AGMA 925A03 Effect of Lubrication on Gear Surface

AGMA INFORMATION SHEET(This Information Sheet is NOT an AGMA Standard)

AGMA925-A03

AGMA 925-A03

AMERICAN GEAR MANUFACTURERS ASSOCIATION

Effect of Lubrication on Gear SurfaceDistress

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 ISPJAEM.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 Gear 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


American Gear ManufacturersAssociation --

Effect of Lubrication onGear Surface Distress

1 Scope

This information sheet is designed to providecurrently available tribological information pertainingto oil lubrication of industrial gears for powertransmission applications. It is intended to serve asa general guideline and source of information aboutgear oils, their properties, and their general tribolog-ical behavior in gear contacts. Manufacturers andend--users are encouraged, however, to work withtheir lubricant suppliers to address specific concernsor special issues that may not be covered here (suchas greases).

The equations provided herein allow the user tocalculate specific oil film thickness and instanta-neous contact (flash) temperature for gears inservice. These two parameters are consideredcritical in defining areas of operation that may lead tounwanted surface distress. Surface distress may bescuffing (adhesive wear), fatigue (micropitting andmacropitting), or excessive abrasive wear (scoring).Each of these forms of surface distress may beinfluenced by the lubricant; the calculations areoffered to help assess the potential risk involved witha given lubricant choice. Flow charts are included asaids to using the equations.

This information sheet is a supplement to ANSI/AGMA 2101--C95 and ANSI/AGMA 2001--C95. Ithas been introduced as an aid to the gear manufac-turing and user community. Accumulation of feed-back data will serve to enhance future developmentsand improved methods to evaluate lubricant relatedsurface distress.

It was clear from the work on the revision of standardANSI/AGMA 2001--C95 (ANSI/AGMA 2101--C95,metric version) that supporting information regard-ing lubricant properties and general tribologicalunderstanding of contacting surfaces would aid inunderstanding of the standard and provide the userwith more tools to make an informed decision aboutthe performance of a geared system. One of the keyparameters is the estimated film thickness. This isnot a trivial calculation, but one that has significantimpact on overall performance of the gear pair. It isconsidered in performance issues such as scuffing,wear, and surface fatigue. This information sheetprovides sufficient information about key lubricantparameters to enable the user to generate reason-able estimates about surface distress based on thecollective knowledge available.

Blok [1] published his contact temperature equationin 1937. It went relatively unnoticed in the U.S. untilKelley [2] showed that Blok’s method gave goodcorrelation with Kelley’s experimental data. Blok’sequation requires an accurate coefficient of friction.Kelley found it necessary to couple the coefficient offriction to surface roughness of the gear teeth.Kelley recognized the importance of load sharing bymultiple pairs of teeth and gear tooth tip relief, but hedid not offer equations to account for those variables.

Dudley [3] modified Kelley’s equation by addingderating factors for application, misalignment anddynamics. He emphasized the need for research oneffects of tip relief, and recommended applyingBlok’s method to helical gears.

In 1958, Kelley [4] changed his surface roughnessterm slightly.

Benedict and Kelley [5] published their equation forvariable coefficient of friction derived from disc tests.

The AGMAAerospace Committee began investigat-ing scuffing in 1960, and Lemanski [6] publishedresults of a computer analysis that contains data for90 spur and helical gearsets, and formed the termsfor AGMA 217.01 [7], which was published in 1965.It used Dudley’s modified Blok/Kelley equation andincluded factors accounting for load sharing and tiprelief.


2

TheSCORING+computer program [8] was releasedin 1985. It incorporated all advancements made byBlok, Kelley, Dudley and AGMA 217.01. In addition,it added several improvements including:

-- Helical gears were analyzed by resolving theload in the normal plane and distributing thenormal load over the minimum length of thecontact lines. The semi--width of the Hertziancontact band was calculated based on the normalrelative radius of curvature;

-- Derating factors for application, misalignmentand dynamics were explicit input data;

-- Options for coefficient of friction were part ofinput data, including a constant 0.06 (as pre-scribed by Kelley and AGMA 217.01), a constantunder user control, and a variable coefficientbased on the Benedict and Kelley equation.

SCORING+ and AGMA 217.01 both use the samevalue for the thermal contact coefficient ofBM = 16.5 N/[mm⋅s0.5⋅K], and they calculate thesame contact temperature for spur gears if allderating factors are set to unity.

Annex A of ANSI/AGMA 2101--C95 and ANSI/AGMA 2001--C95 was based on SCORING+ andincluded methods for predicting risk of scuffingbased on contact temperature and risk of wearbased on specific film thickness.

This information sheet expands the information inannex A of ANSI/AGMA2101--C95 andANSI/AGMA2001--C95 to includemany aspects of gear tribology.

2 References

The following standards contain provisions whichare referenced in the text of this information sheet.At the time of publication, the editions indicated werevalid. All standards are subject to revision, andparties to agreements based on this document areencouraged to investigate the possibility of applyingthe most recent editions of the standards indicated.

ANSI/AGMA 2001--C95, Fundamental Rating Fac-tors and Calculation Methods for Involute Spur andHelical Gear Teeth

ANSI/AGMA 2101--C95, Fundamental Rating Fac-tors and Calculation Methods for Involute Spur andHelical Gear Teeth (Metric Edition)

ANSI/AGMA 1010--E95, Appearance of Gear Teeth-- Terminology of Wear and Failure

ISO 10825:1995, Gears -- Wear and Damage toGear Teeth -- Terminology

3 Symbols and units

The symbols used in this document are shown intable 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 firstused

A Dimensionless constant -- -- Eq 61aw Operating center distance mm Eq 4B Dimensionless constant -- -- Eq 61BM Thermal contact coefficient N/[mm s0.5K] 6.2.3BM1, BM2 Thermal contact coefficient (pinion, gear) N/[mm s0.5K] Eq 84b Face width mm Eq 23bHi

Semi--width of Hertzian contact band mm Eq 57

CA ... CF Distances along line of action mm 4.1.2CRavgx

Surface roughness constant -- -- Eq 85

c Parameter for calculating ηo -- -- Eq 69cM1, cM2 Specific heat per unit mass (pinion, gear) J/[kg K] Eq 89, 90Di Internal gear inside diameter mm 4.1.2d Parameter for calculating ηo -- -- Eq 69

(continued)


3

Table 1 (continued)


E1, E2 Modulus of elasticity (pinion, gear) N/mm2 Eq 58Er Reduced modulus of elasticity N/mm2 Eq 57Ft Actual tangential load N Eq 42(Ft)nom Nominal tangential load N Eq 40Fwn Normal operating load N Eq 43G Materials parameter -- -- Eq 65g Parameter for calculating ηo -- -- Eq 69Hci

Dimensionless central film thickness -- -- Eq 65

h Thickness of element measured perpendicular to flow m Eq 59hci

Central film thickness mm Eq 75

hmin Minimum film thickness mm Eq 102K Flash temperature constant -- -- Eq 84KD Combined derating factor -- -- Eq 41Km Load distribution factor -- -- Eq 41Ko Overload factor -- -- Eq 41Kv Dynamic factor -- -- Eq 41k Parameter for calculating α -- -- Eq 74ksump Parameter for calculating θM -- -- Eq 91Lx Filter cutoff of wavelength x mm Eq 77Lmin Minimum contact length mm Eq 25mn Normal module mm Eq 2n1 Pinion speed rpm Eq 33N Number of load cycles cycles Fig 14na Fractional (non--integer) part of εβ -- -- Eq 25nr Fractional (non--integer) part of εα -- -- Eq 25P Transmitted power kW Eq 40P(x) Probability of survival -- -- 8.2.2p Pressure N/mm2 Eq 64pbn Normal base pitch mm Eq 10pbt Transverse base pitch mm Eq 9px Axial pitch mm Eq 11Q Tail area of the normal probability function -- -- Eq B.2Q(x) Probability of failure -- -- 8.2.2Ravgx

Average of the average values of pinion and gear roughness mm Eq 87

Ra1x, Ra2x Average surface roughness (pinion, gear) at Lx mm Eq 78Rqx Root mean square roughness at Lx mm Eq 79Rqx avg Arithmetic average of Rq1x and Rq2x at Lx mm Eq 99Rq1x, Rq2x Root mean square roughness at Lx (pinion, gear) mm Eq 99r1, r2 Standard pitch radius (pinion, gear) mm Eq 2, 3ra1, ra2 Outside radius (pinion, gear) mm Eq 19, 16rb1, rb2 Base radius (pinion, gear) mm Eq 6, 7rw1 Operating pitch radius of pinion mm Eq 4Sf Contact time ms (sec¢10--3) Eq 97s Parameter for calculating α -- -- Eq 74

(continued)


4

Table 1 (continued)


T Absolute temperature K Eq 61U(i) Speed parameter -- -- Eq 65u Gear ratio (always ≥ 1.0) -- -- Eq 1v Velocity m/s Eq 59vei Entraining velocity m/s Eq 39

vr1i, vr2i

Rolling (tangential) velocity (pinion, gear) m/s Eq 36, 37

vsi Sliding velocity m/s Eq 38

vt Operating pitch line velocity m/s Eq 35W(i) Load parameter -- -- Eq 65wn Normal unit load N/mm Eq 44XW Welding factor -- -- Eq 96XΓ(i)

Load sharing factor -- -- 4.3

Z Active length of line of action mm Eq 21ZN Stress cycle factor -- -- 7.5ZQ Normal probability density function -- -- Eq B.3z1 Number teeth in pinion -- -- Eq 1z2 Number teeth in gear (positive) -- -- Eq 1α Pressure--viscosity coefficient mm2/N Eq 64αn Normal generating pressure angle degrees Eq 5αt Transverse generating pressure angle degrees Eq 5αwn Normal operating pressure angle degrees Eq 14αwt Transverse operating pressure angle degrees Eq 8β Helix angle degrees Eq 2βb Base helix angle degrees Eq 12βw Operating helix angle degrees Eq 13ξ(i) Pinion roll angle at point i along the line of action radians Eq 29ξA ... ξE Pinion roll angle at points A ... E radians Eq 28εα Transverse contact ratio -- -- Eq 22εβ Axial contact ratio -- -- Eq 23η Dynamic viscosity mPa⋅s Eq 59ηatm Viscosity at atmospheric pressure mPa⋅s Eq 64ηP Viscosity at pressure P mPa⋅s Eq 64ηM Dynamic viscosity at gear tooth temperature θM mPa⋅s Eq 67η1, η2 Dynamic viscosity at temperature θ1, θ2 mPa⋅s Eq 70η40, η100 Dynamic viscosity at 40°C, 100°C mPa⋅s Eq 71θBi

Contact temperature °C Eq 92

θB max Maximum contact temperature °C Eq 93θfli

Flash temperature °C Eq 84

θfl max Maximum flash temperature °C Eq 91θfl max, test Maximum flash temperature of test gears °C Eq 96θM Tooth temperature °C Eq 69θM, test Tooth temperature of test gears °C Eq 96

(continued)


5

Table 1 (concluded)


θoil Oil inlet or sump temperature °C Eq 91θS Mean scuffing temperature °C Eq 94θSmet

Method of calculating scuffing temperature, θS -- -- Annex A

θ1, θ2 Temperature at which η1, η2 was measured °C Eq 70λmin Specific film thickness -- -- Eq 104λ2bHi

Specific film thickness at point i with a filter cutoff wavelengthof 2bH

-- -- Eq 76

λM1, λM2 Heat conductivity (pinion, gear) N/[s K] Eq 89, 90λW&H Wellauer and Holloway specific film thickness -- -- Eq 102my Mean value of random variable y -- -- 6.5.5mmi

Mean coefficient of friction -- -- Eq 84

mmet Method for approximating mean coefficient of friction -- -- Annex Amm const Mean coefficient of friction, constant -- -- Eq 85mλ min Mean minimum specific film thickness mm Eq 109ν Kinematic viscosity mm2/s Eq 60ν1, ν2 Poisson’s ratio (pinion, gear) -- -- Eq 58ν40, ν100 Kinematic viscosity at 40°C, 100°C mm2/s Eq 62ρ Density kg/m3 Eq 60ρM1, ρM2 Density (pinion, gear) kg/m3 Eq 89, 90ρ1i

, ρ2iTransverse radius of curvature (pinion, gear) mm 4.1.5

ρni Normal relative radius of curvature mm Eq 32

ρri Transverse relative radius of curvature mm Eq 31

σx Composite surface roughness for filter cutoff wavelength, Lx mm Eq 77σλ min Standard deviation of the minimum specific film thickness mm Eq 109σ2bHi

Composite surface roughness adjusted for a cutoffwavelength equal to the Hertzian contact width

mm Eq 76

τ Shear stress N/mm2 Eq 59ω1, ω2 Angular velocity (pinion, gear) rad/s Eq 33, 34

4 Gear information

4.1 Gear geometry

This clause gives equations for gear geometry usedto determine flash temperature and elastohydrody-namic (EHL) film thickness. The following equationsapply to both spur and helical gears; spur gearing is aparticular case with zero helix angle. Where doublesigns are used (e.g., ¦), the upper sign applies toexternal gears and the lower sign to internal gears.

4.1.1 Basic gear geometry

Gear ratio

(1)u=z2z1

Standard pitch radii

(2)r1=z1 mn2 cos β

(3)r2= r1 u

Operating pitch radius of pinion

(4)rw1=aw

u 1

Transverse generating pressure angle

(5)αt= arctan tanαncos β

Base radii

rb1= r1 cos αt (6)

rb2= rb1 u (7)


6

Transverse operating pressure angle

(8)αwt= arccosrb1rw1

Transverse base pitch

(9)pbt=2 π rb1z1

Normal base pitch

pbn= π mn cos αn (10)

Axial pitch

(11)px=π mnsin β

Base helix angle

(12)βb= arccospbnpbtOperating helix angle

(13)βw= arctan tan βbcosαwt

Normal operating pressure angle

αwn= arcsincos βb sinαwt (14)

4.1.2 Distances along the line of action

Figure 1 is the line of action shown in a transverseplane. 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 ofactive profile (EAP). The lowest and highest point ofsingle--tooth--pair contact (LPSTC and HPSTC) arelocated by distances CB and CD, respectively.Distance CC locates the operating pitch point. CF isthe distance between base circles along the line ofaction.

CF= aw sinαwt (15)

(16)CA= CF− r2a2− r2b20.5

NOTE: For internal gears ra2=Di2.

(17)CC=CF

u 1CD= CA+ pbt (18)

CE= r2a1− r2b10.5

(19)

CB= CE− pbt (20)

Z= CE− CA (21)

aw

rb2

αwtra2

Zpbt

pbtE

D

CF

ra1

CACBCC CD

CErb1

CAB

HPSTC

LPSTCEAP

SAP

Figure 1 -- Distances along the line of action forexternal gears

4.1.3 Contact ratios

Transverse contact ratio

(22)εα= Zpbt

nr is fractional (non--integer) part of εα.

Axial contact ratio

-- for helical gears

(23)εβ=bpx

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 < na

(26)Lmin=εα b − 1− na1− nr px

cos βb-- for spur gears

Lmin= b (27)


7

4.1.4 Roll angles

Pinion roll angles corresponding to the five specificpoints along the line of action shown in figure 1 aregiven by:

ξj=Cjrb1

(28)

where

j = A, B, C, D, E

4.1.5 Profile radii of curvature

Transverse radii of curvature

Figure 2 shows the transverse radii of curvature, Ã1iand Ã2i

, of the gear tooth profiles at a general

contact point defined by the roll angle, ξ(i), where (i) isany point on the line of action from A to E (see figure1).

CFξ(i)

Ãri=

Ã1iÃ2i

Ã2i Ã1i

Ã2iÃ1i

rb1

Figure 2 -- Transverse relative radius ofcurvature for external gears

Ã1i= rb1ξi (29)

where

Ã2i= CF Ã1i

(30)ξA≤ ξ(i)≤ ξE

Transverse relative radius of curvature

(31)Ãri=

Ã1iÃ2i

Ã2i Ã1i

Normal relative radius of curvature

Ãni=

Ãri

cos βb(32)

Ãriand Ãni

are the equivalent radii of cylinders

riding on a flat plate that represent the gear paircurvatures in contact along the line of action.

4.2 Gear tooth velocities and loads

Rotational (angular) velocities

ω1=πn130

(33)

(34)ω2=ω1u

Operating pitch line velocity

vt=ω1 rw11000 (35)

Rolling (tangential) velocities

vr1i=ω1 Ã1i

1000(36)

vr2i=ω2 Ã2i

1000(37)

Sliding velocity (absolute value)

(38)vsi= vr1i − vr2i

Entraining velocity (absolute value)

(39)vei= vr1i + vr2i

Nominal tangential load

(40)Ftnom=1000 P

vtCombined derating factor

(41)KD= Ko Km Kv

where

Ko is overload factor;

Km is load distribution factor;

Kv is dynamic factor.

See ANSI/AGMA 2101--C95 for guidance indetermining Ko, Km and Kv factors.


8

Actual tangential load

(42)Ft= Ftnom KD

Normal operating load

(43)Fwn=Ft

cosαwn cos βwNormal unit load

(44)wn=FwnLmin

4.3 Load sharing factor

The load sharing factor accounts for load sharingbetween succeeding pairs of teeth as influenced byprofilemodification, andwhether the pinion or gear isthe driving member. By convention, the load sharingfactor is represented by a polygonal function on theline of action with magnitude equal to 1.0 betweenpoints B and D (see figure 3).

The load sharing factor is strongly influenced byprofile modification of the tooth flanks of both gears.On the other hand, profile modifications are chosensuch that load sharing follows a desired function.The following equations give the load sharing factorfor unmodified tooth profiles, and for three typicalcases of profile modifications.

For unmodified tooth profiles

If there is no tip or root relief (see figure 3):

(45)

XΓi= 1

3+ 1

3ξi − ξAξB− ξA for ξA≤ ξi < ξB

(46)XΓi= 1 for ξB≤ ξi ≤ ξD

(47)

XΓi= 1

3+ 1

3ξE− ξiξE− ξD for ξD< ξi ≤ ξE

A B D E

13

23

1

Figure 3 -- Load sharing factor -- unmodifiedprofiles

For modified tooth profiles

If adequate tip and root relief is designed for highload capacity, and if the pinion drives the gear (seefigure 4):

(48)XΓi= 6



XΓi= 1

7+ 6


(50)

A B D E

17

67

1

Figure 4 -- Load sharing factor -- pinion driving

If adequate tip and root relief is designed for highload capacity, and if the pinion is driven by the gear(see figure 5):

XΓi= 1

7+ 6


(51)


(53)XΓi= 6


A B D E

17

67

1

Figure 5 -- Load sharing factor -- gear driving


9

For smooth meshing

If adequate tip and root relief is designed for smoothmeshing (see figure 6):

(54)XΓi=ξi − ξAξB− ξA

for ξA≤ ξi < ξB


(56)XΓi=ξE− ξiξE− ξD

for ξD< ξi ≤ ξE

A B D E

1

Figure 6 -- Load sharing factor -- smoothmeshing

4.4 Hertzian contact band

The semi--width of the rectangular contact band isgiven by:

(57)bHi=8 XΓi

wn Ãni

π Er

0.5

where

XΓiis load sharing factor (see 4.3);

wn is normal unit load, N/mm (see equation 44);

Ãniis normal relative radius of curvature, mm

(see equation 32);

Er is reduced modulus of elasticity given by:

Er= 21− ν21E1+

1− ν22

E2−1 (58)

where

ν1, ν2 is Poisson’s ratio (pinion, gear);

E1, E2 is modulus of elasticity, N/mm2 (pinion,gear).

5 Lubrication

5.1 Viscometric information

Lubricants are commonly referred to by their basetype, for example mineral or synthetic, and theirviscosity, usually in relation to a defined viscositygrade. Viscosity is one of the basic and veryimportant properties of a lubricant and is usedextensively in tribological calculations. Viscosity is abulk property of a fluid, semi--fluid or semi--solidsubstance that causes it to resist flow. In addition tothe basic composition and structure of the material,viscosity decreases with increasing temperatureand increases with increasing pressure.

For a liquid under shear, the rate of deformation orshear rate is proportional to the shearing stress. Thisrelationship is Newton’s law, which essentially statesthat the ratio of the stress to the shear rate is aconstant. That constant is viscosity. Dynamicviscosity, η, sometimes referred to as absoluteviscosity, is defined by equation 59.

η= 109 τ

dvdh (59)

where:

η is dynamic viscosity, mPa•s;

τ is shear stress, N/mm2;

v is velocity, m/s;

h is thickness of an element measured per-pendicular to the flow, m;

dvdh is known as the rate of shear [s--1] and

sometimes listed as γ.

Lubricants used in industry today, however, havetheir viscosity measured by capillary viscometerswhich provide a kinematic viscosity. Kinematicviscosity, ν, is the ratio of dynamic viscosity, η, to thedensity, ρ, at a specified temperature and pressure(see equation 60).

ν= 103ηÃ (60)

where:

ν is kinematic viscosity, mm2/s;

ρ is density, kg/m3.

ASTM D445 [9] is the most widely used method formeasuring the kinematic viscosity of lubricants formany different applications. The most commonly


10

used temperatures are 40°C and 100°C; thesemeasurements are generally made at atmosphericpressure.

Under Newton’s law, viscosity is independent ofshear rate. Fluids such as these are referred to asNewtonian fluids. Most conventional, single gradelubricants made with a relatively low molecularweight base stock (non--polymeric) are consideredNewtonian fluids. However, there are fluids that donot exhibit this ideal behavior because their viscosityis not independent of shear rate. These are usuallyfinished blends containing higher molecular weightpolymers (viscosity modifiers or viscosity indeximprovers, as well as pour point depressants) thatare sensitive to shear rate. Some exhibit shearthinning, whereas others result in shear thickening.It is more common in gear lubricant applications tofind shear thinning relationships due to the nature ofthe polymers typically used in these formulations.This shear thinning translates into lower effectiveviscosities in the contact region under operation thanmight be expected from a non--polymer blend ofsimilar viscosity.

5.1.1 Viscosity – temperature relationship

Lubricant viscosity varies inversely with tempera-ture. A truly ideal fluid would have a viscosity that isconstant over all temperature. ASTM method D341[10] can be used to obtain the viscosity--temperaturerelationship. A simplified form can be used toestimate the kinematic viscosity of a fluid at a giventemperature if there is some viscometric informationavailable for the fluid at two other temperatures (seeequation 61).

log10 log10(ν+ 0.7)= A− B× log10T (61)

where:

T is absolute temperature, K;

ν is kinematic viscosity, mm2/s;

A, B are dimensionless constants.

A and B can be determined by solving equation 61simultaneously with equations 62 and 63, using thekinematic viscosity of the fluidmeasured at standardtemperatures of 40°C and 100°C.

(62)B=

log10 log10ν40+ 0.7 − log10 log10ν100+ 0.7log10(373.15)− log10(313.15)

then

(63)

A= log10 log10ν40+ 0.7 + B× log10(313.15)

Another common numeric designation that providesinformation about the viscosity--temperature rela-tionship of a fluid is the viscosity index or VI. Theviscosity index of a fluid can be calculated by ASTMmethod D2270 [11]. This arbitrary measure gives arelative viscosity--temperature sensitivity for a givenoil. The higher the value the less change in viscositywith temperature.

5.1.2 Viscosity--pressure relationship

Equally important to temperature on the fluidviscosity is the pressure acting on it. This isespecially important in highly loaded contacts suchas gears and rolling element bearings where pres-sures can easily exceed 1 GPa. The viscosity oflubricant trapped in a concentrated contact in-creases exponentially with pressure. In 1893, C.Barus established an empirical equation to describethe isothermal viscosity--pressure relationship for agiven 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 andKlaus [12] provided a comparison of the manymodels developed since the Barus equationwas firstintroduced. The continued research aided by thedevelopment of high pressure rheology techniquesto generate empirical information have shown thatthe viscosity--pressure response of a fluid is alsorelated to its chemical structure [13, 14, 15]. This canhave a profound effect on the film forming capabili-ties of the fluid in question and the overall life of thecomponent involved.

5.2 Film thickness equation

Dowson, Higginson and Toyoda have authoredvarious papers on EHL film thickness [16, 17, 18,19]. The film thickness equations given in thesepapers account for the exponential increase oflubricant viscosity with pressure, tooth geometry,velocity of the gear teeth, material elastic propertiesand the transmitted load. The film thicknessdetermines the operating regime of the gearset and


11

has been found to be a useful index of wear relateddistress probability. Wellauer andHolloway [20] alsofound that specific film thickness could be correlatedwith the probability of tooth surface distress. TheDowson and Toyoda [19] equation for line contactcentral EHL film thickness will be used as shownbelow.

Dimensionless central film thickness:

(65)Hci= 3.06

G0.56U0.69i

Wi0.10

where

(i) (as a subscript) defines a point on the line ofaction,

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)Ui =ηM vei2Er Ãni

× 10−6

load parameter, W(i)

(68)Wi =XΓi

wn

Er Ãni

where

ηM is dynamic viscosity at the gear toothtemperature, mPa•s.

ηM= 10g− 0.9 (69)

where

g= 10cθM+ 273.15d

θM is tooth temperature, °C (see 6.3).

The parameters c and d required for calculating ηMcan either be taken from table 2 or calculated withequations 70 and 72, respectively. Equations 70 and72, derived from a modification of the Waltherequation [10], will yield the parameters c and d if twodynamic viscosities, η1 and η2, are known at twocorresponding temperatures, θ1 and θ2.

Since dynamic viscosity is generally available at40°C and 100°C, equations 70 and 72 are modifiedin equations 71 and 73 to incorporate termscorresponding 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=

log10log10η2+0.9log10η1+0.9

log10θ2+273.15θ1+273.15

(70)

when θ1 = 40°C and θ2 = 100°C,

d= 13.13525 log10log10η100+ 0.9log10η40+ 0.9 (71)

− d log10 θ1+ 273.15) (72)

c= log10 log10η1+ 0.9

when θ1 = 40°C and θ2 = 100°C,

c= log10log10η40+ 0.9 − 2.495752 d(73)

α is pressure--viscosity coefficient, mm2/N.Values range from 0.725¢ 10--2 mm2/N to2.9¢ 10--2 mm2/N for typical gear lubri-cants. Values for pressure--viscositycoefficients vs. dynamic viscosity can beobtained from equation 74.

α= k ηsM (74)

Table 2 contains viscosity information for mineraloils, MIL--L spec. oils, polyalphaolefin (PAO) basedsynthetic oils (which contain ester) and polyalkyleneglycol (PAG) based synthetic oils, as well asconstants c, d, k and s for use in the equations 69through 74. These values were obtained from thedata shown in figures 7 through 11 [22]. It isimportant that the film thickness is calculated withvalues 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:

hci= Hci

Ãni× 103 (75)

(see clause 4 for Ãni).


12

Table 2 -- Data for determining viscosity and pressure--viscosity coefficient

Lubricant ISO VG1) η40 η100 c d k sMineral oil 32

46681001502203204606801000150022003200

27.1781639.3587958.6451486.91484131.4335194.2414284.6312412.0824613.8288909.48361374.9312031.4172975.954

4.2941825.4405147.0591639.25119912.2758815.9829620.6070926.3410434.2400338.5678349.5872862.6980578.56109

10.2007610.079339.903559.657089.425269.240599.093008.964208.845729.259439.199469.156469.13012

--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

0.0104710.0104710.0104710.0104710.0104710.0104710.0104710.0104710.0104710.0104710.0104710.0104710.010471

0.13480.13480.13480.13480.13480.13480.13480.13480.13480.13480.13480.13480.1348

PAO -- basedsynthetic non--VI improved oil

15022032046068010001500220032006800

128.5772189.9828278.3370402.8943600.0179868.17101310.3501933.0702827.7266077.362

16.1797121.6093328.6640537.5402053.2042368.6076791.03300118.0509151.2132244.5559

7.994287.799277.630357.497997.164347.120087.076787.061137.065947.11907

--3.07304--2.98154--2.90169--2.83762--2.69277--2.66528--2.63766--2.62221--2.61561--2.62091

0.0103260.0103260.0103260.0103260.0103260.0103260.0103260.0103260.0103260.010326

0.05070.05070.05070.05070.05070.05070.05070.05070.05070.0507

PAG -- basedsynthetic2)

1001502203204606801000

102.630153.950225.790328.430472.130697.9201026.37

19.56027.38040.09056.71077.250113.43163.30

6.425346.195865.765525.493945.350275.060114.85075

--2.45259--2.34616--2.16105--2.04065--1.97254--1.84558--1.75175

0.00470.00470.00470.00470.00470.00470.0047

0.15720.15720.15720.15720.15720.15720.1572

MIL--L--7808KGrade 3

12 11.35364 2.701402 9.58596 --3.82619 0.005492 0.25472

MIL--L--7808KGrade 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 0.16530NOTES:1) ν40 (mm2/s)2) Copolymer of ethylene oxide and propylene oxide in 50% weight ratio.

The specific film thickness is the ratio of filmthickness divided by the composite roughness of thecontacting gear teeth and can be used to assessperformance.

To determine this ratio, the cutoff wavelength for thecomposite surface roughness measurement (σx)should be comparable to the width of the Hertziancontact, 2bHi

. This results in σx becoming σ2bHias

shown in equation 76.

λ2bHi=

hciσ2bHi

(76)

This may not be practical because many surfacemeasuring instruments have a fixed cutoff wave-length (usually 0.8 mm).


13

Dynam

icviscosity

(mPa⋅s)

1

10

100

1000

10 000

100 000

1 000 000

200 250 300 350 400 450 500

Temperature (K)

32

4668

100

150220

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 beapproximated by:

λ2bHi=

hciσx

Lx2bHi

0.5

(77)

σx= Ra21x+ Ra22x0.5

(78)

where

λ2bHiis specific film thickness at point i with a

filter cutoff wavelength of 2bH;

Lx is filter cutoff wavelength used in measuringsurface roughness, mm. Any cutoff length,Lx, can be used (for example, L0.8 = 0.8 mmcutoff);


14

σx is composite surface roughness for filtercutoff 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 roughnessadjustment is developed below.

From Gaussian statistics [24], it is seen that:

Rq2x ∝ Lx (79)

where

Rqx2 is variance or square of the root meansquare roughness, mm.

also [25]:

Rax= 2π Rqx (80)

From equations 79 and 80:

Rax ∝ L0.5x (81)

Dynam

icviscosity

(mPa⋅s)

Temperature (K)

1

10

100

1000

10 000

100 000

1 000 000

200 250 300 350 400 450 500

150

220

320460

6801000

1500

2200

3200

6800

ISO VG

Figure 8 -- Dynamic viscosity versus temperature for PAO--based synthetic non--VI--improved oils


15

Hence, for a 0.8 mm cutoff length,

Ra2bHi= Ra0.82bHiL0.8

0.5

(82)

Substitute equation 82 into equation 78 onceeach for Ra1x and for Ra2x to obtain σ2bHi

.

Using this in equation 76, noting that

σ0.8= Ra210.8+ Ra220.80.5 yields equation 83

which is equation 77 developed for a 0.8 mm cutofflength.

λ2bHi=

hciσ0.8L0.82bHi

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 VG1000680460320220150100

Dynam

icviscosity

(mPa⋅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


16

Dynam

icviscosity

(mPa⋅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 4MIL--L--23699E

Figure 10 -- Dynamic viscosity versus temperature for MIL Spec. oils

Pressure--viscositycoefficient(mm2 /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 oilMIL--L--7808KMIL--L--23699ESynthetic oil (PAO)Synthetic oil (PAG)

Figure 11 -- Pressure--viscosity coefficient versus dynamic viscosity


17

6 Scuffing

6.1 General

The term scuffing as used in this information sheet isdefined as localized damage caused by solid--phasewelding between surfaces in relative motion. It isaccompanied by transfer of metal from one surfaceto another due to welding and subsequent tearing,and may occur in any highly loaded contact wherethe oil film is too thin to adequately separate thesurfaces. Scuffing appears as a matte, rough finishdue to the microscopic tearing at the surface. Itoccursmost commonly at extremeend regions of thecontact path or near points of single tooth contact.Scuffing is also known generically as severeadhesive wear.

Scoring was a term commonly used in the U.S. todescribe the same phenomenon now defined asscuffing (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 byintense frictional heat generated by a combination ofhigh sliding velocity and high contact stress.Scuffing occurs under thin film, boundary lubricationconditions and can be affected by physical andchemical properties of the lubricant, nature of theoxide films, and gear material.

When gear teeth are separated by a thick lubricantfilm, contact between surface asperities is mini-mized and there is usually no scuffing. As lubricantfilm thickness decreases, asperity contact increasesand scuffing becomes more probable. A very thinfilm, such as in boundary lubrication, together with ahigh contact temperature suggests a high probabilityof scuffing is possible in the absence of antiscuffadditives in the lubricant.

6.1.2 Probability of scuffing

Blok’s [1] contact temperature theory states thatscuffing will occur in gear teeth that are sliding underboundary--lubricated conditions, when the maxi-mum contact temperature reaches a criticalmagnitude. The contact temperature is the sum oftwo components: the flash temperature and thetooth temperature. See 6.4.

Scuffing most commonly occurs at one of the twoextreme end regions of the contact path or near thepoints of single tooth contact.

Prediction of the probability of scuffing is possible bycomparing the calculated contact temperature withlimiting scuffing temperature. The limiting scuffingtemperature can be calculated from an appropriategear scuffing test, or can be provided by fieldinvestigations.

For non--additive mineral oils, each combination ofoil and gear materials has a limiting scuffingtemperature that is constant regardless of theoperating conditions. It is believed that the limitingscuffing temperature is not constant for syntheticand high--additive EP lubricants, and it must bedetermined from tests that closely simulate theoperating condition of the gearset.

6.2 Flash temperature

The flash temperature is the calculated increase ingear tooth surface temperature at a given point alongthe line of action resulting from the combined effectsof gear tooth geometry, load, friction, velocity andmaterial properties during operation.

6.2.1 Fundamental formula for flashtemperature, θfli

The fundamental formula is based on Blok’s [1]equation.

(84)×

vr1i − vr2i

BM1vr1i0.5

+ BM2vr2i0.5

θfli= 31.62 K mmi

XΓiwn

bHi0.5

where

K is 0.80, numerical factor valid for a semi--elliptic (Hertzian) distribution of frictionalheat over the instantaneous width, 2 bH, ofthe rectangular contact band;

mmiis mean coefficient of friction (see 6.2.2);

XΓiis load sharing factor (see 4.3);

wn is normal unit load, N/mm (see equation 44);

vr1iis rolling tangential velocity of the pinion,m/s

(see equation 36);


18

vr2iis rolling tangential velocity of the gear, m/s

(see equation 37);

BM1 is thermal contact coefficient of the pinionmaterial, N/[mm s0.5K] (see 6.2.3);

BM2 is thermal contact coefficient of the gearmaterial, N/[mm s0.5K] (see 6.2.3);

bHiis semi--width of Hertzian contact band, mm

(see equation 57);

i (as a subscript) defines a point on the line ofaction.

In this equation, the coefficient of friction may beapproximated by different expressions, for instanceas proposed by Kelley [2, 4] and AGMA 217.01 [7].The influence of surface roughness is incorporatedin the approximation of the coefficient of friction.

6.2.2 Mean coefficient of friction, mmi

The mean coefficient of friction is an approximationof the actual coefficient of friction on the tooth flank,which is an instantaneous and local value dependingon several properties of the oil, surface roughness,lay of the surface irregularities like grinding marks,material properties, tangential velocities, forces anddimensions.

Three methods may be used to determine the valueof mmi

to be used in equation 84.

-- input a value based upon experience, whichis a constant;

-- input a value from equation 85, which is alsoa constant;

-- input a value from equation 88, which variesalong the line of action.

6.2.2.1 Approximation by a constant

A constant coefficient of friction along the line ofaction has been assumed by AGMA 217.01 [7] andKelley [2]:

(85)mmi= 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 operatingin the partial EHL regime. It may be too low for

boundary lubricated gears where mm may be higherthan 0.2, or too high for gears operating in thefull--film regime where mm may be less than 0.01.

The surface roughness is taken as an average of theaverage values:

(87)Ravgx=Ra1x+ Ra2x

2

where

Ra1x is pinion average surface roughness for filtercutoff length, Lx, mm;

Ra2x is gear average surface roughness for filtercutoff length, Lx, mm.

6.2.2.2 Empirical equation

An empirical equation for a variable coefficient offriction is the Benedict and Kelley [5] equation,supplemented with the influence of roughness:

(88)

mmi= 0.0127 CRavgx

log10

29 700 XΓiwn

ηMvsiv2ei

where the surface roughness expression is taken inaccordance with equations 86 and 87. Equation 88is not valid at or near the operating pitch point, as vsgoes to zero.

where

ηM is dynamic viscosity of the oil at gear toothtemperature, θM, mPa•s;

vsiis sliding velocity, m/s (see equation 38);

veiis entraining velocity, m/s (see equation 39).

6.2.3 Thermal contact coefficient, BMThe thermal contact coefficient accounts for theinfluence of the material properties of pinion andgear:

BM1= λM1× ÃM1× cM10.5

(89)

BM2= λM2× ÃM2× cM20.5

(90)

For martensitic steels the range of heat conductivity,λM , is 41 to 52 N/[s K] and the product of densitytimes the specific heat per unit mass, ρM¢ cM isabout 3.8 N/[mm2K], so that the use of the averagevalue BM = 13.6 N/[mm s0.5 K] for such steels will notintroduce a large error when the thermal contactcoefficient is unknown.

6.2.4 Maximum flash temperature

To locate and determine the maximum flash tem-perature, the flash temperature should be calculated


19

at a sufficient number of points (for example, 25 to50) on the line of action. Calculate flash tempera-tures at points between SAP and LPSTC duringdouble tooth contact, at LPSTC and HPSTC forsingle tooth contact, and between HPSTC and EAPduring double tooth contact.

If the contact temperature (see 6.4) is greater thanthe mean scuffing temperature (see 6.5) for thelubricant being used, there is a potential risk forscuffing (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 theyenter the contact zone. In some cases [26], the toothtemperature may be significantly higher than thetemperature 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 oiltemperature, taking into account some impedimentin heat transfer for spray lubrication if applicable, anda portion that depends mainly on the flash tempera-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, see6.2.

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 temperaturebe 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 athermal network analysis [43] (see figure 12).

The tooth temperature is determined by the heat flowbalance in the gearbox. There are several sourcesof frictional heat, of which the most important onesare the tooth friction and the bearing friction. Otherheat sources, like seals and oil flow, may alsocontribute. For gear pitchline velocities above 80m/s, churning loss, expulsion of oil betweenmeshingteeth, and windage loss become important heatsources that should be considered. Heat is con-ducted and transferred to the environment byconduction, 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) thecontact temperature is:

θBi= θM+ θfli

(92)

where

θM is tooth temperature, °C (see 6.3);

θfliis flash temperature, °C (see 6.2).

i (as a subscript) defines a point on the line ofaction.

Bearings

Air

Oil

Case

Frictionpower

Pinion

Gear

Friction power

Shafts

Figure 12 -- Example of thermal network


20

A B D EC

θB max

θfl maxθfli

θBi

θM

Figure 13 -- Contact temperature along the lineof 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 (see6.2).

6.5 Scuffing temperature

The scuffing temperature is the temperature in thetooth contact zone at which scuffing is likely to occurwith the chosen combination of lubricant and gearmaterials. The scuffing temperature is assumed tobe a characteristic value for the material--lubricantsystem of a gear pair, to be determined by gear testswith the same material--lubricant system.

When θB max (see figure 13) reaches the scuffingtemperature of the system, scuffing is likely. Themean scuffing temperature is the temperature atwhich there is a 50% chance of scuffing.

6.5.1 Mean scuffing temperature for mineral oils

Scuffing temperatures for mineral oils with lowconcentrations of antiscuff additives are indepen-dent of operating conditions. Viscosity grade is aconvenient index of oil composition, and thus ofscuffing temperature.

Equations 94 and 95 are approximate guides formineral oils and steels typical of IAE and FZG test

machines. The mean scuffing temperature wasderived from data published by Blok [27].

Equation 94 gives the scuffing temperature fornon--antiscuff mineral oils (R&O in accordance withANSI/AGMA 9005--E02 [28]).

θS= 63+ 33 ln ν40 (94)

where

ν40 is kinematic viscosity at 40°C, mm2/s (table2).

Equation 95 gives the scuffing temperature forantiscuff mineral oils (EP gear oil in accordance withANSI/AGMA 9005--E02).

θS= 118+ 33 ln ν40 (95)

6.5.2 Mean scuffing temperature for oils andsteels typical of aerospace industry

Table 3 gives the mean scuffing temperature for oilswith steels typical of the aerospace industry.

Table 3 -- Mean scuffing temperatures for oilsand steels typical of the aerospace industry

LubricantMean scuffingtemperature, °C

MIL--L--7808 205MIL--L--23699 220DERD2487 225DERD2497 240DOD--L--85734 260ISO VG 32 PAO 280DexronR II1) 290NOTE:1) DexronR is a registered trademark of GeneralMotors Corporation.

6.5.3 Extension of test gear scuffing temperaturefor one steel to other steels

The scuffing temperature determined from testgears with low--additive mineral oils may be ex-tended to different gear steels, heat treatments orsurface treatments by introducing an empiricalwelding factor.

θS= XWθfl max, test+ θM, test (96)

where

XW is welding factor (see table 4);

θfl max, test is maximum flash temperature of testgears, °C;


21

θM, test is tooth temperature of test gears, °C.

6.5.4 Scuffing temperature for oils used inhypoid gear application

Scuffing temperature for high--additive oils (hypoidgear oil) may be dependent on operating conditions.Therefore, the scuffing temperature should beobtained from tests that closely simulate operatingconditions of the gears.

Table 4 -- Welding factors, XW

Material XWThrough hardened steel 1.00Phosphated steel 1.25Copper--plated steel 1.50Bath or gas nitrided steel 1.50Hardened carburized steel-- Less than 20% retained austenite 1.15-- 20 to 30% retained austenite 1.00-- Greater than 30% retained austenite 0.85Austenite steel (stainless steel) 0.45

6.5.5 Scuffing risk

Scuffing risk can be calculated from a Gaussiandistribution of scuffing temperature about the meanvalue. Typically, the coefficient of variation is at least15%. Therefore, use the procedure of annex B tocalculate the probability of scuffing:

where

y = θB max

my = θs

σy = 0.15 θs

Table 5 gives the evaluation of scuffing risk based onthe probability of scuffing [7].

Table 5 -- Scuffing risk

Probability of scuffing Scuffing risk<10% Low

10 to 30% Moderate>30% High

6.6 Alternative scuffing risk evaluation

The calculation of the scuffing load capacity is a verycomplex problem. Several alternative methods are

proposed which may support the gear geometry androtor dimensions most suitable to the gear applica-tion. Gear drives cover a wide field of operatingconditions from relatively low pitch line velocitieswith high specific tooth loads, to very high pitch linevelocities and moderate specific tooth loads.Lubricants vary, as well, between mineral oils withlittle or no additives to antiscuff lubricants withsubstantial additives.

The flash temperature method described in 6.2through 6.5 is based on Blok’s contact temperaturetheory. The flash temperature, θfl, must be added tothe steady gear tooth temperature, θM, to give thetotal contact temperature, θB. The value of thecontact temperature for every point in the contactzone must be less than the mean scuffing tempera-ture of the material--lubricant system or scuffingmayoccur.

6.6.1 Integral temperature method

The integral temperature method [29] has beenproposed as an alternative to the flash temperaturemethod by which the influence of the gear geometryimposes a critical energy level based on theintegrated temperature distribution (for example,numerically integrating using Simpson’s rule) alonga path of contact and adopting a steady gear toothtemperature. Thismethod involves the calculation ofa scuffing load basically independent of speed, butcontrolled by gear geometry. Application requirescomparison of the proposed gearset based on a testrig result to a known test rig gearset and tested oil.

A comparison of the flash temperature method andintegral temperature method has shown thefollowing:

-- Blok’s method and the integral temperaturemethod give essentially the same assessment ofscuffing risk for most gearsets;

-- Blok’s method and the integral temperaturemethod give different assessments of scuffingrisk for those cases where there are localtemperature peaks. These cases usually occur ingearsets that have low contact ratio, contact nearthe base circle, or other sensitive geometries;

-- Blok’s method is sensitive to local tempera-ture peaks because it is concerned with themaximum instantaneous temperature, whereasthe integral temperature method is insensitive tothese peaks because it averages the temperaturedistribution.


22

6.6.2 Other scuffing methods

6.6.2.1 PVT Method

Almen [30] popularized the PVT method forpredicting 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 inautomotive and aircraft industries. It worked well fora narrow range of gear designs, but was unreliablewhen extrapolated to other gear applications.

6.6.2.2 Borsoff scoring factor method

Borsoff [31, 32, 33, 34] conducted many scuffingtests during the 1950’s and found scuffing resistanceincreased when test gears were run at high speeds.Borsoff introduced a scoring factor, Sf:

Sf=2bHvs

(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 totraverse the Hertzian band of the mating tooth.Borsoff’s test data showed a linear relationshipbetween scuffing load and scoring factor, Sf. Borsoffrecommended that a number of considerationsshould be made before using his method for specificapplications.

6.6.2.3 Simplified scuffing criteria for high speedgears

Annex B of ANSI/AGMA 6011--H98 [35] has beenused to evaluate scuffing risk of high speed gearapplications.

There are other methods for evaluating scuffing ofgear teeth not mentioned here. Other methods mayalso have application merit. Most importantly, thegear designer should recognize scuffing as a geardesign criteria.

7 Surface fatigue (micro-- andmacropitting)

7.1 General information

Surface fatigue, commonly referred to as pitting orspalling, is a wear mode that results in loss ofmaterial as a result of repeated stress cycles actingon the surface. There are two major sub--groupsunder surface fatigue known as micro-- and macro-pitting. As their names imply, the type of pitting isrelated to the size of the pit. Macropits usually can beseen with the naked eye as irregular shaped cavitiesin the surface of the tooth. Damage beginning on theorder of 0.5 to 1.0mm in diameter is considered to bea macropit.

The number of stress cycles occurring before failureis referred to as the fatigue life of the component.The surface fatigue life of a gear is inverselyproportional to the contact stress applied. Althoughcontact stress is probably themajor factor governinglife, there are many others that influence life. Theseinclude design factors such as tip relief and crown-ing, surface roughness, physical and chemicalproperties of the lubricant and its additive system,and external contaminants such as water and hardparticulate matter.

7.2 Micropitting

Micropitting is a fatigue phenomenon that occurs inHertzian contacts that operate in elastohydrody-namic or boundary lubrication regimes and havecombined rolling and sliding. Besides operatingconditions such as load, speed, sliding, temperatureand specific film thickness, the chemical composi-tion of a lubricant strongly influences micropitting.Damage can start during the first 105 to 106 stresscycles with generation of numerous surface cracks.The cracks grow at a shallow angle to the surfaceforming micropits that are about 10 – 20 mm deep byabout 25 -- 100 mm long and 10 – 20 mm wide. Themicropits coalesce to produce a continuous frac-tured surface which appears as a dull, matte surfaceto the observer.

Micropitting is the preferred name for this mode ofdamage, but it has also been referred to as greystaining, grey flecking, frosting, and peeling. Al-though micropitting generally occurs with heavilyloaded, 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


23

reduced gear tooth accuracy, increased dynamicloads and noise. Eventually, it can progress tomacropitting and gear failure.

7.2.1 Micropitting risk evaluation

Factors that influence micropitting are gear toothgeometry, surface roughness, lubricant viscosity,coefficient of friction, load, tangential speed, oiltemperature and lubricant additives. Commonmethods suggested for reducing the probability ofmicropitting 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 micropittingresistance;

-- protect gear teeth during run--in with suitablecoatings, such as manganese phosphate, copperor silver plating.

CAUTION: Silver or copper plating of carburized gearelements will cause hydrogen embrittlement, whichcould result in a reduction in bending strength and fa-tigue life. Thermal treatment shortly after plating mayreduce this effect.

Surface roughness strongly influences the tendencyto micropit. Gears finished to a mirrorlike finish havebeen reported to eliminate micropitting [36, 37, 38].Gear teeth have maximum micropitting resistancewhen the teeth of the high speedmember are harderthan the mating teeth and are as smooth as possible[39].

Currently there is no standard test for determiningmicropitting resistance of lubricants. However, FVAInformation Sheet 54/IV describes a test that usesthe FZG C--GF type gears to rank micropittingperformance of oils [40]. At present, the influence oflubricant additives is unresolved. Therefore, themicropitting resistance of a lubricant should bedetermined by field testing on actual gears or bylaboratory tests.

7.3 Macropitting

Macropitting is also a fatigue phenomenon. Crackscan initiate either at or near the surface of a geartooth. The crack usually propagates for a shortdistance 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 thematerial. With gears the origin of the crack is morelikely surface initiated because lubricant film thick-ness is low resulting in a high amount of asperity ormetal--to--metal contact. For high--speed gears withsmooth surface finishes, film thickness is larger andsub--surface initiated crack formationmay dominate.In these cases an inclusion or small void in thematerial is a source for stress concentration.

Laboratory testing commonly uses a 1% limit ontooth surface area damageas a criteria to stop a test.However, for field service applications one shouldalways abide by the equipment manufacturer’srecommendations or guidelines for acceptable limitsof 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 beenrefined to take into account many of the majorvariables that affect gear life. With respect tocalculated stress numbers, variables such as loaddistribution, internally induced dynamic loading andexternally induced dynamic loading are accountedfor by derating factors. Variables such as materialquality, cycle life and reliability are accounted for byallowable stress numbers, stress cycle factors andreliability factors.

Along with these influences, it has been recognizedthat adequate lubrication is necessary for gears torealize their calculated capacity. Indeed, AGMAgearing standards have acknowledged this fact bystating this need as a requirement in order to applythe various rating methods.

Much of the groundwork for lubrication theory cameabout in the 1960’s and 1970’s. This period saw theadvent and proliferation of jet travel, space travel,advanced manufacturing processes and advancedpower needs. These technological and industrialdevelopments led to the need for better gear ratingmethods which, in turn, resulted in rapid progress inindustrial, vehicle and aerospace gearing standards.

High speed gearing was coming into greater use, butit was not as well understood as the industry wouldhave liked. To compensate, designs tended to focuson making higher speed stages of gearing moresuccessful, sometimes to the detriment of slowerspeed stages. This is how the gearing industry


24

started to get its first glimpses into the importance oflubrication on the life of gearing.

It was not uncommon to see a three (3) stageindustrial gear drive with problems as follows: a highspeed set of gears that looked relatively undam-aged, an intermediate speed set of gears that wasexperiencing initial pitting, and a slow speed set ofgears that was experiencing advanced pitting andtooth breakage. In the event that all three stageswere designed to have similar load intensity factors(K--factors and unit loads) the problem could beparticularly puzzling. Rating theory at the timeindicated that with all other things equal, the higherspeed stages of gearing should have been failingsooner than the lower speed stages, due to greaterstress cycles.

At issue was the tribological condition betweensurfaces of two mating teeth. Elastohydrodynamiclubrication (EHL) theory showed that factors likerelative surface velocity and local oil viscosity at thecontact area directly affected thickness of the EHLoilfilm that separated asperities on surfaces of twomating gear teeth. For amultiple stage gear reducer,higher speed stages of gearing, with higher surfacevelocities, tended to produce thicker EHL oil films,better capable of separating asperities on matingteeth. Lower speed stages, with lower surfacevelocities, tended to produce thinner EHL oil films,less capable of separating asperities on matingteeth.

Through the years, a great many researchers andcompanies inside and outside of the gear industryhave sought to quantify the effects of EHL oil filmtheory on the life of gearing. There aremany ways inwhich one could hypothesize the effects of inade-quate oil films on degradation of gear tooth surfacesand its results on the life of gearing. Indeed, acomprehensive treatment of this subject could fillmany volumes. Added to this is the fact that this isstill a very active area of gear research. With this inmind, it is still useful to put forth a simplifieddescription of how inadequate oil films can lead todecreased life of gears. So, very simply put, thinneroil films lead to a greater chance of more frequentand more detrimental degree of contact betweenasperities on mating gear teeth. The more severethis is, the more likely it will lead to pitting, arecognized form of surface fatigue in gearing.

The effects of this phenomenon on the fatigue life ofgearing were introduced by Bowen [41]. Dudley [42]

defined the three regimes of lubrication at theoperating pitch diameter as follows:

-- Regime III: Full EHL oil film is developed andseparates the asperities of gear flanks in motionrelative to one another;

-- Regime II: Partial EHL oil film is developedand there is occasional contact of the asperities ofgear flanks in motion relative to one another;

-- Regime I: Only boundary lubrication existswith essentially no EHL film and contact of theasperities of gear flanks in motion relative to oneanother is pronounced.

The implementation of this theory involves what iscurrently referred to as the stress cycle factor for thesurface durability of gears, ZN, (this used to be calledthe life factor for surface durability). Keeping inmindthat regime of lubrication depends ultimately on thedegree of separation between asperities, Dudleyproposed that the effect could be quantified bymaking proper adjustments to the curves thatdetermine the stress cycle factor. Thus, we have asfollows:

7.4.2 Regime III

This regime of lubrication, characterized by full EHLoil film development, occursmainly when gears haverelatively high pitch line velocity, good care is takento ensure that an adequate supply of clean, cool oil isavailable (of adequate viscosity and formulation),and good surface finishes are achieved on thegearing. As such, aerospace gearing, high speedmarine gearing, and good quality industrial geardrives tend to have gears that operate within regimeIII. Thus, stress cycle factor curves that appear instandards for these gears are the basis for ratinggears that operate within regime III.

7.4.3 Regime II

This regime of lubrication, characterized by partialEHL oil film development, occurs mainly when gearshavemoderate pitch line velocities,moderate care istaken to ensure that an adequate supply of clean,cool oil is available (of adequate viscosity andformulation), and moderately good surface finishesare achieved on the gearing. As such, vehiclegearing is very characteristic of gears that operatewithin regime II. Dudley uses information from thestress cycle factor curves in vehicle standards tocreate a branch from the regime III curve for cyclesgreater than 100 000. It is felt that effects ofoperation within regime II on fatigue life will not beginto be realized until this point in the life of a gear.


25

7.4.4 Regime I

This regime of lubrication, characterized by bound-ary lubrication, occurs mainly when gears have lowpitch line velocities, little care is taken to ensure thatan adequate supply of clean, cool oil is available (ofadequate viscosity and formulation), and relativelyrough surface finishes are achieved on the gearing.Many types of gearing can fall into this range ofoperation, including all types mentioned above.Dudley used fatigue curves generated for ball androller bearings as a basis for regime I stress cyclefactor curves. These curves, first developed in the1940’s, indicated that with a ten--fold increase in

cycles, load capacity of a bearing drops off by afactor of 2.0. Thus, a stress curve for Hertziancontact would drop off by about a factor of 1.41(square root of 2.0). Bearings back in the 1940’scommonly had surface finishes and oil films veryanalogous to gears operating in regime I. Thisinformation is used to create a branch from theregime III curve at cycles greater than 100 000.

Figure 14 shows the curves that result fromDudley’smethod of regimes of lubrication. Below, themethodis described in fuller detail and calculations are givento show how one assesses which regime of lubrica-tion should be applied to a given set of gears.

0.050.060.070.080.090.10

0.20

0.30

0.40

0.50

102 1010109108107106105104103 10121011

0.15

0.600.700.800.901.00

4.00

3.00

2.00

1.50

Number of load cycles, N

Regime I

Regime II

Regime III

Stresscyclefactor,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 durabilityRegime III ZN= 1.47 for N< 10 000 cycles

ZN= 2.46604× N−0.056 for N≥ 10 000 cyclesRegime II ZN= 3.83441× N−0.094 for N≥ 100 000 cyclesRegime I ZN= 7.82078× N−0.156 for N≥ 100 000 cycles


26

7.5 Estimating life with respect to surfacedurability

After calculating the minimum EHL film thicknessbased on 5.2, one must calculate the specific filmthickness. In figure 14, specific film thicknessesgreater than or equal to 1.0 indicate the beginning ofregime III and the end of regime II lubrication.Specific film thicknesses between 0.4 and 1.0indicate operation within regime II and specific filmthicknesses less than or equal to 0.4 indicateregime I.

Once the regime of lubrication is determined, onecan calculate the stress cycle factor, ZN, shown infigure 14. ZN is used to calculate gear rating inANSI/AGMA 2101--C95.

8 Wear

Wear is a term describing change to a gear toothsurface involving removal or displacement of materi-al, due to mechanical, chemical or electrical action.

In the boundary lubrication regime, some wear isinevitable.Many gears, because of practical limits onlubricant viscosity, speed and temperature, mustoperate under boundary lubricated conditions.

Mild wear occurs during running--in and usuallysubsides with time, resulting in a tolerable wear rateand a satisfactory lifetime for the gearset. Wear thatoccurs during running--in may be beneficial if itsmoothes tooth surfaces (increasing specific filmthickness) and increases the area of contact byremoving minor imperfections through local wear.The amount of wear that is tolerable depends on theexpected lifetime for the gearset, and on require-ments for noise and vibration. Wear rate maybecome excessive if tooth profiles are worn to theextent that high dynamic loads are encountered.Excessive wear may also be caused by contamina-tion of the lubricant by abrasive particles.Whenwearbecomes aggressive and is not preempted byscuffing or bending fatigue, wear and pittingwill likelycompete for the predominate failure mode.

8.1 Abrasive wear

Abrasive wear is removal or displacement of materi-al due to the presence of hard particles suspended in

the lubricant or embedded in flanks of mating teeth.The choice of lubricant usually does not have anydirect effect on abrasivewear. Abrasive particles canbe present, however, as debris from other forms ofwear such as fatigue pitting and adhesion. Thelubricant should not react with any systemic materi-als or with any contaminants. Products of thesereactions can be abrasive. In large open gears, thefilm thickness of highly viscous lubricants mayprevent three--body abrasion from small particles.

8.2 Wear risk evaluation

The boundary lubrication regime consists of exceed-ingly complex interactions between additives in thelubricant, metal, and atmosphere making it impossi-ble to assess accurately the chance of wear orscuffing froma single parameter such as specific filmthickness. However, empirical data of figure 15 havebeen used as an approximate guide to the probabilityof wear related distress. Figure 15 is based on datapublished by Wellauer and Holloway [20] that wereobtained from several hundred laboratory tests andfield applications. The curves of figure 15 apply tothrough--hardened steel gears ranging in size from25 mm to 4600 mm in diameter that were lubricatedwith mineral--based, non--EP gear lubricants. Theauthors [20] defined tooth flank surface distress assurface pitting or wear that might be destructive orcould shorten the gear life. Most of the data of figure15 pertain to gears that experienced lives in excessof 10 million cycles.

8.2.1 Adjustments to the surface distress andspecific film thickness curves

The surface distress and specific film thicknesscurves (figure 15) were derived from the Wellauerand Holloway curves. The curves are adjusted toaccount for different definitions of composite surfaceroughness and specific film thickness.

8.2.1.1 Average surface roughness adjustment

Reference [20] used root mean square surfaceroughness. This information sheet uses averagesurface roughness. The relationship between rootmean square and average surface roughness varieswith the machining process. Typically,

(98)Rqx≅ 1.11 Rax


27

Specific

filmthickness,λ

0.01

0.1

1

10

0.1 1 10 100 1000Pitch line velocity (m/s)

5%40%80%

Figure 15 -- Probability of wear related distress

8.2.1.2 Composite surface roughnessadjustment

Reference [20] used an arithmetic average for thecomposite surface roughness:

Rqx avg=Rq1x+ Rq2x

2(99)

where

Rq1x, Rq2x is root mean square surface rough-ness, pinion and gear respectively, forfilter cutoff length, Lx, mm.

Composite surface roughness used in this informa-tion sheet is root mean square average of averagesurface roughness, see equation 78.

If Rq1x = Rq2x and Ra1x = Ra2x (similar surfaceroughnesses),

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 fordifferent definitions of film thickness. The Dowsonand Toyoda equation for central film thickness [19],

hci, of equation 75, provides film thickness values

1.316 times the Dowson and Higginson [17] mini-mum film thickness, hmin, used by the Wellauer andHolloway paper [20].

Specific film thickness adjustment factor is derivedas follows:

Wellauer and Holloway [20] defined λ as:

λW&H=hmin

Rqx avg(102)

This information sheet uses hciand σx defined by

equations 75 and 100:

λi =hciσx

(103)

Substituting adjustment factors into the equation forλ 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 thicknessprovided by Wellauer and Holloway. This verticalaxis adjustment is now reflected in figure 15.


28

Finally, the units of pitch line velocity, vt, wereadjusted 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 thefollowing 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 minimumspecific film thickness, mλ min, and the standarddeviation, σλ min, can be calculated by simultaneoussolution (two equations in two unknowns) using anytwo 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 variabledetermined by probability;

λmin is specific film thickness (equation 105);

mλ min is mean minimum specific film thickness;

σλ min is standard deviation of the minimumspecific film thickness.

Figure 15 and equations 106 through 108 are listedin the percent failure mode, Q(x). This must first beconverted to a percent survival mode, P(x), by theequation P(x)= 1− Q(x). With P(x) known, the value“x” may be determined from the table “NormalProbability 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 tofind how mean minimum specific film thickness,mλ min, and standard deviation of the minimumspecific film thickness, σλ min, vary with pitch linevelocity. An example is shown below:

vt= 5 m∕sλ5%= 0.9849

λ40%= 0.6149

This gives the following equations that are solved forσλ min:

1.6449= 0.9849− mλ minσλ min

0.2534= 0.6149− mλ minσλ min

1.6449 σλ min= 0.9849− mλ min0.2534 σλ min= 0.6149− mλ min

Subtracting the bottom equation from the upperequation yields:

1.3915 σλ min= 0.3700

σλ min=0.37001.3915

= 0.2659

Using σλ min in the first equation, mλ min is found:

1.6449=0.9849− mλ min

0.2659mλ min= 0.9849− 1.6449 (0.2659)

mλ min= 0.5475

This process was repeated for all data points alongthe curves in the following combinations: 5%--40%,40%--80% and 5%--80%. Results of these calcula-tions were averaged and the values are shown intable 7.

Curve--fitting the inverse of themean, 1mλ min

, and the

inverse of the standard deviation, 1σλ 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)


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 witheach pitch line velocity allows the probability of weardistress to be assigned given specific EHL operatingconditions using the procedure of annex B andusing:

y= λmin

my= mλ min

σy= σλ min

Table 7 -- Calculation results

vt (m/s) mλ min σλ min0.25 0.04455408 0.024963020.50 0.08636353 0.047576651.00 0.16271966 0.086895831.50 0.23073618 0.119822982.00 0.29172511 0.147715232.50 0.34673387 0.171581233.00 0.39660952 0.192184593.50 0.44204486 0.210112924.00 0.48361240 0.225824914.50 0.52178951 0.239683315.00 0.55697759 0.2519782510.00 0.80016431 0.3248480115.00 0.93691698 0.3569398520.00 1.02464932 0.3743122925.00 1.08573704 0.3849618530.00 1.13072662 0.3920578235.00 1.16524421 0.3970772740.00 1.19256659 0.4007910445.00 1.21473204 0.4036365550.00 1.23307514 0.40587858100.00 1.32309469 0.41541491150.00 1.35614631 0.41831071200.00 1.37331023 0.41968741250.00 1.38382249 0.42048785


30

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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 beconstrued 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 DataθS met

Tip profile modification0 = none1 = modified for high load capacity2 = modified for smooth meshing

Driver driving member1 = pinion2 = gear

nop number of calculation points along the lineof action (25 recommended)

ηM dynamic viscosity (mPa⋅s) at gear toothtemperature, θM0 = 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 meancoefficient of friction1 = 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 scuffingtemperature, θs0 = from test gears (need to also inputθfl max, test, θM, test and XW from table 41 = R&O mineral oil2 = EP mineral oilOther = enter own value of θs (°C), (seetable 3)


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

nohelical 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

RavgxCRavgxmm const

Lmin (Eq 27)

εβ (Eq 24)


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)




yes

yes

yes

no

i = nop + 6

bH1 (eq 57)

i = i+ 1

P3

no

yes


34

no(ηM & α input)no

P3

θM = 0

P3A

P3A

P4

ηM = 0ηM = 0

mmet = 2

mmet = 1

θM = 0

ηM = 0

|θM1 -- θM| < 0.01

K = 0.8

mm const (Eq 85) mm const = mmetηM* (Eq 69)

α* (Eq 74)

yes

yes

no

no(θM input)

yesmm const (Eq 85)

yes

Call subroutineMax_Flash_Temp

θfl max


θfl maxCall subroutine

Max_Flash_Tempθfl max

θM (Eq 91)

θM1 = θM

ηM* (Eq 69)

α* (Eq 74)

θM (Eq 91)

yes

no(θM input)

no(εo & α input)

ηM (Eq 69)

α (Eq 74)


θfl max


θfl max

θM (Eq 91)

yes

yes

yes

samepage

no(ηM & αinput)

no

* See table 2 for constants in these equations calculated per 71 and 73.

mm const = 0


35

P5

P4

i= nop+ 6

θB max (eq 93)

G (Eq 66)

hmin = 100

λmin = λ2bH(i)

λmin = 100

i = 1

U(i) (Eq 67)

W(i) (Eq 68)

Hc(i) (Eq 65)

hc(i) (Eq 75)

hmin > hc(i)

hmin = hc(i)

λ2bH(i) (Eq 77)

yes

λmin > λ2bH(i)

yes

i = i + 1

yes

no

no

no


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

Pscuff< 0.10

Pscuff≤ 0.30

Srisk= high

Srisk = lowno

Srisk = moderateno

yes

yes

EP Mineral Oil

Enter own value of θs

Rq1x (Eq 98)

Rq2x (Eq 98)

Rqx avg (Eq 99)

λmin (Eq 105)

vt≤ 5 m∕sno

yes

y= λminmy= mλ min

σy= σλ min

Call subroutine “Probability”

Return POF

mλ min (Eq 112)

σλ min (Eq 113)


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


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) < 0, set mm(i) = 0.

νs(i) or XΓ(i)< εmach**

yes

mm(i) = mm constmm(i) (Eq 88)(Benedict and Kelley) mm(i) = 0

mm(i) or bH(i)< εmach**

yes

no

yes

no

θfl(i) (Eq 84)

mm(i) = 0

θfl(i) = 0

yes

θfl(i) > θfl max

no

no

θfl max = θfl(i)

yes

no

i = i + 1

i = nop + 6

yes

Return

no

mm is a (given) constantor calculated by equation85 (AGMA 217.01 and

Kelley)


39

Annex B(informative)

Normal or Gaussian probability


B.1 Normal or Gaussian probability

For random variables that follow normal (Gaussian)distributions, the following procedure [24] can beused to calculate probabilities of failure in the rangeof 5% to 95%:

x=y− myσy

(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 variabley.

Evaluation of Q:

if x > 1.6448, then:

Q = 0.05;

else

Q= ZQ b1t+ b2t2+ b3t

3+ b4t4+ b5t

5(B.2)

where

Q is the tail area of the normal probabilityfunction;

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= 11+ p|x|

(B.4)

are constants given in reference [24].


40

(This page is intentionally left blank.)


41

Annex C(informative)

Test rig gear data


C.1 Test rig gear data

Table C.1 provides a summary of gear data forseveral back to back test rigs that have been used forgear lubrication rating and research.

AGMA925--A

03AMERICANGEARMANUFA

CTURERSASSOCIATION

42

TableC.1--Summaryofgeardataforlubricanttesting

Sym

bol

Units

FZG“A

”FZG“A

10”

FZG“C

”FZG

“C--GF”

NASA

Ryder

AGMA

IAE

Prim

arywear

assessment

Scuffing

Scuffing

Pitting(micro

&macro)

Micropitting

Pitting

Scuffing

Pitting(micro

&macro)

Scuffing

amm

91.5

91.5

91.5

91.5

88.9

88.9

91.5

82.55

mn

mm

4.5

4.5

4.5

4.5

3.175

3.175

3.629

5.08

αn

deg

2020

2020

2022.5

2020

βdeg

00

00

00

00

αwt

deg

22.44

22.44

22.44

22.44

2022.5

21.31

26.25

z 1----

1616

1616

2828

2015

z 2----

2424

2424

2828

3016

bmm

2010

1414

6.35/2.8

6.35

144.76

r a1

mm

44.385

44.385

41.23

41.23

47.625

47.22

40.82

45.02

r a2

mm

56.25

56.25

59.18

59.18

47.625

47.22

58.18

47.69

x 1----

0.8635

0.8635

0.1817

0.1817

00

0.2231

0.3625

x 2----

--0.5103

--0.5103

0.1715

0.1715

00

0.0006

0.3875

Qualitynumber

Qualitystandard

----

5ISO1328

5ISO1328

5DIN

3962

5DIN

3962

13AGMA2000

13AGMA2000

12--13

AGMA2000

5ISO1328

Ra 1

mm0.3--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

Ra 2

mm0.3--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 1rpm

2170

2170

2250

2250

10000

10000

2250

4K--6K

θ oil

degC

90--140

90--120

90--120

9049

--77

7480

70--110

Refdocument

----

ISO14635--1

ASTM

D5182--97

CEC

L--07--A--95

ISO/W

D14635--2

FVA

Info

Sheet

54/7

FVA

Info

Sheet

54/I--IV

NASA

TP--2047

(1982)

ASTM

D1947--83

(1984)

----

IP166/77

(1992)

Piniontorque

range

Nm

3.3--534.5

3.3--534.5

135--376

28--265

0--100

0--270

250--400

20--407


43

Annex D(informative)

Example calculations[The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not beconstrued as a part of AGMA 925--A03, Effect of Lubrication on Gear Surface Distress.]

******************************************************************************SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03SCORING+ EX.#1DATE:2002/04/18 TIME:08:08:23******************************************************************************

***** GENERAL AND GEOMETRY INPUT DATA *****SCORING+ EX.#1Input unit (=1 SI, =2 Inch) (iInputUnit) 1.000000Output unit (=1 SI, =2 Inch) (iOutputUnit) 1.000000Gear type (=1 external, =2 internal) (iType) 1.000000Driving member (=1 pinion, =2 gear) (iDriver) 2.000000Number of pinion teeth (z1) 21.000000Number of gear teeth (z2) 26.000000Normal module (mn) 4.000000 mmHelix angle (Beta) 0.000000 degOperating center distance (aw) 96.000000 mmNormal generating pressure angle (Alphan) 20.000000 degStandard outside radius, pinion (ra1) 46.570900 mmStandard outside radius, gear (ra2) 57.277000 mmFace width (b) 66.040000 mmProfile mod (=0 none, =1 hi load, =2 smooth) (iTip) 1.000000

***** Material input data *****Modulus of elasticity, pinion (E1) 206842.718795 N/mm^2Modulus of elasticity, gear (E2) 206842.718795 N/mm^2Poisson’s ratio, pinion (Nu1) 0.300000Poisson’s ratio, gear (Nu2) 0.300000Average surface roughness at Lx, pinion (Ra1x) 0.508000 mu mAverage surface roughness at Lx, gear (Ra2x) 0.508000 mu mFilter cutoff of wavelength x (Lx) 0.800000 mmMethod for approximate mean coef. friction (Mumet) 1.000000Welding factor (Xw) 1.000000

***** Load data *****Pinion speed (n1) 308.570000 rpmTransmitted power (P) 20.619440 kWOverload factor (Ko) 1.000000Load distribution factor (Km) 1.400000Dynamic factor (Kv) 1.063830

***** Lubrication data *****Lubricant type (=1 Mineral, =2 Synthetic,=3 MIL--L--7808K, =4 MIL--L--23699E) (iLubeType) 1.000000ISO viscosity grade number (nIsoVG) 460.000000Kinematic viscosity at 40 deg C (Nu40) 407.000000 mm^2/s

***** Input temperature data *****Tooth temperature (ThetaM) 82.222222 deg CThermal 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 CParameter for calculating tooth temperature (ksump) 1.000000Dynamic viscosity at gear tooth temperature (EtaM) 43.000000 mPa⋅sPressure--viscosity coefficient (Alpha) 0.022045 mm^2/NMethod of calculating scuffing temperature (Thetasmet) 2.000000Maximum flash temperatrue of test gears (Thetaflmaxtest) 0.000000Tooth temperature of test gear (ThetaMtest) 0.000000Number of calculation points (nNop) 25.000000


44

******************************************************************************SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03SCORING+ EX.#1DATE:2002/04/18 TIME:08:08:23******************************************************************************

***** GEOMETRY CALCULATION *****Gear ratio (u) 1.238095Standard pitch radius, pinion (r1) 42.000000 mmStandard pitch radius, gear (r2) 52.000000 mmPinion operating pitch radius (rw1) 42.893617 mmTransverse generating pressure angle (Alphat) 20.000000 degBase radius, pinion (rb1) 39.467090 mmBase radius, gear (rb2) 48.864016 mmTransverse operating pressure angle (Alphawt) 23.056999 degTransverse base pitch (pbt) 11.808526 mmNormal base pitch (pbn) 11.808526 mmAxial pitch (px) ----------------Base helix angle (Betab) 0.000000 degOperating helix angle (Betaw) 0.000000 degNormal operating pressure angle (Alphawn) 23.056999 degDistance along line of action -- Point A (CA) 7.715600 mmDistance along line of action -- Point B (CB) 12.913884 mmDistance along line of action -- Point C (CC) 16.799142 mmDistance along line of action -- Point D (CD) 19.524126 mmDistance along line of action -- Point E (CE) 24.722409 mmDistance along line of action -- Point F (CF) 37.598080 mmActive length of line of action (Z) 17.006810 mmTransverse contact ratio (EpsAlpha) 1.440214Fractional part of EpsAlpha (nr) 0.440214Axial contact ratio (EpsBeta) 0.000000Fractional part of EpsBeta (na) 0.000000Minimum contact length (Lmin) 66.040000 mm

***** GEAR TOOTH VELOCITY AND LOADS *****Rotational (angular) velocity, pinion (Omega1) 32.313375 rad/sRotational (angular) velocity, gear (Omega2) 26.099264 rad/sOperating pitch line velocity (vt) 1.386038 m/sNominal tangential load (Ftnom) 14876.538066 NCombined derating factor (KD) 1.489362Actual tangential load (Ft) 22156.550486 NNormal operating load (Fwn) 24080.178937 NNormal unit load (wn) 364.630208 N/mm

***** MATERIAL PROPERTY AND TOOTH SURFACE FINISH *****Reduced modulus of elasticity (Er) 227299.690984 N/mm^2Average of pinion and gear average roughness (Ravgx) 0.508000 mu mSurface roughness constant (CRavgx) 1.816720Composite surface roughness at filter cuttoff (Sigmax) 0.718420 mu m


45

**********************************************************************************SCUFFING ANDWEAR RISK ANALYSIS ver 1.0.9 -- AGMA925--A03SCORING+ EX.#1DATE:2002/04/18 TIME:08:08:23**********************************************************************************

***** LOAD SHARING RATIO AND bH *****

IndexRoll

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 8.61978 0.18765 ( 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⋅sDynamic viscosity at 100 deg C (Eta100C) 26.341040 mPa⋅sFactor c (c_coef) 8.964201Factor d (d_coef) --3.424449Factor k (k_coef) 0.010471Factor s (s_coef) 0.134800Mumet -- use Kelley and AGMA 217.01 (Mumet) 1.000000Surface roughness constant (CRavgx) 1.816720Mean coef. of friction, const. (Eq 85) (Mumconst) 0.109003


46


**** 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⋅sPressure--viscosity coefficient (Alpha) 0.022045 mm^2/N


47


********** 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 mMin. specific film thk. found at point (B) (LambdaMin) 0.425354Tooth temperature (ThetaM) 82.222222 deg CMax. flash temperature (Thetaflmax) 25.646608 deg CMinimum film thickness (hmin) 0.207269 mu mMaximum contact temperature (ThetaBmax) 107.868830 deg C--------------------------------------------------------------------------------------------------------------------------------------------------------------------


48


**** P5 -- Calculate risk of scuffing and wear ****

***** Risk of scuffing *****

Method of calculating scuffing temperature (Thetasmet) 2.000000Mean scuffing temperature (Thetas) 316.290835 deg C

***** Probability of scuffing *****

Maximum contact temperature (y) 107.868830 deg CMean scuffing temperature (Muy) 316.290835 deg CApprox. standard deviation of scuffing temp. (Sigmay) 47.443625 deg CStandard normal variable, x = ((y--muy)/Sigmay) --4.393046--------------------------------------------------------------------------------------------------------------------------------------------------------------------Probability of scuffing Pscuff = 5% or lowerBased on AGMA925--A03 Table 5, scuffing risk is low--------------------------------------------------------------------------------------------------------------------------------------------------------------------

**** Risk of wear ****Average surface roughness, pinion (Ra1x) 0.508000 mu mAverage surface roughness, gear (Ra2x) 0.508000 mu mAverage surface roughness (rms), pinion (Rq1x) 0.563880 mu mAverage surface roughness (rms), gear (Rq2x) 0.563880 mu mArithmetic average of rms roughness (Rqxavg) 0.563880 mu mMinimum specific film thickness (Lambdamin) 0.425354Pitchline velocity is less than 5 m/s (vt) 1.386038 m/sMean min. specific film thk. (eq. 110) (MuLambdaMin) 0.215956Std. dev. of min. spec. film thk. (eq. 111) (SigmaLambdaMin) 0.112623

***** Probability of wear *****Minimum specific film thickness (y) 0.425354Mean minimum specific film thickness (muy) 0.215956Standard deviation of the min. specific film (Sigmay) 0.112623Standard normal variable, x = ((y--muy)/Sigmay) 1.859273--------------------------------------------------------------------------------------------------------------------------------------------------------------------Probability of wear Pwear = 5% or lower--------------------------------------------------------------------------------------------------------------------------------------------------------------------


49

Bibliography

The following documents are either referenced in the text of AGMA 925--A03, Effect of Lubrication on GearSurface 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 EngineeringApproach 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 PowerGears, October, 1965.

8. SCORING+, computer program, GEARTECH Software, Inc., 1985.

9. ASTMD445--97, Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (theCalculation 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 at40 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 ofLubricant 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 forSeveral 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 atElevated Pressures and Temperatures, Preprint number 75--LC--3D--1, presented at the ASLE/ASMELubrication 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 andGear 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.


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 pressure -- 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 PrintingOffice, 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 theLubrication 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--HardenedGears, 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’ ofTooth 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, NECBirmingham, 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, ASMEPaper77--DET--122, September 1977.

42. Dudley, D.W.,Characteristics of Regimes of Gear Lubrication, International Symposium on Gearing andPower 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.


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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--SpeedGears, 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 inMachinable Hardness Gear Teeth, AGMA Technical Paper 91FTM17, 1991.

PUBLISHED BYAMERICAN GEAR MANUFACTURERS ASSOCIATION1500 KING STREET, ALEXANDRIA, VIRGINIA 22314

Documents

AGMA 925A03 Effect of Lubrication on Gear Surface