AGMA 925-A03

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AGMA INFORMATION SHEET
(This Information Sheet is NOT an AGMA Standard)
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AGMA 925-A03
AMERICAN GEAR MANUFACTURERS ASSOCIATION
Effect of Lubrication on Gear Surface
Distress
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ii
Effect of Lubrication on Gear Surface Distress
AGMA 925--A03
CAUTION NOTICE: AGMA technical publications are subject to constant improvement,
revision or withdrawal as dictated by experience. Any person who refers to any AGMA
technical publication should be sure that the publication is the latest available from the As-
sociation on the subject matter.
[Tables or other self--supporting sections may be quoted or extracted. Credit lines should
read: Extracted fromAGMA925--A03,Effect of Lubrication onGear SurfaceDistress,with
the permission of the publisher, the AmericanGear Manufacturers Association, 500Mont-
gomery Street, Suite 350, Alexandria, Virginia 22314.]
Approved March 13, 2003
ABSTRACT
AGMA 925--A03 is an enhancement of annex A of ANSI/AGMA 2101--C95. Various methods of gear surface
distress are included, such as scuffing and wear, and in addition, micro andmacropitting. Lubricant viscometric
information has been added, as has Dudley’s regimes of lubrication theory. A flow chart is included in annex A,
Gaussian theory in annexB, a summary of lubricant test rigs in annexC, and an example calculation in annexD.
Published by
American Gear Manufacturers Association
500 Montgomery Street, Suite 350, Alexandria, Virginia 22314
Copyright  2003 by American Gear Manufacturers Association
All rights reserved.
No part of this publication may be reproduced in any form, in an electronic
retrieval system or otherwise, without prior written permission of the publisher.
Printed in the United States of America
ISBN: 1--55589--815--7
American
Gear
Manufacturers
Association
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
iii
Contents
Page
Foreword iv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Scope 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 References 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Symbols and units 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Gear information 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Lubrication 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Scuffing 17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Surface fatigue (micro-- and macropitting) 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Wear 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography 49. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Annexes
A Flow chart for evaluating scuffing risk and oil film thickness 31. . . . . . . . . . . . . .
B Normal or Gaussian probability 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C Test rig gear data 41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D Example calculations 43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figures
1 Distances along the line of action for external gears 6. . . . . . . . . . . . . . . . . . . . . .
2 Transverse relative radius of curvature for external gears 7. . . . . . . . . . . . . . . . .
3 Load sharing factor -- unmodified profiles 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Load sharing factor -- pinion driving 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Load sharing factor -- gear driving 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Load sharing factor -- smooth meshing 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Dynamic viscosity versus temperature for mineral oils 13. . . . . . . . . . . . . . . . . . .
8 Dynamic viscosity versus temperature for PAO--based synthetic
non--VI--improved oils 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Dynamic viscosity versus temperature for PAG--based synthetic oils 15. . . . . .
10 Dynamic viscosity versus temperature for MIL Spec. oils 16. . . . . . . . . . . . . . . .
11 Pressure--viscosity coefficient versus dynamic viscosity 16. . . . . . . . . . . . . . . . .
12 Example of thermal network 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13 Contact temperature along the line of action 20. . . . . . . . . . . . . . . . . . . . . . . . . . .
14 Plot of regimes of lubrication versus stress cycle factor 25. . . . . . . . . . . . . . . . . .
15 Probability of wear related distress 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
1 Symbols and units 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Data for determining viscosity and pressure--viscosity coefficient 12. . . . . . . . .
3 Mean scuffing temperatures for oils and steels typical of the aerospace
industry 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Welding factors, XW 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Scuffing risk 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Stress cycle factor equations for regimes I, II and III 25. . . . . . . . . . . . . . . . . . . .
7 Calculation results 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ture, for which the maximum value is taken:
θM= ksump θoil+ 0.56 θfl max (91)
where
ksump = 1.0 if splash lube; 1.2 if spray lube;
θoil is oil supply or sump temperature, °C;
θfl max is maximum flash temperature, °C, see
6.2.
However, for a reliable evaluation of the scuffing risk,
it is important that instead of the rough approxima-
tion, an accurate value of the gear tooth temperature
be used for the analysis.
6.3.2 Measurement and experience
The tooth temperature can be measured by testing,
or determined according to experience.
6.3.3 Thermal network
The tooth temperature can be calculated from a
thermal network analysis [43] (see figure 12).
The tooth temperature is determined by the heat flow
balance in the gearbox. There are several sources
of frictional heat, of which the most important ones
are the tooth friction and the bearing friction. Other
heat sources, like seals and oil flow, may also
contribute. For gear pitchline velocities above 80
m/s, churning loss, expulsion of oil betweenmeshing
teeth, and windage loss become important heat
sources that should be considered. Heat is con-
ducted and transferred to the environment by
conduction, convection and radiation.
6.4 Contact temperature
6.4.1 Contact temperature at any point
At any point on the line of action (see figure 13) the
contact temperature is:
θBi
= θM+ θfli
(92)
where
θM is tooth temperature, °C (see 6.3);
θfli
is flash temperature, °C (see 6.2).
i (as a subscript) defines a point on the line of
action.
Bearings
Air
Oil
Case
Friction
power
Pinion
Gear
Friction power
Shafts
Figure 12 -- Example of thermal network
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
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A B D EC
θB max
θfl maxθfli
θBi
θM
Figure 13 -- Contact temperature along the line
of action
6.4.2 Maximum contact temperature
The maximum contact temperature is:
θB max= θM+ θfl max (93)
where
θfl max is maximum flash temperature, °C (see
6.2).
6.5 Scuffing temperature
The scuffing temperature is the temperature in the
tooth contact zone at which scuffing is likely to occur
with the chosen combination of lubricant and gear
materials. The scuffing temperature is assumed to
be a characteristic value for the material--lubricant
system of a gear pair, to be determined by gear tests
with the same material--lubricant system.
When θB max (see figure 13) reaches the scuffing
temperature of the system, scuffing is likely. The
mean scuffing temperature is the temperature at
which there is a 50% chance of scuffing.
6.5.1 Mean scuffing temperature for mineral oils
Scuffing temperatures for mineral oils with low
concentrations of antiscuff additives are indepen-
dent of operating conditions. Viscosity grade is a
convenient index of oil composition, and thus of
scuffing temperature.
Equations 94 and 95 are approximate guides for
mineral oils and steels typical of IAE and FZG test
machines. The mean scuffing temperature was
derived from data published by Blok [27].
Equation 94 gives the scuffing temperature for
non--antiscuff mineral oils (R&O in accordance with
ANSI/AGMA 9005--E02 [28]).
θS= 63+ 33 ln ν40 (94)
where
ν40 is kinematic viscosity at 40°C, mm2/s (table
2).
Equation 95 gives the scuffing temperature for
antiscuff mineral oils (EP gear oil in accordance with
ANSI/AGMA 9005--E02).
θS= 118+ 33 ln ν40 (95)
6.5.2 Mean scuffing temperature for oils and
steels typical of aerospace industry
Table 3 gives the mean scuffing temperature for oils
with steels typical of the aerospace industry.
Table 3 -- Mean scuffing temperatures for oils
and steels typical of the aerospace industry
Lubricant
Mean scuffing
temperature, °C
MIL--L--7808 205
MIL--L--23699 220
DERD2487 225
DERD2497 240
DOD--L--85734 260
ISO VG 32 PAO 280
DexronR II1) 290
NOTE:
1) DexronR is a registered trademark of General
Motors Corporation.
6.5.3 Extension of test gear scuffing temperature
for one steel to other steels
The scuffing temperature determined from test
gears with low--additive mineral oils may be ex-
tended to different gear steels, heat treatments or
surface treatments by introducing an empirical
welding factor.
θS= XWθfl max, test+ θM, test (96)
where
XW is welding factor (see table 4);
θfl max, test is maximum flash temperature of test
gears, °C;
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
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θM, test is tooth temperature of test gears, °C.
6.5.4 Scuffing temperature for oils used in
hypoid gear application
Scuffing temperature for high--additive oils (hypoid
gear oil) may be dependent on operating conditions.
Therefore, the scuffing temperature should be
obtained from tests that closely simulate operating
conditions of the gears.
Table 4 -- Welding factors, XW
Material XW
Through hardened steel 1.00
Phosphated steel 1.25
Copper--plated steel 1.50
Bath or gas nitrided steel 1.50
Hardened carburized steel
-- Less than 20% retained austenite 1.15
-- 20 to 30% retained austenite 1.00
-- Greater than 30% retained austenite 0.85
Austenite steel (stainless steel) 0.45
6.5.5 Scuffing risk
Scuffing risk can be calculated from a Gaussian
distribution of scuffing temperature about the mean
value. Typically, the coefficient of variation is at least
15%. Therefore, use the procedure of annex B to
calculate the probability of scuffing:
where
y = θB max
my = θs
σy = 0.15 θs
Table 5 gives the evaluation of scuffing risk based on
the probability of scuffing [7].
Table 5 -- Scuffing risk
Probability of scuffing Scuffing risk
30% High
6.6 Alternative scuffing risk evaluation
The calculation of the scuffing load capacity is a very
complex problem. Several alternative methods are
proposed which may support the gear geometry and
rotor dimensions most suitable to the gear applica-
tion. Gear drives cover a wide field of operating
conditions from relatively low pitch line velocities
with high specific tooth loads, to very high pitch line
velocities and moderate specific tooth loads.
Lubricants vary, as well, between mineral oils with
little or no additives to antiscuff lubricants with
substantial additives.
The flash temperature method described in 6.2
through 6.5 is based on Blok’s contact temperature
theory. The flash temperature, θfl, must be added to
the steady gear tooth temperature, θM, to give the
total contact temperature, θB. The value of the
contact temperature for every point in the contact
zone must be less than the mean scuffing tempera-
ture of the material--lubricant system or scuffingmay
occur.
6.6.1 Integral temperature method
The integral temperature method [29] has been
proposed as an alternative to the flash temperature
method by which the influence of the gear geometry
imposes a critical energy level based on the
integrated temperature distribution (for example,
numerically integrating using Simpson’s rule) along
a pathof contact and adopting a steady gear tooth
temperature. Thismethod involves the calculation of
a scuffing load basically independent of speed, but
controlled by gear geometry. Application requires
comparison of the proposed gearset based on a test
rig result to a known test rig gearset and tested oil.
A comparison of the flash temperature method and
integral temperature method has shown the
following:
-- Blok’s method and the integral temperature
method give essentially the same assessment of
scuffing risk for most gearsets;
-- Blok’s method and the integral temperature
method give different assessments of scuffing
risk for those cases where there are local
temperature peaks. These cases usually occur in
gearsets that have low contact ratio, contact near
the base circle, or other sensitive geometries;
-- Blok’s method is sensitive to local tempera-
ture peaks because it is concerned with the
maximum instantaneous temperature, whereas
the integral temperature method is insensitive to
these peaks because it averages the temperature
distribution.
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
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6.6.2 Other scuffing methods
6.6.2.1 PVT Method
Almen [30] popularized the PVT method for
predicting scuffing where:
P is Hertzian pressure;
V is sliding velocity;
T is distance along line of action.
PVT was used during World War II by designers in
automotive and aircraft industries. It worked well for
a narrow range of gear designs, but was unreliable
when extrapolated to other gear applications.
6.6.2.2 Borsoff scoring factor method
Borsoff [31, 32, 33, 34] conducted many scuffing
tests during the 1950’s and found scuffing resistance
increased when test gears were run at high speeds.
Borsoff introduced a scoring factor, Sf:
Sf=
2bH
vs
(97)
where
Sf is contact time, ms (sec¢ 10--3);
bH is semi--width of Hertzian contact band,mm;
vs is sliding velocity, m/s.
Sf is the time required for a point on one tooth to
traverse the Hertzian band of the mating tooth.
Borsoff’s test data showed a linear relationship
between scuffing load and scoring factor, Sf. Borsoff
recommended that a number of considerations
should be made before using his method for specific
applications.
6.6.2.3 Simplified scuffing criteria for high speed
gears
Annex B of ANSI/AGMA 6011--H98 [35] has been
used to evaluate scuffing risk of high speed gear
applications.
There are other methods for evaluating scuffing of
gear teeth not mentioned here. Other methods may
also have application merit. Most importantly, the
gear designer should recognize scuffing as a gear
design criteria.
7 Surface fatigue (micro-- andmacropitting)
7.1 General information
Surface fatigue, commonly referred to as pitting or
spalling, is a wear mode that results in loss of
material as a result of repeated stress cycles acting
on the surface. There are two major sub--groups
under surface fatigue known as micro-- and macro-
pitting. As their names imply, the type of pitting is
related to the size of the pit. Macropits usually can be
seen with the naked eye as irregular shaped cavities
in the surface of the tooth. Damage beginning on the
order of 0.5 to 1.0mm in diameter is considered to be
a macropit.
The number of stress cycles occurring before failure
is referred to as the fatigue life of the component.
The surface fatigue life of a gear is inversely
proportional to the contact stress applied. Although
contact stress is probably themajor factor governing
life, there are many others that influence life. These
include design factors such as tip relief and crown-
ing, surface roughness, physical and chemical
properties of the lubricant and its additive system,
and external contaminants such as water and hard
particulate matter.
7.2 Micropitting
Micropitting is a fatigue phenomenon that occurs in
Hertzian contacts that operate in elastohydrody-
namic or boundary lubrication regimes and have
combined rolling and sliding. Besides operating
conditions such as load, speed, sliding, temperature
and specific film thickness, the chemical composi-
tion of a lubricant strongly influences micropitting.
Damage can start during the first 105 to 106 stress
cycles with generation of numerous surface cracks.
The cracks grow at a shallow angle to the surface
forming micropits that are about 10 – 20 mm deep by
about 25 -- 100 mm long and 10 – 20 mm wide. The
micropits coalesce to produce a continuous frac-
tured surface which appears as a dull, matte surface
to the observer.
Micropitting is the preferred name for this mode of
damage, but it has also been referred to as grey
staining, grey flecking, frosting, and peeling. Al-
though micropitting generally occurs with heavily
loaded, carburized gears, it also occurs with nitrided,
induction hardened and through--hardened gears.
Micropitting may arrest after running--in. If micropit-
ting continues to progress, however, it may result in
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
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reduced gear tooth accuracy, increased dynamic
loads and noise. Eventually, it can progress to
macropitting and gear failure.
7.2.1 Micropitting risk evaluation
Factors that influence micropitting are gear tooth
geometry, surface roughness, lubricant viscosity,
coefficient of friction, load, tangential speed, oil
temperature and lubricant additives. Common
methods suggested for reducing the probability of
micropitting include:
-- reduce surface roughness;
-- increase film thickness;
-- use higher viscosity oil;
-- reduce coefficient of friction;
-- run at higher speeds if possible;
-- reduce oil temperature;
-- use additives with demonstrated micropitting
resistance;
-- protect gear teeth during run--in with suitable
coatings, such as manganese phosphate, copper
or silver plating.
CAUTION: Silver or copper plating of carburized gear
elements will cause hydrogen embrittlement, which
could result in a reduction in bending strength and fa-
tigue life. Thermal treatment shortly after plating may
reduce this effect.
Surface roughness strongly influences the tendency
to micropit. Gears finished to a mirrorlike finish have
been reported to eliminate micropitting [36, 37, 38].
Gear teeth have maximum micropitting resistance
when the teeth of the high speedmember are harder
than the mating teeth and are as smooth as possible
[39].
Currently there is no standard test for determining
micropitting resistance of lubricants. However, FVA
Information Sheet 54/IV describes a test that uses
the FZG C--GF type gears to rank micropitting
performance of oils [40]. At present, the influence of
lubricant additives is unresolved. Therefore, the
micropitting resistance of a lubricant should be
determined by field testing on actual gears or by
laboratory tests.
7.3 Macropitting
Macropitting is also a fatigue phenomenon. Cracks
can initiate either at or near the surface of a gear
tooth.The crack usually propagates for a short
distance at a shallow angle to the surface before
turning or branching back to the surface. Eventually,
material will dislodge from the surface forming a pit,
an irregular shaped cavity in the surface of the
material. With gears the origin of the crack is more
likely surface initiated because lubricant film thick-
ness is low resulting in a high amount of asperity or
metal--to--metal contact. For high--speed gears with
smooth surface finishes, film thickness is larger and
sub--surface initiated crack formationmay dominate.
In these cases an inclusion or small void in the
material is a source for stress concentration.
Laboratory testing commonly uses a 1% limit on
tooth surface area damageas a criteria to stop a test.
However, for field service applications one should
always abide by the equipment manufacturer’s
recommendations or guidelines for acceptable limits
of damage to any gear or supporting component.
7.4 Regimes of lubrication
7.4.1 Introduction to regimes of lubrication
Gear rating standards have progressed and been
refined to take into account many of the major
variables that affect gear life. With respect to
calculated stress numbers, variables such as load
distribution, internally induced dynamic loading and
externally induced dynamic loading are accounted
for by derating factors. Variables such as material
quality, cycle life and reliability are accounted for by
allowable stress numbers, stress cycle factors and
reliability factors.
Along with these influences, it has been recognized
that adequate lubrication is necessary for gears to
realize their calculated capacity. Indeed, AGMA
gearing standards have acknowledged this fact by
stating this need as a requirement in order to apply
the various rating methods.
Much of the groundwork for lubrication theory came
about in the 1960’s and 1970’s. This period saw the
advent and proliferation of jet travel, space travel,
advanced manufacturing processes and advanced
power needs. These technological and industrial
developments led to the need for better gear rating
methods which, in turn, resulted in rapid progress in
industrial, vehicle and aerospace gearing standards.
High speed gearing was coming into greater use, but
it was not as well understood as the industry would
have liked. To compensate, designs tended to focus
on making higher speed stages of gearing more
successful, sometimes to the detriment of slower
speed stages. This is how the gearing industry
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
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started to get its first glimpses into the importance of
lubrication on the life of gearing.
It was not uncommon to see a three (3) stage
industrial gear drive with problems as follows: a high
speed set of gears that looked relatively undam-
aged, an intermediate speed set of gears that was
experiencing initial pitting, and a slow speed set of
gears that was experiencing advanced pitting and
tooth breakage. In the event that all three stages
were designed to have similar load intensity factors
(K--factors and unit loads) the problem could be
particularly puzzling. Rating theory at the time
indicated that with all other things equal, the higher
speed stages of gearing should have been failing
sooner than the lower speed stages, due to greater
stress cycles.
At issue was the tribological condition between
surfaces of two mating teeth. Elastohydrodynamic
lubrication (EHL) theory showed that factors like
relative surface velocity and local oil viscosity at the
contact area directly affected thickness of the EHLoil
film that separated asperities on surfaces of two
mating gear teeth. For amultiple stage gear reducer,
higher speed stages of gearing, with higher surface
velocities, tended to produce thicker EHL oil films,
better capable of separating asperities on mating
teeth. Lower speed stages, with lower surface
velocities, tended to produce thinner EHL oil films,
less capable of separating asperities on mating
teeth.
Through the years, a great many researchers and
companies inside and outside of the gear industry
have sought to quantify the effects of EHL oil film
theory on the life of gearing. There aremany ways in
which one could hypothesize the effects of inade-
quate oil films on degradation of gear tooth surfaces
and its results on the life of gearing. Indeed, a
comprehensive treatment of this subject could fill
many volumes. Added to this is the fact that this is
still a very active area of gear research. With this in
mind, it is still useful to put forth a simplified
description of how inadequate oil films can lead to
decreased life of gears. So, very simply put, thinner
oil films lead to a greater chance of more frequent
and more detrimental degree of contact between
asperities on mating gear teeth. The more severe
this is, the more likely it will lead to pitting, a
recognized form of surface fatigue in gearing.
The effects of this phenomenon on the fatigue life of
gearing were introduced by Bowen [41]. Dudley [42]
defined the three regimes of lubrication at the
operating pitch diameter as follows:
-- Regime III: Full EHL oil film is developed and
separates the asperities of gear flanks in motion
relative to one another;
-- Regime II: Partial EHL oil film is developed
and there is occasional contact of the asperities of
gear flanks in motion relative to one another;
-- Regime I: Only boundary lubrication exists
with essentially no EHL film and contact of the
asperities of gear flanks in motion relative to one
another is pronounced.
The implementation of this theory involves what is
currently referred to as the stress cycle factor for the
surface durability of gears, ZN, (this used to be called
the life factor for surface durability). Keeping inmind
that regime of lubrication depends ultimately on the
degree of separation between asperities, Dudley
proposed that the effect could be quantified by
making proper adjustments to the curves that
determine the stress cycle factor. Thus, we have as
follows:
7.4.2 Regime III
This regime of lubrication, characterized by full EHL
oil film development, occursmainly when gears have
relatively high pitch line velocity, good care is taken
to ensure that an adequate supply of clean, cool oil is
available (of adequate viscosity and formulation),
and good surface finishes are achieved on the
gearing. As such, aerospace gearing, high speed
marine gearing, and good quality industrial gear
drives tend to have gears that operate within regime
III. Thus, stress cycle factor curves that appear in
standards for these gears are the basis for rating
gears that operate within regime III.
7.4.3 Regime II
This regime of lubrication, characterized by partial
EHL oil film development, occurs mainly when gears
havemoderate pitch line velocities,moderate care is
taken to ensure that an adequate supply of clean,
cool oil is available (of adequate viscosity and
formulation), and moderately good surface finishes
are achieved on the gearing. As such, vehicle
gearing is very characteristic of gears that operate
within regime II. Dudley uses information from the
stress cycle factor curves in vehicle standards to
create a branch from the regime III curve for cycles
greater than 100 000. It is felt that effects of
operation within regime II on fatigue life will not begin
to be realized until thispoint in the life of a gear.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
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7.4.4 Regime I
This regime of lubrication, characterized by bound-
ary lubrication, occurs mainly when gears have low
pitch line velocities, little care is taken to ensure that
an adequate supply of clean, cool oil is available (of
adequate viscosity and formulation), and relatively
rough surface finishes are achieved on the gearing.
Many types of gearing can fall into this range of
operation, including all types mentioned above.
Dudley used fatigue curves generated for ball and
roller bearings as a basis for regime I stress cycle
factor curves. These curves, first developed in the
1940’s, indicated that with a ten--fold increase in
cycles, load capacity of a bearing drops off by a
factor of 2.0. Thus, a stress curve for Hertzian
contact would drop off by about a factor of 1.41
(square root of 2.0). Bearings back in the 1940’s
commonly had surface finishes and oil films very
analogous to gears operating in regime I. This
information is used to create a branch from the
regime III curve at cycles greater than 100 000.
Figure 14 shows the curves that result fromDudley’s
method of regimes of lubrication. Below, themethod
is described in fuller detail and calculations are given
to show how one assesses which regime of lubrica-
tion should be applied to a given set of gears.
0.05
0.06
0.07
0.08
0.09
0.10
0.20
0.30
0.40
0.50
102 1010109108107106105104103 10121011
0.15
0.60
0.70
0.80
0.90
1.00
4.00
3.00
2.00
1.50
Number of load cycles, N
Regime I
Regime II
Regime III
S
tr
es
s
cy
cl
e
fa
ct
or
,Z
N
Figure 14 -- Plot of regimes of lubrication versus stress cycle factor
Table 6 -- Stress cycle factor equations for regimes I, II and III
Regime of lubrication Stress cycle factor for surface durability
Regime III ZN= 1.47 for NAGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
27
S
pe
ci
fic
fil
m
th
ic
kn
es
s,
λ
0.01
0.1
1
10
0.1 1 10 100 1000
Pitch line velocity (m/s)
5%
40%
80%
Figure 15 -- Probability of wear related distress
8.2.1.2 Composite surface roughness
adjustment
Reference [20] used an arithmetic average for the
composite surface roughness:
Rqx avg=
Rq1x+ Rq2x
2
(99)
where
Rq1x, Rq2x is root mean square surface rough-
ness, pinion and gear respectively, for
filter cutoff length, Lx, mm.
Composite surface roughness used in this informa-
tion sheet is root mean square average of average
surface roughness, see equation 78.
If Rq1x = Rq2x and Ra1x = Ra2x (similar surface
roughnesses),
σx= 2 Ra1x= 2 Ra2x (100)
Rqx avg= Rq1x= Rq2x (101)
8.2.1.3 Specific film thickness adjustment
The curves of figure 15 were also adjusted for
different definitions of film thickness. The Dowson
and Toyoda equation for central film thickness [19],
hci
, of equation 75, provides film thickness values
1.316 times the Dowson and Higginson [17] mini-
mum film thickness, hmin, used by the Wellauer and
Holloway paper [20].
Specific film thickness adjustment factor is derived
as follows:
Wellauer and Holloway [20] defined λ as:
λW&H=
hmin
Rqx avg
(102)
This information sheet uses hci
and σx defined by
equations 75 and 100:
λi =
hci
σx
(103)
Substituting adjustment factors into the equation for
λ gives:
λmin=
1.316 (1.11)hmin
2 Rqx avg
(104)
λmin= 1.033 λW&H (105)
and is used to adjust the specific film thickness
provided by Wellauer and Holloway. This vertical
axis adjustment is now reflected in figure 15.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
28
Finally, the units of pitch line velocity, vt, were
adjusted from feet per minute to meters per second.
Note that specific film thickness is dimensionless.
8.2.2 Wear risk probability
The curves of figure 15 can be fitted with the
following equations:
λ5%= 2.68863vt
+ 0.47767−1 (106)
λ40%= 4.90179vt
+ 0.64585−1 (107)
λ80%= 9.29210vt
+ 0.95507−1 (108)
Using the following definition, the mean minimum
specific film thickness, mλ min, and the standard
deviation, σλ min, can be calculated by simultaneous
solution (two equations in two unknowns) using any
two of the adjusted Wellauer and Holloway curves
(5% and 40%, 40% and 80%, or 5% and 80%):
x=
λmin− mλ min
σλ min
(ref [24]) (109)
where
x is value of the standard normal variable
determined by probability;
λmin is specific film thickness (equation 105);
mλ min is mean minimum specific film thickness;
σλ min is standard deviation of the minimum
specific film thickness.
Figure 15 and equations 106 through 108 are listed
in the percent failure mode, Q(x). This must first be
converted to a percent survival mode, P(x), by the
equation P(x)= 1− Q(x). With P(x) known, the value
“x” may be determined from the table “Normal
Probability Function and Derivatives” of reference
[24].
λ5%:
Q(x)= 5%
P(x)= 95%
x5%= 1.64491438
λ40%:
Q(x)= 40%
P(x)= 60%
x40%= 0.25335825
λ80%:
Q(x)= 80%
P(x)= 20%
x80%=− 0.84163389
Use several film thickness values from figure 15 to
find how mean minimum specific film thickness,
mλ min, and standard deviation of the minimum
specific film thickness, σλ min, vary with pitch line
velocity. An example is shown below:
vt= 5 m∕s
λ5%= 0.9849
λ40%= 0.6149
This gives the following equations that are solved for
σλ min:
1.6449= 0.9849− mλ min
σλ min

0.2534= 0.6149− mλ min
σλ min

1.6449 σλ min= 0.9849− mλ min
0.2534 σλ min= 0.6149− mλ min
Subtracting the bottom equation from the upper
equation yields:
1.3915 σλ min= 0.3700
σλ min=
0.3700
1.3915
= 0.2659
Using σλ min in the first equation, mλ min is found:
1.6449=
0.9849− mλ min
0.2659
mλ min= 0.9849− 1.6449 (0.2659)
mλ min= 0.5475
This process was repeated for all data points along
the curves in the following combinations: 5%--40%,
40%--80% and 5%--80%. Results of these calcula-
tions were averaged and the values are shown in
table 7.
Curve--fitting the inverse of themean, 1
mλ min
, and the
inverse of the standard deviation, 1
σλ min
, versus the
inverse of the pitch line velocity, 1vt
, results in the
following:
for vt ≤ 5 m/s
mλ min= 5.43389vt
+ 0.71012−1 (110)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
29
σλ min= 0.01525v2t
+ 9.43942
vt
+ 2.06085−1
(111)
for vt > 5 m/s:
mλ min= 5.47432vt
+ 0.70153−1 (112)
σλ min= 9.7849v2t
+ 6.19681
vt
+ 2.34174−1
(113)
Association of a mean and standard deviation with
each pitch line velocity allows the probability of wear
distress to be assigned given specific EHL operating
conditions using the procedure of annex B and
using:
y= λmin
my= mλ min
σy= σλ min
Table 7 -- Calculation results
vt (m/s) mλ min σλ min
0.25 0.04455408 0.02496302
0.50 0.08636353 0.04757665
1.00 0.16271966 0.08689583
1.50 0.23073618 0.11982298
2.00 0.29172511 0.14771523
2.50 0.34673387 0.17158123
3.00 0.39660952 0.19218459
3.50 0.44204486 0.21011292
4.00 0.48361240 0.22582491
4.50 0.52178951 0.23968331
5.00 0.55697759 0.25197825
10.00 0.80016431 0.32484801
15.00 0.93691698 0.35693985
20.00 1.02464932 0.37431229
25.00 1.08573704 0.38496185
30.00 1.13072662 0.39205782
35.00 1.16524421 0.39707727
40.00 1.19256659 0.40079104
45.00 1.21473204 0.40363655
50.00 1.23307514 0.40587858
100.00 1.32309469 0.41541491
150.00 1.35614631 0.41831071
200.00 1.37331023 0.41968741
250.00 1.38382249 0.42048785
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
30
(This page is intentionally left blank.)AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
31
Annex A
(informative)
Flow chart for evaluating scuffing risk and oil film thickness
[The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be
construed as a part of AGMA 925--A03, Effect of Lubrication on Gear Surface Distress.]
z1, z2, mn, β, aw, αn, ra1, ra2, b, n1,
P, Ko, Km, Kv, E1, E2, ν1, ν2, Ra1x,
Ra2x, nop, Tip, Driver, mmet, θM,
BM1, BM2, θoil, ksump, ηM, α, Lx,
θM,test, XW, ν40, θfl max, test,
START
P1
Get Input Data
θS met
Tip profile modification
0 = none
1 = modified for high load capacity
2 = modified for smooth meshing
Driver driving member
1 = pinion
2 = gear
nop number of calculation points along the line
of action (25 recommended)
ηM dynamic viscosity (mPa⋅s) at gear tooth
temperature, θM
0 = calculate using table 2 and equation 69
¸ 0! input own value (must also input α)
α pressure viscosity coefficient (mm2/N)
0 = calculate using table 2 and equation 74
¸ 0! input own value (must also inputηM)
ksump = 1.0 if splash lube
= 1.2 if spray lube
mmet method for approximating mean
coefficient of friction
1 = Kelley and AGMA 217.01 method
(constant)
2 = Benedict and Kelley method (variable)
Other = enter own value for mm (constant)
θM gear tooth temperature (°C)
0 = program calculates with equation 91
¸ 0! input own value
θS met method of calculating scuffing
temperature, θs
0 = from test gears (need to also input
θfl max, test, θM, test and XW from table 4
1 = R&O mineral oil
2 = EP mineral oil
Other = enter own value of θs (°C), (see
table 3)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
32
u (Eq 1)
r1 (Eq 2)
r2 (Eq 3)
rw1 (Eq 4)
αt (Eq 5)
rb1 (Eq 6)
rb2 (Eq 7)
αwt (Eq 8)
pbt (Eq 9)
pbn (Eq 10)
px (Eq 11)
βb (Eq 12)
βw (Eq 13)
αwn (Eq 14)
P1
CF (Eq 15)
CA (Eq 16)
CC (Eq 17)
CD (Eq 18)
CE (Eq 19)
CB (Eq 20)
Z (Eq 21)
εα (Eq 22)
nr = fractional part of εα
β = 0
yes
no
helical gear
spur gear
εβ (Eq 23)
na = fractional part of εβ
(1− nr)≥ na
Lmin (Eq 25) Lmin (Eq 26)
ω1 (Eq 33)
ω2 (Eq 34)
vt (Eq 35)
(Ft)nom (Eq 40)
KD (Eq 41)
Ft (Eq 42)
Fwn (Eq 43)
wn (Eq 44)
Er (Eq 58)
(Eq 87)
(Eq 86)
(Eq 85)
σx (Eq 78)
yes
no
P2
Ravgx
CRavgxmm const
Lmin (Eq 27)
εβ (Eq 24)
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
33
C1, C2, C3, C4, C5 = CA, CB, CC, CD, CE
P2
ξ1, ξ2, ξ3, ξ4, ξ5 (Eq 28)
ξA, ξB, ξC, ξD, ξE = ξ1, ξ2, ξ3, ξ4, ξ5
i = 1
ξi= ξA+ (i− 6)
ξE− ξA
(nop− 1)
i > 5
Ã1i (Eq 29)
Ã2i (Eq 30)
Ãri (Eq 31)
Ãni (Eq 32)
vr1i (Eq 36)
vr2i (Eq 37)
vsi (Eq 38)
vei (Eq 39)
yes
Tip = 0
Tip = 2
Driver = 1
no
no
no
XΓi (Eq 45)
XΓi (Eq 46)
XΓi (Eq 47)
XΓi (Eq 54)
XΓi (Eq 55)
XΓi (Eq 56)
XΓi (Eq 48)
XΓi (Eq 49)
XΓi (Eq 50)
XΓi (Eq 51)
XΓi (Eq 52)
XΓi (Eq 53)
yes
yes
yes
no
i = nop + 6
bH1 (eq 57)
i = i+ 1
P3
no
yes
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
34
no
(ηM & α input)no
P3
θM = 0
P3A
P3A
P4
ηM = 0
ηM = 0
mmet = 2
mmet = 1
θM = 0
ηM = 0
|θM1 -- θM| hc(i)
hmin = hc(i)
λ2bH(i) (Eq 77)
yes
λmin > λ2bH(i)
yes
i = i + 1
yes
no
no
no
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
36
mλ min (Eq 110)
σλ min (Eq 111)
P5
θS met= 0
θS met= 1
θS met= 2
θS (eq 96)
θs= θS met
y= θB max
my= θs
σy= 0.15 θs
Call subroutine
“Probability”
Return POF
Pscuff = POF
θS (eq 94)
θS (Eq 95)
yes
yes
yes
no
no
no
test gears
(need θfl max, test,
θM test & XW input)
R&O Mineral Oil
PscuffAGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
37
y, my, σy input
Return POF
POF = Q
x (eq B.1)
|x|> 1.6448
t (eq B.4)
ZQ (eq B.3)
Q (eq B.2)
x> 0
Q = 0.05
yes
no
POF = 1.0 -- Q
yes
POF = Probability of failure
Subroutine “Probability”
no
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
38
Subroutine “Max_Flash_Temp
i = 1
θfl max = 0
mm const = 0
**Eq 88 is not valid at vs(i) = 0 or XΓ(i) = 0 or near zero, and Eq 84 is not valid at bH(i) = 0 or near zero.
εmach is a small finite number (e.g., 10--10). In case the calculated mm(i) θfl max
no
no
θfl max = θfl(i)
yes
no
i = i + 1
i = nop + 6
yes
Return
no
mm is a (given) constant
or calculated by equation
85 (AGMA 217.01 and
Kelley)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
39
Annex B
(informative)
Normal or Gaussian probability
[The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be
construed as a part of AGMA 925--A03, Effect of Lubrication on Gear Surface Distress.]
B.1 Normal or Gaussian probability
For random variables that follow normal (Gaussian)
distributions, the following procedure [24] can be
used to calculate probabilities of failure in the range
of 5% to 95%:
x=
y− my
σy
(B.1)
where
x is the standard normal variable;
y is the random variable;
my is the mean value of random variable y;
σy is the standard deviation of random variable
y.
Evaluation of Q:
if x > 1.6448, then:
Q = 0.05;
else
Q= ZQ b1t+ b2t
2+ b3t
3+ b4t
4+ b5t
5
(B.2)
where
Q is the tail area of the normal probability
function;
ZQ is the normal probability density function.
Probability of failure:
if x > 0, then:
probability of failure = 1 -- Q;
else
probability of failure = Q
where
ZQ= 0.3989422804 e
−0.5(x)2
(B.3)
b1= 0.319381530
b2=− 0.356563782
b3= 1.781477937
b4=− 1.821255978
b5= 1.330274429
p= 0.2316419
t= 1
1+ p|x|
(B.4)
are constants given in reference [24].
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
40
(This page is intentionally left blank.)
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
41
Annex C
(informative)
Test rig gear data
[The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be
construed as a part of AGMA 925--A03, Effect of Lubrication on Gear Surface Distress.]
C.1 Test rig gear data
Table C.1 provides a summary of gear data for
several back to back test rigs that have been used for
gear lubrication rating and research.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
A
G
M
A
92
5
--A
03
A
M
E
R
IC
A
N
G
E
A
R
M
A
N
U
FA
C
T
U
R
E
R
S
A
S
S
O
C
IA
T
IO
N
42
Ta
b
le
C
.1
--
S
u
m
m
ar
y
o
f
g
ea
r
d
at
a
fo
r
lu
b
ri
ca
n
t
te
st
in
g
S
ym
b
o
l
U
n
it
s
F
Z
G
“A
”
F
Z
G
“A
10
”
F
Z
G
“C
”
F
Z
G
“C
--
G
F
”
N
A
S
A
R
yd
er
A
G
M
A
IA
E
P
rim
ar
y
w
ea
r
as
se
ss
m
en
t
S
cu
ffi
ng
S
cu
ffi
ng
P
itt
in
g
(m
ic
ro
&
m
ac
ro
)
M
ic
ro
pi
tti
ng
P
itt
in
g
S
cu
ffi
ng
P
itt
in
g
(m
ic
ro
&
m
ac
ro
)
S
cu
ffi
ng
a
m
m
91
.5
91
.5
91
.5
91
.5
88
.9
88
.9
91
.5
82
.5
5
m
n
m
m
4.
5
4.
5
4.
5
4.
5
3.
17
5
3.
17
5
3.
62
9
5.
08
α
n
de
g
20
20
20
20
20
22
.5
20
20
β
de
g
0
0
0
0
0
0
0
0
α
w
t
de
g
22
.4
4
22
.4
4
22
.4
4
22
.4
4
20
22
.5
21
.3
1
26
.2
5
z 1
--
--
16
16
16
16
28
28
20
15
z 2
--
--
24
24
24
24
28
28
30
16
b
m
m
20
10
14
14
6.
35
/2
.8
6.
35
14
4.
76
r a
1
m
m
44
.3
85
44
.3
85
41
.2
3
41
.2
3
47
.6
25
47
.2
2
40
.8
2
45
.0
2
r a
2
m
m
56
.2
5
56
.2
5
59
.1
8
59
.1
8
47
.6
25
47
.2
2
58
.1
8
47
.6
9
x 1
--
--
0.
86
35
0.
86
35
0.
18
17
0.
18
17
0
0
0.
22
31
0.
36
25
x 2
--
--
--
0.
51
03
--0
.5
10
3
0.
17
15
0.
17
15
0
0
0.
00
06
0.
38
75
Q
ua
lit
y
nu
m
be
r
Q
ua
lit
y
st
an
da
rd
--
--
5
IS
O
13
28
5
IS
O
13
28
5
D
IN
39
62
5
D
IN
39
62
13
A
G
M
A
20
00
13
A
G
M
A
20
00
12
--1
3
A
G
M
A
20
00
5
IS
O
13
28
R
a 1
mm
0.
3
--
0.
7
0.
3
--
0.
7
0.
3
--
0.
5
0.
4
--
0.
6
0.
3
--
0.
4
0.
46
--
0.
64
0.
5
--
0.
8
0.
3
--
0.
8
R
a 2
mm
0.
3
--
0.
7
0.
3
--
0.
7
0.
3
--
0.
5
0.
4
--
0.
6
0.
3
--
0.
4
0.
46
--
0.
64
0.
5
--
0.
8
0.
3
--
0.
8
n 1
rp
m
21
70
21
70
22
50
22
50
10
00
0
10
00
0
22
50
4K
--
6K
θ o
il
de
g
C
90
--1
40
90
--1
20
90
--1
20
90
49
--
77
74
80
70
--
11
0
R
ef
do
cu
m
en
t
--
--
IS
O
14
63
5-
-1
A
S
T
M
D
51
82
--9
7
C
E
C
L-
-0
7-
-A
--9
5
IS
O
/W
D
14
63
5-
-2
F
VA
In
fo
S
he
et
54
/7
F
VA
In
fo
S
he
et
54
/I-
-I
V
N
A
S
A
T
P
--
20
47
(1
98
2)
A
S
TM
D
19
47
--8
3
(1
98
4)
--
--
IP
16
6/
77
(1
99
2)
P
in
io
n
to
rq
ue
ra
ng
e
N
m
3.
3
--
53
4.
5
3.
3-
-5
34
.5
13
5
--
37
6
28
--
26
5
0
--
10
0
0
--
27
0
25
0
--
40
0
20
--
40
7
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
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Annex D
(informative)
Example calculations
[The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be
construed as a part of AGMA 925--A03, Effect of Lubrication on Gear Surface Distress.]
******************************************************************************
SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03
SCORING+ EX.#1
DATE:2002/04/18 TIME:08:08:23
******************************************************************************
***** GENERAL AND GEOMETRY INPUT DATA *****
SCORING+ EX.#1
Input unit (=1 SI, =2 Inch) (iInputUnit) 1.000000
Output unit (=1 SI, =2 Inch) (iOutputUnit) 1.000000
Gear type (=1 external, =2 internal) (iType) 1.000000
Driving member (=1 pinion, =2 gear) (iDriver) 2.000000
Number of pinion teeth (z1) 21.000000
Number of gear teeth (z2) 26.000000
Normal module (mn) 4.000000 mm
Helix angle (Beta) 0.000000 deg
Operating center distance (aw) 96.000000 mm
Normal generating pressure angle (Alphan) 20.000000 deg
Standard outside radius, pinion (ra1) 46.570900 mm
Standard outside radius, gear (ra2) 57.277000 mm
Face width (b) 66.040000 mm
Profile mod (=0 none, =1 hi load, =2 smooth) (iTip) 1.000000
***** Material input data *****
Modulus of elasticity, pinion (E1) 206842.718795 N/mm^2
Modulus of elasticity, gear (E2) 206842.718795 N/mm^2
Poisson’s ratio, pinion (Nu1) 0.300000
Poisson’s ratio, gear (Nu2) 0.300000
Average surface roughness at Lx, pinion (Ra1x) 0.508000 mu m
Average surface roughness at Lx, gear (Ra2x) 0.508000 mu m
Filter cutoff of wavelength x (Lx) 0.800000 mm
Method for approximate mean coef. friction (Mumet) 1.000000
Welding factor (Xw) 1.000000
***** Load data *****
Pinion speed (n1) 308.570000 rpm
Transmitted power (P) 20.619440 kW
Overload factor (Ko) 1.000000
Load distribution factor (Km) 1.400000
Dynamic factor (Kv) 1.063830
***** Lubrication data *****
Lubricant type (=1 Mineral, =2 Synthetic,
=3 MIL--L--7808K, =4 MIL--L--23699E) (iLubeType) 1.000000
ISO viscosity grade number (nIsoVG) 460.000000
Kinematic viscosity at 40 deg C (Nu40) 407.000000 mm^2/s
***** Input temperature data *****
Tooth temperature (ThetaM) 82.222222 deg C
Thermal contact coefficient, pinion (BM1) 16.533725 N/[mm s^.5K]
Thermal contact coefficient, gear (BM2) 16.533725 N/[mm s^.5K]
Oil inlet or sump temperature (Thetaoil) 71.111111 deg C
Parameter for calculating tooth temperature (ksump) 1.000000
Dynamic viscosity at gear tooth temperature (EtaM) 43.000000 mPa⋅s
Pressure--viscosity coefficient (Alpha) 0.022045 mm^2/N
Method of calculating scuffing temperature (Thetasmet) 2.000000
Maximum flash temperatrue of test gears (Thetaflmaxtest) 0.000000
Tooth temperature of test gear (ThetaMtest) 0.000000
Number of calculation points (nNop) 25.000000
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
44
******************************************************************************
SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03
SCORING+ EX.#1
DATE:2002/04/18 TIME:08:08:23
******************************************************************************
***** GEOMETRY CALCULATION *****
Gear ratio (u) 1.238095
Standard pitch radius, pinion (r1) 42.000000 mm
Standard pitch radius, gear (r2) 52.000000 mm
Pinion operating pitch radius (rw1) 42.893617 mm
Transverse generating pressure angle (Alphat) 20.000000 deg
Base radius, pinion (rb1) 39.467090 mm
Base radius, gear (rb2) 48.864016 mm
Transverse operating pressure angle (Alphawt) 23.056999 deg
Transverse base pitch (pbt) 11.808526 mm
Normal base pitch (pbn) 11.808526 mm
Axial pitch (px) ----------------
Base helix angle (Betab) 0.000000 deg
Operating helix angle (Betaw) 0.000000 deg
Normal operating pressure angle (Alphawn) 23.056999 deg
Distance along line of action -- Point A (CA) 7.715600 mm
Distance along line of action -- Point B (CB) 12.913884 mm
Distance along line of action -- Point C (CC) 16.799142 mm
Distance along line of action -- Point D (CD) 19.524126 mm
Distance along line of action -- Point E (CE) 24.722409 mm
Distance along line of action -- Point F (CF) 37.598080 mm
Active length of line of action (Z) 17.006810 mm
Transverse contact ratio (EpsAlpha) 1.440214
Fractional part of EpsAlpha (nr) 0.440214
Axial contact ratio (EpsBeta) 0.000000
Fractional part of EpsBeta (na) 0.000000
Minimum contact length (Lmin) 66.040000 mm
***** GEAR TOOTH VELOCITY AND LOADS *****
Rotational (angular) velocity, pinion (Omega1) 32.313375 rad/s
Rotational (angular) velocity, gear (Omega2) 26.099264 rad/s
Operating pitch line velocity (vt) 1.386038 m/s
Nominal tangential load (Ftnom) 14876.538066 N
Combined derating factor (KD) 1.489362
Actual tangential load (Ft) 22156.550486 N
Normal operating load (Fwn) 24080.178937 N
Normal unit load (wn) 364.630208 N/mm
***** MATERIAL PROPERTY AND TOOTH SURFACE FINISH *****
Reduced modulus of elasticity (Er) 227299.690984 N/mm^2
Average of pinion and gear average roughness (Ravgx) 0.508000 mu m
Surface roughness constant (CRavgx) 1.816720
Composite surface roughness at filter cuttoff (Sigmax) 0.718420 mu m
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
45
**********************************************************************************
SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03
SCORING+ EX.#1
DATE:2002/04/18 TIME:08:08:23
**********************************************************************************
***** LOAD SHARING RATIO AND bH *****
Index
Roll
Ang(rad) XGamma Rhon(mm) bH Index
(A) 0.19549 0.14286 6.13226 0.05982 (A)
(B) 0.32721 1.00000 8.47833 0.18610 (B)
(C) 0.42565 1.00000 9.29314 0.19484 (C)
(D) 0.49469 1.00000 9.38554 0.19581 (D)
(E) 0.62641 0.00000 8.46633 0.00000 (E)
( 1) 0.19549 0.14286 6.13226 0.05982 ( 1)
( 2) 0.21345 0.25970 6.53669 0.08327 ( 2)
( 3) 0.23140 0.37654 6.91441 0.10313 ( 3)
( 4) 0.24936 0.49339 7.26541 0.12101 ( 4)
( 5) 0.26731 0.61023 7.58971 0.13755 ( 5)
( 6) 0.28527 0.72708 7.88729 0.15306 ( 6)
( 7) 0.30322 0.84392 8.15816 0.16770 ( 7)
( 8) 0.32118 0.96076 8.40233 0.18160 ( 8)
( 9) 0.33913 1.00000 8.619780.18765 ( 9)
( 10) 0.35709 1.00000 8.81052 0.18971 ( 10)
( 11) 0.37504 1.00000 8.97455 0.19147 ( 11)
( 12) 0.39300 1.00000 9.11187 0.19293 ( 12)
( 13) 0.41095 1.00000 9.22247 0.19410 ( 13)
( 14) 0.42890 1.00000 9.30637 0.19498 ( 14)
( 15) 0.44686 1.00000 9.36356 0.19558 ( 15)
( 16) 0.46481 1.00000 9.39403 0.19589 ( 16)
( 17) 0.48277 1.00000 9.39780 0.19593 ( 17)
( 18) 0.50072 0.81791 9.37485 0.17698 ( 18)
( 19) 0.51868 0.70106 9.32520 0.16342 ( 19)
( 20) 0.53663 0.58422 9.24883 0.14857 ( 20)
( 21) 0.55459 0.46737 9.14575 0.13214 ( 21)
( 22) 0.57254 0.35053 9.01596 0.11362 ( 22)
( 23) 0.59050 0.23369 8.85946 0.09196 ( 23)
( 24) 0.60845 0.11684 8.67625 0.06435 ( 24)
( 25) 0.62641 0.00000 8.46633 0.00000 ( 25)
**** P3 -- Calculate flash temperature ****
Dynamic viscosity at 40 deg C (Eta40C) 412.082400 mPa⋅s
Dynamic viscosity at 100 deg C (Eta100C) 26.341040 mPa⋅s
Factor c (c_coef) 8.964201
Factor d (d_coef) --3.424449
Factor k (k_coef) 0.010471
Factor s (s_coef) 0.134800
Mumet -- use Kelley and AGMA 217.01 (Mumet) 1.000000
Surface roughness constant (CRavgx) 1.816720
Mean coef. of friction, const. (Eq 85) (Mumconst) 0.109003
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
46
**********************************************************************************
SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03
SCORING+ EX.#1
DATE:2002/04/18 TIME:08:08:23
**********************************************************************************
**** Calculate flash temperature ****
Index K Mum XGamma bH (mm) vs (m/s) vr1 (m/s) vr2 (m/s) Thetafl (C) Index
(A) 0.80 0.1090 0.1429 0.059822 0.5306 0.2493 0.7799 13.6320 (A)
(B) 0.80 0.1090 1.0000 0.186102 0.2269 0.4173 0.6442 22.0835 (B)
(C) 0.80 0.1090 1.0000 0.194840 0.0000 0.5428 0.5428 0.0000 (C)
(D) 0.80 0.1090 1.0000 0.195806 0.1592 0.6309 0.4717 14.7688 (D)
(E) 0.80 0.0000 0.0000 0.000000 0.4628 0.7989 0.3360 0.0000 (E)
( 1) 0.80 0.1090 0.1429 0.059822 0.5306 0.2493 0.7799 13.6320 ( 1)
( 2) 0.80 0.1090 0.2597 0.083275 0.4892 0.2722 0.7614 19.2004 ( 2)
( 3) 0.80 0.1090 0.3765 0.103129 0.4478 0.2951 0.7429 22.7228 ( 3)
( 4) 0.80 0.1090 0.4934 0.121010 0.4064 0.3180 0.7244 24.7713 ( 4)
( 5) 0.80 0.1090 0.6102 0.137549 0.3650 0.3409 0.7059 25.6466 ( 5)
( 6) 0.80 0.1090 0.7271 0.153056 0.3236 0.3638 0.6874 25.5359 ( 6)
( 7) 0.80 0.1090 0.8439 0.167704 0.2822 0.3867 0.6689 24.5661 ( 7)
( 8) 0.80 0.1090 0.9608 0.181595 0.2408 0.4096 0.6505 22.8276 ( 8)
( 9) 0.80 0.1090 1.0000 0.187648 0.1995 0.4325 0.6320 19.2753 ( 9)
( 10) 0.80 0.1090 1.0000 0.189713 0.1581 0.4554 0.6135 15.1349 ( 10)
( 11) 0.80 0.1090 1.0000 0.191471 0.1167 0.4783 0.5950 11.0832 ( 11)
( 12) 0.80 0.1090 1.0000 0.192930 0.0753 0.5012 0.5765 7.1033 ( 12)
( 13) 0.80 0.1090 1.0000 0.194098 0.0339 0.5241 0.5580 3.1799 ( 13)
( 14) 0.80 0.1090 1.0000 0.194979 0.0075 0.5470 0.5395 0.7011 ( 14)
( 15) 0.80 0.1090 1.0000 0.195577 0.0489 0.5699 0.5210 4.5531 ( 15)
( 16) 0.80 0.1090 1.0000 0.195895 0.0903 0.5928 0.5025 8.3886 ( 16)
( 17) 0.80 0.1090 1.0000 0.195934 0.1317 0.6157 0.4840 12.2201 ( 17)
( 18) 0.80 0.1090 0.8179 0.176983 0.1731 0.6386 0.4655 13.8125 ( 18)
( 19) 0.80 0.1090 0.7011 0.163420 0.2145 0.6615 0.4470 15.2621 ( 19)
( 20) 0.80 0.1090 0.5842 0.148569 0.2559 0.6844 0.4285 15.9136 ( 20)
( 21) 0.80 0.1090 0.4674 0.132141 0.2973 0.7073 0.4100 15.6888 ( 21)
( 22) 0.80 0.1090 0.3505 0.113623 0.3386 0.7302 0.3915 14.4671 ( 22)
( 23) 0.80 0.1090 0.2337 0.091964 0.3800 0.7531 0.3730 12.0443 ( 23)
( 24) 0.80 0.1090 0.1168 0.064352 0.4214 0.7760 0.3545 7.9953 ( 24)
( 25) 0.80 0.0000 0.0000 0.000000 0.4628 0.7989 0.3360 0.0000 ( 25)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
The max. flash temp. occurs at point (10) (Thetaflmax) 25.646608 deg C
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
Dynamic viscosity at the gear tooth temperature (EtaM) 43.000000 mPa⋅s
Pressure--viscosity coefficient (Alpha) 0.022045 mm^2/N
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
47
**********************************************************************************
SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03
SCORING+ EX.#1
DATE:2002/04/18 TIME:08:08:23
**********************************************************************************
********** P4 -- Specific film thickness **********
Material parameter (eq 66) (G) 5010.821688
Index U W Hc hc (mu m) Lambda2bH Index
(A) 1.587561e--11 0.000037 3.539329e--05 0.217041 0.781203 (A)
(B) 1.184300e--11 0.000189 2.458469e--05 0.208437 0.425354 (B)
(C) 1.105036e--11 0.000173 2.365326e--05 0.219813 0.438395 (C)
(D) 1.111223e--11 0.000171 2.376807e--05 0.223076 0.443804 (D)
(E) 1.267961e--11 0.000000 0.000000e+00 0.000000 0.000000 (E)
( 1) 1.587561e--11 0.000037 3.539329e--05 0.217041 0.781203 ( 1)
( 2) 1.495710e--11 0.000064 3.220166e--05 0.210492 0.642142 ( 2)
( 3) 1.420027e--11 0.000087 3.010396e--05 0.208151 0.570609 ( 3)
( 4) 1.357156e--11 0.000109 2.854084e--05 0.207361 0.524768 ( 4)
( 5) 1.304655e--11 0.000129 2.730927e--05 0.207269 0.491992 ( 5)
( 6) 1.260712e--11 0.000148 2.630903e--05 0.207507 0.466937 ( 6)
( 7) 1.223958e--11 0.000166 2.548198e--05 0.207886 0.446895 ( 7)
( 8) 1.193348e--11 0.000183 2.479093e--05 0.208301 0.430320 ( 8)
( 9) 1.168076e--11 0.000186 2.439213e--05 0.210255 0.427292 ( 9)
( 10) 1.147515e--11 0.000182 2.414785e--05 0.212755 0.430014 ( 10)
( 11) 1.131183e--11 0.000179 2.395433e--05 0.214979 0.432510 ( 11)
( 12) 1.118707e--11 0.000176 2.380784e--05 0.216934 0.434789 ( 12)
( 13) 1.109806e--11 0.000174 2.370556e--05 0.218624 0.436856 ( 13)
( 14) 1.104277e--11 0.000172 2.364541e--05 0.220053 0.438717 ( 14)
( 15) 1.101981e--11 0.000171 2.362595e--05 0.221223 0.440375 ( 15)
( 16) 1.102840e--11 0.000171 2.364633e--05 0.222134 0.441830 ( 16)
( 17) 1.106830e--11 0.000171 2.370628e--05 0.222787 0.443084 ( 17)
( 18) 1.113982e--11 0.000140 2.428942e--05 0.227710 0.476505 ( 18)
( 19) 1.124380e--11 0.000121 2.481221e--05 0.231379 0.503875 ( 19)
( 20) 1.138168e--11 0.000101 2.546118e--05 0.235486 0.537840 ( 20)
( 21) 1.155550e--11 0.000082 2.627996e--05 0.240350 0.582071 ( 21)
( 22) 1.176804e--11 0.000062 2.735014e--05 0.246588 0.644006 ( 22)
( 23) 1.202294e--11 0.000042 2.885557e--05 0.255645 0.742128 ( 23)
( 24) 1.232482e--11 0.000022 3.139471e--05 0.272388 0.945273 ( 24)
( 25) 1.267961e--11 0.000000 0.000000e+00 0.000000 0.000000 ( 25)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
Minimum film thickness found at point(5) (hmin) 0.207269 mu m
Min. specific film thk. found at point (B) (LambdaMin) 0.425354
Tooth temperature(ThetaM) 82.222222 deg C
Max. flash temperature (Thetaflmax) 25.646608 deg C
Minimum film thickness (hmin) 0.207269 mu m
Maximum contact temperature (ThetaBmax) 107.868830 deg C
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
48
**********************************************************************************
SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03
SCORING+ EX.#1
DATE:2002/04/18 TIME:08:08:23
**********************************************************************************
**** P5 -- Calculate risk of scuffing and wear ****
***** Risk of scuffing *****
Method of calculating scuffing temperature (Thetasmet) 2.000000
Mean scuffing temperature (Thetas) 316.290835 deg C
***** Probability of scuffing *****
Maximum contact temperature (y) 107.868830 deg C
Mean scuffing temperature (Muy) 316.290835 deg C
Approx. standard deviation of scuffing temp. (Sigmay) 47.443625 deg C
Standard normal variable, x = ((y--muy)/Sigmay) --4.393046
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
Probability of scuffing Pscuff = 5% or lower
Based on AGMA925--A03 Table 5, scuffing risk is low
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
**** Risk of wear ****
Average surface roughness, pinion (Ra1x) 0.508000 mu m
Average surface roughness, gear (Ra2x) 0.508000 mu m
Average surface roughness (rms), pinion (Rq1x) 0.563880 mu m
Average surface roughness (rms), gear (Rq2x) 0.563880 mu m
Arithmetic average of rms roughness (Rqxavg) 0.563880 mu m
Minimum specific film thickness (Lambdamin) 0.425354
Pitchline velocity is less than 5 m/s (vt) 1.386038 m/s
Mean min. specific film thk. (eq. 110) (MuLambdaMin) 0.215956
Std. dev. of min. spec. film thk. (eq. 111) (SigmaLambdaMin) 0.112623
***** Probability of wear *****
Minimum specific film thickness (y) 0.425354
Mean minimum specific film thickness (muy) 0.215956
Standard deviation of the min. specific film (Sigmay) 0.112623
Standard normal variable, x = ((y--muy)/Sigmay) 1.859273
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
Probability of wear Pwear = 5% or lower
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
49
Bibliography
The following documents are either referenced in the text of AGMA 925--A03, Effect of Lubrication on Gear
Surface Distress, or indicated for additional information.
1. Blok, H., Les Températures de Surface dans les Conditions de Graissage sans Pression Extrême,
Second World Petroleum Congress, Paris, June, 1937.
2. Kelley, B.W., A New Look at the Scoring Phenomena of Gears, SAE transactions, Vol. 61, 1953,
pp. 175--188.
3. Dudley, D.W., Practical Gear Design, McGraw--Hill, New York, 1954.
4. Kelley, B.W., The Importance of Surface Temperature to Surface Damage, Chapter in Engineering
Approach to Surface Damage, Univ. of Michigan Press, Ann Arbor, 1958.
5. Benedict, G. H. and Kelley, B. W., Instantaneous Coefficients of Gear Tooth Friction, ASLE transactions,
Vol. 4, 1961, pp. 59--70.
6. Lemanski, A.J., “AGMA Aerospace Gear Committee Gear Scoring Project”, March 1962.
7. AGMA 217.01, AGMA Information Sheet -- Gear Scoring Design for Aerospace Spur and Helical Power
Gears, October, 1965.
8. SCORING+, computer program, GEARTECH Software, Inc., 1985.
9. ASTMD445--97, Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (the
Calculation of Dynamic Viscosity).
10. ASTM D341--93(1998), Standard Viscosity -- Temperature Charts for Liquid Petroleum Products.
11. ASTM D2270--93(1998), Standard Practice for Calculating Viscosity Index From Kinematic Viscosity at
40 and 100°C.
12. So, B. Y. C. and Klaus, E. E., Viscosity--Pressure Correlation of Liquids, ASLE Transactions, Vol. 23, 4,
409--421, 1979.
13. Novak, J. D. and Winer, W. O., Some Measurements of High Pressure Lubricant Rheology, Journal of
Lubricant Technology, Transactions of the ASME, Series F, Vol. 90, No. 3, July 1968, pp. 580 – 591.
14. Jones, W. R., Johnson, R. L., Winer, W. O. and Sanborn, D. M., Pressure--Viscosity Measurements for
Several Lubricants to 5.5x108 N/m2 (8x104 psi) and 149°C (300°F), ASLE Transactions, 18, pp. 249 – 262,
1975.
15. Brooks, F. C. and Hopkins, V., Viscosity and Density Characteristics of Five Lubricant Base Stocks at
Elevated Pressures and Temperatures, Preprint number 75--LC--3D--1, presented at the ASLE/ASME
Lubrication Conference, Miami Beach, FL, October 21 – 23, 1975.
16. Dowson, D. and Higginson, G. R., New Roller -- Bearing Lubrication Formula, Engineering, (London),
Vol. 192, 1961, pp. 158--159.
17. Dowson, D. and Higginson, G.R., Elastohydrodynamic Lubrication -- The Fundamentals of Roller and
Gear Lubrication, Pergamon Press (London), 1966.
18. Dowson, D., Elastohydrodynamics, Paper No. 10, Proc. Inst. Mech. Engrs., Vol. 182, Pt. 3A, 1967,
pp. 151--167.
19. Dowson, D. and Toyoda, S., A Central Film Thickness Formula for Elastohydrodynamic Line Contacts,
5th Leeds--Lyon Symposium Proceedings, Paper 11 (VII), 1978, pp. 60--65.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
50
20. Wellauer, E. J. and Holloway, G.A., Application of EHD Oil Film Theory to Industrial Gear Drives,
Transactions of ASME, J. Eng., Ind., Vol. 98., series B, No 2, May 1976, pp. 626--634.
21. Moyer, C. A. and Bahney, L.L., Modifying the Lambda Ratio to Functional Line Contacts, STLE Trib.
Trans. Vol. 33 (No. 4), 1990, pp. 535--542.
22. Viscosity and pressureAGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
iv
Foreword
[The foreword, footnotes and annexes, if any, in this document are provided for
informational purposes only and are not to be construed as a part of AGMA Information
Sheet 925--A03, Effect of Lubrication on Gear Surface Distress.]
The purpose of this information sheet is to provide the user with information pertinent to the
lubrication of industrial metal gears for power transmission applications. It is intended that
this document serve as a general guideline and source of information about conventional
lubricants, their properties, and their general tribological behavior in gear contacts. This
information sheet was developed to supplement ANSI/AGMA Standards 2101--C95 and
2001--C95. It has been introduced as an aid to the gearmanufacturing and user community.
Accumulation of feedback data will serve to enhance future developments and improved
methods to evaluate lubricant related wear risks.
It was clear from the work initiated on the revision of AGMA Standards 2001--C95 and
2101--C95 (metric version) that supporting information regarding lubricant properties and
general tribological knowledge of contacting surfaces would aid in the understanding of
these standards. The information would also provide the user with more tools to help make
a more informed decision about the performance of a geared system. This information
sheet provides sufficient information about the key lubricant parameters to enable the user
to generate reasonable estimates about scuffing and wear based on the collective
knowledge of theory available for these modes at this time.
In 1937 Harmon Blok published his theory about the relationship between contact
temperature and scuffing. This went largely unnoticed in the U.S. until the early 1950’s
when Bruce Kelley showed that Blok’s method and theories correlated well with
experimental data he had generated on scuffing of gear teeth. The Blok flash temperature
theory began to receive serious consideration as a predictor of scuffing in gears. The
methodology and theories continued to evolve through the 1950’s with notable
contributions from Dudley, Kelley and Benedict in the areas of application rating factors,
surface roughness effects and coefficient of friction. The 1960’s saw the evolution of gear
calculations and understanding continue with computer analysis and factors addressing
load sharing and tip relief issues. The AGMA Aerospace Committee began using all the
available information to produce high quality products and help meet its long--term goal of
manned space flight. R. Errichello introduced the SCORING+ computer program in 1985,
which included all of the advancements made by Blok, Kelley, Dudley and the Aerospace
Committee to that time. It became the basis for annex A of ANSI/AGMA 2101--C95 and
2001--C95 which helped predict the risk of scuffing and wear. In the 1990s, this annex
formed the basis for AGMA’s contribution to ISO 13989--1.
Just as many others took the original Blok theories and expanded them, the Tribology
Subcommittee of the Helical Gear Rating Committee has attempted to expand the original
annex A of ANSI/AGMA 2001--C95 and 2101--C95. Specifically, the subcommittee
targeted the effect lubricationmay have on gear surface distress. As discussions evolved, it
became clear that this should be a stand alone document which will hopefully serve many
other gear types. This should be considered awork in progress asmore is learned about the
theories and understanding of the various parameters and how they affect the life of the
gear. Some of these principles are also mentioned in ISO/TR 13989--1.
AGMA 925--A03 was was approved by the AGMA Technical Division Executive Committee
on March 13, 2003.
Suggestions for improvement of this document will be welcome. They should be sent to the
AmericanGearManufacturers Association, 500Montgomery Street, Suite 350, Alexandria,
Virginia 22314.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
v
PERSONNEL of the AGMA Helical Rating Committee and Tribology SubCommittee
Chairman: D. McCarthy Dorris Company. . . . . . . . . . . . . . . . . . . . . . . . .
Vice Chairman: M. Antosiewicz The Falk Corporation. . . . . . . . . . . . . . . . . .
SubCommittee Chairman: H. Hagan The Cincinnati Gear Company. . . . . . . . . . . . . .
COMMITTEE ACTIVE MEMBERS
K.E. Acheson The Gear Works--Seattle, Inc.. . .
J.B. Amendola MAAG Gear AG. .
T.A. Beveridge Caterpillar, Inc.. .
M.J. Broglie Dudley Technical Group, Inc.. . . . .
A.B. Cardis Exxon Mobil Research. . . . .
M.F. Dalton General Electric Company. . . . .
G.A. DeLange Prager, Incorporated. . .
D.W. Dudley Consultant. . . .
R.L. Errichello GEARTECH. . .
D.R. Gonnella Equilon Lubricants. . .
M.R. Hoeprich The Timken Company. .
O.A. LaBath The Cincinnati Gear Co.. . . .
G. Lian Amarillo Gear Company. . . . . . . . .
J.V. Lisiecki The Falk Corporation. . . . .
L. Lloyd Lufkin Industries, Inc.. . . . . . . .
J.J. Luz General Electric Company. . . . . . . .
D.R. McVittie Gear Engineers, Inc.. . . .
A.G. Milburn Milburn Engineering, Inc.. . . .
G.W. Nagorny Nagorny & Associates. . .
M.W. Neesley Philadelphia Gear Corp.. . .
B. O’Connor The Lubrizol Corporation. . . .
W.P. Pizzichil Philadelphia Gear Corp.. . .
D.F. Smith Solar Turbines, Inc.. . . . . .
K. Taliaferro Rockwell Automation/Dodge. . . .
COMMITTEE ASSOCIATE MEMBERS
M. Bartolomeo New Venture Gear, Inc.. .
A.C. Becker Nuttall Gear LLC. . . .
E. Berndt Besco. . . . . . .
E.J. Bodensieck Bodensieck Engineering Co..
D.L. Borden D.L. Borden, Inc.. . . .
M.R. Chaplin Contour Hardening, Inc.. . . .
R.J. Ciszak Euclid--Hitachi Heavy Equip. Inc.. . . . .
A.S. Cohen Engranes y Maquinaria Arco SA. . . . .
S. Copeland Gear Products, Inc.. . . .
R.L. Cragg Consultant. . . . .
T.J. Dansdill General Electric Company. . . .
F. Eberle Rockwell Automation/Dodge. . . . . . .
L. Faure C.M.D.. . . . . . . .
C. Gay Charles E. Gay & Company, Ltd.. . . . . . . . .
J. Gimper Danieli United, Inc.. . . . . .
T.C. Glasener Xtek, Incorporated. . .
G. Gonzalez Rey ISPJAE
M.A. Hartman ITW. . .
J.M. Hawkins Rolls--Royce Corporation. . .
G. Henriot Consultant. . . . . .
G. Hinton Xtek, Incorporated. . . . . . .
M. Hirt Renk AG. . . . . . . . .
R.W. Holzman Milwaukee Gear Company, Inc.. .
R.S. Hyde The Timken Company. . . . . .
V. Ivers Xtek, Incorporated. . . . . . . .
A. Jackson Exxon Mobil. . . . .
H.R. Johnson The Horsburgh & Scott Co.. . .
J.G. Kish Sikorsky Aircraft Division. . . . . . .
R.H. Klundt The Timken Company. . . . .
J.S. Korossy The Horsburgh & Scott Co.. . . .
I. Laskin Consultant. . . . . . . .
J. Maddock The Gear Works -- Seattle, Inc.. . . . .
J. Escanaverino ISPJAE.
G.P. Mowers Consultant. . . .
R.A. Nay UTC Pratt & Whitney Aircraft. . . . . . .
M. Octrue CETIM. . . . . .
T. Okamoto Nippon Gear Company, Ltd.. . . . .
J.R. Partridge Lufkin Industries, Inc.. . .
J.A. Pennell Univ. of Newcastle--Upon--Tyne. . . . .
A.E. Phillips Rockwell Automation/Dodge. . . . .
J.W. Polder Delft University of Technology. . . . .
E. Sandberg Det Nordske Veritas. . . .
C.D. Schultz Pittsburgh Gear Company. . . .
E.S. Scott The Alliance Machine Company. . . . . .
A. Seireg University of Wisconsin. . . . . . .
Y. Sharma Philadelphia Gear Corporation. . . . . .
B.W. Shirley Emerson Power Transmission. . . .
L.J. Smith Invincible-- viscosity data supplied by Mobil Technology Company and Kluber Lubrication.
23. Sayles, R.S. and Thomas, T.R., Surface Topography as a Nonstationary RandomProcess, Nature, 271,
pp. 431--434, February 1978.
24. Handbook of Mathematical Functions, National Bureau of Standards (NIST), U.S. Government Printing
Office, Washington, D.C., 1964.
25. Rough Surfaces, edited by Thomas, T.R., Longman, Inc., New York, 1982, p. 92.
26. Errichello, R., Friction, Lubrication andWear of Gears, ASMHandbook, Vol. 18, Oct. 1992, pp. 535--545.
27. Blok, H., The Postulate About the Constancy of Scoring Temperature, Interdisciplinary Approach to the
Lubrication of Concentrated Contacts, NASA SP--237, 1970, pp. 153--248.
28. ANSI/AGMA 9005--E02, Industrial Gear Lubrication.
29. Winter, H. andMichaelis, K.,Scoring LoadCapacity of Gears Lubricated with EP--Oils, AGMAPaper No.
P219.17, October, 1983.
30. Almen, J.O., Dimensional Value of Lubricants in Gear Design, SAE Journal, Sept. 1942, pp. 373--380.
31. Borsoff, V.N., Fundamentals of Gear Lubrication, Summary Report for Period March 1953 to May 1954,
Bureau of Aeronautics, Shell Development Company, Contract No. 53--356c, p. 12.
32. Borsoff, V.N., On the Mechanism of Gear Lubrication, ASME Journal of Basic Engineering, Vol. 81,
pp. 79--93, 1959.
33. Borsoff, V.N. and Godet, M.R., A Scoring Factor for Gears, ASLE Transactions, Vol. 6, No. 2, 1963,
pp. 147--153.
34. Borsoff, V.N., Predicting the Scoring of Gears, Machine Design, January 7, 1965, pp. 132--136.
35. ANSI/AGMA 6011--H98, Specification for High Speed Helical Gear Units.
36. Nakanishi, T. and Ariura, Y., Effect of Surface--Finishing on Surface Durability of Surface--Hardened
Gears, MPT ‘91, JSME International Conference on Motion and Power Transmissions, 1991, pp. 828--833.
37. Tanaka, S., et al, Appreciable Increases in Surface Durability of Gear Pairs with Mirror--Like Finish,
ASME Paper No. 84--DET--223, 1984, pp. 1--8.
38. Ueno, T., et al, Surface Durability of Case--Carburized Gears on a Phenomenon of ‘Gray Staining’ of
Tooth Surface, ASME Paper No. 80--C2/DET--27, 1980, pp. 1--8.
39. Olver, A.V., Micropitting of Gear Teeth -- Design Solutions, presented at Aerotech 1995, NEC
Birmingham, October 1995, published by I. Mech. E., 1995.
40. FVA Information Sheet “Micropitting”, No. 54/7 (July, 1993) Forschungsvereinigung Antriebstechnik e.V.,
Lyoner Strasse 18, D--60528, Frankfurt/Main.
41. Bowen, C. W., The Practical Significance of Designing to Gear Pitting Fatigue Life Criteria, ASMEPaper
77--DET--122, September 1977.
42. Dudley, D.W.,Characteristics of Regimes of Gear Lubrication, International Symposium on Gearing and
Power Transmissions, Tokyo, Japan, 1981.
43. Blok, H., The Thermal--Network Method for Predicting Bulk Temperatures in Gear Transmissions, Proc.
7th Round Table Discussion on Marine Reduction Gears held in Finspong, Sweden, 9--10 September 1969.
44. Blok, H., Thermo--Tribology -- Fifty Years On, keynote address to the Int. Conf. Tribology; Friction,
Lubrication and Wear -- 50 Years On, Inst. Mech. Engrs., London, 1--3 July 1987, Paper No. C 248/87.
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
51
45. Ku, P.M. and Baber, B.B., The Effect of Lubricants on Gear Tooth Scuffing, ASLE Transactions, Vol. 2,
No. 2, 1960, pp. 184--194.
46. Winter, H., Michaelis, K. and Collenberg, H.F., Investigations on the Scuffing Resistance of High--Speed
Gears, AGMA Fall Technical Meeting Paper 90FTM8, 1990.
47. ANSI/AGMA 6002--B93, Design Guide for Vehicle Spur and Helical Gears.
48. Barish, T., How Sliding Affects Life of Rolling Surfaces, Machine Design, 1960.
49. Massey, C., Reeves, C. and Shipley, E.E., The Influence of Lubrication on the Onset of Surface Pitting in
Machinable Hardness Gear Teeth, AGMA Technical Paper 91FTM17, 1991.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PUBLISHED BY
AMERICAN GEAR MANUFACTURERS ASSOCIATION
1500 KING STREET, ALEXANDRIA, VIRGINIA 22314Gear Company. . . . . .
L. Spiers Emerson Power Trans. Corp.. . . . . . .
A.A. Swiglo IIT Research Institute/INFAC. . . . .
J.W. Tellman Dodge. . . .
F.A. Thoma F.A. Thoma, Inc.. . . . .
D. Townsend NASA/Lewis Research Center. . . .
L. Tzioumis Dodge. . . . .
F.C. Uherek Flender Corporation. . . . .
A. Von Graefe MAAG Gear AG. . .
C.C. Wang 3E Software & Eng. Consulting. . . . .
B. Ward Recovery Systems, LLC. . . . . . . .
R.F. Wasilewski Arrow Gear Company.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
vi
SUBCOMMITTEE ACTIVE MEMBERS
K.E. Acheson The Gear Works -- Seattle, Inc.. . .
J.B. Amendola MAAG Gear AG. .
T.A. Beveridge Caterpillar, Inc.. .
M.J. Broglie Dudley Technical Group, Inc.. . . . .
A.B. Cardis Exxon Mobil Research. . . . .
R.L. Errichello GEARTECH. . .
D.R. Gonnella Equilon Lubricants. . .
M.R. Hoeprich The Timken Company. .
G. Lian Amarillo Gear Company. . . . . . . . .
D. McCarthy Dorris Company. . . .
D.R. McVittie Gear Engineers, Inc.. . . .
A.G. Milburn Milburn Engineering, Inc.. . . .
G.W. Nagorny Nagorny & Associates. . .
B. O’Connor The Lubrizol Corporation. . . .
D.F. Smith Solar Turbines, Inc.. . . . . .
K. Taliaferro Rockwell Automation/Dodge. . . .
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
American Gear Manufacturers
Association --
Effect of Lubrication on
Gear Surface Distress
1 Scope
This information sheet is designed to provide
currently available tribological information pertaining
to oil lubrication of industrial gears for power
transmission applications. It is intended to serve as
a general guideline and source of information about
gear oils, their properties, and their general tribolog-
ical behavior in gear contacts. Manufacturers and
end--users are encouraged, however, to work with
their lubricant suppliers to address specific concerns
or special issues that may not be covered here (such
as greases).
The equations provided herein allow the user to
calculate specific oil film thickness and instanta-
neous contact (flash) temperature for gears in
service. These two parameters are considered
critical in defining areas of operation that may lead to
unwanted surface distress. Surface distress may be
scuffing (adhesive wear), fatigue (micropitting and
macropitting), or excessive abrasive wear (scoring).
Each of these forms of surface distress may be
influenced by the lubricant; the calculations are
offered to help assess the potential risk involved with
a given lubricant choice. Flow charts are included as
aids to using the equations.
This information sheet is a supplement to ANSI/
AGMA 2101--C95 and ANSI/AGMA 2001--C95. It
has been introduced as an aid to the gear manufac-
turing and user community. Accumulation of feed-
back data will serve to enhance future developments
and improved methods to evaluate lubricant related
surface distress.
It was clear from the work on the revision of standard
ANSI/AGMA 2001--C95 (ANSI/AGMA 2101--C95,
metric version) that supporting information regard-
ing lubricant properties and general tribological
understanding of contacting surfaces would aid in
understanding of the standard and provide the user
with more tools to make an informed decision about
the performance of a geared system. One of the key
parameters is the estimated film thickness. This is
not a trivial calculation, but one that has significant
impact on overall performance of the gear pair. It is
considered in performance issues such as scuffing,
wear, and surface fatigue. This information sheet
provides sufficient information about key lubricant
parameters to enable the user to generate reason-
able estimates about surface distress based on the
collective knowledge available.
Blok [1] published his contact temperature equation
in 1937. It went relatively unnoticed in the U.S. until
Kelley [2] showed that Blok’s method gave good
correlation with Kelley’s experimental data. Blok’s
equation requires an accurate coefficient of friction.
Kelley found it necessary to couple the coefficient of
friction to surface roughness of the gear teeth.
Kelley recognized the importance of load sharing by
multiple pairs of teeth and gear tooth tip relief, but he
did not offer equations to account for those variables.
Dudley [3] modified Kelley’s equation by adding
derating factors for application, misalignment and
dynamics. He emphasized the need for research on
effects of tip relief, and recommended applying
Blok’s method to helical gears.
In 1958, Kelley [4] changed his surface roughness
term slightly.
Benedict and Kelley [5] published their equation for
variable coefficient of friction derived from disc tests.
The AGMAAerospace Committee began investigat-
ing scuffing in 1960, and Lemanski [6] published
results of a computer analysis that contains data for
90 spur and helical gearsets, and formed the terms
for AGMA 217.01 [7], which was published in 1965.
It used Dudley’s modified Blok/Kelley equation and
included factors accounting for load sharing and tip
relief.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
2
TheSCORING+computer program [8] was released
in 1985. It incorporated all advancements made by
Blok, Kelley, Dudley and AGMA 217.01. In addition,
it added several improvements including:
-- Helical gears were analyzed by resolving the
load in the normal plane and distributing the
normal load over the minimum length of the
contact lines. The semi--width of the Hertzian
contact band was calculated based on the normal
relative radius of curvature;
-- Derating factors for application, misalignment
and dynamics were explicit input data;
-- Options for coefficient of friction were part of
input data, including a constant 0.06 (as pre-
scribed by Kelley and AGMA 217.01), a constant
under user control, and a variable coefficient
based on the Benedict and Kelley equation.
SCORING+ and AGMA 217.01 both use the same
value for the thermal contact coefficient of
BM = 16.5 N/[mm⋅s0.5⋅K], and they calculate the
same contact temperature for spur gears if all
deratingfactors are set to unity.
Annex A of ANSI/AGMA 2101--C95 and ANSI/
AGMA 2001--C95 was based on SCORING+ and
included methods for predicting risk of scuffing
based on contact temperature and risk of wear
based on specific film thickness.
This information sheet expands the information in
annex A of ANSI/AGMA2101--C95 andANSI/AGMA
2001--C95 to includemany aspects of gear tribology.
2 References
The following standards contain provisions which
are referenced in the text of this information sheet.
At the time of publication, the editions indicated were
valid. All standards are subject to revision, and
parties to agreements based on this document are
encouraged to investigate the possibility of applying
the most recent editions of the standards indicated.
ANSI/AGMA 2001--C95, Fundamental Rating Fac-
tors and Calculation Methods for Involute Spur and
Helical Gear Teeth
ANSI/AGMA 2101--C95, Fundamental Rating Fac-
tors and Calculation Methods for Involute Spur and
Helical Gear Teeth (Metric Edition)
ANSI/AGMA 1010--E95, Appearance of Gear Teeth
-- Terminology of Wear and Failure
ISO 10825:1995, Gears -- Wear and Damage to
Gear Teeth -- Terminology
3 Symbols and units
The symbols used in this document are shown in
table 1.
NOTE: The symbols and definitions used in this docu-
ment may differ from other AGMA standards.
Table 1 -- Symbols and units
Symbol Description Units Where first
used
A Dimensionless constant -- -- Eq 61
aw Operating center distance mm Eq 4
B Dimensionless constant -- -- Eq 61
BM Thermal contact coefficient N/[mm s0.5K] 6.2.3
BM1, BM2 Thermal contact coefficient (pinion, gear) N/[mm s0.5K] Eq 84
b Face width mm Eq 23
bHi
Semi--width of Hertzian contact band mm Eq 57
CA ... CF Distances along line of action mm 4.1.2
CRavgx
Surface roughness constant -- -- Eq 85
c Parameter for calculating ηo -- -- Eq 69
cM1, cM2 Specific heat per unit mass (pinion, gear) J/[kg K] Eq 89, 90
Di Internal gear inside diameter mm 4.1.2
d Parameter for calculating ηo -- -- Eq 69
(continued)
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
3
Table 1 (continued)
Symbol Description Units Where first
used
E1, E2 Modulus of elasticity (pinion, gear) N/mm2 Eq 58
Er Reduced modulus of elasticity N/mm2 Eq 57
Ft Actual tangential load N Eq 42
(Ft)nom Nominal tangential load N Eq 40
Fwn Normal operating load N Eq 43
G Materials parameter -- -- Eq 65
g Parameter for calculating ηo -- -- Eq 69
Hci
Dimensionless central film thickness -- -- Eq 65
h Thickness of element measured perpendicular to flow m Eq 59
hci
Central film thickness mm Eq 75
hmin Minimum film thickness mm Eq 102
K Flash temperature constant -- -- Eq 84
KD Combined derating factor -- -- Eq 41
Km Load distribution factor -- -- Eq 41
Ko Overload factor -- -- Eq 41
Kv Dynamic factor -- -- Eq 41
k Parameter for calculating α -- -- Eq 74
ksump Parameter for calculating θM -- -- Eq 91
Lx Filter cutoff of wavelength x mm Eq 77
Lmin Minimum contact length mm Eq 25
mn Normal module mm Eq 2
n1 Pinion speed rpm Eq 33
N Number of load cycles cycles Fig 14
na Fractional (non--integer) part of εβ -- -- Eq 25
nr Fractional (non--integer) part of εα -- -- Eq 25
P Transmitted power kW Eq 40
P(x) Probability of survival -- -- 8.2.2
p Pressure N/mm2 Eq 64
pbn Normal base pitch mm Eq 10
pbt Transverse base pitch mm Eq 9
px Axial pitch mm Eq 11
Q Tail area of the normal probability function -- -- Eq B.2
Q(x) Probability of failure -- -- 8.2.2
Ravgx
Average of the average values of pinion and gear roughness mm Eq 87
Ra1x, Ra2x Average surface roughness (pinion, gear) at Lx mm Eq 78
Rqx Root mean square roughness at Lx mm Eq 79
Rqx avg Arithmetic average of Rq1x and Rq2x at Lx mm Eq 99
Rq1x, Rq2x Root mean square roughness at Lx (pinion, gear) mm Eq 99
r1, r2 Standard pitch radius (pinion, gear) mm Eq 2, 3
ra1, ra2 Outside radius (pinion, gear) mm Eq 19, 16
rb1, rb2 Base radius (pinion, gear) mm Eq 6, 7
rw1 Operating pitch radius of pinion mm Eq 4
Sf Contact time ms (sec¢10--3) Eq 97
s Parameter for calculating α -- -- Eq 74
(continued)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
4
Table 1 (continued)
Symbol Description Units Where first
used
T Absolute temperature K Eq 61
U(i) Speed parameter -- -- Eq 65
u Gear ratio (always ≥ 1.0) -- -- Eq 1
v Velocity m/s Eq 59
vei Entraining velocity m/s Eq 39
vr1i
, vr2i
Rolling (tangential) velocity (pinion, gear) m/s Eq 36, 37
vsi Sliding velocity m/s Eq 38
vt Operating pitch line velocity m/s Eq 35
W(i) Load parameter -- -- Eq 65
wn Normal unit load N/mm Eq 44
XW Welding factor -- -- Eq 96
XΓ(i)
Load sharing factor -- -- 4.3
Z Active length of line of action mm Eq 21
ZN Stress cycle factor -- -- 7.5
ZQ Normal probability density function -- -- Eq B.3
z1 Number teeth in pinion -- -- Eq 1
z2 Number teeth in gear (positive) -- -- Eq 1
α Pressure--viscosity coefficient mm2/N Eq 64
αn Normal generating pressure angle degrees Eq 5
αt Transverse generating pressure angle degrees Eq 5
αwn Normal operating pressure angle degrees Eq 14
αwt Transverse operating pressure angle degrees Eq 8
β Helix angle degrees Eq 2
βb Base helix angle degrees Eq 12
βw Operating helix angle degrees Eq 13
ξ(i) Pinion roll angle at point i along the line of action radians Eq 29
ξA ... ξE Pinion roll angle at points A ... E radians Eq 28
εα Transverse contact ratio -- -- Eq 22
εβ Axial contact ratio -- -- Eq 23
η Dynamic viscosity mPa⋅s Eq 59
ηatm Viscosity at atmospheric pressure mPa⋅s Eq 64
ηP Viscosity at pressure P mPa⋅s Eq 64
ηM Dynamic viscosity at gear tooth temperature θM mPa⋅s Eq 67
η1, η2 Dynamic viscosity at temperature θ1, θ2 mPa⋅s Eq 70
η40, η100 Dynamic viscosity at 40°C, 100°C mPa⋅s Eq 71
θBi
Contact temperature °C Eq 92
θB max Maximum contact temperature °C Eq 93
θfli
Flash temperature °C Eq 84
θfl max Maximum flash temperature °C Eq 91
θfl max, test Maximum flash temperature of test gears °C Eq 96
θM Tooth temperature °C Eq 69
θM, test Tooth temperature of test gears °C Eq 96
(continued)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
5
Table 1 (concluded)
Symbol Description UnitsWhere first
used
θoil Oil inlet or sump temperature °C Eq 91
θS Mean scuffing temperature °C Eq 94
θSmet
Method of calculating scuffing temperature, θS -- -- Annex A
θ1, θ2 Temperature at which η1, η2 was measured °C Eq 70
λmin Specific film thickness -- -- Eq 104
λ2bHi
Specific film thickness at point i with a filter cutoff wavelength
of 2bH
-- -- Eq 76
λM1, λM2 Heat conductivity (pinion, gear) N/[s K] Eq 89, 90
λW&H Wellauer and Holloway specific film thickness -- -- Eq 102
my Mean value of random variable y -- -- 6.5.5
mmi
Mean coefficient of friction -- -- Eq 84
mmet Method for approximating mean coefficient of friction -- -- Annex A
mm const Mean coefficient of friction, constant -- -- Eq 85
mλ min Mean minimum specific film thickness mm Eq 109
ν Kinematic viscosity mm2/s Eq 60
ν1, ν2 Poisson’s ratio (pinion, gear) -- -- Eq 58
ν40, ν100 Kinematic viscosity at 40°C, 100°C mm2/s Eq 62
ρ Density kg/m3 Eq 60
ρM1, ρM2 Density (pinion, gear) kg/m3 Eq 89, 90
ρ1i
, ρ2i
Transverse radius of curvature (pinion, gear) mm 4.1.5
ρni Normal relative radius of curvature mm Eq 32
ρri Transverse relative radius of curvature mm Eq 31
σx Composite surface roughness for filter cutoff wavelength, Lx mm Eq 77
σλ min Standard deviation of the minimum specific film thickness mm Eq 109
σ2bHi
Composite surface roughness adjusted for a cutoff
wavelength equal to the Hertzian contact width
mm Eq 76
τ Shear stress N/mm2 Eq 59
ω1, ω2 Angular velocity (pinion, gear) rad/s Eq 33, 34
4 Gear information
4.1 Gear geometry
This clause gives equations for gear geometry used
to determine flash temperature and elastohydrody-
namic (EHL) film thickness. The following equations
apply to both spur and helical gears; spur gearing is a
particular case with zero helix angle. Where double
signs are used (e.g., ¦), the upper sign applies to
external gears and the lower sign to internal gears.
4.1.1 Basic gear geometry
Gear ratio
(1)u=
z2
z1
Standard pitch radii
(2)r1=
z1 mn
2 cos β
(3)r2= r1 u
Operating pitch radius of pinion
(4)rw1=
aw
u 1
Transverse generating pressure angle
(5)αt= arctan tanαn
cos β

Base radii
rb1= r1 cos αt (6)
rb2= rb1 u (7)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
6
Transverse operating pressure angle
(8)αwt= arccosrb1rw1

Transverse base pitch
(9)pbt=
2 π rb1
z1
Normal base pitch
pbn= π mn cos αn (10)
Axial pitch
(11)px=
π mn
sin β
Base helix angle
(12)βb= arccospbnpbt
Operating helix angle
(13)βw= arctan tan βbcosαwt

Normal operating pressure angle
αwn= arcsincos βb sinαwt (14)
4.1.2 Distances along the line of action
Figure 1 is the line of action shown in a transverse
plane. Distances Cj are measured from the interfer-
ence point of the pinion along the line of action.
Distance CA locates the pinion start of active profile
(SAP) and distance CE locates the pinion end of
active profile (EAP). The lowest and highest point of
single--tooth--pair contact (LPSTC and HPSTC) are
located by distances CB and CD, respectively.
Distance CC locates the operating pitch point. CF is
the distance between base circles along the line of
action.
CF= aw sinαwt (15)
(16)CA= CF− r2a2− r2b2
0.5
NOTE: For internal gears ra2=
Di
2
.
(17)CC=
CF
u 1
CD= CA+ pbt (18)
CE= r2a1− r2b1
0.5
(19)
CB= CE− pbt (20)
Z= CE− CA (21)
aw
rb2
αwt
ra2
Z
pbt
pbt
E
D
CF
ra1
CA
CB
CC CD
CErb1
CA
B
HPSTC
LPSTC
EAP
SAP
Figure 1 -- Distances along the line of action for
external gears
4.1.3 Contact ratios
Transverse contact ratio
(22)εα= Z
pbt
nr is fractional (non--integer) part of εα.
Axial contact ratio
-- for helical gears
(23)εβ=
b
px
na is fractional (non--integer) part of εβ.
-- for spur gears
εβ= 0.0 (24)
Minimum contact length
-- for helical gears, case 1,where 1− nr  ≥ na
(25)Lmin=
εαb − na nr px
cos βb
-- for helical gears, case 2,where 1− nr driving member. By convention, the load sharing
factor is represented by a polygonal function on the
line of action with magnitude equal to 1.0 between
points B and D (see figure 3).
The load sharing factor is strongly influenced by
profile modification of the tooth flanks of both gears.
On the other hand, profile modifications are chosen
such that load sharing follows a desired function.
The following equations give the load sharing factor
for unmodified tooth profiles, and for three typical
cases of profile modifications.
For unmodified tooth profiles
If there is no tip or root relief (see figure 3):
(45)
XΓi
= 1
3
+ 1
3ξi − ξAξB− ξA
 for ξA≤ ξicontacts such
as gears and rolling element bearings where pres-
sures can easily exceed 1 GPa. The viscosity of
lubricant trapped in a concentrated contact in-
creases exponentially with pressure. In 1893, C.
Barus established an empirical equation to describe
the isothermal viscosity--pressure relationship for a
given liquid as shown in equation 64.
(64)ηP= ηatm eαp
where
ηP is viscosity at pressure, p, mPa•s;
ηatm is viscosity at atmospheric pressure,
mPa•s;
α is pressure--viscosity coefficient, mm2/N.
Today the model continues to be refined. So and
Klaus [12] provided a comparison of the many
models developed since the Barus equationwas first
introduced. The continued research aided by the
development of high pressure rheology techniques
to generate empirical information have shown that
the viscosity--pressure response of a fluid is also
related to its chemical structure [13, 14, 15]. This can
have a profound effect on the film forming capabili-
ties of the fluid in question and the overall life of the
component involved.
5.2 Film thickness equation
Dowson, Higginson and Toyoda have authored
various papers on EHL film thickness [16, 17, 18,
19]. The film thickness equations given in these
papers account for the exponential increase of
lubricant viscosity with pressure, tooth geometry,
velocity of the gear teeth, material elastic properties
and the transmitted load. The film thickness
determines the operating regime of the gearset and
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
11
has been found to be a useful index of wear related
distress probability. Wellauer andHolloway [20] also
found that specific film thickness could be correlated
with the probability of tooth surface distress. The
Dowson and Toyoda [19] equation for line contact
central EHL film thickness will be used as shown
below.
Dimensionless central film thickness:
(65)Hci
= 3.06
G0.56U0.69
i
Wi
0.10
where
(i) (as a subscript) defines a point on the line of
action,
and the dimensionless parameters G, U(i) and W(i)
are defined below:
materials parameter, G
G= α Er (66)
speed parameter, U(i)
(67)Ui =
ηM vei
2Er Ãni
× 10−6
load parameter, W(i)
(68)Wi =
XΓi
wn
Er Ãni
where
ηM is dynamic viscosity at the gear tooth
temperature, mPa•s.
ηM= 10g− 0.9 (69)
where
g= 10cθM+ 273.15d
θM is tooth temperature, °C (see 6.3).
The parameters c and d required for calculating ηM
can either be taken from table 2 or calculated with
equations 70 and 72, respectively. Equations 70 and
72, derived from a modification of the Walther
equation [10], will yield the parameters c and d if two
dynamic viscosities, η1 and η2, are known at two
corresponding temperatures, θ1 and θ2.
Since dynamic viscosity is generally available at
40°C and 100°C, equations 70 and 72 are modified
in equations 71 and 73 to incorporate terms
corresponding to those temperatures.
η1 is dynamic viscosity at temperature θ1,
mPa•s;
η2 is dynamic viscosity at temperature θ2,
mPa•s;
θ1 is temperature at which η1 was determined,
°C;
θ2 is temperature at which η2 was determined,
°C.
d=
log10log10η2+0.9log10η1+0.9

log10θ2+273.15θ1+273.15

(70)
when θ1 = 40°C and θ2 = 100°C,
d= 13.13525 log10log10η100+ 0.9
log10η40+ 0.9  (71)
− d log10 θ1+ 273.15) (72)
c= log10 log10η1+ 0.9
when θ1 = 40°C and θ2 = 100°C,
c= log10log10η40+ 0.9 − 2.495752 d
(73)
α is pressure--viscosity coefficient, mm2/N.
Values range from 0.725¢ 10--2 mm2/N to
2.9¢ 10--2 mm2/N for typical gear lubri-
cants. Values for pressure--viscosity
coefficients vs. dynamic viscosity can be
obtained from equation 74.
α= k ηsM (74)
Table 2 contains viscosity information for mineral
oils, MIL--L spec. oils, polyalphaolefin (PAO) based
synthetic oils (which contain ester) and polyalkylene
glycol (PAG) based synthetic oils, as well as
constants c, d, k and s for use in the equations 69
through 74. These values were obtained from the
data shown in figures 7 through 11 [22]. It is
important that the film thickness is calculated with
values of viscosity and pressure--viscosity coeffi-
cient for the gear tooth temperature, θM, (see 6.3).
The central film thickness at a given point is:
hci
= Hci
Ãni
× 103 (75)
(see clause 4 for Ãni
).
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
12
Table 2 -- Data for determining viscosity and pressure--viscosity coefficient
Lubricant ISO VG1) η40 η100 c d k s
Mineral oil 32
46
68
100
150
220
320
460
680
1000
1500
2200
3200
27.17816
39.35879
58.64514
86.91484
131.4335
194.2414
284.6312
412.0824
613.8288
909.4836
1374.931
2031.417
2975.954
4.294182
5.440514
7.059163
9.251199
12.27588
15.98296
20.60709
26.34104
34.24003
38.56783
49.58728
62.69805
78.56109
10.20076
10.07933
9.90355
9.65708
9.42526
9.24059
9.09300
8.96420
8.84572
9.25943
9.19946
9.15646
9.13012
--4.02279
--3.95628
--3.86833
--3.75377
--3.64563
--3.55832
--3.48706
--3.42445
--3.36585
--3.52128
--3.48702
--3.46064
--3.44157
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.010471
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
0.1348
PAO -- based
synthetic non--
VI improved oil
150
220
320
460
680
1000
1500
2200
3200
6800
128.5772
189.9828
278.3370
402.8943
600.0179
868.1710
1310.350
1933.070
2827.726
6077.362
16.17971
21.60933
28.66405
37.54020
53.20423
68.60767
91.03300
118.0509
151.2132
244.5559
7.99428
7.79927
7.63035
7.49799
7.16434
7.12008
7.07678
7.06113
7.06594
7.11907
--3.07304
--2.98154
--2.90169
--2.83762
--2.69277
--2.66528
--2.63766
--2.62221
--2.61561
--2.62091
0.010326
0.010326
0.010326
0.010326
0.010326
0.010326
0.010326
0.010326
0.010326
0.010326
0.0507
0.0507
0.0507
0.0507
0.0507
0.0507
0.0507
0.0507
0.0507
0.0507
PAG -- based
synthetic2)
100
150
220
320
460
680
1000
102.630
153.950
225.790
328.430
472.130
697.920
1026.37
19.560
27.380
40.090
56.710
77.250
113.43
163.30
6.42534
6.19586
5.76552
5.49394
5.35027
5.06011
4.85075
--2.45259
--2.34616
--2.16105
--2.04065
--1.97254
--1.84558
--1.75175
0.0047
0.0047
0.0047
0.0047
0.0047
0.0047
0.0047
0.1572
0.1572
0.1572
0.1572
0.1572
0.1572
0.1572
MIL--L--7808K
Grade 3
12 11.35364 2.701402 9.58596 --3.82619 0.005492 0.25472
MIL--L--7808K
Grade 4
17 16.09154 3.609883 9.08217 --3.60300 0.005492 0.25472
MIL--L--23699E 23 22.56448 4.591235 8.91638 --3.51779 0.006515 0.16530
NOTES:
1) ν40 (mm2/s)
2) Copolymer of ethylene oxide and propylene oxide in 50% weight ratio.
The specific film thickness is the ratio of film
thickness divided by the composite roughness of the
contacting gear teeth and can be used to assess
performance.
To determinethis ratio, the cutoff wavelength for the
composite surface roughness measurement (σx)
should be comparable to the width of the Hertzian
contact, 2bHi
. This results in σx becoming σ2bHi
as
shown in equation 76.
λ2bHi
=
hci
σ2bHi
(76)
This may not be practical because many surface
measuring instruments have a fixed cutoff wave-
length (usually 0.8 mm).
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
13
D
yn
am
ic
vi
sc
os
ity
(m
P
a⋅
s)
1
10
100
1000
10 000
100 000
1 000 000
200 250 300 350 400 450 500
Temperature (K)
32
46
68
100
150
220
320
460
680
1000
1500
2200
3200
ISO VG
Figure 7 -- Dynamic viscosity versus temperature for mineral oils
Following the concepts in [21], equation 76 can be
approximated by:
λ2bHi
=
hci
σx


Lx
2bHi



0.5
(77)
σx= Ra21x+ Ra22x
0.5
(78)
where
λ2bHi
is specific film thickness at point i with a
filter cutoff wavelength of 2bH;
Lx is filter cutoff wavelength used in measuring
surface roughness, mm. Any cutoff length,
Lx, can be used (for example, L0.8 = 0.8 mm
cutoff);
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
14
σx is composite surface roughness for filter
cutoff wavelength Lx, mm;
Ra1x is pinion average surface roughness for Lx,
mm;
Ra2x is gear average surface roughness for Lx,
mm.
Use of the radical term in equation 77 for roughness
adjustment is developed below.
From Gaussian statistics [24], it is seen that:
Rq2x ∝ Lx (79)
where
Rqx2 is variance or square of the root mean
square roughness, mm.
also [25]:
Rax= 2
π
 Rqx (80)
From equations 79 and 80:
Rax ∝ L0.5x (81)
D
yn
am
ic
vi
sc
os
ity
(m
P
a⋅
s)
Temperature (K)
1
10
100
1000
10 000
100 000
1 000 000
200 250 300 350 400 450 500
150
220
320
460
680
1000
1500
2200
3200
6800
ISO VG
Figure 8 -- Dynamic viscosity versus temperature for PAO--based synthetic non--VI--improved oils
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
15
Hence, for a 0.8 mm cutoff length,
Ra2bHi
= Ra0.8


2bHi
L0.8



0.5
(82)
Substitute equation 82 into equation 78 once
each for Ra1x and for Ra2x to obtain σ2bHi
.
Using this in equation 76, noting that
σ0.8= Ra210.8+ Ra220.8
0.5 yields equation 83
which is equation 77 developed for a 0.8 mm cutoff
length.
λ2bHi
=
hci
σ0.8


L0.8
2bHi



0.5
(83)
1
10
100
1000
10000
100000
1000000
10000000
200 225 250 275 300 325 350 375 400 425 450 475 500
ISO VG
1000
680
460
320
220
150
100
D
yn
am
ic
vi
sc
os
ity
(m
P
a⋅
s)
Temperature (K)
10 000 000
1 000 000
100 000
10 000
1000
100
10
1
Figure 9 -- Dynamic viscosity versus temperature for PAG--based synthetic oils
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
16
D
yn
am
ic
vi
sc
os
ity
(m
P
a⋅
s)
Temperature (K)
0.1
1
10
100
1000
200 250 300 350 400 450 500
MIL--L--7808K Grade 3
MIL--L--7808K Grade 4
MIL--L--23699E
Figure 10 -- Dynamic viscosity versus temperature for MIL Spec. oils
P
re
ss
ur
e-
-v
is
co
si
ty
co
ef
fic
ie
nt
(m
m
2 /
N
)
Dynamic viscosity (mPa⋅s)
0.1 1 10 100 1000 10 000 100 000 1 000 000
0.001
0.01
0.1
1
Mineral oil
MIL--L--7808K
MIL--L--23699E
Synthetic oil (PAO)
Synthetic oil (PAG)
Figure 11 -- Pressure--viscosity coefficient versus dynamic viscosity
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
17
6 Scuffing
6.1 General
The term scuffing as used in this information sheet is
defined as localized damage caused by solid--phase
welding between surfaces in relative motion. It is
accompanied by transfer of metal from one surface
to another due to welding and subsequent tearing,
and may occur in any highly loaded contact where
the oil film is too thin to adequately separate the
surfaces. Scuffing appears as a matte, rough finish
due to the microscopic tearing at the surface. It
occursmost commonly at extremeend regions of the
contact path or near points of single tooth contact.
Scuffing is also known generically as severe
adhesive wear.
Scoring was a term commonly used in the U.S. to
describe the same phenomenon now defined as
scuffing (welding and tearing of mating surfaces).
See ANSI/AGMA 1010--E95 or ISO 10825:1995.
6.1.1 Mechanism of scuffing
The basic mechanism of scuffing is caused by
intense frictional heat generated by a combination of
high sliding velocity and high contact stress.
Scuffing occurs under thin film, boundary lubrication
conditions and can be affected by physical and
chemical properties of the lubricant, nature of the
oxide films, and gear material.
When gear teeth are separated by a thick lubricant
film, contact between surface asperities is mini-
mized and there is usually no scuffing. As lubricant
film thickness decreases, asperity contact increases
and scuffing becomes moreprobable. A very thin
film, such as in boundary lubrication, together with a
high contact temperature suggests a high probability
of scuffing is possible in the absence of antiscuff
additives in the lubricant.
6.1.2 Probability of scuffing
Blok’s [1] contact temperature theory states that
scuffing will occur in gear teeth that are sliding under
boundary--lubricated conditions, when the maxi-
mum contact temperature reaches a critical
magnitude. The contact temperature is the sum of
two components: the flash temperature and the
tooth temperature. See 6.4.
Scuffing most commonly occurs at one of the two
extreme end regions of the contact path or near the
points of single tooth contact.
Prediction of the probability of scuffing is possible by
comparing the calculated contact temperature with
limiting scuffing temperature. The limiting scuffing
temperature can be calculated from an appropriate
gear scuffing test, or can be provided by field
investigations.
For non--additive mineral oils, each combination of
oil and gear materials has a limiting scuffing
temperature that is constant regardless of the
operating conditions. It is believed that the limiting
scuffing temperature is not constant for synthetic
and high--additive EP lubricants, and it must be
determined from tests that closely simulate the
operating condition of the gearset.
6.2 Flash temperature
The flash temperature is the calculated increase in
gear tooth surface temperature at a given point along
the line of action resulting from the combined effects
of gear tooth geometry, load, friction, velocity and
material properties during operation.
6.2.1 Fundamental formula for flash
temperature, θfli
The fundamental formula is based on Blok’s [1]
equation.
(84)×
vr1i − vr2i

BM1vr1i
0.5
+ BM2vr2i
0.5
θfli
= 31.62 K mmi
XΓi
wn
bHi
0.5
where
K is 0.80, numerical factor valid for a semi--
elliptic (Hertzian) distribution of frictional
heat over the instantaneous width, 2 bH, of
the rectangular contact band;
mmi
is mean coefficient of friction (see 6.2.2);
XΓi
is load sharing factor (see 4.3);
wn is normal unit load, N/mm (see equation 44);
vr1i
is rolling tangential velocity of the pinion,m/s
(see equation 36);
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AGMA 925--A03 AMERICAN GEAR MANUFACTURERS ASSOCIATION
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vr2i
is rolling tangential velocity of the gear, m/s
(see equation 37);
BM1 is thermal contact coefficient of the pinion
material, N/[mm s0.5K] (see 6.2.3);
BM2 is thermal contact coefficient of the gear
material, N/[mm s0.5K] (see 6.2.3);
bHi
is semi--width of Hertzian contact band, mm
(see equation 57);
i (as a subscript) defines a point on the line of
action.
In this equation, the coefficient of friction may be
approximated by different expressions, for instance
as proposed by Kelley [2, 4] and AGMA 217.01 [7].
The influence of surface roughness is incorporated
in the approximation of the coefficient of friction.
6.2.2 Mean coefficient of friction, mmi
The mean coefficient of friction is an approximation
of the actual coefficient of friction on the tooth flank,
which is an instantaneous and local value depending
on several properties of the oil, surface roughness,
lay of the surface irregularities like grinding marks,
material properties, tangential velocities, forces and
dimensions.
Three methods may be used to determine the value
of mmi
to be used in equation 84.
-- input a value based upon experience, which
is a constant;
-- input a value from equation 85, which is also
a constant;
-- input a value from equation 88, which varies
along the line of action.
6.2.2.1 Approximation by a constant
A constant coefficient of friction along the line of
action has been assumed by AGMA 217.01 [7] and
Kelley [2]:
(85)mmi
= mm const= 0.06× CRavgx
The surface roughness constant, CRavgx
, is limited
to a maximum value of 3.0:
(86)1.0≤ CRavgx
= 1.13
1.13− Ravgx
≤ 3.0
Equation 85 gives a typical value for gears operating
in the partial EHL regime. It may be too low for
boundary lubricated gears where mm may be higher
than 0.2, or too high for gears operating in the
full--film regime where mm may be less than 0.01.
The surface roughness is taken as an average of the
average values:
(87)Ravgx=
Ra1x+ Ra2x
2
where
Ra1x is pinion average surface roughness for filter
cutoff length, Lx, mm;
Ra2x is gear average surface roughness for filter
cutoff length, Lx, mm.
6.2.2.2 Empirical equation
An empirical equation for a variable coefficient of
friction is the Benedict and Kelley [5] equation,
supplemented with the influence of roughness:
(88)
mmi
= 0.0127 CRavgx
log10


29 700 XΓi
wn
ηMvsi
v2ei



where the surface roughness expression is taken in
accordance with equations 86 and 87. Equation 88
is not valid at or near the operating pitch point, as vs
goes to zero.
where
ηM is dynamic viscosity of the oil at gear tooth
temperature, θM, mPa•s;
vsi
is sliding velocity, m/s (see equation 38);
vei
is entraining velocity, m/s (see equation 39).
6.2.3 Thermal contact coefficient, BM
The thermal contact coefficient accounts for the
influence of the material properties of pinion and
gear:
BM1= λM1× ÃM1× cM1
0.5
(89)
BM2= λM2× ÃM2× cM2
0.5
(90)
For martensitic steels the range of heat conductivity,
λM , is 41 to 52 N/[s K] and the product of density
times the specific heat per unit mass, ρM¢ cM is
about 3.8 N/[mm2K], so that the use of the average
value BM = 13.6 N/[mm s0.5 K] for such steels will not
introduce a large error when the thermal contact
coefficient is unknown.
6.2.4 Maximum flash temperature
To locate and determine the maximum flash tem-
perature, the flash temperature should be calculated
 
 
 
 
 
 
AGMA 925--A03AMERICAN GEAR MANUFACTURERS ASSOCIATION
19
at a sufficient number of points (for example, 25 to
50) on the line of action. Calculate flash tempera-
tures at points between SAP and LPSTC during
double tooth contact, at LPSTC and HPSTC for
single tooth contact, and between HPSTC and EAP
during double tooth contact.
If the contact temperature (see 6.4) is greater than
the mean scuffing temperature (see 6.5) for the
lubricant being used, there is a potential risk for
scuffing (see 6.5.5).
6.3 Tooth temperature
The tooth temperature, θM, is the equilibrium tem-
perature of the surface of the gear teeth before they
enter the contact zone. In some cases [26], the tooth
temperature may be significantly higher than the
temperature of the oil supplied to the gear mesh.
6.3.1 Rough approximation
For a very rough approximation, the tooth tempera-
ture may be estimated by the sum of the oil
temperature, taking into account some impediment
in heat transfer for spray lubrication if applicable, and
a portion that depends mainly on the flash tempera-