TECHNICAL ISO/TS

SPECIFICATION 14521

First edition
2020-04

Gears — Calculation of load capacity

of worm gears
Engrenages — Calcul de la capacité de charge des engrenages à vis

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Reference number
ISO/TS 14521:2020(E)

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ISO/TS 14521:2020(E)


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Contents Page

Foreword......................................................................................................................................................................................................................................... vi
Introduction............................................................................................................................................................................................................................... vii
1 Scope.................................................................................................................................................................................................................................. 1
2 Normative references....................................................................................................................................................................................... 1
3 Terms, definitions and symbols............................................................................................................................................................. 1
3.1 Terms and definitions........................................................................................................................................................................ 1
3.2 Symbols.......................................................................................................................................................................................................... 2
4 General consideration..................................................................................................................................................................................... 7
4.1 Worm gear load capacity rating criteria............................................................................................................................ 7
4.2 Basis of the method.............................................................................................................................................................................. 8
4.3 Concept of absolute and relative parameters................................................................................................................ 8
4.4 Applicability............................................................................................................................................................................................... 9
4.5 Validity......................................................................................................................................................................................................... 10
4.6 System considerations.................................................................................................................................................................... 11
4.7 Calculation methods A, B, C........................................................................................................................................................ 11
4.7.1 Generality on methods A, B and C................................................................................................................... 11
4.7.2 Notes on numerical formulae............................................................................................................................. 12
4.7.3 Base conditions, interaction................................................................................................................................. 12
4.7.4 Other notes......................................................................................................................................................................... 13
4.8 iTeh STANDARD PREVIEW
Standard reference gear................................................................................................................................................................ 13
5 Required date for calculation...............................................................................................................................................................13
5.1
(standards.iteh.ai)
Input variable......................................................................................................................................................................................... 13
5.2 Safety factors.......................................................................................................................................................................................... 15
ISO/TS 14521:2020
6 Forces, speeds and parameters for the calculation of stresses..........................................................................15
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6.1 General.........................................................................................................................................................................................................
15de51b1bbd6/iso-ts-14521-2020 15
6.2 Tooth forces............................................................................................................................................................................................. 15
6.2.1 Application factor.......................................................................................................................................................... 15
6.2.2 Dynamic factor................................................................................................................................................................. 15
6.2.3 Load distribution factor........................................................................................................................................... 15
6.2.4 Tooth force components.......................................................................................................................................... 16
6.3 Sliding velocity at reference diameter.............................................................................................................................. 17
6.4 Physical parameters......................................................................................................................................................................... 17
6.4.1 Generality on physical parameters................................................................................................................ 17
6.4.2 Parameter for the mean Hertzian stress................................................................................................... 18
6.4.3 Parameter for the mean lubricant film thickness.............................................................................. 19
6.4.4 Parameter for the mean sliding path............................................................................................................ 20
6.5 Calculation of mean contact stress...................................................................................................................................... 21
6.6 Calculation of mean lubricant film thickness............................................................................................................. 22
6.7 Calculation of the wear path..................................................................................................................................................... 23
6.8 Calculation of the lubricant kinematic viscosity...................................................................................................... 23
7 Efficiency and power loss..........................................................................................................................................................................23
7.1 General......................................................................................................................................................................................................... 23
7.2 Total efficiency...................................................................................................................................................................................... 24
7.2.1 Method A............................................................................................................................................................................... 24
7.2.2 Method B............................................................................................................................................................................... 24
7.3 Total power loss................................................................................................................................................................................... 24
7.3.1 Methods of calculation.............................................................................................................................................. 24
7.3.2 Idle running power loss........................................................................................................................................... 25
7.3.3 Bearing load power loss.......................................................................................................................................... 25
7.3.4 Sealing power loss........................................................................................................................................................ 25
7.3.5 Adaptation of the calculation procedure to a specific test........................................................ 26
7.4 Gear efficiency....................................................................................................................................................................................... 26

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7.4.1 Efficiency calculation................................................................................................................................................. 26

7.4.2 Base coefficient of friction, µOT, of the standard reference gear........................................... 26
7.4.3 Size factor............................................................................................................................................................................. 28
7.4.4 Geometry factor.............................................................................................................................................................. 29
7.4.5 Material factor.................................................................................................................................................................. 29
7.4.6 Roughness factor........................................................................................................................................................... 29
7.4.7 Adaptation of the calculation procedure to a specific test........................................................ 29
7.5 Meshing power loss.......................................................................................................................................................................... 30
7.5.1 Method A............................................................................................................................................................................... 30
7.5.2 Method B............................................................................................................................................................................... 30
7.5.3 Method C............................................................................................................................................................................... 30
8 Wear load capacity...........................................................................................................................................................................................30
8.1 General......................................................................................................................................................................................................... 30
8.2 Wear safety factor............................................................................................................................................................................... 30
8.3 Expected wear....................................................................................................................................................................................... 31
8.3.1 Method A............................................................................................................................................................................... 31
8.3.2 Methods B, C...................................................................................................................................................................... 31
8.4 Permissible wear................................................................................................................................................................................. 35
8.5 Adaptation of the calculation procedure to a specific test.............................................................................. 36
9 Surface durability (pitting resistance)........................................................................................................................................36
9.1 General......................................................................................................................................................................................................... 36
9.2 Pitting safety factor........................................................................................................................................................................... 36
9.3 Actual contact stress........................................................................................................................................................................ 37
9.3.1 Method A............................................................................................................................................................................... 37
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9.3.2 Methods B, C...................................................................................................................................................................... 37
9.4 (standards.iteh.ai)
Limiting value of contact stress.............................................................................................................................................. 37
9.5 Adaptation of the calculation procedure to specific test.................................................................................. 38
10 Deflection...................................................................................................................................................................................................................
ISO/TS 14521:2020 38
10.1 General......................................................................................................................................................................................................... 38
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10.2 Deflection safety factor..................................................................................................................................................................
15de51b1bbd6/iso-ts-14521-2020 39
10.3 Actual deflection.................................................................................................................................................................................. 39
10.3.1 Method A............................................................................................................................................................................... 39
10.3.2 Method B............................................................................................................................................................................... 39
10.3.3 Method C............................................................................................................................................................................... 39
10.4 Limiting value of deflection....................................................................................................................................................... 40
11 Tooth root strength..........................................................................................................................................................................................40
11.1 Safety factor for tooth breakage............................................................................................................................................. 40
11.2 Actual tooth root stress................................................................................................................................................................. 40
11.2.1 Method A............................................................................................................................................................................... 40
11.2.2 Method B............................................................................................................................................................................... 40
11.2.3 Method C............................................................................................................................................................................... 40
11.3 Limiting value of shear stress at tooth root................................................................................................................. 42
11.3.1 General................................................................................................................................................................................... 42
11.3.2 Shear endurance limit, τF lim T ........................................................................................................................... 42
11.3.3 Life factor, YNL ................................................................................................................................................................. 42
11.4 Adaptation of the calculation procedure to a specific test.............................................................................. 44
12 Temperature safety factor........................................................................................................................................................................44
12.1 Temperature safety factor for splash lubrication................................................................................................... 44
12.1.1 General................................................................................................................................................................................... 44
12.1.2 Determination of oil sump temperature................................................................................................... 45
12.1.3 Limiting values................................................................................................................................................................ 46
12.2 Temperature safety factor for oil spray lubrication.............................................................................................. 46
12.2.1 General................................................................................................................................................................................... 46
12.2.2 Cooling capacity PK ..................................................................................................................................................... 46
13 Determination of the wheel bulk temperature..................................................................................................................47

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13.1 Wheel bulk temperature with splash lubrication................................................................................................... 47

13.1.1 General................................................................................................................................................................................... 47
13.1.2 Method A............................................................................................................................................................................... 48
13.1.3 Method B............................................................................................................................................................................... 48
13.1.4 Method C............................................................................................................................................................................... 48
13.2 Wheel bulk temperature with spray lubrication..................................................................................................... 48
13.2.1 General................................................................................................................................................................................... 48
13.2.2 Method A............................................................................................................................................................................... 48
13.2.3 Method B............................................................................................................................................................................... 48
13.2.4 Method C............................................................................................................................................................................... 49
Annex A (informative) Notes on physical parameters......................................................................................................................50
Annex B (normative) Methods for the determination of the parameters...................................................................51
Annex C (normative) Lubricant film thickness according to the Elasto Hydrodynamic
Lubrication (EHL) theory..........................................................................................................................................................................56
Annex D (normative) Wear path definition.................................................................................................................................................58
Annex E (informative) Notes on calculation wear................................................................................................................................61
Annex F (informative) Notes on tooth root strength..........................................................................................................................62
Annex G (informative) Adaptation of formulae for the reference gear with results from testing.....63
Annex H (informative) Life time estimation for worm gears with a high risk of pitting damage.......66
Annex I (informative) Examples..............................................................................................................................................................................68
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Annex J (informative) Examples of limit load capacity in a range of working conditions..........................84
(standards.iteh.ai)
Bibliography.............................................................................................................................................................................................................................. 87

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ISO/TS 14521:2020(E)


Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www​.iso​.org/​directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www​.iso​.org/​patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
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World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www​.iso​.org/​
iso/​foreword​.html. (standards.iteh.ai)
This document was prepared by Technical committee ISO/TC 60, Gears, Subcommittee SC 1,
Nomenclature and wormgearing. ISO/TS 14521:2020
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This first edition cancels and replaces ISO/TR 14521:2010, which has been technically revised.
15de51b1bbd6/iso-ts-14521-2020
The main changes compared to the previous edition are as follows:
— the orginal Clause 6 which focused on geometry has been deleted and ISO/TR 10828 has been
referenced.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www​.iso​.org/​members​.html.

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Introduction
This document was developed for the rating and design of enclosed or open single enveloping worm
gears with cylindrical worms, and worm-geared motors having either solid or hollow output shafts.
This document is only applicable when the flanks of the worm wheel teeth are conjugate to those of the
worm threads.
The particular shapes of the rack profiles from tip to root do not affect the conjugacy when the worm
and worm wheel hobs have the same profiles; thus worm wheels have proper contact with worms and
the motions of worm gear pairs are uniform.
This document can apply to wormgearing with cylindrical helicoidal worms as defined in ISO/TR 10828
having the following thread forms: A, C, I, N, K.
Other than those mentioned in the three preceding paragraphs, no restrictions are placed on the
manufacturing methods used.
In order to ensure proper mating and because of the many different thread profiles in use, it is generally
desirable that worms and worm wheels be supplied by the same manufacturer.
In this document, the permissible torque for a worm gear is limited by considerations of surface stress
(conveniently referred to as wear or pitting) or bending stress (referred to as strength) in both worm
threads and worm wheel teeth, deflection of worm or thermal limitation.

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Consequently, the load capacity of a pair of gears is determined using calculations concerned with all
criteria described in the scope and 6.4. The permissible torque on the worm wheel is the least of the
calculated values. (standards.iteh.ai)
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TECHNICAL SPECIFICATION ISO/TS 14521:2020(E)

Gears — Calculation of load capacity of worm gears

1 Scope
This document specifies formulae for calculating the load capacity of cylindrical worm gears and covers
load ratings associated with wear, pitting, worm deflection, tooth breakage and temperature. Scuffing
and other failure modes are not covered by this document.

The load rating and design procedures are only valid for tooth surface sliding velocities, vg , less than or
equal to 25 m/s and contact ratios greater than 2,1. For wear, load rating and design procedures are
only valid for tooth surface sliding velocities which are above 0,1 m/s. The rules and recommendations
for the dimensioning, lubricants or materials selected by this document only apply to centre distances
of 50 mm and larger. For centre distances below 50 mm, method A applies.
The choice of appropriate methods of calculation requires knowledge and experience. This document is
intended for use by experienced gear designers who can make informed judgements concerning factors.
It is not intended for use by engineers who lack the necessary experience. See 4.7.
WARNING — The geometry of worm gears is complex, therefore the user of this document is
encouraged to make sure that a valid working geometry has been established.
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2 Normative references (standards.iteh.ai)
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. ISO/TSFor dated references, only the edition cited applies. For
14521:2020
undated references, the latest edition of the referenced document (including any amendments) applies.
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15de51b1bbd6/iso-ts-14521-2020
ISO 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 1122-2, Vocabulary of gear terms — Part 2: Definitions related to worm gear geometry
ISO 6336-6, Calculation of load capacity of spur and helical gears — Part 6: Calculation of service life under
variable load
DIN 3974-1, Accuracy of worms and wormgears — Part 1: General bases
DIN 3974-2, Accuracy of worms and wormgears — Part 2: Tolerances for individual errors

3 Terms, definitions and symbols

3.1 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 1122-1, ISO 1122-2 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://​w ww​.iso​.org/​obp
— IEC Electropedia: available at http://​w ww​.electropedia​.org/​
3.1.1
actual gear
worm gear set designed by this document

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3.2 Symbols
NOTE Where applicable, the symbols are in accordance with ISO 701.

Table 1 — Symbols for worm gears

Symbols Description Unit Figure Formula
a centre distance mm Figure 1
a1 centre distance of the gear concerned mm Figure 1
a0, a1, a2 oil sump temperature coefficients (118) to (124)
aT centre distance of standard reference gear mm Figure 1
aV centre distance of a gear operating or test mm Table 4
experiences are available
b2H effective wheel facewidth mm
b2H,std standard effective worm wheel facewidth mm (10)
b2R wheel rim width mm (132)
bH half Hertzian contact width mm Annex D (D.2)
ck coefficient for heat transition coefficient (133)
coil specific heat capacity of the oil Ws/(kg.K) (128)
(for temperature calculation with spray
lubrication)
cα iTeh STANDARDmPREVIEW
proximity value for the viscosity pressure
exponent α
/N 2 (22)/(24)

da 1 worm tip diameter (standards.iteh.ai)

mm (89)
da 2 worm wheel throat diameter mm
ISO/TS 14521:2020
de 2 worm wheel outside diameter mm
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dF force transmitted by a segment of the con- N
15de51b1bbd6/iso-ts-14521-2020 Figure B.2 (B.3)
tact line
dl length of contact line segment mm (B.1) to (B.6)
df 1 worm root diameter mm (104)
df 2 worm wheel root diameter mm (111)
dm1 worm reference diameter mm
dm2 worm wheel reference diameter mm (41) to (43)
dm1T reference diameter of the worm, from mm Table 4 (44), (45)
standard reference gear
dm2T reference diameter of the wheel, from mm Table 4
standard reference gear

ex unit vector pointing in direction of the x-axis mm (B.4)
fh worm wheel face width factor for the pa- — (16)
rameter for the minimum mean lubricant
film thickness
fp worm wheel face width factor for the pa- — (17)
rameter for the mean Hertzian stress
Δf relative deviation between a quantity of the — Figure 1
gear concerned and a reference gear
Δf T relative deviation between the centre dis- — Figure 1
tance of the gear concerned and the stand-
ard reference gear
Δf V relative deviation between the centre — Figure 1
distance of the gear concerned and a gear
operating or test experiences are available

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 ISO/TS 14521:2020(E)


Table 1 (continued)
Symbols Description Unit Figure Formula
ham1 worm tooth reference addendum in axial mm (86)
section
hmin minimum lubricant film thickness μm (C.1)
hmin m minimum mean lubricant film thickness μm (21)
h* parameter for minimum mean lubricant film — (14)/(15)
thickness
hT* parameter for minimum mean lubricant film — Table 4
thickness of the standard reference gear
k lubricant constant 1/K (27)/(29)
l1 spacing of the worm shaft bearings mm (103)
l11, l12 bearing spacing of the worm shaft mm Figure 5 (103)
mx 1 axial module mm
Δm lim material loss limit mg (88)
Δs tooth thickness loss mm (111)
Δs lim allowable tooth thickness loss mm (87)

n normal vector (B.5)
n1 rotational speed of the worm shaft min−1
pH Hertzian stress N/mm 2 (B.1)/(B.6)
pHm
iTeh STANDARD
Hertzian stress; mean value for the total
PREVIEW
N/mm 2 (B.7)
contact area (standards.iteh.ai)—
pm
* parameter for the mean Hertzian stress (11)/(12)/(B.8)
parameter for the mean Hertzian ISO/TS 14521:2020
stress of — Table 4
pmT
*
the standard reference gear
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q1 diameter quotient
15de51b1bbd6/iso-ts-14521-2020mm

r radius from the axis of the worm wheel to mm (B.4)
the contact point B
sf2 mean tooth root thickness of the wheel mm (111)
teeth in the spur section
sft2 mean tooth root thickness of the wheel mm (111)
teeth in the spur section
sgB sliding path of the worm flanks within the mm (D.3)/(D.5)
Hertzian contact of the wheel flank per
number of cycles of the wheel, around the
contact point (local value)
sgm mean sliding path mm (D.7)
sm2 tooth thickness at the reference diameter of mm (111)
the worm wheel
sK rim thickness mm Figure 6 (113)
s Wm wear path inside of the required life ex- mm (30)/(D.1)
pectancy
smx1 worm tooth thickness in axial section mm
smx1
* worm tooth thickness in axial section — (111)
coefficient
s* parameter for the mean sliding path — (17)/(18)/(D.8)
sT* parameter for the mean sliding path of the — Table 4
standard reference gear
Δs tooth thickness loss (111)

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Table 1 (continued)
Symbols Description Unit Figure Formula
Δslim allowable tooth thickness loss (87)/(111)
tcontact time of contact s (D.2)
u gear ratio (1)
uT gear ratio of the standard reference gear Table 4

v1 velocity of a flank point of the worm m/s Figure B.1

v2 velocity of a flank point of a worm wheel m/s Figure B.1
v1n worm velocity component normal to the m/s Figure B.2
contact line
v2n wheel velocity component normal to the m/s Figure B.2 (D.2)
contact line

vgB sliding velocity normal to the line of contact m/s (D.3)/(D.5)/(D.6)
in flank direction
vg sliding velocity at reference diameter m/s (9)/(49)/(50)/(51)/
(H.2)/(H.3)/(H.5)
vref reference sliding velocity m/s (H.2) to (H.5)
v Σn sum velocity in normal direction m/s (11)/(C.4)
x2 worm wheel profile shift coefficient —
z1 number of threads in worm —
z2
iTeh STANDARD
number of teeth in worm wheel
PREVIEW
—
A (standards.iteh.ai)
coefficient for kinematic viscosity (33)
Afl total flank surface of the worm wheel mm2 (89)
AR dominant cooled surface of the gear ISO/TS
set 14521:2020 m2 (132)
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B coefficient for kinematic viscosity — (34)
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B coefficient for h* mm (14)
E1 modulus of elasticity of the worm N/mm2
E2 modulus of elasticity of the worm wheel N/mm2
Ered equivalent modulus of elasticity N/mm2 Table 4 (20)
Fxm1 axial force to the worm shaft N (4)/(7)
Fxm2 axial force to the worm wheel N (3)/(6)
Frm1 radial force to the worm shaft N (5)
Frm2 radial force to the worm wheel N (11)
Ftm1 circumferencial or tangential force to the N (4)/(6)
worm shaft
Ftm2 circumferencial or tangential force to the N (3)/(7)
worm wheel
dF/dl specific loading N/mm (C.5)
JOT reference wear intensity — Figure 4 (69) to (79)
JOI, JOII, JOIII reference wear intensity for stage I, II, III — (H.6) to (H.7)
JW wear intensity — (68)
JWP wear intensity — (H.6)
Kn rotational speed factor/wheel bulk tem- — (135)
perature
KHα transverse load distribution factor — 6.2.3
KHβ longitudinal load distribution factor — 6.2.3
KS size factor/wheel bulk temperature — (137)

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 ISO/TS 14521:2020(E)


Table 1 (continued)
Symbols Description Unit Figure Formula
KA application factor — 6.2.1
Kv dynamic factor — 6.2.2
KW lubricant film thickness parameter — (80)
Kν viscosity factor/wheel bulk temperature — (136)
K1 factor — (G.5)
Lh life time h
NL number of stress cycles of the worm wheel — (31)
NLI, NLII, NLIII number of stress cycles of the worm wheel — (H.1)
for stage I to III
NS number of starts per hour — (70)
P1 input power to the worm shaft W
P2 output power from the worm wheel shaft W
PK cooling capacity of the oil with spray lubri- W (127) (125)
cation
PV total power loss of the worm gear unit W (38)
P VO idle running power loss W (38)/(39)/(G.1)
P Vz1-2 meshing power loss in reducer W (62)
P Vz2-1 meshing power loss in increaser W (64)
P VD
iTeh STANDARD
sealing power loss
PREVIEW
W (44)/(45)
P VLP bearing power loss(standards.iteh.ai)
through loading W (40) to (43)
Qoil spray quantity m3/s (127)
Ra1 arithmetic mean roughness ISO/TS 14521:2020
for worm μm Table 4
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RaT arithmetic mean roughness for reference
15de51b1bbd6/iso-ts-14521-2020μm (62)
gear
Rz1 mean roughness depth μm 7.4.6
SF tooth breakage safety factor — (106)
SF min minimum tooth breakage safety factor — (107)
SH pitting safety factor — (91)
SHmin minimum pitting safety factor — (92)
ST temperature safety factor — (115)/(125)
ST min minimum temperature safety factor — (116)/(126)
SW wear safety factor — (65)
S W min minimum wear safety factor — (66)
Sδ deflection safety factor — (101)
Sδ min limit of deflection safety factor — (102)
T1 input torque to the worm shaft Nm (1)
T1N nominal input torque to the worm shaft Nm (1)
T2 output torque from the worm wheel Nm (2)/(B.4)/(B.5)
T2N nominal output torque from the worm wheel Nm (2)
VSUMn sum of velocities at contact point (C.1)
WH — (84)/(85)
WML material — lubricant factor — Table 7
WNS start factor — (83)
WP damage factor — (H.8)
WS lubricant structure factor — (81)/(82)

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ISO/TS 14521:2020(E)


Table 1 (continued)
Symbols Description Unit Figure Formula
YF form factor/tooth breakage — (110)
YG geometry factor/coefficient of friction — (59)/(60)
YK rim thickness factor/tooth breakage — (113)
YNL life factor/tooth breakage — Figure 7 a)/b) Table 11
YR roughness factor/coefficient of friction — (61)/(62)
YS size factor/coefficient of friction — (57)/(58)
YW material factor/coefficient of friction —
Yε contact factor/tooth breakage — (109)
Yγ lead factor/tooth breakage — (112)
Zh life factor/pitting — (94)
Zoil lubricant factor/pitting — (100)
ZS size factor/pitting — (96)/(97)
Zu gear ratio factor — (98)/(99)
Zv velocity factor/pitting — (95)
α pressure viscosity factor m2/N 6.6
αL heat transition coefficient for immersed W/(m2K) (133)
wheel teeth
αn normal pressure angle
iTeh STANDARD PREVIEW °
α0 normal pressure angle (5), (86)
γm1 (standards.iteh.ai)
reference lead angle of worm ° (86)
δlim limiting value of deflection mm (105)
ISO/TS 14521:2020
δm incurred deflection mm
https://standards.iteh.ai/catalog/standards/sist/d09c2c9b-feaa-4504-9a3a- (103)/(104)
δWn flank loss from wheel through abrasive wear mm
15de51b1bbd6/iso-ts-14521-2020 (67)
in the normal section
δW lim limiting value of flank loss mm (90)
δW lim n limiting value of flank loss in normal section mm (86) to (88)
ηges total efficiency in reducer — (35)
ηges1-2 total efficiency worm driving wheel — (35)
ηges2-1 total efficiency wheel driving worm — (36)
η'ges total efficiency in increaser — (36)
ηz1-2 gear efficiency in reducer — (46)/(63)
ηz2-1 gear efficiency in increaser — (47)/(64)
η0M dynamic viscosity of lubricant at ambient Ns/m2 (25)/(C.1)
pressure and wheel bulk temperature
θ temperature °C
Δθ temperature difference between oil sump °C (131)
and worm wheel bulk temperature
θin oil entrance temperature °C (129)
θ0 ambient temperature °C
θoil spray temperature °C (129)
Δθoil oil temperature difference between input °C (129)
and output cooling system
θM wheel bulk temperature °C (130)/(134)
θS oil sump temperature °C (117)/(119)
θS lim limiting value of oil sump temperature °C (115)

6  © ISO 2020 – All rights reserved

 ISO/TS 14521:2020(E)


Table 1 (continued)
Symbols Description Unit Figure Formula
μ0T base coefficient of friction — (49) to (52)
μzm mean tooth coefficient of friction — (48)
ν1 POISSON ratio of the worm — (20)
ν2 POISSON ratio for the worm wheel — (20)
νθ kinematic viscosity at oil temperature θ mm2/s (32)
ν40 kinematic viscosity at 40 °C mm2/s (32)
ν100 kinematic viscosity at 100 °C mm2/s
νM kinematic viscosity at wheel bulk tempera- mm2/s (25)
ture
ρ1, ρ2 local radius of curvature mm (B.2)
ρoil lubricant density kg/dm3 (127)
ρg friction angle for the tooth coefficient of (5)
friction
ρoil15 lubricant density at 15 °C kg/dm3 (25)
ρoilM lubricant density at wheel bulk temperature kg/dm3 (26)
ρred equivalent radius of curvature mm (B.2)
ρz friction angle for the tooth coefficient of ° (5)
friction
ρRad iTeh STANDARD PREVIEW
material density of the wheel mg/mm Table 8 3 (88)
σH lim T pitting strength (standards.iteh.ai)
N/mm Table 9 2

σHm mean contact stress N/mm2 (19) (91)

σHG limiting value for the meanISO/TS
contact stress
14521:2020 N/mm2 (93) (91)
τF https://standards.iteh.ai/catalog/standards/sist/d09c2c9b-feaa-4504-9a3a-
shear stress at tooth root N/mm2 (108) (106)
15de51b1bbd6/iso-ts-14521-2020
τF lim T shear endurance strength N/mm 2 Table 10
τFG limiting value for shear stress at tooth root N/mm2 (114) (106)

4 General consideration

4.1 Worm gear load capacity rating criteria

The load capacity of a worm gear corresponds to the torque (or the power) which can be transmitted
without the occurrence of tooth breakage or the appearance of excessive damage on the active flanks of
the teeth during the design life of the gearing.
Conditions shown in Table 2 can limit the rated load capacity.

Table 2 — Significant factors affecting failure mode and performance (valid for same gear set)
Failure modes
Influencing factors Wear Pitting Tooth- Worm shaft Scuffing Efficiency
breakage deflection
Load (Hertzian pressure) x x x x x x
Worm speed x x x x
Oil viscosity x x x x
Contact Pattern x x x x x
Worm surface waviness and x x x x
roughness

© ISO 2020 – All rights reserved  7