Paula J. Dempsey, Robert F. Handschuh, and Irebert R. Delgado

Glenn Research Center, Cleveland, Ohio

Integrating Condition Indicators and Usage 

Parameters for Improved Spiral Bevel 

Gear Health Monitoring

NASA/TM—2013-217896

June 2013
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Paula J. Dempsey, Robert F. Handschuh, and Irebert R. Delgado

Glenn Research Center, Cleveland, Ohio

Integrating Condition Indicators and Usage 

Parameters for Improved Spiral Bevel 

Gear Health Monitoring

NASA/TM—2013-217896

June 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2013-217896 1

Integrating Condition Indicators and Usage Parameters for 

Improved Spiral Bevel Gear Health Monitoring

Paula J. Dempsey, Robert F. Handschuh, and Irebert R. Delgado

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

The objective of this study was to illustrate the importance 

of combining Health Usage Monitoring Systems (HUMS) data 

with usage monitoring system data when detecting rotorcraft 

transmission health. Three gear sets were tested in the NASA 

Glenn Spiral Bevel Gear Fatigue Rig. Damage was initiated 

and progressed on the gear and pinion teeth. Damage 

progression was measured by debris generation and 

documented with inspection photos at varying torque values.

A contact fatigue analysis was applied to the gear design 

indicating the effect temperature, load and reliability had on 

gear life. Results of this study illustrated the benefits of 

combining HUMS data and actual usage data to indicate 

progression of damage for spiral bevel gears. 

Background

Power train health is a critical part of a rotorcraft health 

management system since no other air vehicle relies on the 

propulsion system for propulsion, lift and maneuvering 

through a transmission with critical single load paths. Many 

rotorcraft are equipped with on-board Health Usage 

Monitoring Systems (HUMS) to detect anomalies in 

transmission dynamic mechanical components by monitoring 

vibration signatures produced by the damaged component. 

The results from vibration signatures, referred to as condition 

indicators (CI), are used to indicate component health or 

condition. Some failure modes of transmission components 

generate and introduce debris into the oil. Measurement of 

debris in the oil can be used to help assess transmission health.

Oil debris measurements can be off-line, performing oil 

analysis at periodic maintenance intervals or on-line, using oil 

debris sensors installed on board the aircraft to detect metallic 

debris in real-time (Ref. 1).

Usage monitoring is another important HUMS function.

Helicopter transmission components are designed per assumed 

flight regimes and usage spectrums. Usage monitoring consists 

of measuring torque, operating hours, flight regimes and 

operating conditions to track component “actual” usage. If 

“actual” usage is measured, and component usage is less severe 

than the life it was designed for, the time in operation of a 

component may be increased as shown in the green in Figure 1.

If component usage is more severe than the life it was designed 

for, the time in operation of a component should be decreased 

for safety reasons as shown in the red in Figure 1.

In practice, fatigue critical components in helicopters are 

designed to a specific service life in hours and removed from 

service before they reach those operational hours. The service 

life hours are determined using the following information 

(Ref. 3):

1. Fatigue strength S-N (stress-cycles) curves that relate 

component design, stress, number of cycles, operating 

conditions and reliability.

2. Load usage spectra from flight regimes from assumed 

mission profiles.

3. Cumulative fatigue damage calculations that tie loads 

back to fatigue life. The Palmgren-Miner Rule is one 

fatigue damage theory that is applied to the component 

properties to determine life. Applying this theory, the total 

life of a part is estimated by adding the percentages of 

applied load cycles per allowable cycles for critical loads 

and calculating a damage fraction.

However, fatigue life calculations do not take into 

consideration manufacturing defects or damage due to the 

aircraft environmental conditions or operational conditions 

that can cause premature failure of components. These types 

of unanticipated failures can be detected by the condition 

indicators in the HUMS.

Typically, within a HUMS system, the CI and usage data 

are acquired, stored, tracked, trended and monitored separately

(Ref. 1). Passing key information between both systems and 

integrating this information has the potential to improve the 

performance and reliability of both systems. An indication 

from the CI that damage has occurred can be fed into the 

usage monitoring system to increase the damage fraction, 

while the torques and rotor turn times monitored by the usage 

monitoring system can be fused with the CI to indicate 

progression of damage and remaining time in operation.

The objective of the research is a first step in illustrating

how key operational parameters measured by the usage 

monitoring system can be used to improve determination of

the health state of a dynamic mechanical component. The 

targeted components are spiral bevel gears. Oil debris 

generated and operational parameters were measured during 

tests performed on spiral bevel gear sets (pinion/gear) in the 

NASA Glenn Spiral Bevel Gear Fatigue Rig when pitting

fatigue damage occurred on gear and pinion teeth. The effect 

of torque on damage progression, once gear tooth damage was 

initiated, were compared to the rate of oil debris generated.

Cycles and loads were correlated to gear fatigue life through
NASA/TM—2013-217896 2

Figure 1.—Illustration of life consumption based on usage

(Ref. 2).

the definition of an S-N curve based on the allowable contact 

stress, number of cycles and operating conditions. Results of 

this analysis will illustrate the benefits of combining usage 

operational parameters with condition indicators when 

detecting gear health.

Test Facility

Tests were performed in the NASA Glenn Spiral Bevel 

Gear Test Rig at NASA Glenn Research Center. A detailed 

description of this test facility can be found in References 4 

and 5. The Spiral Bevel Gear Test Facility is illustrated in 

Figure 2. In addition to developing gear health monitoring 

tools, the test facility has been used to study the effects of gear 

material, gear tooth design, and lubrication on the fatigue 

strength of gears. Two sets of spiral bevel gears are installed 

in the test rig and tested simultaneously. Facing the gearboxes 

per Figure 3, the left gear set (pinion/gear) is referenced as left 

and the right gear set (pinion/gear) is referenced as right.

Figure 3 shows the cross-sectional view of the rig driveline.

The facility operates in a closed-loop arrangement where the 

load is locked into the loop via a split shaft and a thrust piston 

that forces a floating helical gear axially into mesh. The drive 

motor supplies the facility with rotation and loop losses via vbelts to the axially stationary helical gear. The spiral bevel gears 

on the left side operates where the pinion drives the gear in the 

normal speed reducer mode and the right side of the facility acts 

as a speed increaser. However, the concave side of the pinion is 

always in contact with the convex side of the gear on either side 

of the test facility. Load and speed of the left side gear output 

shaft are monitored by torque and speed sensors. 

Turbine engine oil that meets DOD-L-87354 specifications 

is used in the test rig. Both gear sets are lubricated with oil jets 

pumped from an oil reservoir. The lubrication from the 

gearbox then exits the gearbox and flows through an oil debris 

sensor. A strainer and a 3 μm filter are located downstream of 

the oil debris (OD) sensor to capture any debris before 

returning to the sensor and gearbox. 

Figure 2.—Spiral Bevel Gear Fatigue Rig.

Figure 3.—Cross section of Spiral Bevel Gear Fatigue Rig.

A non-contact rotary transformer shaft mounted torque 

sensor was used to measure torque during testing. Speed was 

measured by an optical tachometer mounted on the right gear 

shaft that measures a pulse per each gear shaft revolution.

Thermocouples were used to measure inlet and outlet oil 

temperatures. An inductance type oil debris sensor was used to 

measure the debris generated during fatigue damage to the 

gear teeth. The sensor measures the number of ferrous 

particles and their average size based on user defined particle 

size ranges or bins that is in turn used to calculate the 

cumulative mass by average particle size and the density of 

steel. Data was recorded once every minute with a facility data 

acquisition system.
NASA/TM—2013-217896 3

The gears tested were prototypes of gears designed and 

specified to represent a rotorcraft drive system gear mesh and fit 

within the space available in the spiral bevel gear fatigue rig 

gearboxes. The gears were made from a steel alloy CEVM 

9310, carburized, hardened and ground. However, the three gear 

sets tested, consisting of left pinion/gear and right pinion gear 

sets, differed from the final design in that they were not shot 

peened, the surface roughness on the pinion ranged from 11 to 

15 μin. and the surface roughness on the gears ranged from 26 

to 35 μin. In addition, copper plating used for masking parts of 

the gear during carburization was not removed from the edge of 

the gear teeth for this prototype design.

The prototype gear sets tested have 6.4 in. diametral pitch, 

20° pressure angle, 25° spiral angle, 0.94 in. face width and 

2.15:1 gear ratio. The gears have 41 teeth and the pinions have 

19 teeth. The test gears were designed to operate at a gear 

speed of 3500 rpm and torque of 8000 in.-lb, pinion speed of 

7553 rpm and torque of 3707 in.-lb and 240 to 265 °F inlet oil 

temperatures with an American Gear Manufacturers 

Association (AGMA) calculated contact stress of 237 ksi.

Experimental Data 

For this study, three gear sets were tested at a gear speed of 

3500 rpm and pinion speed of 7553 rpm. Gear torque varied 

from 4000 to 8000 in.-lb and pinion torque varied from 1854 

to 3707 in.-lb. At the start of each test, a run-in was performed 

for a minimum of 1 hr at 4000 in.-lb gear torque/3500 rpm

gear speed and 1854 in.-lb pinion torque/7553 rpm pinion 

speed. Contact cycles accumulated at a rate of 210,000 per 

hour for the gear and 453,180 per hour for the pinion.

At completion of the run-in, inspection photos were taken of 

the left and right gear and pinion teeth. Inspection photos were 

then taken throughout the test to document damage 

progression to the gear teeth.

Damage progression on the gear teeth depends on several 

factors that include: 1) the size, shape and location of the 

initiating flaw; 2) the type of failure mode; and 3) the gear set 

operational conditions. The effect of operational conditions 

and variance in damage progression rates indicates the 

importance of a diagnostic tool that can both detect the 

presence and location of damage and quantify the level, 

magnitude and rate of damage progression.

This preliminary study focuses on the effect measured 

torque has on the progression of damage to the gear and pinion 

teeth. The failure modes observed for this study were defined 

by class (contact fatigue), general mode (macropitting) and 

degree (progressive) per AGMA standards for gear wear 

terminology outlined in Reference 6.

Using Reference 6 for tooth damage terminology, a 

numbering scheme per Reference 7 was developed to 

streamline the identification of gear damage. Table 1

illustrates this numbering scheme for the types of damage 

observed during these tests. Table 2, Table 3, and Table 4

summarize the observed failure modes observed on the gear 

teeth during each inspection interval. The tests ran until 

macropitting/spalling (4.3.4) was observed on two or more 

teeth. The reader should note that damage mode 6.0, fracture, 

was a failure mode observed due to the prototype gear design.

In the prototype design, the edges of the teeth were not 

chamfered per design specifications and the copper masking 

was left on the edge of the teeth. This caused copper edges to 

fracture during testing. Since the oil debris sensor does not 

measure non-ferrrous particles, this type of debris was not 

measured by the sensor.

TABLE 1.—NUMBERING SCHEME FOR NOMENCLATURE 

OF GEAR FAILURE MODES (REF. 6)

Class General mode Specific mode or 

degree

2.0 Scuffing 2.1 Scuffing

2.1.1 Mild

2.1.2 Moderate

2.1.3 Severe

4.0 Contact Fatigue 4.1 Subcase Fatigue

4.2 Micropitting

4.3 Macropitting

4.3.1 Initial

4.3.2 Progressive

4.3.3 Flake

4.3.4 Spall

6.0 Fracture 6.0 Fracture

TABLE 2.—FAILURE MODES DURING TEST 1

Test 1 Rdg (min) Hour(s) Gear left Pinion left Gear right Pinion right

Start 0 0.00 N/A N/A N/A N/A

Run-in 60 1.00 N/A N/A N/A N/A

Inspection 108 1.80 N/A N/A N/A N/A

Inspection 379 6.32 6.0 at et 4.2 2t 6.0 at et, 2.1.2 at 4.2 at, 2.1.3 at

Inspection 559 9.32 6.0 at et 4.3.2 3t, 4.3.4 2t 6.0 at et, 2.1.2 at 4.2 at, 2.1.3 at

Inspection 662 11.03 6.0 at et 4.3.4 5t 6.0 at et, 2.1.2 at 4.2 at, 2.1.3 at

Key: xt= number of teeth; at=all teeth; et=edges of teeth
NASA/TM—2013-217896 4

TABLE 3.—FAILURE MODES DURING TEST 2

Test 2 Rdg (min) Hour(s) Gear left Pinion left Gear right Pinion right

Start 0 0.00 N/A N/A N/A N/A

Run-in 69 1.15 N/A N/A N/A N/A

Inspection 184 3.07 6.0 at et N/A N/A N/A

Inspection 520 8.67 6.0 at et 4.3.2 at 6.0 at et, 2.1.2 at 6.0 at et, 2.1.2 at, 4.3.4 1t

Inspection 686 11.43 6.0 at et 4.3.2 at, 4.3.4 1t 6.0 at et, 2.1.2 at 6.0 at et, 2.1.2 at, 4.3.4 5t, 4.3.2 4t

Key: xt= number of teeth; at=all teeth; et=edges of teeth

TABLE 4.—FAILURE MODES DURING TEST 3

Test 3 Rdg (min) Hour(s) Gear left Pinion left Gear right Pinion right

Start 0 0.00 N/A N/A N/A N/A

Run-in 60 1.00 N/A N/A N/A N/A

Inspection 489 8.15 6.0 at et N/A 6.0 at et, 2.1.2 at 4.3.1 at, 2.1.2 at

Inspection 901 15.02 6.0 at et 6.0 at et, 4.3.1 at 6.0 at et, 2.1.2 at 4.3.1 at, 2.1.2 at

Inspection 1196 19.93 6.0 at et 6.0 at et, 4.3.1 at 6.0 at et, 2.1.2 at 4.3.1 at, 2.1.2 at

Inspection 1829 30.48 6.0 at et 6.0 at et, 4.3.1 at 6.0 at et, 2.1.2 at 4.3.1 at, 2.1.2 at

Inspection 4034 67.23 6.0 at et, 4.3.4 5t, 4.3.2 6t 6.0 at et, 4.3.1 at 6.0 at et, 2.1.2 at 4.3.1 at, 2.1.2 at

Key: xt= number of teeth; at=all teeth; et=edges of teeth

Figure 4 to Figure 9 are plots of the damage progression to 

the gear teeth and the effect of torque during the testing of the 

three gear sets. The first plot in Figure 4, Figure 6 and Figure 8, 

torque, in inch-pounds (in.-lb), plotted in blue per the left y-axis.

Debris generated in milligrams, an indication of fatigue damage 

progressing, is plotted in orange per the right y-axis. The yellow 

diamonds on the x-axis indicate hours for gear teeth inspections. 

Representative photos of gear and pinion teeth damage modes 

and their progression at the inspections intervals are shown in 

the second figure. The six figures will be discussed in the 

following paragraphs.

Table 5 to Table 7 are summaries of the rate of debris 

generated during damage progression during each test per time 

in operation in hours. The debris generated per hour based on 

the inspection intervals is shown in the last column. Note that 

the amount of debris generated varied for each test due to the 

varying failure modes of the gear set. This data combined with 

the damage within each inspection interval is to be used to 

assess the overall trends of damage progression based on 

changes in torque applied to the gear set. 

For test 1, Figure 5 illustrates the progression of damage to 

five left pinion teeth. The other photos are representative 

pictures of one left gear tooth, on right gear tooth and one 

pinion tooth. The damage to these gears did not change after 

the initial inspection. For the left pinion, no macropitting was 

observed on the pinion teeth 6 hr into the test. Nine hours into 

the test, 4.3.4 was observed on two pinion teeth. Eleven hours 

into the test, 4.3.4 was observed on five teeth.

For test 1, Table 5 displays the rate of debris generation 

measured was at 8.96 mg/hr when progressive macropitting 

(4.3.2) was first observed on several teeth as seen in Figure 4

and Figure 5. The rate decreased to 3.75 mg/hr when the 

torque dropped to 4000 in.-lb. The debris generated then 

increased from 3.75 to 27.69 mg/hr when torque increased 

from 4000 to 8000 in.-lb, and spalling macropitting (4.3.4) 

was observed on five gear teeth as seen in Figure 5. 

For test 2, Figure 7 illustrates the progression of damage to 

six right and left pinion teeth. No macropitting was observed 

on the pinion teeth 3 hr into the test. Eight hours into the test, 

a pit was observed on a right pinion tooth. Several more pits 

were observed 11 hr into the test on the right pinion teeth and 

one pit on a left pinion tooth.

For test 2, Table 6 displays the rate of debris generation 

measured increased when torque increased from 6,000 to 8,000 

in.-lb per Figure 6. For this test, the torque was not decreased 

when the macropitting was observed on the teeth per Figure 7. 

The 6.37 mg/hr rate of debris generation when spalling 

macropitting (4.3.4) was observed at 8,000 in.-lb was higher 

than the 3.75 mg/hr rate of debris generation when spalling 

macropitting (4.3.4) was observed at 4,000 in.-lb for test 1.
NASA/TM—2013-217896 5

Figure 4.—Debris generated and torque during test 1.

Figure 5.—Damage conditions on teeth during test 1.

TABLE 5.—TEST 1 DEBRIS GENERATED DURING DAMAGE PROGRESSION

Test 1 Rdg (min) Hour(s) Torque ODM Δ ODM Δ hr mg/hr

Start 0 0.00 0 4.15

Run-in 60 1.00 4,000 4.69

Inspection 108 1.80 4,000 4.69 0.00 0.80 0.00

202 3.37 4,000 5.70 1.01 1.57 0.64

Inspection 379 6.32 8,000 7.72 2.02 2.95 0.68

468 7.80 4,000 8.59 0.87 1.48 0.59

Inspection 559 9.32 8,000 22.18 13.59 1.52 8.96

632 10.53 4,000 26.75 4.57 1.22 3.75

Inspection 662 11.03 8,000 40.59 13.84 0.50 27.69
NASA/TM—2013-217896 6

Figure 6.—Debris generated and torque during test 2.

Figure 7.—Damage conditions on teeth during test 2.

TABLE 6.—TEST 2 DEBRIS GENERATED DURING DAMAGE PROGRESSION.

Test 2 Rdg (min) Hour(s) Torque ODM Δ ODM Δ hr mg/hr

Start 0 0.00 4,000 0.63

Run-in 69 1.15 4,000 2.20

Inspection 184 3.07 6,000 3.08 0.87 1.92 0.45

367 6.12 6,000 3.08 0.00 3.05 0.00

Inspection 520 8.67 8,000 6.68 3.60 2.55 1.41

Inspection 686 11.43 8,000 24.30 17.62 2.77 6.37
NASA/TM—2013-217896 7

For test 3, Figure 9 illustrate no macropitting was observed 

on the pinion teeth 30 hr into the test. Sixty-seven hours into 

the test, several pits were observed on the left gear teeth and 

micropitting on both the left and right pinion teeth. The torque 

remained at 6000 in.-lb during the test.

For test 3, Table 7 displays the rate of debris generation 

measured was at 0.51 mg/hr rate of debris generation when 

spalling macropitting (4.3.4) was observed at 6000 in.-lb per 

Figure 8 and Figure 9. This rate was lower than the 3.75 mg/hr 

rate of debris generation when spalling macropitting (4.3.4) 

was observed at 4000 in.-lb for test 1, and lower than the 

6.37 mg/hr rate of debris generation when spalling 

macropitting (4.3.4) was observed at 8000 in.-lb for test 2.

Based on this preliminary analysis, for test 1 and 2, the rate 

of debris generated and damage progression to the gear and 

pinion teeth increased with increased torque values. Since 

damage progression depends on the size, location and shape of 

the initiating flaw, further testing is required to determine if 

once initiated, the damage progression can be slowed by 

decreasing the torque value. 

TABLE 7.—TEST 3 DEBRIS GENERATED DURING DAMAGE PROGRESSION.

Test 3 Rdg (min) Hour(s) Torque ODM Δ ODM Δ hr mg/hr

Start 0 0.00 4,000 4.96

Run-in 60 1.00 4,000 4.96

Inspection 489 8.15 6,000 12.86 7.89 7.15 1.10

Inspection 901 15.02 6,000 19.82 6.96 6.87 1.01

Inspection 1196 19.93 6,000 23.40 3.59 4.92 0.73

Inspection 1829 30.48 6,000 41.07 17.67 10.55 1.67

Inspection 4034 67.23 6,000 59.74 18.66 36.75 0.51

Figure 8.—Debris generated and torque during test 3.
NASA/TM—2013-217896 8

Figure 9.—Damage conditions on teeth during test 3.
NASA/TM—2013-217896 9

AGMA Discussion

The previous section of this paper provides a preliminary 

assessment of the effect actual usage, using torque and 

rotational hours, has on damage progression to gear teeth. 

Although contact fatigue analysis applied to a new gear design 

defines a specific service life, aircraft environmental 

conditions can cause premature failure of components.

Sometimes these conditions, such as operational climate and 

use, are not accounted for in the original design. A component 

failure per Reference 1 is defined as when a component cannot 

perform its intended function or the level of damage has 

reached a detectable level. Some component damage 

progresses slowly and the component can continue to function 

with a detectable level of damage. 

From an operations standpoint, if the type of component 

failure mode is dependent on load, and the HUMS CI is 

capable of indicating this type of failure mode before the fault 

reaches a critical size, it may be possible to modify an 

operational condition, such as decrease the load, to extend the 

useful life of the component. However, contact fatigue 

analysis is used to define the probability of survival, to avoid 

initiation of surface durability damage. Once the flaw initiates 

and starts to progress, based on varying operational 

conditions, a new approach may be required.

A preliminary contact fatigue analysis was applied to this 

gear design and its operational conditions to show the effect 

on the life of these gears based on their operational conditions.

The spiral bevel gear pinion was evaluated for various loading 

scenarios at different operational temperatures, to determine 

the effect on the expected time for damage initiation at a 

predetermined level of reliability.

The pinion design information and operational conditions 

within the Spiral Bevel Gear Fatigue Rig were utilized in a 

computer program (Ref. 8) that provides contact and bending 

stress indices. The design information included gear material, 

heat treatment, lubricant and desired reliability. The 

operational conditions included rotational speed, input torque 

and operating temperature. For a given design, rotational 

speed, and torque transmitted, the analysis provides the 

contact and bending stress indices. Contact and bending stress 

indices are criteria used to define gear tooth load capacity 

between mating teeth and its resistance to pitting damage on 

the gear tooth contact surface and the gear tooth base for 

bending (Ref. 9).

All of the input information described above has an effect on 

the allowable stress indices. Based on the input data, the 

program then calculates the margin of safety for the input 

design and operational conditions for the contact and bending 

fatigue behavior of the gear mesh. Note that 100 percent gear 

torque is 8000 in.-lb. The effect of torque on contact stress and 

bending stress indices in (ksi) for this design is given in Table 8.

TABLE 8.—EFFECT OF TORQUE ON 

CONTACT AND BENDING STRESS INDICES

% 

torque

Contact stress 

index, 

ksi

Bending stress 

index,

ksi

10 75.1 4.2

20 106.1 8.4

30 130 12.7

40 150.1 16.9

50 167.8 21.1

60 183.8 25.3

70 198.6 29.6

80 212.3 33.8

90 225.1 38

100 237.3 42.2

110 248.9 46.5

120 260 50.7

130 270.6 54.9

140 280.8 59.1

150 290.7 63.4

Gear and pinion temperatures and applied loads have 

significant effects on gear and pinion life. The effect of load 

on the progression of damage to the gear teeth was observed in 

Figure 5, Figure 7 and Figure 9. The applied torque affects 

contact and bending stresses on all spiral bevel geared 

systems. In many cases the gears must operate at elevated 

temperatures. Elevated temperatures can also have detrimental 

effects on the aspects of a design that have to do with bending 

fatigue (material capability to carry load at elevated 

temperatures), contact fatigue (pitting—surface degradation) 

and scoring (surface interaction through the lubricating film 

thickness) that decrease the life of the gears.

In addition to loads and temperatures, the risk associated 

with a given design must be assessed. This is known as the 

reliability of the design. This is typically described as a 

percentage of reliability for a given load(s) for a number of 

hours (or cycles) of operation. The non-uniform loading a gear 

mesh might see can be evaluated utilizing a “Miner’s Rule” 

summation (Ref. 10). The level of reliability the gears must 

maintain also affects gear and pinion life. Reliability refers to 

the probability the gear will fail. A 99 percent reliability is 

defined as 99 out of 100 gears will survive to x number of 

cycles at a given load. A 50 percent reliability is defined as 

one out of two gears will survive x number of cycles at a given 

load. These effects are illustrated in Table 9. Per the last 

column of the table, if you can accept a lower reliability, you 

can increase the number of life cycles since lower reliability 

allows higher allowable stress indices.
NASA/TM—2013-217896 10

TABLE 9.—CALCULATED LIFE ASSESSMENT IN CYCLES 

FOR PINION AT DIFFERENT OPERATING CONDITIONS

% 

torque

500 °F life 

cycles 

(millions) 

99% 

reliability

400 °F life 

cycles 

(millions) 

99% 

reliability

300 °F life 

cycles 

(millions) 

99% 

reliability

500 °F life 

cycles 

(millions)

50% 

reliability

10 >10,000 >10,000 >10,000 >10,000

20 >10,000 >10,000 >10,000 >10,000

30 >10,000 >10,000 >10,000 >10,000

40 >10,000 >10,000 >10,000 >10,000

50 >10,000 >10,000 >10,000 >10,000

60 700 7,000 >10,000 >10,000

70 340 1,600 >10,000 6,000

75 160 1,100 10,000 3,300

80 100 600 5,000 1,800

90 40 240 2,000 700

100 19 100 700 300

110 8 44 340 140

120 3.6 23 160 64

Per the highlighted line in Table 9 at 100% torque (8000 in.-

lb gear torque), the life cycles at 500 °F pinion temperature is 

significantly lower than at 400 and 300 °F. An S-N curve of 

cycles versus allowable stress index was generated for the 

contact fatigue reliability based on blank or gear tooth 

temperatures for this gear design and is shown in Figure 10. The 

number of cycles is shown on the x-axis and the contact stress 

index is shown on the y-axis. The red dashed horizontal line is 

the contact stress index at 8000 in.-lb gear torque, 3707 in.-lb

pinion torque. The blank temperature is the pinion tooth 

temperature. During the three gear tests the inlet oil 

temperatures ranged from 240 to 265 °F. The gear and pinion 

temperatures can be significantly higher than the inlet oil 

temperatures. Pinion tooth root temperatures were measured in 

this test rig on another gear design with 100 °F oil inlet 

temperatures at comparable load that ranged from 200 to 

225 °F, over 100 °F above the oil inlet temperature (Ref. 11).

Methods to calculate pinion temperature based on operating 

conditions and pinion design were researched in the literature.

Based on the operating conditions of the test rig, pinion 

temperatures were calculated using methods outlined in 

Reference 12. The method uses the following equations and 

parameters to calculate pinion temperatures.

0.6875 0.3125 0.75

1 50

50 P T Pd np s C K

C

G T 



 





− ∆ = (1)

1.2096 1= C

CP (2)

C F

T C C K v

P o m T = (3)

Where ΔT is the temperature rise in °F; G is a geometry 

factor; C1 is a thermal constant for gear material; Cp is an 

elastic coefficient; KT is a load factor; s is the surface finish in 

micro-inches; Pd is the transverse diametral pitch in (1/in.); np

is the pinion speed in rpm; factors Co, overload, Cm, load 

distribution, and Cv, dynamic, are set equal to 1; and F is equal 

to the gear face width. Per Equations (1) through (3), if the 

pinion surface finish is 10 μin., the pinion temperature is 

calculated as 561 °F. This value increases to 631 °F if the 

surface finish of the pinion is 20 μin.

Table 10 is a summary of the hours the pinions will be free 

of contact fatigue damage at 99 percent reliability at the rig 

operating conditions of 8000 and 6000 in.-lb gear 

torque/3500 rpm gear speed and 3707 and 2780 in.-lb pinion 

torque/7553 rpm pinion speed at pinion temperatures of 300, 

400, and 500 °F. The gear sets were tested at these conditions 

during test 1 and 2 as shown in Figure 4 and Figure 6. Per 

Table 10, 1 out of 100 gears tested should have failed at 42 hr

at 8000 in.-lb torque. Based on the damage progression data 

collected during the three tests, macropitting was observed 

less than 10 hr into each test. For tests 1 and 2, 8000 in.-lb

torque was applied for less than 5 of the 10 hr. For test 3, 

macropitting was observed within 10 hr at 6000 in.-lb load.

This AGMA analysis over predicted the life of this gear 

design. 

TABLE 10.—CALCULATED LIFE ASSESSMENT IN 

HOURS FOR PINION AT TEST CONDITIONS

% 

torque

500 °F life 

cycles,

hr,

99% 

reliability

400 °F life 

cycles,

hr,

99% 

reliability

300 °F life 

cycles,

hr,

99% 

reliability

500 °F life 

cycles,

hr,

50% 

reliability

75 353 2,427 22,067 7,282

100 42 221 1,545 662

At this time, surface finish effects are not part of the input 

data to the AGMA analysis. However, the effect of surface 

finish on contact fatigue has been documented in previous 

studies (Ref. 13). If surface finish effects were part of the 

input data for the AGMA contact stress calculations, the stress 

levels would have been calculated to be a higher value or have 

a lower allowable index stress decreasing the life of the gears. 

Using a pinion temperature higher than 500 °F would have 

also decreased the calculated life of these gears. Further 

studies, outside the scope of this paper, are required to capture 

these other design and operational conditions into the AGMA 

to more accurately predict gear life. 
NASA/TM—2013-217896 11

Figure 10.—Blank temperature effects on allowable contact stress, 

99 percent reliability.

Summary

The benefit of combining usage operational parameters with 

HUMS condition indicators has the potential to improve the 

performance and reliability of both systems to indicate 

progression of damage and remaining time in operation. This 

analysis illustrates the importance of combining gear condition 

indicators and gear operational conditions, such as load and 

temperature, to indicate spiral bevel gear health. Decreasing both 

temperature and load can increase the fatigue life of the 

components. Per accepted AGMA practice, torque and 

temperature have significant influence on time for damage to 

appear. Once surface fatigue damage was initiated, the 

experimental data indicated decreasing load can slow the 

progression of damage to the gear teeth. Further studies are 

required to determine if usage monitoring of temperature and 

torque can be used to increase operational life for rotorcraft gears.

References

1. U.S. Army Aeronautical Design Standard for Condition 

Based Maintenance, ADS79 Handbook. August 2012.

2. Chapter 37: Rotorcraft Systems Health Management, 

System Health Management: With Aerospace 

Applications, Wiley Online Library. Web. 13 Dec. 2011.

3. Vaughan, R.E. and Tipps, D.O.: Condition Based 

Maintenance Approach to Fleet Management. American 

Helicopter Society CBM specialist Workshop, 

Huntsville, AL, Feb. 12-13 2008.

4. Handschuh, R.F.: Thermal Behavior of Spiral Bevel 

Gears. NASA TM-106518, 1995.

5. Handschuh, R.F.: Testing of Face-Milled Spiral Bevel 

Gears at High-Speed and Load. NASA/TM—2001-

210743, 2001.

6. ANSI/AGMA 1010-E95. Appearance of Gear Teeth –

Terminology of Wear and Failure.

7. Delgado, Irebert; Dempsey, Paula; Antolick, Lance and 

Wade, Dan: Continued Evaluation of Gear Condition 

Indicator Performance on Rotorcraft Fleet.

Airworthiness, CBM, and HUMS Specialists' Meeting, 

Feb. 11-13, 2013, Huntsville, AL.

8. Bevel Gear Rating Suite by AGMA, American Gear 

Manufacturers Association, Version 1.0.12, 2007.

9. American National Standard (ANSI)/American Gear 

Manufacturers Association (AGMA) Rating Resistance 

and Bending Strength of Generated Straight Bevel, Zero 

Bevel and Spiral Bevel Gear Teeth. ANSA/AGMA 

2003-C10.

10. Juvinal, R.: Engineering Considerations of Stress, Strain, 

and Strength, McGraw-Hill Book Company, 1967.

11. Handschuh, R.F.: Effect of Lubricant Jet Location on 

Spiral Bevel Gear Operating Temperatures. NASA TM105656, 1992.

12. American Gear Manufacturers Association Gleason Gear 

Engineering Standard, 1977.

13. Krantz, T.: The Influence of Roughness on Gear Surface 

Fatigue. NASA/TM—2005-213958 and ARL-TR-3134, 

Oct. 2005.
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Integrating Condition Indicators and Usage Parameters for Improved Spiral Bevel Gear 

Health Monitoring 

5a. CONTRACT NUMBER

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Dempsey, Paula, J.; Handschuh, Robert, F.; Delgado, Irebert, R. 

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WBS 380046.02.03.02.02.03 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The objective of this study was to illustrate the importance of combining Health Usage Monitoring Systems (HUMS) data with usage 

monitoring system data when detecting rotorcraft transmission health. Three gear sets were tested in the NASA Glenn Spiral Bevel Gear 

Fatigue Rig. Damage was initiated and progressed on the gear and pinion teeth. Damage progression was measured by debris generation and 

documented with inspection photos at varying torque values. A contact fatigue analysis was applied to the gear design indicating the effect 

temperature, load and reliability had on gear life. Results of this study illustrated the benefits of combining HUMS data and actual usage 

data to indicate progression of damage for spiral bevel gears.

15. SUBJECT TERMS

Health monitoring; Gears; Usage 

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