for a normal life of more than IO” cycles.
Extensive prototype testing is normally excluded because of the cost. As a consequence, the load capacity
ratings of turbine gears tend to be conservative with relatively high safety factors.
Safety factors
4.1.3
It is necessary to distinguish between the safety factor relative to pitting, S,, and the safety factor relative to
tooth breakage, S,.
For a given application, adequate gear load capacity is demonstrated by the computed values of S, and S,
being equal to or greater than the values SH min and SF min, respectively.
Certain minimum values for safety factors shall be determined. Recommendations concerning these minimum
values are made in IS0 6336, but values are not proposed.
An appropriate probability of failure and the safety factor shall be carefully chosen to meet the required reliability
at a justifiable cost. If the performance of the gears can be accurately appraised through testing of the actual
unit under actual load conditions, a lower safety factor and more economical manufacturing procedures may be
permissible.
Modified allowable stress number
Safety factor =
Calculated stress
Safety factors based on load are permitted. When they are based on load the safety factor equals the specific
When the factor is based on load,
calculated load capacity divided by the specific operating load transmitted.
this shall be stated clearly.
IS0 6336-1 :1996(E)
0 IS0
NOTE 1 - Safety factors based on load (power) relative to tooth bending are proportional to SF. Safety factors based on
load (power) relative to pitting are proportional to SH2.
In addition to the general requirements mentioned and the special requirements for surface durability, pitting,
(IS0 6336-2) and tooth bending strength (IS0 6336-3) the safety factors shall be chosen after careful
consideration of the following influences:
reliability of material data (The allowable stress numbers used in the calculation are valid for a given
probability of failure, the material values in IS0 6336-5 are valid for 1% probability of damage. This risk of
damage reduces with the increase of the safety factor and vice versa);
reliability of load values used for calculation (If loads or the response of the system to vibration, are
estimated rather than measured, a larger factor of safety should be used);
variations in gear geometry due to manufacturing tolerances;
variations in alignment;
variations in material due to process variations in chemistry, cleanliness and microstructure (material
quality and heat treatment);
variations in lubrication and its maintenance over the service life of the gears.
Depending on the reliability of the assumptions on which the calculations are based (e.g. load assumptions) and
according to the reliability requirements (consequences of damage occurrence), a corresponding safety factor
is to be chosen.
Where gears are produced under a specification or a request for proposal (quotation), in which the gear supplier
is to provide gears or assembled gear drives having specified calculated capacities (ratings) in accordance with
IS0 6336, the value of the safety factor for each mode of failure (pitting, tooth breakage) is to be agreed upon
between the parties.
4.1.4 Testing
The most reliable known approach to the appraisal of overall system performance is that of testing a proposed
new design. Where sufficient field or test experience is available, satisfactory results can be obtained by
extrapolation of previous tests or field data.
When suitable test results or field data are not available, values for the rating factors should be chosen
conservatively.
4.1.5 Manufacturing tolerances
Evaluation of rating factors should be based on the minimum accuracy grade limits specified for the component
parts in the manufacturing process.
4.1.6 implied accuracy
Where empirical values for rating factors are given by curves, curve fitting equations are provided to facilitate
computer programming. The constants and coefficients used in curve fitting often have significant digits in excess
of those appropriate to the reliability of the empirical data.
4.1.7
Other considerations
In addition to the factors considered in IS0 6336 influencing pitting resistance and bending strength, other
interrelated system factors can have a significant influence on overall transmission performance. The following
factors are particularly significant.
0 IS0
IS0 6336-l :1996(E)
4.1.7.1 Lubrication. The ratings determined by these formulae are valid only if the gear teeth are operated
with a lubricant of proper viscosity and additives for the load, speed, and surface finish, and if there is a sufficient
quantity of lubricant supplied to the gear teeth and bearings to lubricate and maintain an acceptable operating
temperature.
Many gear systems depend on external supports such
4.1.7.2 Misalignment and deflection of foundations.
If these supports are poorly designed, initially
as machinery foundations to maintain alignment of the gear mesh.
misaligned, or become misaligned during operation through elastic or thermal deflection or other influences,
overall gear system performance will be adversely affected.
4.1.7.3 Deflections of gear teeth, gear blanks, gear shafts, bearings and housings affect performance and
distribution of total tooth load over meshing flanks. Since these deflections vary with load, it is impossible to
obtain optimum tooth contact at different loads in those transmissions that encounter variable load. When gear
tooth flanks are not modified, the face load factor increases with increasing deflection, thereby lowering rated
capacity.
4.1.7.4 System dynamics. The method of analysis used in IS0 6336 provides a dynamic factor in the formulae
by derating the gears for increased loads caused by gear tooth inaccuracies and for harmonic effects. In
general, simplified values are given for easy application. The dynamic response of the system results in
additional gear tooth loads due to the relative motions of the connected masses of the driver and the driven
equipment. The application factor, Kay is intended to account for the operating characteristics of the driving and
driven equipment. It must be recognized, however, that if the operating roughness of the driver, gearbox, or
driven equipment causes an excitation with a frequency that is near to one of the system ’s major natural
frequencies, resonant vibrations may cause severe overloads which may be several times higher than the
nominal load.
For critical service applications, it is recommended that a vibration analysis be performed. This analysis shall
include the total system of driver, gearbox, driven equipment, couplings, mounting conditions, and sources of
excitation. Natural frequencies, mode shapes, and the dynamic response amplitudes should be calculated. The
resulting load spectrum cumulative fatigue effect calculation, if necessary or required, is given in ISO/TR 10495.
The teeth of most cylindrical gears are modified in both profile and lengthwise
4.1.7.5 Contact pattern.
directions during the manufacturing operation to accommodate deflection of the mountings. This results in a
localized contact pattern during roll testing under light loads. Under design load, the contact should spread over
the tooth flank without any concentration of the pattern at the edges. This influence shall be taken into account
by the corresponding load distribution factor.
4.1.7.6 Corrosion of gear tooth surfaces can significantly reduce the bending strength and pitting resistance
of the teeth. Quantifying the extent of these reductions is beyond the scope of IS0 6336.
4.1.8 Influence factors
The influence factors presented in IS0 6336 are derived from results of research and field service. It is
convenient to distinguish between the following:
a) Factors which are determined by gear geometry or which have been established by convention. They shall
be calculated in accordance with the equations given in IS0 6336.
b) Factors which account for several influences and which are dealt with as independent of each other, but,
which may nevertheless influence each other to a degree for which no numerical value can be assigned.
These include the factors KA, Kv, KHa, KHp, or KFa and the factors influencing allowable stress.
The factors Kv, KHp, and KHa also depend on the magnitudes of the profile and helix modifications. Profile and
helix modifications are only effective if they are significantly larger than the manufacturing deviations. For this
reason, the influence of the profile and helix modifications may only be taken into consideration if the gear
manufacturing deviations do not exceed specific limit values. The minimum required gear manufacturing
accuracy is stated, together with reference to IS0 1328-1, for each factor.
The influence factors can be determined by various methods. These are qualified, as necessary, by adding
subscripts A through E to the symbols. Unless otherwise specified, e.g. in an application standard, the more
0 IS0 IS0 6336=1:1996(E)
accurate of the methods is to be preferred for important transmissions. In cases of dispute, when proof of
accuracy and reliability is supplied, method A is superior to method B, and method B to method C, etc.
NOTE 2 - It is recommended that supplementary subscripts be used whenever the method used for evaluation of a factor
would not be readily identifiable.
In some applications it may be necessary to choose between factors which have been determined using
alternative methods (e.g. the alternatives for the determination of the equivalent misalignment). When
necessary, the relevant method can be indicated by extending the subscript, e.g. KHp Bl.
IS0 6336 is primarily intended for verifying the load capacity of gears for which essential calculation data are
available by way of detail drawings, or in similar form.
The data available at the primary design stage is usually restricted. It is therefore necessary, at this stage, to
make use of approximations or empirical values for some factors.
For given fields of application or for rough calculations, it is often permissible to substitute unity or some other
In doing so, it is necessary to verify that a good margin of safety is assured.
constant for some factors.
Otherwise, the safety factor shall
...
SLOVENSKI STANDARD
01-julij-2002
,]UDþXQQRVLOQRVWLUDYQR]RELKLQSRãHYQR]RELK]REQLNRYGHO 2VQRYHXYDMDQMH
LQNRHILFLHQWL
Calculation of load capacity of spur and helical gears -- Part 1: Basic principles,
introduction and general influence factors
Calcul de la capacité de charge des engrenages cylindriques à dentures droite et
hélicoïdale -- Partie 1: Principes de base, introduction et facteurs généraux d'influence
Ta slovenski standard je istoveten z: ISO 6336-1:1996
ICS:
21.200 Gonila Gears
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL
IS0
STANDARD
6336-1
First edition
1996-05-15
Calculation of load capacity of spur and
helical gears -
Part 1:
Basic principles, introduction and general
influence factors
Calcul de la capacitg de charge des engrenages cylindriques ;i dentures
droite et h6licoi ’dale -
Partie I: Principes de base, introduction et facteurs g&W-aux d/influence
Reference number
IS0 6336-1:1996(E)
IS0 6336-l :I 996(E)
Contents
Page
................................. iv
Introduction
Scope .
.......................... 2
Normative references
..................... 3
Definitions symbols and units
.............................. 13
Basic principles
.......................... 19
Application factor KA
...................... 19
Internal dynamic factor Kv
................... 37
Face load factors K,+ and KFP
..............
Transverse load factors KHa and KFa
............... 77
Tooth stiffness parameters c’ and cr
Annexes
Guide values for crowning and end relief
A
of teeth of cylindrical gears . . . . . . . . . . . . . . . . . . . . . 85
Guide values for the application factor KA . . . . . . . . . s . 87
B
Derivations and explanatory notes . . . . . . . . . . . . . . . . 90
C
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
D
0 IS0 1996
All rights reserved. Unless otherwise specified, no part of this publication may be
reproduced or utilized in any form or by any means, electronic or mechanical, including
photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
ii
IS0 6336-l :I 996(E)
0 IS0
Foreword
IS0 (the International Organization for Standardization) is a
worldwide federation of national standards bodies (IS0 member
The work of preparing International Standards is
bodies).
normally carried out through IS0 technical committees. Each
member body interested in a subject for which a technical
committee has been established has the right to be represented
International organizations, governmental
on that committee.
and non-governmental, in liaison with ISO, also take part in the
work. IS0 collaborates closely with the International
Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
Draft International Standards adopted by the technical
committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at
least 75 % of the member bodies casting a vote.
International standard IS0 6336-l was prepared by Technical
Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear
capacity calculation.
IS0 6336 consists of the following parts, under the general title
Calculation of load capacity of spur and helical gears:
- Part 7: Basic principles, introduction and general influence
factors
- Part 2: Calculation of surface durability (pitting)
- Part 3: Calculation of tooth bending strength
Part 5: Strength and quality of materials
-
Annexes A to D of this part of IS0 6336 are for information only.
. . .
III
IS0 6336-l :1996(E)
0 IS0
Introduction
This part of IS0 6336 and parts 2, 3 and 5 provide the principles
for a coherent system of procedures for the calculation of the
load capacity of cylindrical involute gears with external or
internal teeth. IS0 6336 is designed to facilitate the application
of future knowledge and developments, also the exchange of
information gained from experience.
Design considerations to prevent fractures emanating from stress
raisers in the tooth flank, tip chipping and failures of the gear
blank through the web or hub should be analyzed by general
machine design methods.
Several methods for the calculation of load capacity, also for the
calculation of various factors are permitted (see 4.1.8). The
directions in IS0 6336 are thus complex, but also flexible. As
appropriate, the more detailed or simplified versions should be
chosen for inclusion in application standards derived from this
basic standard. Such application standards cover the following
fields:
- industrial gears (detailed and simplified method);
- high-speed gears and gears of similar requirements;
- marine gears;
- vehicle gears.
These application standards feature clear, and to some extent
simplified, rules for the calculations.
Included in the formulae are the major factors which are
presently known to affect gear tooth pitting and fractures at the
root fillet. The formulae are in a form that will permit the
addition of new factors to reflect knowledge gained in the future.
IV
IS0 6336-l :I 996(E)
INTERNATIONAL STANDARD 0 IS0
Calculation of load capacity of spur and helical gears
Part 1: Basic principles, introduction and general influence factors
.
1 Scope
11 l Intended use
This part of IS0 6336, together with parts 2, 3 and 5, provides a method by which different gear designs can
be compared. It is not intended to assure the performance of assembled drive gear systems. It is not intended
for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who
is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs
and awareness of the effects of the items discussed.
The formulae in IS0 6336 are intended to establish a uniformly acceptable method for calculating the pitting
resistance and bending strength capacity of cylindrical gears with straight or helical teeth.
IS0 6336 includes procedures based on testing and theoretical studies such as those of Hirt [l], Strasser [2],
and Brossman [3]. The results of rating calculations made by following this method are in good agreement with
previously accepted gear calculations methods (see references [4] through [8]), for normal working pressure
angles up to 25’ and reference helix angles up to 30 ”.
For larger pressure angles and larger helix angles the trends of products YF Ys YP and respectively Z,, Zc Zp
are not the same as those of some earlier methods. The user of IS0 6336 is cautioned that when the methods
in IS0 6336 are used for other helix angles and pressure angles, the calculated results should be confirmed by
experience.
12 . Exceptions
The formulae in IS0 6336 are not applicable when any of the following conditions exist:
- spur gears with transverse contact ratios less than 1 ,O;
- spur or helical gears with transverse contact ratios greater than 2,5;
- where interference exists between tooth tips and root fillets;
- when teeth are pointed;
- when backlash is zero.
The rating formulae in IS0 6336 are not applicable to other types of gear tooth deterioration such as plastic
yielding, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where
there may be an unpredictable profile breakdown The bending strength formulae are applicable to fractures
at the tooth fillet, but are not applicable to fractures on the tooth working surfaces, failure of the gear rim, or
failures of the gear blank through web and hub. IS0 6336 does not apply to teeth finished by forging or
sintering. It is not applicable to gears which have a poor contact pattern.
0 IS0
IS0 6336-l :1996(E)
based on pitting and tooth-root
The procedures in IS0 6336 provide for the calculation of load capacity,
breakage. At pitch line velocities below 1 m/s the gear load capacity is often limited by abrasive wear (see other
literature for information on the calculation for this).
1.2.1
Scuffing
Formulae for scuffing resistance on cylindrical gear teeth are not included in IS0 6336. At the present time,
there is insufficient agreement concerning the method for designing cylindrical gears to resist scuffing failure.
1.2.2 Wear
Very little attention and concern have been devoted to the study of gear tooth wear. This subject primarily
concerns gear teeth with low surface hardness or gears with improper lubrication. No attempt has been made
to cover the subject in IS0 6336.
1.2.3 Micropitting
IS0 6336 does not cover micropitting, which is an additional type of surface distress that may occur on gear
teeth.
1.2.4 Plastic yielding
IS0 6336 does not extend to stress levels greater than those permissible at IO3 cycles or less, since stresses
in this range may exceed the elastic limit of the gear tooth in bending or in surface compressive stress.
Depending on the material and the load imposed, a single stress cycle greater than the limit level at < 1 O3
cycles could result in plastic yielding of the gear tooth.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions of this part
of IS0 6336. At the time of publication, the editions indicated were valid. All standards are subject to revision,
and parties to agreements based on this part of IS0 6336 are encouraged to investigate the possibility of
applying the most recent edition of the standards indicated below. Members of IEC and IS0 maintain registers
of currently valid International Standards.
Cylindrical gears for general and heavy engineering - Basic rack.
IS0 53: 1974,
IS0 468: 1982, Surface roughness - Parameters, their values and general rules for specifying
requirements.
International gear notation
IS0 701: 1976, - Symbols for geometrical data.
IS0 1122-l : 1983, Glossary of gear terms - Part I : Geometrical definitions.
IS0 1328-1: 1995, Cylindrical gears - IS0 system of accuracy - Part I : Definitions and allowable values
of deviations relevant to corresponding flanks of gear teeth.
Calculation of load capacity of spur and helical gears - Part 2: Calculation of surface
IS0 6336-2: 1996,
durability (pitting).
IS0 6336-3: 1996, Calculation of load capacity of spur and helical gears - Part 3: Calculation of tooth
bending strength.
IS0 6336-5: 1996, Calculation of load capacity of spur and helical gears - Part 5: Strength and quality of
material.
ISO/TR 10495: 1996 Calculation of cylindrical gears
- Calculation of service life under variable load.
IS0 6336-l :I 996(E)
0 IS0
3 Definitions, symbols and units
For the purposes of IS0 6336, the definitions given in IS0 1122-I apply.
Symbols are based on and are extensions of the symbols given in IS0 701 and IS0 1328-I. Only symbols for
quantities used for the calculation of the particular factors treated in IS0 6336 are given, together with preferred
units. Table 1 list the symbols used in the calculations for all parts of IS0 6336.
Table 1 - Symbols and abbreviations used within IS0 63364, 2, 3 and 5
Description
Symbol Unit
Principal symbols and abbreviations
-11
center distance mm
facewidth mm
constant
d diameter (without subscript, reference diameter) mm
I
I
auxiliary quantity
deviation, tooth deformation
Pm
path of contact mm
tooth depth (without subscript, root circle to tip circle) mm
i transmission ratio
I
I -1
k addendum truncation factor
I I I
I ( bearing span mm
I I
m module,
mm
mass
kg
n
rotational speed s-’ or min-’
pitch, mm
P
number of planet gears
~~
auxiliary factor,
flexibility of pair of meshing teeth, see clause 9
(mm=pm)/N
material allowance for finish machining, see clause 5 of IS0 6336-3 mm
radius (without subscript, reference radius) mm
tooth thickness, distance between mid-plane of pinion and the middle of the bearing
mm
span
u gear ratio (z2 / z,) 2 1 ‘)
V tangential velocity (without subscript, at the reference circle M tangential velocity at
m/s
pitch circle)
W specific load (per unit facewidth, Ft / b) N/mm
X profile shift coefficient
running-in allowance (only with subscript a or p)
Y
Pm
I I I
~~ ~
Z number of teeth ’)
A, B, C, D, E points on path of contact (pinion root to pinion tip, regardless of whether pinion or
wheel drives, only for geometrical considerations)
total facewidth of double helical gear including gap width mm
I I -1
1) For external gearing a, z,, and z2 are positive; for internal gearing a and z2 have a negative sign, z, has a positive.
0 IS0
IS0 6336-l :I 996(E)
Description Unit
Symbol
constant, coefficient,
C
relief of tooth flank
Pm
mm
D diameter (design)
N/mm2
modulus of elasticity
E
material designation for case-hardening steel, case hardened
Eh
mm
case depth, see IS0 6336-5
Eht
F composite and cumulative deviations,
“N”
force or load
N/mm2
G shear modulus
material designation for grey cast iron
GG
material designation for cast iron (perlitic, bainitic, ferritic structure)
GGG
GTS material designation for black malleable cast iron (perlitic structure)
HB Brine11 hardness
HRC Rockwell hardness (C scale)
HR 30N Rockwell hardness (30 N scale), see IS0 6336-5
Vickers hardness
HV
HV 1 Vickers hardness at load F = 9,81 N, see IS0 6336-5
HV 10 Vickers hardness at load F = 98,lO N, see IS0 6336-5
IF material designation for steel and GGG, flame or induction hardened
Jominy hardenability, see IS0 6336-5
J
K constant, factors concerning tooth load
L lengths (design) mm
moment of a force Nm
M
MX
ME symbols identifying material and heat-treatment requirements, see IS0 6336-5
MQ
ML
N number, exponent, number of load cycles, resonance ratio
material designation for nitriding steel, nitrided
NT
NV material designation for through-hardening and case-hardening steel, nitrided (nitr.),
nitrocarburized (nitrocar.)
P transmitted power kW
S safety factor
St material designation for steel (Ok < 800 N/mm2)
T torque, Nm
tolerance
Pm
V
material designation for through-hardening steel, through-hardened (Ok 2
800 N/mm2)
W weighing factor
Y factor related to tooth-root stress
factor related to contact stress
z
0 IS0 IS0 6336-l :I 996(E)
ISymbol 1 Description Unit
a pressure angle (without subscript, at reference cylinder)
I I
helix angle (without subscript, at reference cylinder)
P
I I I
auxiliary angle,
Y
shear strain,
pinion offset factor, see equations in clause 7
6 deflection
Pm
I
& contact ratio, overlap ratio, relative eccentricity (see clause 7)
r I
effective dynamic viscosity of the oil wedge at the mean temperature of wedge
mPa s
rl
I I I
temperature
I I OC 1
coefficient of friction
P
I I I
V Poisson ’s ratio,
-2
kinematic viscosity of the oil mm /s
radius of curvature,
P
density (for steel, p = 7,83x10m6)
normal stress N/mm2
I I I
z shear stress N/mm2
I I
running-in factor
x
auxiliary angle,
w
relative bearing clearance (see clause 7)
1 angular velocity
radls
r
1 parameter on the line of action
I I
Y reduction of area on fracture
%
I
Subscripts to symbols
reference values (without subscript)
a addendum,
tooth tip
ann annulus gear
b base circle,
facewidth
be bearing
I --I
ca case
cal calculated
co contact pattern
I 1
dynamic
I --I
e outer limit of single pair tooth contact
I -1
effective value, real stress
eff
I I
tooth-root, dedendum
internal
k
tooth truncation,
values related to the notched test piece
lim value of reference strength
I
\ 5
IS0 6336-l :I 996(E)
Description Unit
Symbol
mean or average value (mean section)
m
ma manufacturing
max maximum value
minimum value
min
n normal *plane,
virtual spur gear of a helical gear,
number of revolutions
oil oil
pitch,
P
values related to the smooth polished test piece
parallel
Par
planet gear
Pla
r radial
red reduced
rel relative
S tooth thickness,
notch effect
sh shaft
stat static (load)
sun sun pinion, sun gear
t transverse plane
th theoretical
V velocity,
losses
W working (this subscript may replace the apostrophe)
running-in,
Y
any point on the tooth flank
A application,
external shock loads
pitch point,
C
profile and helix modification
D speed transformation,
reducing or increasing
E elasticity of material,
resonance
F tooth-root stress
G geometry
H Hertzian stress (contact stress)
L lubrication
M material
N number (a specific number may be inserted after the subscript N in the life factor)
IS0 6336-l :1996(E)
0 IS0
Description Unit
Symbol
P permissible value,
rack profile
R roughness,
rows
T
test gear,
values related to the standard reference test gear
W pairing of materials
X dimension (absolute)
Z sun
I I I
a transverse contact,
profile
total (total value)
Y
A rough specimen
1 contact ratio
I
I
0 basic value,
tool
1 pinion
I
I
2 wheel
1 .9
general numbering
I 1
end relief,
WI)
reference (nonreference) face
I
single-flank (subscript w possible) single-pair tooth contact
I I
If
double-flank contact (simultaneous contact between working and non-working flanks)
I
Combined symbols
length of journal bearing mm
bbe
I
I I
b calculated facewidth (figure 9) mm
cal I
I I
b length of tooth bearing pattern at no load (contact marking)
mm
co
I I I
reduced facewidth (facewidth minus end reliefs)
b mm
red
I -7
I
web thickness
bs -7 mm I
I I
1 facewidth of one helix on a double helical gear mm
I
I
length of end relief mm
bl(ll)
I T I
I bottom clearance between basic rack profile and mating profile
mm
cP I-
I
mean value of mesh stiffness per unit facewidth N/(mm=pm)
C’ maximum tooth stiffness per unit facewidth (single stiffness) of a tooth pair Nl(mm-pm)
theoretical single stiffness
---j-- N/mmYm) 1
“th
I
tip diameter mm
da
base diameter mm
db
diameter of circle through outer point of single pair tooth contact -7 mm 1
de
I
IS0 6336-l :I 996(E) 0 IS0
Description Unit
Symbol
root diameter mm
df
root diameter of internal gear mm
df2
mm
d external diameter of shaft, nominal for bending deflection
sh
internal diameter of a hollow shaft mm
d
shi
mm
pitch diameter
dw
ball diameter (ball bearing) mm
dB
mm
reference diameter of pinion (or wheel)
q2
component of equivalent misalignment2) due to bearing deformation
Pm
fbe
f component of equivalent misalignment2) due to case deformation
W-J
ca
profile form deviation (the value for the total profile deviation Fa may be used
IJm
ffa
alternatively for this, if tolerances complying with IS0 1328-I are used)
f mesh misalignment2) due to manufacturing deviations
Pm
ma
transverse single pitch deviation
Pm
fP
f non-parallelism of pinion and wheel axes (manufacturing deviation) 2,
Pm
Par
transverse base pitch deviation (the values of fpt may be used for calculations in
P-lm
fPb
accordance with IS0 6336, using tolerances complying with IS0 1328-l)
f component of equivalent misalignment2) due to deformations of pinion and wheel
Pm
sh
shafts
f component of misalignment due to shaft and pinion deformation measured at a
Pm
shT
partial load
f shaft deformation under specific load2) pm=mm/N
sh0
helix slope deviation (the value for the total helix deviation Fp may be used
Pm
fw
alternatively for this, if tolerances complying with IS0 1328-I are used)
tolerance on helix slope deviation for IS0 accuracy grade 6
Pm
fHp 6
length of path of contact mm
sol
h addendum of basic rack of cylindrical gears mm
aP
h tool addendum mm
a0
dedendum of basic rack of cylindrical gears mm
hfP
tool dedendum mm
hfo
dedendum of tooth of an internal gear
mm
hf2
h minimum lubricant film thickness mm
min
bending moment arm for tooth-root stress
mm
hF
bending moment arm relevant to load application at the tooth tip (defined by the mm
hFa
contact point of the 30” tangents)
bending moment relevant to load application at the outer point of single pair tooth mm
hF,
contact
effective length of roller (roller bearings) mm
‘a
m* relative individual gear mass per unit facewidth referenced to line of action
kg/mm
normal module mm
mn
The components in the plane of action are determinant.
2)
0 IS0 IS0 6336-l :I 996(E)
Symbol Description
Unit
I I I
reduced gear pair mass per unit facewidth referenced to the line of action
kg/mm
mred
I I
transverse module
mm
“t
I
I
rotation speed of pinion (or wheel)
min-’ or s-l
“I,2
resonance speed
min-’
“E
I
normal base pitch mm
Pbn
I I
transverse base pitch
mm
Pbt
I
I
minimum value for the flexibility of a pair of meshing teeth
(mmmpm)/N
9’
I I
protuberance of the tool, see figure 2 of IS0 6336-3
mm
4pr
I I
notch parameter, qs = sFn / 2@
9s
I I
notch parameter of the notched test piece
%k
I
notch parameter of the standard reference test gear, qsT = 2,5
%T
I
auxiliary factor
%t
I I
film thickness of marking compound used in contact pattern determination
sC Pm
I I
residual fillet undercut, s
mm
= 9pr-9
SPr Pr
tooth-root chord at the critical section
-17
‘Fn
I
rim thickness
mm
c
SR
maximum depth of grinding notch
mm
( mean specific load (per unit facewidth)
wm
tangential force per unit tooth width, including overload factors
N/mm
wt
rack shift coefficient for adjustment of tooth thickness
XE
addendum modification coefficient of pinion (or wheel)
x1 ,2
running-in allowance for a gear pair
Pm
ya
running-in allowance (equivalent misalignment)
Pm
yP
virtual number of teeth of a helical gear
‘n
I I
~~
number of teeth of pinion (or wheel) ‘), see page 3
=I ,2
I
B
constant, see equations in clause 7
I
tip relief
Pm
‘a
I
basic rack factor (same rack for pinion and wheel)
cB
basic rack factor (pinion), see 9.3.1.4
‘Bl
basic rack factor (wheel), see 9.3.1.4
‘B2
correction factor, see clause 9
cM
gear blank factor, see clause 9
cR
factors for determining lubricant film factors, see 11.2 of Part 2
‘ZL, ZR, Zv
crowning height
I
end relief
bearing bore diameter (plain bearings)
mm
Dbe
D
journal diameter (plain bearings)
mm
sh
radial force on bearing
N
Fbe r
0 IS0
IS0 6336-l :I 996(E)
F initial equivalent misalignment (before running-in)
Pm
Px
initial equivalent misalignment for the determination of the crowning height
F
Pm
px cv
(estimate)
equivalent misalignment measured under a partial load
Pm
FX
P T
F effective equivalent misalignment (after running-in)
Pm
PY
K constant for the pinion position in relation to the torqued end
dynamic factor
KV
application factor
KA
transverse load factor (root stress)
KFcl
face load factor (root stress)
KFP
transverse load factor (contact stress)
KHCt
face load factor (contact stress)
Kw
mesh load factor (takes into account the uneven distribution of the load between
KY
meshes for multiple transmission paths)
J” moment of inertia per unit facewidth kg=mm2/mm
number of balls (or rollers) per row
NB
exponent
NF
number of load cycles
NL
number of mesh contacts per revolution (normally 1, for idler 2)
NM
number of rows per bearing
NR
resonance ratio in the main resonance range
NS
number of webs
Nw
arithmetic mean roughness value, R, = l/6 Rz
P’
Ra
mean peak-to-valley roughness (as specified in IS0 468)
Pm
Rz
R mean peak-to-valley roughness of the notched, rough test piece
Pm
zk
R mean peak-to-valley roughness of the standard reference test gear, RzT = 10
Pm
zT
factor of safety from tooth breakage
SF
k
0 IS0 IS0 6336-l :I 996(E)
Description Unit
Symbol
factor of safety from pitting
sH
Sommerfeld number
so
nominal torque at the pinion (or wheel) Nom
T1,2
tooth form factor, for the influence on nominal tooth-root stress with load applied at
yF
the outer point of single pair tooth contact
form factor, for the influence on nominal tooth-root stress with load applied at the
‘Fa
tooth tip
tip factor, equal (Y Fa YSa), accounts for influences covered by YFa and Ysa
‘FS
life factor for tooth-root stress, relevant to the notched test piece
‘Nk
life factor for tooth-root stress, relevant to the plain polished test piece
yNP
life factor for tooth-root stress for reference test conditions
‘NT
tooth-root surface factor (relevant to the plain polished test piece)
yR
relative roughness factor, the quotient of the gear tooth-root surface factor of
‘R rel k
interest divided by the notch test piece factor, YR rel k = YR/YRk
relative surface factor, the quotient of the gear tooth-root surface factor of interest
‘R rel T
divided by the tooth-root surface factor of the reference test gear,
‘R rel T = ‘RIYRT
stress correction factor, for the conversion of the nominal bending stress,
yS
determined for application of load at the outer point of single pair tooth contact, to
the local tooth-root stress
stress correction factor, for the conversion of the nominal bending stress
‘Sa
determined for load application at the tooth tip, to the local tooth-root stress
stress correction factors for teeth with grinding notches
‘Sag? ‘Sg
stress correction factor, relevant to the notched test piece
‘Sk
stress correction factor, relevant to the dimensions of the reference test gears
‘ST
size factor (tooth-root)
yX
helix angle factor (tooth-root)
yP
notch sensitivity factor of the actual gear (relative to a polished test piece)
ys
sensitivity factor of a notched test piece, relative to a smooth polished test piece
‘Sk
sensitivity factor of the standard reference test gear, relative to the smooth polished
yST
test piece
test relative notch sensitivity factor, the quotient of the gear notch sensitivity factor
‘6 rel k
of interest divided by the notched test piece factor, Ys rel k = Ys /Y&
relative notch sensitivity factor, the quotient of the gear notch sensitivity factor of
‘8 rel T
interest divided by the standard test gear factor, Ys rel T = Ys /Y&T
contact ratio factor (tooth-root)
yE
velocity factor
=V
single pair tooth contact factors for the pinion, for the wheel
=B7 =D
elasticity factor
=E
Jiijiis
zone factor
=H
lubricant factor
=L
life factor for contact stress
=N
IS0 6336-l :I 996(E) 0 IS0
Symbol Description Unit
life factor for contact stress for reference test conditions
‘NT
roughness factor affecting surface durability
=R
work-hardening factor
=W
size factor (pitting)
=X
helix angle factor (pitting)
=I3
contact ratio factor (pitting)
=E
tip pressure angle of a virtual spur gear
aan
form-factor pressure angle, pressure angle at the outer point of single pair tooth
aen
contact of virtual spur gears
normal pressure angle
%
transverse pressure angle
cCt or aWt pressure angle at the pitch cylinder
tip load angle, angle relevant to direction of application of load at the tooth tip of
aFan
virtual spur gears
load direction angle, relevant to direction of application of load at the outer point of
aFen
single pair tooth contact of virtual spur gears
normal pressure angle of the basic rack for cylindrical gears
aPn
tip helix angle (at the tip surface of a gear)
P
a
base helix angle
Pb
form-factor helix angle, helix angle at the outer point of single tooth contact
P
e
deformation of bearing (1, 2) in direction of load
pm, mm
%,2
combined deflection of mating teeth assuming even load distribution over the
Pm
‘b th
facewidth
difference in feeler gauge thickness measurement of mesh misalignment fma
Pm
6g
elongation on fracture
%
%
transverse contact ratio
%
E virtual contact ratio, transverse contact ratio of a virtual spur gear
an
E overlap ratio
P
total contact ratio, lY = E, + 8P
%
addendum contact ratio of the pinion, cl = CE/Pbt
cl
addendum contact ratio of the wheel, ~~ = AC/Pbt
“2
tip radius of the tool
mm
Pa0
root fillet radius of the basic rack for cylindrical gears
mm
PfP
radius of grinding notch
mm
%
radius of relative curvature
mm
Prel
radius of relative curvature at the pitch surface
mm
PC
tooth-root radius at the critical section
mm
PF
slip-layer thickness
P’ mm
nominal notched-bar stress number (bending)
N/mm2
Ok lim
0 IS0 IS0 6336-l :I 996(E)
Description Description
Symbol Symbol Unit Unit
r--- I I I
pp-;;; 1 nominal nominal plain-bar plain-bar stress stress number number (bending) (bending) N/mm2 N/mm2
Op lim
I I
tensile tensile strength strength N/mm2 N/mm2 1
OB
I I
tooth-root tooth-root stress stress N/mmN/mm2 ’
““F F
I I I
nominal nominal stress stress number number (bending) (bending) N/mm2 N/mm2
OF OF iim iim
I I I I
allowable stress number (bending), CTFE = OF lim YsT N/mm2 N/mm2 I
allowable stress number (bending), CJFE = OF lim YsT
OFE OFE I I
tooth-root tooth-root stress stress limit limit N/mm2 N/mm2
OFG OFG
I I I
permissible permissible tooth-root tooth-root stress stress N/mm2 N/mm2
OFP OFP
r I I I
nominal nominal tooth-root tooth-root stress stress N/mmN/mm’ ’ I
OF0 OF0 I I
calculated contact stress N/mm2 N/mm2 I
calculated contact stress
OH I I
allowable allowable stress stress number number (contact) (contact) N/mm2 N/mm2 ~~~
OH OH lim lim
I I I I
modified modified allowable allowable stress stress number, number, GHG GHG = = 0f-t CYH fim fim SH SH N/mm2 N/mm2
OHG OHG
r--- I I ~~~~ 1
permissible permissible contact contact stress stress N/mm2 N/mm2
OHP OHP
I I
nominal nominal contact contact stress stress N/mm2 N/mm2 I
OH0 OH0
I I
yield yield stress stress N/mmN/mm2 ’
OS OS
N/mm2 N/mm2
proof proof stress stress (0,2 (0,2 % % permanent permanent set) set)
Oo,2 Oo,2
relative relative stress stress gradient gradient in in the the root root of of a a notch notch mm-mm-’ ’
x* x*
factor factor characterizing characterizing the the equivalent equivalent misalignment misalignment after after running-in running-in
xl3 xl3
I
relative relative stress stress gradient gradient in in a a smooth smooth polished polished test test piece piece mm-mm-’ ’
x*P x*P
angular angular velocity velocity of of pinion pinion (or (or wheel) wheel) radk radk
92 92
4 Basic principles
4.1 Application
Refer to 1 .I for intended use.
4.1 .I Particular categories
Pitting resistance and bending strength rating systems for a particular category of cylindrical gearing may be
established by selecting proper values for the factors used in these general formulae.
4.1.2 Specific applications
For the design of gears it is very important to recognize that requirements for different fields of application vary
considerably. Use of IS0 6336 procedures for specific applications demands a realistic and knowledgeable
appraisal of all applicable considerations, particularly of the:
allowable stress of the material and the number of load repetitions;
consequences of any percentage of failure (failure rate);
appropriate factor of safety.
The following three application fields exemplify the requirements of the above mentioned characteristics.
0 IS0
IS0 6336-l :1996(E)
4.1.2.1 Vehicle final drive gears, which are relatively low speed, coarse pitch teeth are chosen for adequate
strength. As a consequence, pinions have small numbers of teeth (z, of about 14), whereas a value zI of about
Thus, the tooth bending strength of
28 would be chosen for a comparatively high speed gear of similar size.
the former would be about twice that of the latter.
The computed reliability of vehicle gears can be as low as 80% to 90 % whereas that of high speed industrial
gears should be at least 99 %.
In general, the material used in high volume vehicle gear production may be of more uniform quality than that
used for gears produced in small numbers.
Comparison of applied gear designs has indicated that for about 10 000 cycles, the load transmitted by truck
final drive gears is about four times greater than that transmitted by aircraft or space vehicle gears, where the
material, the quality, the size and the design are the same.
For low speed vehicle gears which are intended to have short lives (less than 100 000 cycles), small amounts
Consequently, the levels of surface
of plastic deformation, pitting and abrasive wear can usually be tolerated.
stress which are permissible are substantially higher than would be permissible for long life, high speed gears.
4.1.2.2 Main drive for aircraft and space vehicles, which are found in helicopter rotor drives and the main
pump drives of space vehicle boosters, where gears of the highest quality material and accuracy are used. Such
gears are extensively tested. For example, 10 to 20 transmissions of the same production series may be tested
The tolerable wear rate is established on the basis of test
under operational conditions for the full design life.
results. Lubricant spray rate, position of injection points and direction of spray is optimized.
For these reasons, higher loading is permissible for a design life up to 100 times longer (in cycles of tooth
loading), and speeds about 10 times greater than those of a typical vehicle transmission. The probability of
damage in such cases shall not exceed O,l% to 1 %. Overall loading cannot be as high as for vehicle gears
since neither surface wear nor minor damage can be tolerated.
4.1.2.3 Industrial turbine gears, where the pitch line velocities exceed 50 m/s, the pinions are usually designed
with 30 or more teeth with the objective of minimizing the risk of scuffing and wear. A typical gear pair would
consist of a pinion with 45 teeth and a wheel with 248.
Industrial turbine gearing should be better than 99 % reliable for a normal life of more than IO” cycles.
Extensive prototype testing is normally excluded because of the cost. As a consequence, the load capacity
ratings of turbine gears tend to be conservative with relatively high safety factors.
Safety factors
4.1.3
It is necessary to distinguish between the safety factor relative to pitting, S,, and the safety factor relative to
tooth breakage, S,.
For a given application, adequate gear load capacity is demonstrated by the computed values of S, and S,
being equal to or greater than the values SH min and SF min, respectively.
Certain minimum values for safety factors shall be determined. Recommendations concerning these minimum
values are made in IS0 6336, but values are not proposed.
An appropriate probability of failure and the safety factor shall be carefully chosen to meet the required reliability
at a justifiable cost. If the performance of the gears can be accurately appraised through testing of the actual
unit under actual load conditions, a lower safety factor and more economical manufacturing procedures may be
permissible.
Modified allowable stress number
Safety factor =
Calculated stress
Safety factors based on load are permitted. When they are based on load the safety factor equals the specific
When the factor is based on load,
calculated load capacity divided by the specific operating load transmitted.
this shall be stated clearly.
IS0 6336-1 :1996(E)
0 IS0
NOTE 1 - Safety factors based on load (power) relative to tooth bending are proportional to SF. Safety factors based on
load (power) relative to pitting are proportional to SH2.
In addition to the general requirements mentioned and the special requirements for surface durability, pitting,
(IS0 6336-2) and tooth bending strength (IS0 6336-3) the safety factors shall be chosen after careful
consideration of the following influences:
reliability of material data (The allowable stress numbers used in the calculation are valid for a given
probability of failure, the material values in IS0 6336-5 are valid for 1% probability of damage. This risk of
damage reduces with the increase of the safety factor and vice versa);
reliability of load values used for calculation (If loads or the response of the system to vibration, are
estimated rather than measured, a larger factor of safety should be used);
variations in gear geometry due to manufacturing tolerances;
variations in alignment;
variations in material due to process variations in chemistry, cleanliness and microstructure (material
quality and heat treatment);
variations in lubrication and its maintenance over the service life of the gears.
Depending on the reliability of the assumptions on which the calculations are based (e.g. load assumptions) and
according to the reliability requirements (consequences of damage occurrence), a corresponding safety factor
is to be chosen.
Where gears are produced under a specification or a request for proposal (quotation), in which the gear supplier
is to provide gears or assembled gear drives having specified calculated capacities (ratings) in accordance with
IS0 6336, the value of the safety factor for each mode of failure (pitting, tooth breakage) is to be agreed upon
between the parties.
4.1.4 Testing
The most reliable known approach to the appraisal of overall system performance is that of testing a proposed
new design. Where sufficient field or test experience is available, satisfactory results can be obtained by
extrapolation of previous tests or field data.
When suitable test results or field data are not available, values for the rating factors should be chosen
conservatively.
4.1.5 Manufacturing tolerances
Evaluation of rating factors should be based on the minimum accuracy grade limits specified for the component
parts in the manufacturing process.
4.1.6 implied accuracy
Where empirical values for rating factors are given by curves, curve fitting equations are provided to facilitate
computer programming. The constants and coefficients used in curve fitting often have significant digits in excess
of those appropriate to the reliability of the empirical data.
4.1.7
Other considerations
In addition to the factors considered in IS0 6336 influencing pitting resistance and bending strength, other
interrelated system factors can have a significant influence on overall transmission performance. The following
factors are particularly significant.
0 IS0
IS0 6336-l :1996(E)
4.1.7.1 Lubrication. The ratings determined by these formulae are valid only if the gear teeth are operated
with a lubricant of proper viscosity and additives for the load, speed, and surface finish, and if there is a sufficient
quantity of lubricant supplied to the gear teeth and bearings to lubricate and maintain an acceptable operating
temperature.
Many gear systems depend on external supports such
4.1.7.2 Misalignment and deflection of foundations.
If these supports are poorly designed, initially
as machinery foundations to maintain alignment of the gear mesh.
misaligned, or become misaligned during operation through elastic or thermal deflection or other influences,
overall gear system performance will be adversely affected.
4.1.7.3 Deflections of gear teeth, gear blanks, gear shafts, bearings and housings affect performance and
distribution of total tooth load over meshing flanks. Since these deflections vary with load, it is impossible to
obtain optimum tooth contact at different loads in those transmissions that encounter variable load. When gear
tooth flanks are not modified, the face load factor increases with increasing deflection, thereby lowering rated
capacity.
4.1.7.4 System dynamics. The method of analysis used in IS0 6336 provides a dynamic factor in the formulae
by derating the gears for increased loads caused by gear tooth inaccuracies and for harmonic effects. In
general, simplified values are given for easy application. The dynamic response of the system results in
additional gear tooth loads due to the relative motions of the connected masses of the driver and the driven
equipment. The application factor, Kay is intended to account for the operating characteristics of the driving and
driven equipment. It must be recognized, however, that if the operating roughness of the driver, gearbox, or
driven equipment causes an excitation with a frequency that is near to one of the system ’s major natural
frequencies, resonant vibrations may cause severe overloads which may be several times higher than the
nominal load.
For critical service applications, it is recommended that a vibration analysis be performed. This analysis shall
include the total system of driver, gearbox, driven equipment, couplings, mounting conditions, and sources of
excitation. Natural frequencies, mode shapes, and the dynamic response amplitudes should be calculated. The
resulting load spectrum cumulative fatigue effect calculation, if necessary or required, is given in ISO/TR 10495.
The teeth of most cylindrical gears are modified in both profile and lengthwise
4.1.7.5 Contact pattern.
directions during the manufacturing operation to accommodate deflection of the mountings. This results in a
localized contact pattern during roll testing under light loads. Under design load, the contact should spread over
the tooth flank without any concentration of the pattern at the edges. This influence shall be taken into account
by the corresponding load distribution factor.
4.1.7.6 Corrosion of gear tooth surfaces can significantly reduce the bending strength and pitting resistance
of the teeth. Quantifying the extent of these reductions is beyond the scope of IS0 6336.
4.1.8 Influence factors
The influence factors presented in IS0 6336 are derived from results of research and field service. It is
convenient to distinguish between the following:
a) Factors which are determined by gear geometry or which have been established by convention. They shall
be calculated in accordance with the equations given in IS0 6336.
b) Factors which account for several influences and which are dealt with as independent of each other, but,
which may nevertheless influence each other to a degree for which no numerical value can be assigned.
These include the factors KA, Kv, KHa, KHp, or KFa and the factors influencing allowable stress.
The factors Kv, KHp, and KHa also depend on the magnitudes of the profile and helix modifications. Profile and
helix modifications are only effective if they are significantly larger than the manufacturing deviations. For this
reason, the influence of the profile and helix modifications may only be taken into consideration if the gear
manufacturing deviations do not exceed specific limit values. The minimum required gear manufacturing
accuracy is stated, together with reference to IS0 1328-1, for each factor.
The influence factors can be determined by various methods. These are qualified, as necessary, by adding
subscripts A through E to the symbols. Unless otherwise specified, e.g. in an application standard, the more
0 IS0 IS0 6336=1:1996(E)
accurate of the methods is to be preferred for important transmissions. In cases of dispute, when proof of
accuracy and reliability is supplied, method A is superior to method B, and method B to method C, etc.
NOTE 2 - It is recommended that supplementary subscripts be used whenever the method used for evaluation of a factor
would not be readily identifiable.
In some applications it may be necessary to choose between factors which have been determined using
alternative methods (e.g. the alternatives for
...
NORME ISO
INTERNATIONALE 6336-1
Première édition
1996-05-15
Calcul de la capacité de charge des
engrenages cylindriques à dentures droite
et hélicoïdale —
Partie 1:
Principes de base, introduction et facteurs
généraux d’influence
Calculation of load capacity of spur and helical gears —
Part 1: Basic principles, introduction and general influence factors
Numéro de référence
©
ISO 1996
PDF – Exonération de responsabilité
Le présent fichier PDF peut contenir des polices de caractères intégrées. Conformément aux conditions de licence d'Adobe, ce fichier peut
être imprimé ou visualisé, mais ne doit pas être modifié à moins que l'ordinateur employé à cet effet ne bénéficie d'une licence autorisant
l'utilisation de ces polices et que celles-ci y soient installées. Lors du téléchargement de ce fichier, les parties concernées acceptent de fait la
responsabilité de ne pas enfreindre les conditions de licence d'Adobe. Le Secrétariat central de l'ISO décline toute responsabilité en la
matière.
Adobe est une marque déposée d'Adobe Systems Incorporated.
Les détails relatifs aux produits logiciels utilisés pour la création du présent fichier PDF sont disponibles dans la rubrique General Info du
fichier; les paramètres de création PDF ont été optimisés pour l'impression. Toutes les mesures ont été prises pour garantir l'exploitation de
ce fichier par les comités membres de l'ISO. Dans le cas peu probable où surviendrait un problème d'utilisation, veuillez en informer le
Secrétariat central à l'adresse donnée ci-dessous.
© ISO 1996
Droits de reproduction réservés. Sauf prescription différente, aucune partie de cette publication ne peut être reproduite ni utilisée sous quelque
forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l'accord écrit de l’ISO à
l’adresse ci-après ou du comité membre de l’ISO dans le pays du demandeur.
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.ch
Web www.iso.ch
Version française parue en 2002
Imprimé en Suisse
ii © ISO 1996 – Tous droits réservés
Sommaire Page
Avant-propos .iv
Introduction.v
1 Domaine d'application.1
2 Références normatives.2
3 Définitions, symboles et unités.3
4 Principes de base .14
5 Facteur d'application K .20
A
6 Facteur dynamique interne K .21
v
7 Facteurs de distribution longitudinale de la charge K et K .42
Hβ Fβ
8 Facteurs de distribution transversale de la charge K , K .81
Hα Fα
9 Rigidités de denture c′ et c .89
γ
Annexe A (informative) Valeurs indicatives pour le bombé et les dépouilles d’extrémité des dents
d’engrenages cylindriques .98
Annexe B (informative) Valeurs indicatives pour le facteur d’application K .101
A
Annexe C (informative) Dérivations et notes explicatives.104
Bibliographie.108
© ISO 1996 – Tous droits réservés iii
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée aux
comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du comité
technique créé à cet effet. Les organisations internationales, gouvernementales et non gouvernementales, en
liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec la Commission
électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les projets de Normes internationales adoptés par les comités techniques sont soumis aux comités membres pour
vote. Leur publication comme Normes internationales requiert l'approbation de 75 % au moins des comités
membres votants.
La Norme internationale ISO 6336-1 a été élaborée par le comité technique ISO/TC 60, Engrenages, sous-comité
SC 2, Calcul de la capacité des engrenages.
L'ISO 6336 comprend les parties suivantes, présentées sous le titre général Calcul de la capacité de charge des
engrenages cylindriques à dentures droite et hélicoïdale:
Partie 1: Principes de base, introduction et facteur généraux d'influence
Partie 2: Calcul de la résistance à la pression de contact (piqûres)
Partie 3: Calcul de la résistance à la flexion en pied de dent
Partie 5: Résistance et qualité des matériaux
Les annexes A à D de la présente partie de l’ISO 6336 sont données uniquement à titre d’information.
iv © ISO 1996 – Tous droits réservés
Introduction
La présente partie de l’ISO 6336 et les parties 2, 3 et 5 fournissent les principes d'un système cohérent de
méthodes pour le calcul de la capacité de charge des engrenages cylindriques à denture intérieure ou extérieure et
à profil en développante de cercle. L’ISO 6336 est conçue pour faciliter l’application des résultats des travaux et
développements futurs, mais aussi des échanges d'informations issues de l'expérience.
Il convient d’analyser, par des méthodes générales de conception d'éléments de machine, les particularités de
conception destinées à éviter les ruptures émanant d'un niveau de contrainte élevé au niveau du flanc de dent, de
l'ébréchage des têtes de dents et des ruptures du corps de roue au niveau du voile ou de la jante.
Pour le calcul de la capacité de charge, mais aussi pour celui de plusieurs facteurs, diverses méthodes sont
admises (voir 4.1.8). Les prescriptions contenues dans l’ISO 6336 sont complexes mais aussi adaptables. Il
convient de choisir suivant le cas, la méthode la plus détaillée ou la plus simplifiée pour l’inclure dans les normes
d'application qui sont issues de la norme de base. De telles normes d'application concernent les domaines
suivants:
engrenages industriels (méthode détaillée et simplifiée);
engrenages à grande vitesse et ceux d'application similaire;
engrenages marins;
engrenages pour véhicules industriels.
Ces normes d'application éclaircissent et, dans une certaine mesure, simplifient les règles de calcul.
Les équations contiennent les principaux facteurs d'influence sur les engrenages vis-à-vis de la formation des
piqûres et des ruptures en pied de dent, qui sont connus à ce jour. Les équations sont écrites de manière à
permettre l'introduction de nouveaux facteurs d'influence issus de connaissances qui pourront être acquises dans
l'avenir.
© ISO 1996 – Tous droits réservés v
NORME INTERNATIONALE ISO 6336-1:1996(F)
Calcul de la capacité de charge des engrenages cylindriques à
dentures droite et hélicoïdale —
Partie 1:
Principes de base, introduction et facteurs généraux d'influence
1 Domaine d'application
1.1 Utilisation souhaitée
La présente partie de l’ISO 6336, associée aux parties 2, 3 et 5 fournit une méthode qui permet de comparer
différentes conceptions d'engrenages. Elle n'a pas pour but de déterminer les performances d'une transmission de
puissance par engrenages complète. Elle n'a pas non plus pour but d'être employée par des concepteurs
généralistes en mécanique. Par contre, elle a pour but d'être utilisée par des concepteurs d'engrenages
expérimentés, capables de sélectionner, pour chacun des facteurs employés dans les équations, des valeurs
raisonnables sur la base de leurs connaissances en matière de conception d'engrenages similaires et conscients
des effets des points particuliers discutés.
Les équations de l’ISO 6336 ont pour but d'établir une méthode homogène pour le calcul de la capacité de charge
vis-à-vis de la pression de contact et de la contrainte de flexion en pied de dent des roues cylindriques à denture
droite ou hélicoïdale.
L’ISO 6336 contient des méthodes basées sur des résultats d'essais et d'études théoriques telles que celles de
Hirt [1], Strasser [2], et Brossmann [3]. Les résultats de l'évaluation de la capacité de charge effectuée suivant la
présente partie de l’ISO 6336 sont en bon accord avec ceux obtenus par des méthodes antérieurement reconnues
(voir références [4] à [8]), pour des angles de pression normaux allant jusqu'à 25° et des angles d'hélice de
référence allant jusqu'à 30°.
Pour des angles de pression et des angles d'hélice de référence plus grands, l'évolution des produits Y Y Y et
F S β
Z Z Z n'est pas la même que celle obtenue par les méthodes antérieures. L'utilisateur de l’ISO 6336 est mis en
H ε β
garde sur le fait que, lors de l’utilisation d’une des méthodes de l’ISO 6336 pour des angles d'hélice ou des angles
de pression plus importants, il est recommandé de confirmer par l'expérience les valeurs calculées.
1.2 Exceptions
Les équations de l’ISO 6336 ne sont pas applicables si l'une des conditions suivantes existe:
engrenages à denture droite ou hélicoïdale avec un rapport de conduite inférieur à 1,0;
engrenages à denture droite ou hélicoïdale avec un rapport de conduite apparent supérieur à 2,5;
quand il existe une interférence de fonctionnement entre les profils en pieds de dents et les têtes de dents;
quand les dents sont pointues;
quand le jeu entre dents est nul.
Les équations de calcul de la capacité de charge de l’ISO 6336 ne s’appliquent pas à d'autres dégradations telles
que la déformation plastique, le grippage, la dislocation, l'adhésion ou l'usure, ni lorsque les conditions vibratoires
sont telles qu'elles peuvent conduire à une rupture de dent imprévisible. Les équations de calcul de contrainte de
flexion ne sont applicables que vis-à-vis de la rupture en pied de dent et non vis-à-vis de la rupture au niveau du
© ISO 1996 – Tous droits réservés 1
profil actif, de la jante ou du corps de la roue, au travers du voile ou du moyeu. L’ISO 6336 ne s’applique pas aux
dentures réalisées par forgeage ou roulage, ni aux engrenages qui ont une mauvaise marque de portée.
Les procédures de l’ISO 6336 concernent le calcul de la capacité de charge vis-à-vis de la formation des piqûres et
de la rupture en pied de dent. Avec une vitesse tangentielle inférieure à 1 m/s, l'usure abrasive limite la capacité de
charge (voir d'autres références pour des informations sur ce calcul).
1.2.1 Grippage
Les équations du calcul de la capacité de charge des engrenages cylindriques vis-à-vis du grippage ne sont pas
contenues dans l’ISO 6336. Actuellement, il n'existe pas d’accord suffisant concernant une méthode de conception
des dentures basée sur la tenue au grippage.
1.2.2 Usure
Il y a très peu d'intérêt relatif à l'étude de l'usure des dents d'engrenages. Ce sujet concerne essentiellement les
dentures qui ont une faible dureté superficielle ou les engrenages qui fonctionnent avec une lubrification inadaptée.
Aucune tentative n’a été réalisée pour couvrir ce sujet dans l’ISO 6336.
1.2.3 Micropiqûres
L’ISO 6336 ne traite pas des micropiqûres, qui sont une catégorie supplémentaire de dégradation de surface
pouvant apparaître sur les flancs des dents.
1.2.4 Déformation plastique
L’ISO 6336 ne s’étend pas aux niveaux de contraintes supérieures à celles admissibles pour 10 cycles ou moins,
puisque, dans ce domaine, les contraintes peuvent dépasser la limite élastique du matériau de la denture, que ce
soit à la flexion ou à la pression de contact. En fonction du matériau et de la charge, un seul cycle produisant une
contrainte supérieure à celle admissible pour un nombre de cycles < 10 peut entraîner une déformation plastique
de la dent.
2 Références normatives
Les normes suivantes contiennent des dispositions qui, par suite de la référence qui y est faite, constituent des
dispositions valables pour la présente partie de l'ISO 6336. Au moment de la publication, les éditions indiquées
étaient en vigueur. Toute norme est sujette à révision et les parties prenantes des accords fondés sur la présente
partie de l’ISO 6336 sont invitées à rechercher la possibilité d’appliquer les éditions les plus récentes des normes
indiquées ci-après. Les membres de l'ISO et de la CEI possèdent le registre des Normes internationales en vigueur
à un moment donné.
ISO 53:1974, Engrenages cylindriques de mécanique générale et de grosse mécanique — Crémaillère de
référence
ISO 468:1982, Rugosité de surface — Paramètres, leur valeur et les règles générales de la détermination des
spécifications
ISO 701:1976, Notation internationale des engrenages — Symboles de données géométriques
ISO 1122-1:1983, Vocabulaire des engrenages — Partie 1: Définitions géométriques
ISO 1328-1:1995, Engrenages cylindriques — Système ISO de précision — Partie 1: Définitions et valeurs
admissibles des écarts pour les flancs homologues de la denture
ISO 6336-2:1996, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 2: Calcul de la résistance à la pression de contact (piqûres)
ISO 6336-3:1996, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 3: Calcul de la résistance à la flexion en pied de dent
2 © ISO 1996 – Tous droits réservés
ISO 6336-5:1996, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 5: Résistance et qualité des matériaux
ISO/TR 10495, Engrenages cylindriques — Calcul de la durée de vie en service sous charge variable —
Conditions pour les engrenages cylindriques conformément à l’ISO 6336
3 Définitions, symboles et unités
Pour les besoins de l’ISO 6336, les définitions données dans l’ISO 1122-1 s'appliquent.
Les symboles sont basés sur une extension des symboles donnés dans l’ISO 701 et ISO 1328-1. Sont donnés
uniquement les symboles des quantités particulières qui sont utilisées dans le calcul des facteurs traités dans l’ISO
6336 ainsi que les unités qu'il est préférable d'utiliser dans les calculs. Le Tableau 1 énumère les symboles utilisés
dans les calculs de toutes les parties de l’ISO 6336.
Tableau 1 — Symboles et abréviations utilisés dans l’ISO 6336-1, l’ISO 6336-2, l’ISO 6336-3 et l’ISO 6336-5
Symbole Description Unité
Symboles principaux et abréviations
1)
a entraxe mm
b largeur de denture mm
c constante —
d diamètre (sans indice, diamètre de référence) mm
e quantité auxiliaire —
f écart, déformation de dent µm
g longueur de ligne de conduite mm
h hauteur de denture (sans indice, du cercle de pied au cercle de tête) mm
i rapport de transmission —
k facteur de troncature —
l distance entre paliers mm
module, mm
m
masse kg
−1 −1
n vitesse de rotation s ou min
pas, mm
p
nombre de satellites —
facteur auxiliaire, —
.
q flexibilité d’une paire de dents en contact, voir article 9, (mm µm)/N
surépaisseur d’ébauche, voir article 5 de l’ISO 6336-3 mm
r rayon (sans indice, rayon de référence) mm
épaisseur de denture, distance entre la mi-largeur du pignon et le milieu de la distance
s mm
entre paliers
1)
u rapport d’engrenage (z /z ) W 1 —
2 1
vitesse tangentielle (sans indice, sur le cercle de référence ≈ vitesse tangentielle sur le
v m/s
cercle primitif de fonctionnement)
1)
Pour les engrenages à denture extérieure, a , z , et z sont positifs; pour les engrenages à denture intérieure, a et z ont un
1 2 2
signe négatif, z a un signe positif.
© ISO 1996 – Tous droits réservés 3
Symbole Description Unité
w charge spécifique (par unité de largeur de denture, F /b) N/mm
t
x coefficient de déport —
y tolérance de rodage (seulement avec les indices α ou β) µm
1)
z nombre de dents —
points de la ligne d’action (du pied du pignon au sommet du pignon, indépendant du fait
A, B, C, D, E —
que le pignon ou la roue soit menant, seulement pour des considérations géométriques)
B largeur totale d’une roue à denture hélicoïdale double y compris la gorge centrale mm
constante, coefficient, —
C
dépouille sur les flancs de dents µm
D diamètre (conception) mm
E module d’élasticité N/mm
Eh désignation du matériau pour les aciers de cémentation, cémentés —
Eht profondeur de cémentation, voir l’ISO 6336-5 mm
écarts composé et total, µm
F
force ou charge N
G module de cisaillement N/mm
GG désignation du matériau pour les fontes grises —
GGG désignation du matériau pour les fontes (structure perlitique, bainitique, ferritique) —
GTS désignation du matériau pour les fontes malléables (structure perlitique) —
HB dureté Brinell —
HRC dureté Rockwell (échelle C) —
HR 30N dureté Rockwell (échelle 30 N), voir l’ISO 6336-5 —
HV dureté Vickers —
HV 1 dureté Vickers sous la charge F = 9,81 N, voir l’ISO 6336-5 —
HV 10 dureté Vickers sous la charge F = 98,10 N, voir l’ISO 6336-5 —
désignation du matériau pour les aciers et GGG, durcis superficiellement à la flamme ou
IF —
par induction
J trempabilité Jominy, voir l’ISO 6336-5 —
K constante, facteurs concernant la charge sur les dents —
L longueurs (conception) mm
M moment d’une force Nm
MX
ME symboles identifiant les exigences sur le matériau et le traitement thermique, voir
—
MQ l’ISO 6336-5
ML
N nombre, exposant, nombre de cycles de mise en charge, facteur de résonance —
NT désignation du matériau pour les aciers de nitruration, nitrurés —
désignation du matériau pour les aciers traités dans la masse et les aciers de
NV —
cémentation, nitrurés (nitr.), nitrocarburés (nitrocar.)
P puissance transmise kW
4 © ISO 1996 – Tous droits réservés
Symbole Description Unité
S coefficient de sécurité —
St désignation du matériau pour les aciers (σ < 800 N/mm ) —
B
couple, Nm
T
tolérance µm
V désignation du matériau pour les aciers traités dans la masse, (σ W 800 N/mm ) —
B
W facteur de chargement —
Y facteur relatif à la contrainte en pied de dent —
Z facteur relatif à la pression de contact —
α angle de pression (sans indice, sur le cylindre de référence) °
β angle d’hélice (sans indice, sur le cylindre de référence) °
angle auxiliaire, °
γ contrainte de cisaillement, —
facteur de décalage du pignon, voir équations dans l’article 7 µm
δ déflection µm
ε rapport de conduite, rapport de recouvrement, excentricité relative (voir l’article 7) —
η viscosité dynamique effective du bain d’huile à la température moyenne du bain mPa⋅s
ϕ température °C
µ coefficient de frottement —
coefficient de Poisson, —
ν
viscosité cinématique de l’huile mm /s
rayon de courbure, mm
ρ
−6 3
densité (pour l’acier, ρ = 7,83 × 10 ) kg/mm
σ contrainte normale N/mm
τ contrainte de cisaillement N/mm
χ facteur de rodage —
angle auxiliaire, °
ψ
jeu relatif du palier (voir article 7) —
ω vitesse angulaire rad/s
Γ paramètre sur la ligne d’action —
Ψ striction %
Indices des symboles
— valeurs de référence (sans indice)
saillie,
a
tête de dent
ann couronne
cercle de base,
b
largeur de denture
be palier
ca carter
© ISO 1996 – Tous droits réservés 5
Symbole Description Unité
cal calculé
co marque de portée
dyn dynamique
e point le plus haut de contact unique
eff valeur effective, contrainte effective
f pied de dent, creux
i interne
troncature,
k
valeurs relatives à l’éprouvette entaillée
lim valeur pour la contrainte de référence
m moyenne ou valeur moyenne (plan moyen)
ma fabrication
max valeur maximale
min valeur minimale
plan normal,
n engrenage virtuel équivalent à denture droite d’un engrenage à denture hélicoïdale,
nombre de tours
oil huile
pas,
p
valeurs relatives à l’éprouvette lisse
par parallèle
pla satellite
r radial
red réduit
rel relatif
épaisseur de dent,
s
effet d’entaille
sh arbre
stat statique (charge)
sun pignon solaire, roue solaire, planétaire
t plan apparent
th théorique
vitesse,
v
pertes
w fonctionnement (cet indice peut remplacer l’apostrophe)
rodage,
y
tout point du flanc de dent
application,
A
surcharges extérieures
6 © ISO 1996 – Tous droits réservés
Symbole Description Unité
point primitif,
C
correction de profil d’hélice
transformation de vitesse,
D
réducteur ou multiplicateur
élasticité du matériau,
E
résonance
F contrainte en pied de dent
G géométrie
H pression de Hertz (pression de contact)
L lubrification
M matériau
nombre (un nombre spécifique peut être introduit après l’indice N dans le facteur de
N
durée de vie)
valeur admissible,
P
profil de la crémaillère de référence
rugosité,
R
colonnes
roue d’essai,
T
valeurs relatives à la roue d’essai de référence normalisée
W appairage des matériaux
X dimension (absolue)
z solaire
conduite apparente,
α
profil
hélice,
β largeur de denture,
bombé
total (valeur totale)
γ
témoin de rugosité
∆
rapport de conduite
ε
valeur de base,
outil
1 pignon
2 roue
1.9 numérotation générale
dépouille d’extrémité,
I(II)
face de référence (face de non-référence)
contact monoflanc (indice w possible) une seule paire de dents en contact tangentiel
′
contact sur deux flancs (contact simultané entre les flancs actif et non actif)
″
© ISO 1996 – Tous droits réservés 7
Symbole Description Unité
Symboles combinés
largeur de palier hydrodynamique mm
b
be
b largeur de denture calculée (Figure 9) mm
cal
b largeur de la marque de portée sans charge (marquage du contact) mm
c0
b largeur de denture réduite (largeur moins les dépouilles d’extrémité) mm
red
b épaisseur de voile mm
s
b largeur de denture d’une des hélices d’une roue à denture hélicoïdale double mm
B
b largeur de dépouille d’extrémité mm
I(II)
c vide à fond de dent entre la crémaillère de référence et le profil conjugué mm
P
c valeur moyenne de la rigidité d’engrènement par unité de largeur de denture N/(mm⋅µm)
γ
c′ rigidité maximum par unité de largeur de denture (rigidité simple) d’une paire de dents N/(mm⋅µm)
c′ rigidité simple théorique N/(mm⋅µm)
th
d diamètre de tête mm
a
d diamètre de base mm
b
d diamètre du cercle au point le plus haut de contact unique mm
e
d diamètre de pied mm
f
d diamètre de pied d’une couronne à denture intérieure mm
f2
d diamètre extérieur d’un arbre, nominal pour la déformée élastique de flexion mm
sh
d diamètre intérieur d’un arbre creux mm
shi
d diamètre primitif mm
w
d diamètre de bille (roulement à billes) mm
B
d diamètre de référence du pignon (ou de la roue) mm
1,2
2)
f composante du désalignement équivalent due à la déformation des paliers µm
be
2)
f composante du désalignement équivalent due à la déformation du carter µm
ca
écart de forme du profil (la valeur de l’écart total de profil F peut être utilisée à la place,
α
f µm
fα
si les tolérances définies suivant l’ISO 1328-1 sont utilisées)
2)
f désalignement d’engrènement dû aux écarts de fabrication µm
ma
f écart individuel de pas apparent µm
p
2)
f non-parallélisme des axes du pignon et de la roue (écarts de fabrication) µm
par
écart de pas de base apparent (la valeur de f peut être utilisée pour les calculs suivant
pb
f µm
pb
l’ISO 6336, en utilisant les tolérances définies suivant l’ISO 1328-1)
2)
composante du désalignement équivalent dû à la déformation des arbres du pignon et
f µm
sh
de la roue
composante du désalignement dû aux déformations de l’arbre et du pignon mesurées
f µm
shT
sous charge partielle
2)
.
f déformation de l’arbre sous la charge spécifique (mm µm)/N
sh0
écart d’inclinaison d’hélice (la valeur de l’écart total d’hélice F peut être utilisée à la
β
f µm
Hβ
place, si les tolérances déterminées suivant l’ISO 1328-1 sont utilisées)
f écart admissible d’inclinaison d’hélice pour la classe de précision ISO 6 µm
Hβ 6
g longueur de la ligne d’action mm
α
2)
Les composantes dans le plan d’action sont à considérer.
8 © ISO 1996 – Tous droits réservés
Symbole Description Unité
h saillie de la crémaillère de référence des roues dentées cylindriques mm
aP
h saillie d’outil mm
a0
h creux de la crémaillère de référence des roues dentées cylindriques mm
fP
h creux d’outil mm
f0
h creux de la dent d’une roue à denture intérieure mm
f2
h épaisseur minimale du film lubrifiant mm
min
h hauteur du bras de levier pour la contrainte de flexion en pied de dent mm
F
hauteur du bras de levier dans le cas de l’application de la charge au sommet de dent
h mm
Fa
(défini par le point d’intersection des deux tangentes à 30°)
bras de levier dans le cas de l’application de la charge au point le plus haut de contact
h mm
Fe
unique
l longueur effective d’un rouleau (roulements à rouleaux) mm
a
m* moment d’inertie d’une roue par unité de largeur de denture rapporté à la ligne d’action kg/mm
m module normal mm
n
masse réduite d’un couple de roues dentées par unité de largeur de denture relativement
m kg/mm
red
à la ligne d’action
m module apparent mm
t
−1 −1
n vitesse de rotation du pignon (ou la roue) min ou s
1,2
-1
n vitesse de résonance min
E
p pas de base normal mm
bn
p pas de base apparent mm
bt
.
q′ valeur minimale de la flexibilité d’une paire de dents en contact (mm µm)/N
q protubérance de l’outil, voir Figure 2 de l’ISO 6336-3 mm
pr
q paramètre d’entaille, q = s /2 ρ —
s s Fn F
q paramètre d’entaille de l’éprouvette entaillée —
sk
q paramètre d’entaille de l’engrenage de référence normalisée, q = 2,5 —
sT sT
q facteur auxiliaire —
α
épaisseur du film de produit de marquage utilisé pour la détermination de la marque de
s µm
c
portée
s interférence de taillage résiduelle, s = q − q mm
pr pr pr
s section en pied de dent dans la section critique mm
Fn
s épaisseur de jante mm
R
t profondeur maximum de crique de rectification mm
g
w charge spécifique moyenne (par unité de largeur de denture) N/mm
m
w force tangentielle par unité de largeur de denture, incluant les facteurs de surcharge N/mm
t
x coefficient de déport pour l’obtention de l’épaisseur de dent —
E
x coefficient de déport du pignon (ou de la roue) —
1,2
© ISO 1996 – Tous droits réservés 9
Symbole Description Unité
y tolérance de rodage pour une paire de roues dentées µm
α
y tolérance de rodage (désalignement équivalent) µm
β
z nombre de dents virtuel d’une roue à denture hélicoïdale —
n
1)
z nombre de dents du pignon (ou de la roue) , voir page 3 —
1,2
B* constante, voir équations dans l’article 7 —
C dépouille de tête µm
a
C facteur de crémaillère de référence (même crémaillère pour le pignon et la roue) —
B
C facteur de crémaillère de référence (pignon), voir 9.3.1.4 —
B1
C facteur de crémaillère de référence (roue), voir 9.3.1.4 —
B2
C facteur de correction, voir article 9 —
M
C facteur de corps de roue, voir article 9 —
R
C , , facteurs pour la détermination des facteurs du film lubrifiant, voir 11.2 de la partie 2 —
ZL ZR Zv
C hauteur de bombé µm
β
C dépouille d’extrémité µm
I(II)
D diamètre de l’alésage du palier (paliers lisses) mm
be
D diamètre du tourillon (paliers lisses) mm
sh
F force radiale appliquée au palier N
be r
F force (nominale), normale à la ligne de contact N
bn
F force nominale apparente dans le plan d’action (plan tangent aux cylindres de base) N
bt
effort tangentiel apparent moyen sur le cercle de référence issu des calculs
F N
m
d’engrènement, F = (F K K )
m t A v
F effort tangentiel apparent moyen partiel sur le cercle de référence N
m T
F effort tangentiel maximum pour l’engrènement calculé N
max
F force tangentielle (nominale) sur le cylindre de référence N
t
F effort tangentiel dans le plan apparent déterminant pour K et K F = F K K K N
tH Hα Fα, tH t A v Hβ
F écart total du profil µm
α
F écart total d’hélice µm
β
F écart total d’hélice admissible pour la classe de précision ISO 6 µm
β6
F désalignement équivalent initial (avant rodage) µm
βx
désalignement équivalent initial pour la détermination de la hauteur du bombé
F µm
βx cv
(estimation)
F désalignement équivalent mesuré sous charge partielle µm
βx T
F désalignement équivalent effectif (après rodage) µm
βy
′
K constante pour la détermination de la position du pignon par rapport à l’entrée du couple —
K facteur dynamique —
v
K facteur d’application —
A
K facteur de distribution transversale de la charge (contrainte en pied de dent) —
Fα
10 © ISO 1996 – Tous droits réservés
Symbole Description Unité
K facteur de distribution longitudinale de la charge (contrainte en pied de dent) —
Fβ
K facteur de distribution transversale de la charge (pression de contact) —
Hα
K facteur de distribution longitudinale de la charge (pression de contact) —
Hβ
facteur de répartition de charge (tient compte d’une distribution inégale de la charge
K —
γ
entre les engrènements d’une transmission à couple divisé)
J* moment d’inertie par unité de largeur de denture kg⋅mm /mm
N nombre de billes (ou rouleaux) par rangée —
B
N exposant —
F
N nombre de cycles de mise en charge —
L
N nombre d’engrènements par tour (normalement 1, pour les roues intermédiaires 2)
—
M
N nombre de rangées par roulement
—
R
N facteur de résonance dans le domaine de résonance principale —
S
N nombre de voiles —
w
R rugosité arithmétique moyenne, R = 1/6 R
µm
a a z
R rugosité moyenne crête à crête (comme spécifié dans l’ISO 468)
µm
z
R rugosité moyenne crête à crête de l’éprouvette de rugosité entaillée µm
zk
rugosité moyenne crête à crête de l’engrenage de référence normalisé,
R µm
zT
R = 10
zT
S coefficient de sécurité vis-à-vis de la rupture en pied de dent —
F
S coefficient de sécurité vis-à-vis de la formation des piqûres —
H
So nombre de Sommerfeld
—
.
T couple nominal sur le pignon (ou sur la roue) N m
1,2
facteur de forme, correspondant à l’influence sur la contrainte en pied de dent nominale
Y —
F
avec la charge appliquée sur le point le plus haut de contact unique
facteur de forme, correspondant à l’influence sur la contrainte en pied de dent avec la
Y
—
Fa
charge appliquée au sommet de dent
facteur combiné de forme et de concentration de contrainte, égal à (Y Y ), qui tient
Fa Sa
Y —
FS
compte des influences couvertes par Y et Y
Fa Sa
facteur de durée de vie correspondant à la contrainte en pied de dent, déterminé sur
Y —
Nk
éprouvette entaillée
facteur de durée de vie correspondant à la contrainte en pied de dent, déterminé sur
Y
—
Np
éprouvette lisse
facteur de durée de vie correspondant à la contrainte en pied de dent dans les conditions
Y —
NT
d’essais de référence
Y facteur d’état de surface en pied de dent (déterminé sur éprouvette lisse)
—
R
facteur de rugosité relative, quotient du facteur d’état de surface en pied de dent de la
Y roue dentée concernée par le facteur déterminé sur éprouvette entaillée,
—
R rel k
Y Y /Y
R rel k = R Rk
facteur de rugosité relative, quotient du facteur de rugosité en pied de dent de la roue
Y
dentée concernée par le facteur de rugosité de la roue dentée de référence, —
R rel T
Y Y /Y
R rel T = R RT
facteur de concentration de contrainte, pour la conversion de la contrainte de flexion
Y nominale, déterminé pour l’application de la charge au point le plus haut de contact
—
S
unique, en contrainte locale en pied de dent
© ISO 1996 – Tous droits réservés 11
Symbole Description Unité
facteur de concentration de contrainte, pour la conversion de la contrainte nominale en
Y pied de dent, déterminé pour l’application de la charge en sommet de dent, en contrainte —
Sa
locale en pied de dent
Y , Y facteur de concentration de contrainte pour les dents avec entaille de rectification —
Sag Sg
Y facteur de concentration de contrainte, déterminé sur éprouvette d’essai entaillée —
Sk
facteur de concentration de contrainte, déterminé pour les dimensions de la roue dentée
Y —
ST
de référence
Y facteur de dimension (contrainte en pied de dent) —
X
Y facteur d’angle d’hélice (contrainte en pied de dent) —
β
facteur de sensibilité à l’entaille de la roue concernée (relativement à l’éprouvette d’essai
Y —
δ
lisse)
facteur de sensibilité d’une éprouvette entaillée d’essai, relativement à une éprouvette
Y —
δk
d’essai lisse
facteur de sensibilité à l’entaille d’une roue dentée de référence normalisée, relativement
Y —
δT
à l’éprouvette d’essai lisse
facteur de sensibilité relative d’essai, quotient du facteur de sensibilité à l’entaille de la
Y roue dentée concernée par le facteur de sensibilité de l’éprouvette d’essai entaillée,
δ rel k
Y = Y /Y
δ rel k δ δk
facteur de sensibilité relative à l’entaille, quotient du facteur de sensibilité à l’entaille de la
Y roue dentée concernée par le facteur de sensibilité à l’entaille de l’engrenage d’essai de —
δ rel T
référence normalisée, Y = Y /Y
δ rel T δ δT
Y facteur de rapport de conduite (contrainte en pied de dent) —
ε
Z facteur de vitesse —
v
Z , Z facteur de contact unique pour le pignon, pour la roue —
B D
Z facteur d’élasticité N/mm
E
Z facteur géométrique —
H
Z facteur lubrifiant —
L
Z facteur de durée de vie pour la pression de contact —
N
facteur de durée de vie pour la pression de contact dans les conditions d’essai de
Z —
NT
référence
Z facteur de rugosité pour la pression de contact —
R
Z facteur de rapport de dureté —
W
Z facteur de dimension (pression de contact) —
x
Z facteur d’angle d’hélice (pression de contact) —
β
Z facteur de rapport de conduite (pression de contact) —
ε
α angle d’incidence au sommet de dent de l’engrenage droit équivalent °
an
angle d’incidence pour le facteur de forme, angle d’incidence au point le plus haut de
α °
en
contact unique de l’engrenage droit équivalent
α angle de pression normal °
n
α angle de pression apparent °
t
12 © ISO 1996 – Tous droits réservés
Symbole Description Unité
α′ ou α angle de pression sur le cylindre primitif de fonctionnement °
t wt
angle d’incidence en sommet de dent concernant la direction de l’application de la
α °
Fan
charge en sommet de dent de la roue dentée droite équivalente
angle de direction de la charge concernant la direction de la charge appliquée au point le
α °
Fen
plus haut de contact unique de la roue dentée droite équivalente
α angle de pression normale du tracé de référence pour engrenages cylindriques °
Pn
β angle d’hélice en sommet de dent (sur la surface de tête de la roue dentée) °
a
β angle d’hélice de base °
b
angle d’hélice pour le facteur de forme, angle d’hélice au point le plus haut de contact
β °
e
unique
δ déformation élastique du palier (1, 2) dans la direction de la charge µm, mm
1,2
déflection combinée des dents conjuguées en supposant une distribution uniforme de la
δ µm
b th
charge sur la largeur de denture
différence d’épaisseur des jauges d’épaisseur pour la mesure du désalignement
δ µm
g
équivalent d’engrènement f
ma
δ striction %
S
ε rapport de conduite apparent —
α
rapport de conduite équivalent, rapport de conduite apparent de l’engrenage équivalent à
ε —
αn
denture droite
ε rapport de recouvrement —
β
ε rapport de conduite total, ε = ε + ε —
γ γ α β
ε rapport de retraite, ε = CE/p —
1 1 bt
ε rapport d’approche, ε = AC/p —
2 2 bt
ρ rayon d’arrondi de tête de dent de l’outil mm
a0
rayon du profil de raccordement en pied du tracé de référence pour les engrenages
ρ mm
fP
cylindriques
ρ rayon de l’entaille de rectification mm
g
ρ rayon de courbure équivalent mm
rel
ρ rayon de courbure équivalent au point primitif mm
C
ρ rayon d’arrondi en pied de dent dans la section critique mm
F
ρ′ épaisseur superficielle affectée par le glissement mm
σ contrainte nominale de l’éprouvette entaillée (flexion) N/mm
k lim
σ contrainte nominale de l’éprouvette lisse (flexion) N/mm
p lim
σ résistance mécanique N/mm
B
σ contrainte effective en pied de dent N/mm
F
σ contrainte nominale de référence (flexion) N/mm
F lim
σ contrainte admissible de référence (flexion), σ = σ Y N/mm
FE FE F lim ST
σ contrainte limite de flexion en pied de dent N/mm
FG
σ contrainte de flexion admissible en pied de dent N/mm
FP
© ISO 1996 – Tous droits réservés 13
Symbole Description Unité
σ contrainte de base en pied de dent N/mm
F0
σ pression de contact effective N/mm
H
σ contrainte nominale de référence (pression de contact) N/mm
H lim
σ pression de contact admissible modifiée, σ = σ S N/mm
HG HG H lim H
σ pression de contact admissible N/mm
HP
σ pression de contact de base N/mm
H0
σ limite élastique N/mm
S
σ limite élastique conventionnelle (0,2 % d’allongement permanent) N/mm
0,2
−1
χ* gradient de contrainte relatif dans le fond d’une entaille mm
χ facteur caractérisant le désalignement équivalent après rodage —
β
−1
χ* gradient de contrainte relatif sur une éprouvette d’essai lisse mm
p
ω vitesse angulaire du pignon (ou de la roue) rad/s
1,2
4 Principes de base
4.1 Application
Se référer à 1.1 pour l'utilisation souhaitée.
4.1.1 Catégories particulières
Le calcul de la capacité de charge vis-à-vis de la pression de contact ou de la contrainte de flexion en pied de dent
pour des catégories particulières d'engrenages cylindriques peut être basé sur un choix spécifique de valeurs pour
chacun des facteurs employés dans ces équations générales.
4.1.2 Applications spécifiques
Dans la conception des engrenages, il est très important de noter que les exigences varient considérablement d'un
domaine d'application à l'autre. L'utilisation des procédures de l’ISO 6336 pour des applications particulières
demande une analyse réaliste en toute connaissance de tous les paramètres à prendre en compte, en particulier:
de la contrainte admissible du matériau et du nombre de cycles de mise en charge;
des conséquences de toute probabilité de défaillance (taux de défaillance);
de la valeur appropriée du coefficient de sécurité.
Les trois domaines d'application suivants illustrent les exigences correspondant aux critères mentionnés ci-dessus.
4.1.2.1 Engrenages de pont de véhicule, qui tournent à des vitesses relativement faibles: des dents à gros
module sont choisies compte tenu de l'effort à transmettre. En conséquence, les pignons ont un petit nombre de
dents (z de l'ordre de 14), alors que z de l'ordre de 28 serait choisi pour un engrenage de dimension similaire
1 1
tournant à grande vitesse. Ainsi, la résistance à la flexion de dent du premier devra être environ le double de celle
du dernier.
La fiabilité calculée d'un engrenage automobile peut être assez faible, de l'ordre de 80 % à 90 %, alors qu’il
convient que celle des engrenages industriels tournant à grande vitesse soit de l'ordre d’au moins 99 %.
En général, les matériaux utilisés pour la production d’engrenages automobiles en grande série peuvent avoir des
caractéristiques beaucoup plus uniformes que ceux utilisés pour les engrenages produits en faible quantité.
14 © ISO 1996 – Tous droits réservés
La comparaison de différentes conceptions de dentures a montré que pour une durée de vie d'environ
10 000 cycles, un engrenage d'un pont arrière de camion peut supporter une charge quatre fois supérieure à celle
d'un engrenage d’engin aéronautique ou spatial, lorsque le matériau, la qualité, les dimensions et la conception
sont identiques.
Sur les engrenages automobiles tournant à faible vitesse, et destinés à avoir une courte durée de vie (moins de
100 000 cycles), de légers fluages, des piqûres ou une légère usure abrasive sont généralement tolérés. De ce
fait, les niveaux de pression de contact admissibles sont nettement plus élevés que ceux admis pour les
engrenages qui tournent à grande vitesse et sont conçus pour une durée de vie plus longue.
4.1.2.2 Transmissions principales d'engins aéronautiques et spatiaux, qu'on trouve dans les
transmissions de rotor d'hélicoptère et d'entraînement des pompes principales des propulseurs de véhicules
spatiaux pour lesquelles on utilise des engrenages de la plus grande qualité et de la plus haute précision. De tels
engrenages sont très largement testés: par exemple 10 à 20 trains de la même série de production peuvent être
testés avec les conditions de chargement de service pour une durée de vie complète. Le taux d'usure admissible
est établi sur la base de résultats d'essais. La quantité de lubrifiant pulvérisé, la position des ajutages et la direction
des flux sont optimisées.
Pour les raisons mentionnées ci-dessus, des charges plus importantes sont admissibles pour une durée de vie
d’environ 100 fois supérieure (en cycles de mise en charge de la dent) et une vitesse 10 fois supérieure à celle
d'un engrenage classique de transmission de véhicule. Dans de tels cas, la probabilité de détérioration ne doit pas
dépasser 0,1 % à 1 %. La charge globale ne peut pas être aussi élevée que celle d'un engrenage d'un véhicule
puisque aucune usure ou détérioration mineure de surface ne peut être tolérée.
4.1.2.3 Engrenages de turbines industrielles, où la vitesse tangentielle au cercle primitif dépasse 50 m/s,
les pignons comportent très souvent 30 dents ou plus, afin de diminuer le risque d'usure ou de grippage. Une
conception classique consiste en un pignon de 45 dents conjugué à une roue de 248 dents.
Il convient que la fiabilité d'un engrenage de turbine industrielle soit supérieure à 99 % pour une durée de vie
normale de plus de 10 cycles. Les essais complets de prototypes sont en principe exclus en raison du coût. De
ce fait, les calculs de la capacité de charge de ces engrenages de turbine sont traditionnels, avec des coefficients
de sécurité relativement élevés.
4.1.3 Coefficients de sécurité
Il est nécessaire de différencier le coefficient de sécurité relatif à la formation des piqûres S , de celui relatif à la
H
rupture en pied de dent S .
F
Pour une application donnée, la justification d'une capacité de charge adaptée consiste à calculer une valeur du
coefficient de sécurité S , respectivement S qui doit être supérieure ou égale à celle de S , respectivement
H F, H min
S .
F min
Certaines valeurs minimales doivent être
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.
Loading comments...