Timothy L. Krantz

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Ahmet Kahraman

The Ohio State University, Columbus, Ohio

An Experimental Investigation of the Influence

of the Lubricant Viscosity and Additives on

Gear Wear

NASA/TM—2005-213956

October 2005

ARL–TR–3126

U.S. ARMY

RESEARCH LABORATORY
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Timothy L. Krantz

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Ahmet Kahraman

The Ohio State University, Columbus, Ohio

An Experimental Investigation of the Influence

of the Lubricant Viscosity and Additives on

Gear Wear

NASA/TM—2005-213956

October 2005

National Aeronautics and

Space Administration

Glenn Research Center

ARL–TR–3126

U.S. ARMY

RESEARCH LABORATORY
Acknowledgments

The authors thank Gurinder Singh for measuring the gear surfaces and for processing the data to determine

wear amounts. They also thank M&M Precision Systems, Inc. for making the gear coordinate measurement

machine available.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2005-213956 1

An Experimental Investigation of the Influence 

of the Lubricant Viscosity and Additives 

on Gear Wear 

Timothy L. Krantz 

U.S. Army Research Laboratory 

Glenn Research Center 

Cleveland, Ohio 44135 

Ahmet Kahraman 

The Ohio State University 

Columbus, Ohio 43210 

Abstract 

The influence of lubricant viscosity and additives on the average wear rate of spur gear pairs was 

investigated experimentally. The gear specimens of a comprehensive gear durability test program that 

made use of seven lubricants covering a range of viscosities were examined to measure gear tooth wear. 

The measured wear was related to the as-manufactured surface roughness, the elastohydrodynamic film 

thickness, and the experimentally determined contact fatigue lives of the same specimens. In general, the 

wear rate was found to be inversely proportional to the viscosity of the lubricant and to the lambda ratio 

(also sometimes called the specific film thickness). The data also show an exponential trend between the 

average wear rates and the surface fatigue lives. Lubricants with similar viscosities but differing additives 

and compositions had somewhat differing gear surface fatigue lives and wear rates. 

1. Introduction 

Surface wear is considered to be one of the important failure modes in gear systems. Gear contact 

surface wear can significantly impair the functionality of any gear system. Apart from the direct material 

loss that leads to functional failure, wear can also lead to changes in vibration and noise behavior (refs. 1 

to 3). In addition, wear can change the patterns of gear contact such that the altered load distributions and 

contact stresses will accelerate the occurrence of other failure modes (ref. 4). Therefore, a better 

understanding of gear wear, including its impact on noise and durability, is needed. 

Wear of contacting surfaces is a complex phenomenon that is influenced by a large number of 

parameters. Gear wear is further complicated since the mechanics of the contact are dictated not only by 

the geometry but also by both tooth contact and tooth bending deformations. In addition, many 

automotive and aerospace gearing applications operate in mixed elastohydrodynamic (EHD) or boundary 

lubrication regimes where asperity contacts are possible (ref. 5). Hence, parameters influencing the 

lubricant film and boundary layer properties are also critical. The strong coupling between the actual 

geometries of the worn contacting surfaces and the resulting contact conditions is often ignored in widely 

used models to estimate stresses and surface fatigue life. Such a simplified approach can perhaps provide 

unrealistic life predictions. 

The study of wear is becoming one of the emerging areas of gear research. A number of recent wear 

modeling efforts (refs. 6 to 10) form a solid foundation for studying gear wear. The common thread to 

these studies is that almost all of them use the well-known Archard’s wear model (ref. 11) in conjunction 

with a gear contact model and relative sliding calculations. Archard’s wear equation can be expressed for 

a local point on one of the contacting gear surfaces as 
NASA/TM—2005-213956 2

kP

ds

dh = (1) 

where k is an experimentally determined wear coefficient, h is the wear depth accumulated, P is the 

contact pressure, and s is the sliding distance between the mating surfaces at the point of interest. From 

equation (1) to calculate the wear depth h, the contact pressure P and the sliding distance s must be 

determined. Flodin and Andersson (refs. 7 to 9) and Bajpai et al. (ref. 10) proposed wear models for spur 

and helical gears, and the focus was to determine P and s. The tooth contact pressures P were computed 

in these models using either simplified Hertzian contact (refs. 7 through 9) or boundary element (ref. 10) 

formulations under quasi-static conditions. Sliding distance s calculations were determined from gearing 

kinematics, and Archard’s wear model (ref. 11) was used with an empirical wear coefficient to compute 

the surface wear distribution. 

Perhaps the most significant shortcoming of these models is that they consider wear depth to be a 

function of only two parameters, contact pressure, P and sliding distance, s. All other influences, such as 

surface material, surface roughness and lubrication at the contact interface, are all accounted for by the 

wear coefficient k (ref. 12). When all of the parameters including lubricant type, temperature, flow rate, 

gear material composition, surface topography, and surface hardness are consistent, then it is possible to 

define k using a small number of controlled experiments (ref. 10). However, if all of the stated properties 

are not consistent, then determining a wear rate coefficient might become a challenging task. In addition, 

the influence of such parameters on wear cannot be described by these models. 

The main objective of this study is to investigate the influence of lubricant viscosity and additives on 

the wear rate of spur gear pairs. It is the intention of this study to demonstrate experimentally that the 

lubricant viscosity influences the wear characteristics of gears significantly. The gear specimens of a 

comprehensive gear durability test program, using seven lubricants covering a range of viscosity, are 

examined to measure gear tooth surface wear. Wear rates are related to the lubrication conditions (lambda 

ratios) and the resultant contact fatigue lives of the same specimens. This study is provided to help guide 

future efforts such that gear wear could be modeled in a more general manner including direct 

consideration of the lubricant properties and lubrication conditions. 

2. Test Methodology 

2.1 Background 

The gear experiments of this study were conducted by Townsend and Shimski (ref. 13). The purpose 

of the experiments was to investigate the influence of lubricant viscosity and additives on gear surface 

fatigue lives. The comprehensive test program demonstrated and quantified the increase in gear surface 

fatigue life owing to increased lubricant viscosity. Test specimens and test records were available for 

further inspection and analysis for the present study of gear wear. The test apparatus, specimens, 

lubricants, and procedures were reported by Townsend and Shimski (ref. 13). The information needed to 

document the present research is repeated herein for completeness. 

2.2 Test Apparatus 

The gear fatigue tests were performed in the NASA Glenn Research Center’s gear test apparatus. The 

test rig is shown in figure 1 and described in reference 14. The rig uses the four-square principle of 

applying test loads, and thus the input drive only needs to overcome the frictional losses in the system. 

The test rig is belt driven by a variable speed electric motor. All tests reported herein were conducted at a 

constant speed of 10,000 rpm. Four tests rigs were used and operated 24 hours a day to provide for the 

large numbers of test cycles required for surface fatigue testing. 
NASA/TM—2005-213956 3
NASA/TM—2005-213956 4

The loads on the test gears are provided using hydraulic pressure. A schematic of the apparatus is 

shown in figure 1(b). Oil pressure and leakage replacement flow is supplied to the load vanes through a 

shaft seal. As the oil pressure is increased on the load vanes located inside one of the slave gears, torque is 

applied to its shaft. This torque is transmitted through the test gears and back to the slave gears. In this 

way, power is circulated, and the desired load and corresponding stress level on the test gear teeth may be 

obtained by adjusting the hydraulic pressure. The two identical test gears may be started under no load, 

and the load can then be applied gradually. In order to enable testing at the desired contact stress, the 

gears are tested with the faces offset as shown in figure 1. By utilizing the offset testing arrangement for 

both faces of the gear teeth, a total of four surface fatigue tests can be run for each pair of gears. 

Separate lubrication systems are provided for the test and slave gears. The two lubrication systems are 

separated at the gearbox shafts by pressurized labyrinth seals, with nitrogen as the seal gas. Inlet and 

outlet oil temperatures were continuously monitored. Cooled lubricant was supplied to the inlet of the 

gear mesh at 0.8 liter/min (0.2 gal/min) and 320±7 K (116±13 °F). The lubricant outlet temperature was 

recorded and observed to have been maintained at 348±4.5 K (166±8 °F). The lubricant was circulated 

through a 5-μm- (200-μin.-) nominal fiberglass filter to remove wear particles. For each test, 3.8 liter 

(1 gal) of lubricant was used. 

The purpose of tests by Townsend and Shimski (ref. 13) was to measure gear surface fatigue lives. A 

vibration transducer mounted on the gearbox was used to automatically stop the test rig when gear surface 

fatigue damage occurred. Surface fatigue damage caused an increase in the broad-band (root-meansquared magnitude) acceleration. The gearbox is also automatically stopped if there is a loss of oil flow to 

either the slave gearbox or the test gears, if the test gear oil overheats, or if there is a loss of seal gas 

pressurization. 

2.3 Test Specimens 

The test gears used for this work were manufactured from a single heat of consumable-electrode 

vacuum-melted (CVM) AISI 9310 steel. The gears were manufactured in two lots to the same 

specifications. The nominal chemical composition of the AISI 9310 material is given in table 1. The gears 

were case carburized and heat treated according to table 2. The nominal properties of the carburized gears 

were a case hardness of Rockwell C60, a case depth of 0.97 mm (0.038 in.), and a core hardness of 

Rockwell C38. The measured hardness profile of the gears is provided in figure 2. From figure 2, the 

hardness profile is considered to have not been changed significantly with running. Examined 

microstructure and typical residual stress profiles for such test gears have been reported (refs. 14 and 15). 

TABLE 1.—NOMINAL CHEMICAL COMPOSITION 

OF AISI 9310 GEAR MATERIAL 

Element Weight % 

Carbon 0.10 

Nickel 3.22 

Chromium 1.21 

Molybdenum 0.12 

Copper 0.13 

Manganese 0.63 

Silicon 0.27 

Sulfur 0.005 

Phosphorous 0.005 

Iron balance 
NASA/TM—2005-213956 5

TABLE 2.—HEAT TREATMENT FOR AISI 9310 GEARS 

Step Process Temperature Time, hr 

 K oF 

1 Preheat in air ------ ------ ------ 

2 Carburize 1,172 1,650 8 

3 Air cool to room temperature ------ ------ ------ 

4 Copper plate all over ------ ------ ------ 

5 Reheat 922 1,200 2.5 

6 Air cool to room temperature ------ ------ ------ 

7 Austentize 1,117 1,550 2.5 

8 Oil quench ------ ------ ------ 

9 Subzero cool 180 –120 3.5 

10 Double temper 450 350 2 each 

11 Finish grind ------ ------ ------ 

12 Stress relieve 450 350 2 

The dimensions for the test gears are given in table 3. The gear pitch diameter was 89 mm (3.5 in.,) 

and the tooth form was a 20° involute profile modified to provide a tip relief of 0.013 mm (0.0005 in.) 

starting at the highest point of single tooth contact. The gears have zero lead crowning but do have a 

nominal 0.13-mm- (0.005-in.-) radius edge break at the tips and sides of the teeth. The gear tooth surface 

finish after final grinding was specified as a maximum of 0.406 μm (16 μin.) rms. Tolerances for the gear 

geometries were specified to meet AGMA (American Gear Manufacturers Association) quality level 

class 12. 
NASA/TM—2005-213956 6

TABLE 3.—SPUR TEST GEAR DESIGN PARAMETERS 

GEAR TOLERANCES ARE PER AGMA CLASS 12 

Number of teeth 28 

Module, mm 3.175 

Diametral pitch (1/in.) 8 

Circular pitch, mm (in.) 9.975 (0.3927) 

Whole depth, mm (in.) 7.62 (0.300) 

Addendum, mm (in.) 3.18 (.125) 

Chordal tooth thickness ref. mm (in.) 4.85 (0.191) 

Pressure angle, deg. 20 

Pitch diameter, mm (in.) 88.90 (3.500) 

Outside diameter, mm (in.) 95.25 (3.750) 

Root fillet, mm (in.) 1.02 to 1.52 (0.04 to 0.06) 

Measurement over pins, mm (in.) 96.03 to 96.30 (3.7807 to 3.7915) 

Pin diameter, mm (in.) 5.49 (0.216) 

Backlash reference, mm (in.) 0.254 (0.010) 

Tip relief, mm (in.) 0.010 to 0.015 (0.0004 to 0.0006) 

2.4 Test Procedure 

The test gears were cleaned to remove the preservative and assembled on the test rig. The test gears 

were run with the tooth faces offset by 3.3 mm (0.130 in.). All tests were run-in at a load (tangent to the 

pitch circle) per unit face width of 123 N/mm (700 lb/in.) for one hour. The load was then increased to the 

test load of 580 N/mm (3300 lb/in.), which resulted in a 1.7 GPa (250 ksi) pitch-line maximum Hertz 

stress. The Hertz stress just stated is an idealized stress value assuming static equilibrium, perfectly 

smooth surfaces, and an even load distribution across a 2.79 mm (0.110 in.) line contact (the line length is 

less than the face width allowing for the face offset and the radius edge break). Typical dynamic tooth 

forces using the same rigs and gears of the same specification have been measured (ref. 15), and the 

results are provided in figure 3. The tooth forces reported in figure 3 are the dynamic forces normal to the 

tooth surface (or in other words tangent to the base circle) for a nominal pitch-line test load intensity of 

580 N/mm (3,300 lb/in.). The static contact force (tangent to the base circle) used for stress calculations 

for such test load intensity was 1,720 N (387 lb). This value for the contact force is the value required for 

static torque equilibrium at the pitch-point, and it is somewhat less than the measured typical dynamic 

forces. 

The fatigue tests ran continuously and unattended (24 hr/day). The test was stopped when the rootmean-squared acceleration level of the gearbox housing exceeded a limit. The gears were tested at 

10,000 rpm, which gave a pitch-line velocity of 46.5 m/s (9,154 ft/min). If a gear pair operated for more 

than 500 hours (corresponding to 300 million stress cycles) without fatigue failure, the test was 

suspended. 

The pitch line elastohydrodynamic (EHD) film thickness was calculated using the rectangular conjunction 

formula of Dowson and Higginson (ref. 16). For calculating the film thickness, it was assumed that the 

gear temperature was equal to the oil outlet temperature. The results of film thickness calculations and the 

values used for absolute viscosity and the pressure-viscosity coefficient are provided in table 4. The 

lubricant properties used for EHD calculations are extrapolations using measured values for kinematic 

viscosity and typical values for specific gravity and pressure-viscosity coefficients at the test temperature 

(table 4). Also provided in table 4 are specific film thickness (lambda ratio) values, calculated as the 

minimum film thickness divided by the initial specified composite surface roughness. 
NASA/TM—2005-213956 7

TABLE 4.—LUBRICANT PROPERTIES 

Lubricant 

Parameter A B C D E G H 

Kinematic viscosity, (cSt) 

at 311 K (100 °F) 

at 372 K (210 °F) 

21.0 

4.31 

29.78 

5.39 

12.2 

3.2 

27.6 

5.18 

34.4 

7.37 

52.4 

8.98 

28.4 

5.37 

Flash point, K (°F) 

Pour point, K (°F) 

516 (470) 

200 (–100) 

539 (510) 

217 (–70) 

489 (420) 

----------- 

544 (520) 

211(–80) 

519 (475) 

214 (–75) 

561 (550)

213 (–76) 

525 (485) 

217 (–70) 

Specific gravity 

at 289 k (60 °F) 

1.00 1.00 ----------- 0.995 0.947 0.986 0.990 

Total acid number 

(tan) Mg Koh/g oil 

0.07 0.03 0.15 0.40 0.06 1.01 0.09 

Absolute viscosity, (N-s/m2) 

at 348 K (167 °F) * 

0.014 0.018 0.010 0.017 0.022 0.028 0.017 

Pressure-viscosity 

coefficient, (m2

/N) * 

9.×10–9 10.5×10–9 7.5×10–9 11.×10–9 12.×10–9 11.×10–9 11.×10–9

Film thickness, μm (μin) 

Lambda ratio ** 

0.40 (16) 

0.69 

0.52 (20) 

0.90 

0.28 (11) 

0.49 

0.51 (20) 

0.89 

0.65 (25) 

1.12 

0.73 (29)

1.26 

0.51 (20) 

0.89 

Specification None*** MIL-L-23699 MIL-L-7808J DOD-L-85734 DERD-2478 None DOD-L-85734 

* data used for film thickness calculations 

** Lambda ratio = calculated minimum film thickness/initial composite surface roughness 

*** basestock oil 

2.5 Measurement of Surface Profiles 

A gear coordinate measurement machine is used in this study to quantify the wear depths. Figure 4 

shows the inspection machine used in this study while inspecting one of the test specimens. Two types of 

inspections were performed here. The first type of inspection used was a standard inspection as used by 
NASA/TM—2005-213956 8

the gear industry. These inspections include the measurements of lead traces (from one side to the other at 

given constant radii) and involute traces (from the root to the tip of a tooth at given constant lead 

locations). In figure 5, such inspections of a new test specimen are shown. Here, four teeth at nearly 

90 degrees spacing were inspected. For each tooth inspected, two involute traces (traces A and B at onethird lead locations) and two lead traces (trace A in the addendum and trace B in the dedendum region) 

are shown in figure 5. It is evident from this figure that the profiles were machined very precisely with 

straight lead traces and a designed amount of tip relief. Figure 6 shows the lead charts for the teeth of a 

specimen at the end of its test. Since the actual contact occurred at the left portion of the face width only 

(due to face off-set described earlier), the section to the right represents the unworn original tooth surface 

and the large step down to the left represents wear. It is obvious here that the wear magnitudes are rather 

significant and can be quantified by comparing the worn surface location (left) to the unworn surface 

location (right). It is also clear, and typical, that the wear amount is much larger in dedendum region 

(traces B) than those in addendum region (traces A). 

While standard inspections are useful to visualize the surface wear in any given direction (lead or 

involute), a large number of such traces are required to determine the maximum wear depth. For this 

purpose, the three-dimensional (3-D) topographical gear inspection method developed by Bajpai, et al. 

(ref. 10) was employed. When this method was applied to all the teeth of a test specimen, it was 

commonly observed that the maximum wear depth varies from tooth to tooth. In figure 7, a worn 

specimen that has a significant variation of maximum wear depths from tooth to tooth is shown. Here, a 

sinusoidal distribution of wear is evident. The maximum wear amount on tooth 27 is nearly zero while 

tooth 13 has nearly 160 μm maximum wear. Figure 8 shows the 3-D topographical inspections of four 

teeth of the same gear. Most of the gears had a more uniform wear distribution than shown by this 

extreme example illustrated in figures 7 and 8. Measuring the maximum wear amounts on all the teeth on 

all gears was considered as excessively time consuming and hence not practical. In order to be able to 

represent the wear amount of a given gear by a single number, an average maximum wear parameter was 

defined as ( ) 1 8 15 22 4

1 h = h + h + h + h . In other words, the wear values of four equally spaced teeth (1, 8, 
NASA/TM—2005-213956 9

15, and 22) were used to define h. From the average maximum wear parameter h, the wear rate was 

defined as h = h /C where C is the recorded number of revolutions of the gear pair in millions (or 

millions of meshing cycles). For the majority of specimens, the value of C is equal to the measured 

surface fatigue life for the particular gear pair. For some specimens, C is the number of cycles completed 

without surface fatigue (the fatigue testing procedure made use of a nominal 300 million cycle limit to 

reduce the total test time for the fatigue life evaluations). 
NASA/TM—2005-213956 10
NASA/TM—2005-213956 11

3. Test Lubricants 

The lubricants used had been selected to study the effects of lubricants with similar base stocks but 

differing viscosities on the surface fatigue lives of AISI 9310 spur gears. Fatigue data were reported for 

seven lubricants (ref. 13) that were identified as lubricants A through G. For tests using lubricant F, there 

were insufficient numbers of tested gears available for wear measurements, and so lubricant F was not 

included as part of the present study. Subsequent to the publication of reference 13, Townsend and 

Shimski conducted additional tests using other lubricants. Although these fatigue data have not yet been 

published, the test results, records, and some of the specimens were available to the present investigators. 

For the present wear study, gear specimens tested using a lubricant designated as H in this article were 

analyzed for wear. 

Properties of the lubricants studied are provided in table 4, and descriptions of the lubricants follow. 

Lubricant A is an unformulated base stock lubricant with no additives, and it has a viscosity in between 

that required for the MIL-L-7808J and MIL-L-23699 specifications. Lubricant B is a 5 cSt lubricant 

meeting the MIL-L-23699 specification, and it has a small amount of boundary lubrication additive. 

Lubricant C is a 3 cSt lubricant meeting the MIL-L-7808J specification. Lubricant C has the lowest 

viscosity of all the lubricants included in the study, and it has a proprietary extreme pressure additive 

package. Lubricants D and H are lubricants developed for helicopter gearboxes, and both lubricants meet 

the DOD-L-85734 specification. Lubricants D and H are 5 cSt lubricants with extreme pressure additive 

packages, and these two lubricants were obtained from two different manufacturers. Lubricant E is a 

7.5 cSt lubricant with an extreme pressure additive, and this lubricant meets the development 
NASA/TM—2005-213956 12

specification DERD-2487. Lubricant G is a 9 cSt base stock industrial grade lubricant. Six of the seven 

lubricants included in this study could be classified as synthetic polyol-ester base stock lubricants. 

Lubricant E is a polyalkylene-glycol base stock with a small amount of boundary lubricant additive. 

4. Results and Discussion 

4.1 Amounts and Descriptions of Wear 

A total of 112 gear specimens were inspected using a gear coordinate measuring machine to evaluate 

the average wear depth and wear rate using the methodology described in section 2.5. The number of 

samples for each lubricant test population was dependent on the availability of the test specimens. Gears 

tested with lubricant C had the lowest number of samples, N = 8, and gears tested with lubricant H had 

the largest number of samples, N = 23. Four teeth on each gear specimen were inspected (a total of 

448 teeth), and wear amounts were averaged to determine the average wear rate for each gear. Table 5 

summarizes the measured wear amounts and wear rates (mean and standard deviation values) and the 

sample sizes for each lubricant. The amount of scatter of the wear data from gear specimen to specimen is 

quite significant. The distribution of wear rates is illustrated in figure 9. From table 5 and figure 9, it is 

clear that lubricant C resulted in the most severe wear rates while lubricant G performed the best. Other 

lubricants resulted in levels of wear between these extremes. 
NASA/TM—2005-213956 13

TABLE 5.—WEAR AMOUNT, h AND WEAR RATE, h PARAMETERS FOR THE SEVEN TEST LUBRICANTS. 

Wear amounts, h

(μm) 

Wear rates, h 

Lubricant (μm/million cycles) 

Mean Stnd. dev. Mean Stnd. dev. 

Sample size 

A 66 19 1.7 1.2 13 

B 73 55 1.4 1.8 13 

C 79 62 2.6 2.2 8 

D 49 38 1.2 1.6 20 

E 55 30 0.46 0.3 17 

G 8.1 13 0.11 0.2 18 

H 66 70 0.61 0.6 23 

To help document and characterize the wear, photos of worn gear teeth, one for each lubricant tested, 

are provided in figure 10. In general, the wear can be described as a mild, polishing wear over most of the 

tooth profile. Near the start and end of contact, there exists some evidence of abrasive and/or light 

adhesive wear (scoring-like marks). In general, the scoring-like marks that appeared at the positions of 

high sliding tended to be less severe for lubricants with higher viscosities. It is evident that lesser wear 

amounts occurred near the pitch line where sliding velocities are small as compared to the roots and tips 

of the teeth. The worn surfaces in some cases were remarkable in that worn and very smooth regions can 

be found a slight distance from the pitch point while the grinding patterns were still visible at the 
NASA/TM—2005-213956 14

pitch point. The photograph for the tooth tested with lubricant G demonstrates that for this lubricant and 

for the chosen test conditions, the working surfaces were well protected with few direct asperity contacts 

and, for practical purposes, nearly zero wear. 

The maximum wear depths invariably occurred in the dedendum region of the teeth, that is somewhat 

below the pitch-line. In the regions of maximum wear depth, the worn surfaces have a worked and 

polished appearance. Any scratching marks in the direction of sliding that were present in this region of 

maximum wear can be characterized as minor scratching consistent with abrasive wear. There was no 

evidence of destructive scoring (scuffing), spalling, pitting, nor micropitting (grey-staining) failures on 

the teeth selected for wear measurements. Some teeth on the gears had surface fatigue damage (the intent 

of the original study (ref. 13)), but care was taken to select teeth without such damage for measurements 

of wear. Illustrations of teeth with surface fatigue damage for these tests were provided by Townsend and 

Shimski (ref. 13). 

4.2 Influence of Lubricant Type on Gear Wear 

To characterize differences in wear owing to different lubricants, wear rates are plotted as a function 

of key lubrication parameters. Figure 11 shows h as a function of the absolute viscosity of the lubricants 

at the testing temperature as listed in table 4. It is clear from this figure that the wear rates are an inverse 

function of the viscosity of the lubricant. Lubricant C has the lowest viscosity (0.010 N-s/m2

) resulting in 

the most severe wear rate of nearly 2.6 μm per million cycles while lubricant G with the highest viscosity 

value (0.028 N-s/m2

) resulted in the lowest wear rate of about 0.11 μm per million cycles. The other 

lubricants generally are ordered in sequence relative to their viscosity values. From figure 11, the 

lubricants B, D, and H have differing wear rates but similar viscosity values. It is perhaps significant that 

lubricant B meets the specification MIL-L-23699 (turbine engine lubricants) while lubricants D and H 

meet the specification DOD-L-85734 (helicopter transmission lubricants). One might expect lubricants D 

and H developed for gearing to perform better than lubricant B in a gear test. This scatter in the wear 

results for lubricant B, D, and H (in spite of nearly equal viscosities) highlights that lubricant composition 

and additive packages along with viscosity strongly influence the lubricant’s capability for wear 

protection. 
NASA/TM—2005-213956 15

A very similar behavior is observed when h is plotted as a function of the lambda ratio that is 

defined as the ratio of central film thickness (determined by using the smooth surface EHL formulas of 

Dowson and Higginson (ref. 16)) to the initial specified composite surface roughness of mating gear 

surfaces. The specified root-mean-square roughness of 0.4 μm results in a composite roughness of about 

0.57 μm. In figure 12, the relative ranking of the test lubricants for their wear performance remain 

inversely proportional to the lambda ratio (the same order as fig. 11). The lubricant C having the lowest 

viscosity results in a very thin film and a very low lambda ratio (about 0.49) as listed in table 4. As a 

result, mixed lubrication conditions with significant asperity interactions occurred along with extensive 

wear. The opposite is true for lubricant G that allows a relatively large lambda ratio of 1.26 minimizing 

the amount of surface wear. Other lubricants are ordered between these two extremes depending on the 

lambda ratio. 

4.2 Wear versus Contact Fatigue Life 

The gear fatigue experiments that were conducted by Townsend and Shimski (ref. 13) established and 

quantified the influence of lubricant viscosity on gear surface fatigue lives. The surface fatigue life results 

are summarized in table 6. The table is sorted by the measured 10 and 50 percent lives. These percentile 

life estimates were determined by modeling the life dispersions as Weibull distributions and employing 

the regression methods of Johnson (ref. 17) to determine the values for the Weibull slope and scale 

parameters. In figure 13, estimated 10- and 50-percent surface fatigue lives corresponding to each 

lubricant are plotted against the viscosity of the lubricant. The results demonstrate that, in general, the 

greater the viscosity of the lubricant the longer the surface fatigue lives. The solid lines in figure 13 

represents exponential relationships observed as linear lines since the surface fatigue lives are displayed 

using a log scale. 
NASA/TM—2005-213956 16

TABLE 6.—SURFACE FATIGUE TEST RESULTS (REF. 13) 

Gear System lives, millions 

of cycles 

Lubricant 

code 

Lubricant basestock 

10 percent 50 percent 

Weibull 

slope 

Failure 

index 

Lubricant viscosity 

(cSt) at 372 °K 

(210 °F) 

A polyol-ester 5.1 20 1.4 30/30 4.3 

C polyol-ester 5.7 21 1.5 20/20 3.2 

D polyol-ester 12 51 1.3 17/20 5.2 

B polyol-ester 12 76 1.0 20/20 5.4 

H polyol-ester 35 79 1.6 19/24 5.4 

E polyalkylene-glycol 47 152 1.6 15/19 7.4 

G polyol-ester 103 568 1.1 5/18 9.0 
NASA/TM—2005-213956 17

From figures 13 and 14, it is evident that the lubricant viscosity has a similar trend for both surface 

fatigue life and wear. For the lubricants tested here, the larger the viscosity of the lubricant the longer the 

fatigue lives and smaller the wear amounts. In figure 14, the fatigue lives and wear rates for each lubricant 

group are plotted to show the correlation. The relationship between the wear rates and surface fatigue 

lives is exponential. This correlation highlights the dominant role of the lubricant viscosity. The 

relationship depicted in figure 14 shows that a lubricant that functioned well in terms of surface fatigue 

life also tended to function well in termed of wear. Likewise, it can be stated that very low wear rates 

indicates a relatively favorable lubrication condition that also tended to promote long surface fatigue life. 

Lastly, lubricants with nearly equal viscosity but differing additives offer differing levels of protection for 

wear and surface fatigue 

5. Conclusion 

In this study, the influence of lubricant viscosity and additives on the wear rate of spur gear pairs was 

investigated experimentally. The gear specimens from a comprehensive gear durability test program that 

includes seven different lubricants were inspected to demonstrate the influence of the lubrication 

condition on gear tooth surface wear. The results indicate that the wear rates are strongly related to the 

viscosity of the lubricant. Lubricants with larger viscosity result in larger lambda ratios and lower wear 

rates. A similar strong influence of the lubricant viscosity was previously observed for surface fatigue 

lives as well. An exponential relationship between the surface fatigue lives and the average wear rates 

was found. The data suggest that viscosity plays a dominant role. There were also considerable 

differences in wear amounts for three lubricants with differing additive packages but similar compositions 

and viscosities. 
NASA/TM—2005-213956 18

References 

1. Choy, F.K., Polyshchuk, V. and Zakrajsek, J.J., Handschuh, R.F. and Townsend, D.P., 1996, 

“Analysis of the Effects of Surface Pitting and Wear on the Vibration of a Gear Transmission 

System,” Tribology International, 29, 77–83. 

2. Mackaldener, M. Flodin, A. and Andersson, S., 2001, “Robust Noise Characteristics of Gears Due to 

their Applications, Manufacturing Errors and Wear,” JSME International Conference on Motion and 

Power Transmission, MPT 2001, Fukuoka, Japan, 21–26. 

3. Kuang, J.H. and Lin, A.D., 2001, “The Effect of Tooth Wear on the Vibration Spectrum of a Spur 

Gear Pair,” ASME Journal of Vibration and Acoustics, 123, 311–317. 

4. Chen, Y. and Matubara, M., 2001, “Effect of Automatic Transmission Fluid on Pitting Fatigue 

Strength of Carburized Gears,” JSME International Conference on Motion and Power Transmission, 

MPT 2001, Fukuoka, Japan, 151–156. 

5. Cioc, C., Cioc, S., Kahraman, A. and Keith, T.G., 2002, “A Deterministic Elastohydrodynamic 

Lubrication Model of High-Speed Transmission Components,” Tribology Transactions, 45, 556–562. 

6. Shifeng, W. and Cheng, H.S., 1993, “Sliding Wear Calculation in Spur Gears,” Journal of Tribology, 

115, 493–503. 

7. Flodin, A. and Andersson, S., 1997, “Simulation of Mild Wear in Spur Gears,” Wear, 207, 123–128. 

8. Flodin, A. and Andersson, S., 2000, “Simulation of Mild Wear in Helical Gears,” Wear, 241, 

123–128. 

9. Flodin, A. and Andersson, S., 2001, “A Simplified Model for Wear Prediction in Helical Gears,” 

Wear, 249, 285–292. 

10. Bajpai, P., Kahraman, A., and Anderson, N., 2003, “Development of Surface Wear Model for Helical 

Gear Pairs,” In review, ASME Journal of Tribology. 

11. Archard, J.F., 1953, “Contact of Rubbing Flat Surfaces,” Journal of Applied Physics, 24, 981–988. 

12. Challen, J.M. and Oxley P.L.B., 1986, “Prediction of Archard’s Wear Coefficient for Sliding Metallic 

Sliding Friction Assuming Low Cycle Fatigue Wear Mechanism,” Wear, 111, 275–288. 

13. Townsend, D.P., and Shimski, J., 1994, “Evaluation of the EHL Film Thickness and Extreme 

Pressure Additives on Gear Surface Fatigue,” NASA TM-106663. 

14. Townsend, D.P., Chevalier, J.L., and Zaretsky, E.V., 1973, “Pitting Fatigue Characteristics of AISI 

M–50 and Super Nitralloy Spur Gears,” NASA TN D–7261. 

15. Krantz, T.L., 2002, “The Influence of Roughness on Gear Surface Fatigue,” Ph.D. Thesis, Case 

Western Reserve University, Cleveland, Ohio. 

16. Dowson, D. and Higginson, G., 1966, Elasto-Hydrodynamic Lubrication, Pergamon Press. 

17. Johnson, L., 1964, The Statistical Treatment of Fatigue Experiments, Elsevier, New York, NY. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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NASA TM—2005-213956

ARL–TR–3126

E–15272

24

An Experimental Investigation of the Influence of the Lubricant Viscosity

and Additives on Gear Wear

Timothy L. Krantz and Ahmet Kahraman

Gear; Wear; Lubrication; Elastodynamics

Unclassified -Unlimited

Subject Category: 37

WBS–22–714–09–16

1L161102AF20

Timothy L. Krantz, U.S. Army Research Laboratory, NASA Glenn Research Center; and Ahmet Kahraman, The Ohio

State University, 190 N. Oval Mall, Columbus, Ohio 43210. Responsible person, Timothy L. Krantz, organization

code RSM, 216–433–3580.

The influence of lubricant viscosity and additives on the average wear rate of spur gear pairs was investigated

experimentally. The gear specimens of a comprehensive gear durability test program that made use of seven lubricants

covering a range of viscosities were examined to measure gear tooth wear. The measured wear was related to the

as-manufactured surface roughness, the elastohydrodynamic film thickness, and the experimentally determined contact

fatigue lives of the same specimens. In general, the wear rate was found to be inversely proportional to the viscosity

of the lubricant and to the lambda ratio (also sometimes called the specific film thickness). The data also show an

exponential trend between the average wear rates and the surface fatigue lives. Lubricants with similar viscosities

but differing additives and compositions had somewhat differing gear surface fatigue lives and wear rates.