A New High-Speed, High-Cycle, Gear-Tooth

Bending Fatigue Test Capability

NASA/TM—2011-217039

June 2011

David B. Stringer, Brian D. Dykas, and Kelsen E. LaBerge

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

Andrew J. Zakrajsek

Purdue University, West Lafayette, Indiana

Robert F. Handschuh

Glenn Research Center, Cleveland, Ohio

ARL–TR–5506

U.S. ARMY

RESEARCH LABORATORY
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A New High-Speed, High-Cycle, Gear-Tooth

Bending Fatigue Test Capability

NASA/TM—2011-217039

June 2011

David B. Stringer, Brian D. Dykas, and Kelsen E. LaBerge

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

Andrew J. Zakrajsek

Purdue University, West Lafayette, Indiana

Robert F. Handschuh

Glenn Research Center, Cleveland, Ohio

ARL–TR–5506

U.S. ARMY

RESEARCH LABORATORY

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

67th Annual Forum and Technology Display (Forum 67)

sponsored by the American Helicopter Society

Virginia Beach, Virginia, May 3–5, 2011
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Hanover, MD 21076–1320

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only. Their usage does not constitute an official endorsement, 

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Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-217039 1

A New High-Speed, High-Cycle, Gear-Tooth

Bending Fatigue Test Capability

David B. Stringer, Brian D. Dykas, and Kelsen E. LaBerge

U.S. Army Research Laboratory

Glenn Research Center

Cleveland, Ohio 44135

Andrew J. Zakrajsek

Purdue University

West Lafayette, Indiana 47907

Robert F. Handschuh

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

A new high-speed test capability for determining the highcycle bending-fatigue characteristics of gear teeth has been 

developed. Experiments were performed in the test facility 

using a standard spur gear test specimens designed for use in 

NASA Glenn’s drive system test facilities. These tests varied 

in load condition and cycle-rate. The cycle-rate varied from 50 

to 1000 Hz. The loads varied from high-stress, low-cycle loads 

to near infinite life conditions. Over 100 tests were conducted 

using AISI 9310 steel spur gear specimen. These results were 

then compared to previous data in the literature for correlation.

Additionally, a cycle-rate sensitivity analysis was conducted 

by grouping the results according to cycle-rate and comparing 

the data sets. Methods used to study and verify load-path and 

facility dynamics are also discussed.

Introduction

The helicopter community’s shift toward a Condition-Based 

Maintenance (CBM) strategy seeks to extend the useful life of 

gears and bearings in order to increase the overall affordability 

of the aircraft. Fatigue failures, to include gear-tooth bending 

fatigue, take on considerable importance as the number of 

cycles increases. Fatigue data historically has only extended to 

the 106 to 107 cycle range. With the emphasis on longer useful 

life, gear technology continues to reach further into the infinite 

life area of the s-n curve, a region that is still largely unknown.

The time required to acquire data in this region has been 

considerable and to date, out of reach. The required enabler is 

a high-speed test apparatus that will allow the accumulation of 

108 to 109 cycles in a reasonable amount of time. The only 

way to repeatedly achieve these high-cycle accumulations is to 

develop and validate a high-speed test rig that can operate at 

or near 1000 Hz. At this cycle rate, a facility can achieve 108

cycles in 27.8 hr, and 109 cycles in 11.6 days.

Background

The fatigue life of gears has been studied extensively over 

the past five decades (Refs. 1 to 14). Gear-tooth bending 

fatigue is a key characteristic of the gear itself and varies with 

geometry, material, residual stress, surface finish, and 

hardness, among other variables. It is a highly variable and 

stochastic failure property. The primary goal of fatigue testing 

is to optimize gear design by studying the effects of these 

variables on the fatigue characteristics of the gear. The Society 

of Automotive Engineers has developed a standard for 

conducting single gear-tooth bending fatigue experiments 

(Ref. 15), with testing established at low-frequency cycle rates 

of 10 to 20 Hz.

Many tooth-bending test facilities have been established 

around the world (Refs. 16 to 19). However, none of these 

existing facilities has the capability to achieve the high cycle 

rates required for infinite-life testing. Furthermore, most of 

these test facilities require the removal of gear teeth for 

mounting in the test apparatus. Therefore, after crack 

initiation, specimens are unusable in other rotating mesh test 

facilities. In many cases, it might be desirable to operate the 

failed specimen in another test apparatus in order to 

characterize post-failure gear performance in support of health 

or vibration monitoring initiatives. The destructive removal of 

specimen gear teeth for use in bending fatigue facilities 

prohibits such a capability. 

Apparatus

NASA Glenn Research Center and the Army Research 

Laboratory (ARL) teamed together to develop the high-speed 

Single Gear-Tooth Bending Test Facility. The centerpiece of 

the facility is the 1000 Hz High-Cycle Fatigue Test System 

produced by MTS Systems Corporation. The servo-hydraulic 

system is capable of maintaining high waveform fidelity at 
NASA/TM—2011-217039 2

high frequency. It has a static load capacity of ±5500 lb force 

and maximum displacement capability of ±1 in. at an 

operating frequency of 1000 Hz, the gear tooth is experiencing 

the bending equivalent to a gear rotating at a speed of

60,000 rpm.

A layout of the test apparatus is provided in Figure 1. A 

loading arm enters the top of the gearbox through a bushing 

and rests on the test gear-tooth at the highest point of singletooth contact. The oscillating load applicator of the load frame 

contacts the loading arm and transmits the load to the test 

tooth. A reaction tooth rests on an anvil, maintaining the gear 

in a stationary position. The test tooth and reaction tooth are 

separated by an intermediate gear-tooth. The reaction anvil is 

connected to the reaction arm, which runs through the floor of 

the gearbox and transfers the load to a load cell. Though the 

gear itself is keyed, it is mounted on a keyless shaft such that 

all of the reaction force is provided by the reaction tooth. The 

reaction tooth rests on the anvil contacting at the root of the 

tooth to ensure that the test tooth experiences higher bending 

stress than the reaction tooth. During testing, the applicator, 

loading arm, test specimen, and reaction interfaces are always 

in contact with a small nominal load in order to maintain the 

test and reaction teeth in constant compression and prevent 

impact of the loading arm on the test tooth. Instrumentation 

measures load, displacement, and acceleration.

A circulating oil bath of MIL-PRF 23699 aviation turbine 

oil is contained in the gearbox and conditions the test 

specimen. The bath allows the operator to control the 

temperature of the test condition through an oil heater. The 

temperature ranges from approximately 50 to 300 °F, although 

this functionality has yet to be fully implemented. 

The spur-gear test specimens for this study are manufactured 

from AISI 9310 steel. The specimen design has been 

documented and used extensively in many NASA/ARL studies 

over the past four decades for a variety of experiments oriented 

toward bending fatigue, contact fatigue, wear, crack 

propagation, and health monitoring (Refs. 5, 20 to 21). The 

gears are case-carburized and heat-treated, with a case hardness 

of Rockwell C60, a case depth of 0.038 in., and a core hardness 

of Rockwell C38. Depending upon the specimen, gear 

tolerances meet the standards for AGMA Quality Class 11 to 

Class 13 gears. Table 1 lists the design parameters of the 

specimens.

TABLE 1.—TEST SPECIMEN DESIGN PARAMETERS

Number of teeth 28

Diametral pitch (1/in.) 8

Circular pitch (in.) 0.3927

Whole depth (in.) 0.3000

Addendum (in.) 0.125

Chordal tooth thickness ref (in.) 0.191

Pressure angle (deg) 20

Pitch diameter (in.) 3.500

Outside diameter (in.) 3.750

Root fillet (in.) 0.040 to 0.060

Measurement over pins (in.) 3.7867 to 3.7915

Pin diameter (in.) 0.216

Backlash reference (in.) 0.010

Tip relief (in.) 0.010 to 0.015

Each specimen can be used for multiple tests. One bending 

experiment consumes four teeth. The first is the test tooth, 

followed by an intermediate gear-tooth. The third is the 

reaction tooth, followed by a second intermediate tooth. 

Continuing this pattern around the gear results in seven test 

sections per specimen. The intermediate gear-teeth are not 

tested due to the unknown bending stress interaction effects 

from the adjacent test and reaction gear-teeth.

Test Methodology

Table 2 lists the user-defined test parameters. The cycle rate 

and maximum number of cycles are user-defined. The no-load 

stroke, xo, defines the baseline displacement for measuring the 

relative displacement during a test. The no-load stroke is 

measured by applying a nominal static load of 2 lbf on the 

gear-tooth.
NASA/TM—2011-217039 3

TABLE 2.—TEST MACHINE SOFTWARE

PRE-LOAD PARAMETERS

Parameter Symbol Value

Cycle rate f User-defined

Maximum number of cycles n User-defined

No-load stroke (2 lbf) xo Measured

Minimum cyclic load Fmin 200 lbf

Maximum cyclic load Fmax User-defined

Maximum cyclic load stroke xmax Measured

Crack initiation stroke xcrack 1.02(xmax – xo)

Maximum load limit Flim 5.5 kips

Maximum stroke limit xlim User-defined

Data sample rate n/a 6144 Hz 

(maximum)

The minimum cyclic load, Fmin, is pre-defined at 200 lbf. The 

maximum cyclic load, Fmax, is the load corresponding to the 

maximum bending stress desired during the test. The minimum 

cyclic load is established to ensure that the components in the 

load path are in constant contact with adjacent components and 

to eliminate the possibility of damage to the gear teeth or failure 

due to impact between components.

The maximum cyclic load stroke, xmax, is the displacement 

corresponding to Fmax. The maximum cyclic load stroke 

determines the displacement associated with crack initiation, 

xcrack. Based upon previous work (Ref. 5), crack initiation is 

assumed to occur when the displacement increases by

2 percent of the maximum load stroke, or, in this case, a 

change of approximately 0.0002 in. The test is allowed to 

continue until the stroke increases an additional 0.0075 in., 

which is defined as the maximum stroke limit, xlim. At this 

limit, the crack is clearly visible and extends from 25 to

50 percent of the tooth thickness at the root. Upon exceeding 

this limit, the rig automatically terminates the test.

The test matrix incorporated loading conditions comparable 

to existing data points in the literature. The loads were chosen 

to avoid the infinite life region of the s-n curve and achieve 

fatigue failures in less than 106 cycles. The test matrix follows 

in Table 3. This matrix is repeated for cycle rates of 50, 100, 

200, 400, 600, 800, and 1000 Hz.

Using the raw data to determine the actual tooth loading 

conditions, the bending stress and the unit load can be 

calculated. The bending stress, σb, is calculated using the 

American Gear Manufacturer’s Association (AGMA) stress 

equation for Imperial units, provided in Equation (1). The 

AGMA parameters are defined in Table 4 (Refs. 22 and 23), 

along with the values used in this study.

b t vomsB

P W KKK KK

FJ

σ = (1)

TABLE 3.—SINGLE GEAR-TOOTH

BENDING TEST MATRIX

Tooth Nominal load,

lbf

Approximate bending

stress,

ksi

1 4015 389

2 3825 370

3 3060 296

4 2675 259

5 2485 241

6 2295 222

7 3440 333

TABLE 4.—AGMA BENDING STRESS PARAMETERS

Definition Value

Wt Tangential load cos( ) W W t = α

P Diametral pitch 8

F Face width 0.251

J AGMA geometry factor 0.36

Kv Dynamic factor 1.0

Ko Overload factor 1.0

Km Mounting factor 1.1

Ks Size factor 1.052

KB Rim thickness factor 1.0

The unit load, σunit, is defined as the original Lewis 

equation minus the Lewis form factor. It has been used as a 

“geometrically dimensionless” stress parameter for comparing 

the bending fatigue characteristics of gears of differing size 

and shape (Ref. 1). Rather than the conventional stress units of 

kips per square inch (ksi), the unit load notation is given in 

kips-per-inch per-inch (kips/in./in.). The unit load in this effort 

is used in order to provide consistent units for validating 

ARL/NASA bending fatigue results against a sizable amount 

of AISI 9310 fatigue data from the literature. The unit load 

equation is given in Equation (2), with the parameters having 

the same definition and value as in Table 4.

unit

W Pt

F

σ = (2)
NASA/TM—2011-217039 4

Results and Discussion

Figure 2 displays results representative of each fatigue 

experiment. Figure 2(a) and (b) provide the load signal and 

stroke data for operation at 100 Hz, respectively. Figure 2(b)

also displays the crack initiation and maximum displacement 

limits. To reduce data file size at lower cycle rates, data was 

acquired at periodic increments during the test. Test 

termination subsequently occurred between data acquisitions, 

resulting in an absence of recorded data where the stroke 

exceeded the limit. Figure 2(c) displays the frequency content 

of the load signal. The data at 100 Hz depicts a clean trace 

with peaks at 100 Hz and its harmonics. Figure 2(d) depicts a 

post-test image of the test specimen with the fatigue crack 

clearly visible at the base of the tooth.

The raw data at each load and cycle rate was screened for 

abnormalities in transient behavior and frequency content. The 

data different cycle rates exhibited differences in amplitudes, 

transient conditions, and frequency content in the applied load 

signals. When analyzed together, the observed differences 

create a map of preferred cycle rates for test facility operation.

For operation at 50, 100, and 200 Hz, the loading and 

displacement curves display constant amplitude and a 

negligible transient state. Although not included here, the 

frequency domains also show clean traces with defined peaks 

at the harmonic frequencies. These characteristics define good 

testing conditions.

At a test frequency of 400 Hz, the data begins to show 

different characteristics, as depicted in Figure 3. At 400 Hz, 

(Fig. 3(a)), the loading and displacement amplitudes are no 

longer constant, but slightly decreasing until failure. A larger 

transient period also exists. Additionally, frequency 

contributions from non-harmonic frequencies become 

apparent. Perhaps the most radical dynamic characteristics 
NASA/TM—2011-217039 5

occur at 600 and 800 Hz, Figures 3(b) and (c), respectively.

Figure 3(b) shows a large transient period greater than 100 sec

at 600 Hz. The frequency domain also shows significant 

frequency content symmetrically placed around 600 Hz as 

illustrated in Figure 4. The loading and displacement data for 

800 Hz, Figure 3(c), displays the most extreme characteristics.

These include significant amplitude spikes, following a 

lengthy transient period of approximately 90 sec. The 

frequency content shows corresponding variations (not 

depicted). These two conditions clearly illustrate that testing at 

600 and 800 Hz should be avoided. It is unclear whether the 

dynamic characteristics of this regime are a result of 

mechanical dynamic influence, controller algorithm 

influences, or a combination of both.

At 1000 Hz, the characteristics display similar conditions as

at 50, 100, and 200 Hz (Fig. 3(d)). The frequency domain 

does, however, show significant frequency content, although 

at a lower power distribution than at 600 and 800 Hz. The 

relatively benign effects at this cycle rate indicate that 

operation at 1000 Hz is feasible and valid.

The effects of cycle rate are best shown in Figure 5, which 

compares the cycle-rate effects on the loading conditions of 

Table 3, grouped by test tooth. Each tooth was tested at a 

different nominal bending stress, represented by the first bar in 

each series. This is the load requested by the test software. The 

remaining bars in each series are the measured bending 

stresses at each operational cycle-rate. From this comparison, 

it is apparent that facility operation between 400 and 800 Hz is 

not recommended for any loading condition.

Recommended operation at 1000 Hz is also dependent upon 

the loading condition. At bending stress loads less than

300 ksi, 1000-Hz operating conditions compare closely with 

the results from cycle-rates between 50 and 200 Hz,. Since the 

loads of interest in the high-cycle (infinite life) fatigue region 

are on the order of 150 ksi, operation within this loading 

region is not expected to cause deleterious effects at 1000 Hz.

The fatigue data collected from the test rig used in this 

study was compared against other data from two sources. The 

first is a set of low-cycle bending fatigue tests conducted at the 

NASA Glenn Research Center on a fatigue tester capable of 
NASA/TM—2011-217039 6

 

operating at a maximum cycle-rate of 50 Hz (Ref. 5). The 

second is a comprehensive fatigue study conducted by General 

Motors Corporation in the late 1960s (Ref. 1). Figure 6 depicts

how well data from the current work compares to those two 

studies.

Load-Path Verification

Due to the facility’s varied behavior at different cycle rates, 

several methods were used to ensure proper load-path between 

the load applicator and the load cell. Such tests included loadcell validation, strain-gage measurement, finite element 

modeling, and three-dimensional optical strain measurement.

After several million cycles, the loading arm showed 

fretting damage, an indicator of friction between the loading 

arm and the bushing through which the arm passes into the 

gearbox. It exhibited this damage even though the loading 

arm-bushing interface was lubricated prior to each test. This 

created a concern that the test apparatus was transferring 

energy to the load-cell via other dynamic mechanical paths, 

rather than the required loading path. Figure 7 shows the 

loading bar with minor fretting damage.

Three experiments were conducted to determine the 

bushing’s static effects on load-cell output. The first experiment 

was a static load of nominal weight, placed on the gearbox, but 

not in contact with the loading rod. The load display was 

monitored to see if the load reading changed. There were no 

noticeable load changes due to added weight on the gearbox.

The second experiment used a dial indicator to detect any 

horizontal motion of the loading arm. As the load steadily 

increased, the dial indicator was monitored for any increases in 

horizontal displacement. No significant readings were observed.

The third experiment consisted of a static loading test using 

a 500-lbf load-cell. The load-cell was placed inside the 

gearbox between the loading arm and reaction arm. Load was 

applied in approximately 50-lbf increments from 0 to 500 lbf.

The 500-lbf load-cell consistently read the same values as the 

load frame within the measurement uncertainty.
NASA/TM—2011-217039 7

Additionally, a strain-gage instrumented spur gear was 

placed in the test rig to measure root-fillet strain in the gear 

under static load and dynamic load cycling to determine if 

dynamic attenuation would reduce the root stress under given 

peak-to-peak cyclic loads measured by the load frame.

Static measurements were taken from 0 to 3000 lbf of applied 

load. A series of dynamic loading experiments was conducted at 

20, 100, 300, 600, and 1000 Hz for a cyclic load between 200 

and 1000 lbf. However, damage to the strain-gages after the first 

experiments prevented strain measurements at higher dynamic 

loads. Sample results for 20 and 1000 Hz are presented in 

Figures 8(a) and (b), respectively.

The dynamic experiments showed that high frequency 

single tooth bending experiments on spur gears are valid up to 

the 1000 Hz maximum rate tested, although the actual strain 

experienced in the gear teeth may be on the order of

25 percent lower than anticipated. For the load cycle used in 

this study, the data does not show monotonically decreasing 

root strain as the load cycle rate increases. In other words, 

attenuation did not necessarily increase with load. However, 

some load adjustment is likely required for load rates of

100 Hz and above to account for the decreased cyclic strain 

measured in the test tooth.

Further investigation could provide improved understanding 

of the cyclic strain attenuation at various load rates and allow 

for more accurate corrections to be applied to the fatigue data to 

reduce scatter and bias error. A second instrumented strain-gage 

specimen will be used to perform a more comprehensive root 

strain study. However, the absence of a clear trend toward 

decreasing cyclic strain with increased loading rate is 

encouraging and suggests that data may continue to be collected 

using the test rig as is, with correction factors applied later.
NASA/TM—2011-217039 8

Other load-path verification methods to include finite 

element modeling and three-dimensional optical surface strain 

measurement were conducted, but have been omitted here.

Conclusions

Experiments and validation efforts were performed to 

demonstrate a new high-speed, high-cycle, gear-tooth, bending 

fatigue capability co-operated by the NASA Glenn Research 

Center and the U.S. Army Research Laboratory. Such a 

facility provides the ability to explore the infinite-life region 

of the stress-cycle curve at bending stress loads of 

approximately 150 ksi and below in support of CBM and other 

component life-extension initiatives. A description of the 

facility was provided, as was data showing typical results from 

over 100 fatigue experiments. Characteristics of test results at 

different cycle rates were discussed and compared. These 

efforts support the following conclusions.

1. The NASA/ARL Single Gear Tooth Bending Test 

Facility is a unique test rig capable of conducting highspeed bending-fatigue tests. It enhances further research 

in the infinite-life regions of the stress-cycle curve, by 

enabling experiments in the 108 to 109-cycle range in the 

shortest amount of time possible.

2. Effective load output is dependent upon cycle-rate.

Operation between 400 and 800 Hz is not recommended 

for any loading condition. The results demonstrate 

excessive dynamic anomalies within this range.

3. Experiments conducted at 1000 Hz did not exhibit 

adverse dynamic/transient loading effects, as 

demonstrated through data results and strain-gage 

measurement.

4. Fatigue data compared closely with previous data results 

in the literature.

5. A thorough sequence of additional strain-gage testing is 

necessary to determine strain/load correction factors and 

attenuation at different loading conditions and cyclerates, as well as to decrease variability and eliminate bias 

in the results. This is currently underway.

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1. REPORT DATE (DD-MM-YYYY)

01-06-2011 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

A New High-Speed, High-Cycle, Gear-Tooth Bending Fatigue Test Capability 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Stringer, David, B.; Dykas, Brian, D.; LaBerge, Kelsen, E.; Zakrajsek, Andrew, J.; 

Handschuh, Robert, F. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 877868.02.07.03.01.01.01 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-17745 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

and 

U.S. Army Research Laboratory 

Adelphi, Maryland 20783-1145 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA, ARL 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2011-217039; ARL-TR-5506 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 07 and 37 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

A new high-speed test capability for determining the high-cycle bending-fatigue characteristics of gear teeth has been developed. 

Experiments were performed in the test facility using a standard spur gear test specimens designed for use in NASA Glenn’s drive system 

test facilities. These tests varied in load condition and cycle-rate. The cycle-rate varied from 50 to 1000 Hz. The loads varied from highstress, low-cycle loads to near infinite life conditions. Over 100 tests were conducted using AISI 9310 steel spur gear specimen. These 

results were then compared to previous data in the literature for correlation. Additionally, a cycle-rate sensitivity analysis was conducted by 

grouping the results according to cycle-rate and comparing the data sets. Methods used to study and verify load-path and facility dynamics 

are also discussed. 

15. SUBJECT TERMS

Bending fatigue; Gear tooth crack; Fatigue failure; High-cycle fatigue 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

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18. NUMBER

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15 

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STI Help Desk (email:help@sti.nasa.gov) 

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