David G. Lewicki

Glenn Research Center, Cleveland, Ohio

Nicholas A. Lambert and Robert S. Wagoner

Ridgetop Group Inc., Tucson, Arizona

Evaluation of MEMS-Based Wireless Accelerometer 

Sensors in Detecting Gear Tooth Faults in

Helicopter Transmissions

NASA/TM—2015-218722

April 2015
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated 

to the advancement of aeronautics and space science. 

The NASA Scientifi c and Technical Information (STI) 

Program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI Program provides access 

to the NASA Technical Report Server—Registered 

(NTRS Reg) and NASA Technical Report Server—

Public (NTRS) thus providing one of the largest 

collections of aeronautical and space science STI in 

the world. Results are published in both non-NASA 

channels and by NASA in the NASA STI Report 

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counter-part of peer-reviewed formal 

professional papers, but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or of 

specialized interest, e.g., “quick-release” reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or co-sponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 757-864-6500

• Telephone the NASA STI Information Desk at

 757-864-9658

• Write to:

NASA STI Program

 Mail Stop 148

 NASA Langley Research Center

 Hampton, VA 23681-2199
David G. Lewicki

Glenn Research Center, Cleveland, Ohio

Nicholas A. Lambert and Robert S. Wagoner

Ridgetop Group Inc., Tucson, Arizona

Evaluation of MEMS-Based Wireless Accelerometer 

Sensors in Detecting Gear Tooth Faults in

Helicopter Transmissions

NASA/TM—2015-218722

April 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

Level of Review: This material has been technically reviewed by technical management. 

NASA STI Program

Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681-2199

National Technical Information Service

5285 Port Royal Road

Springfi eld, VA 22161

703-605-6000

This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/
NASA/TM—2015-218722 1 

Evaluation of MEMS-Based Wireless Accelerometer Sensors in 

Detecting Gear Tooth Faults in Helicopter Transmissions 

David G. Lewicki 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Nicholas A. Lambert and Robert S. Wagoner 

Ridgetop Group Inc. 

Tucson, Arizona 85741 

Abstract 

The diagnostics capability of micro-electro-mechanical systems (MEMS) based rotating 

accelerometer sensors in detecting gear tooth crack failures in helicopter main-rotor transmissions was 

evaluated. MEMS sensors were installed on a pre-notched OH-58C spiral-bevel pinion gear. Endurance 

tests were performed and the gear was run to tooth fracture failure. Results from the MEMS sensor were 

compared to conventional accelerometers mounted on the transmission housing. Most of the four 

stationary accelerometers mounted on the gear box housing and most of the CI’s used gave indications of 

failure at the end of the test. The MEMS system performed well and lasted the entire test. All MEMS 

accelerometers gave an indication of failure at the end of the test. The MEMS systems performed as well, 

if not better, than the stationary accelerometers mounted on the gear box housing with regards to gear 

tooth fault detection. For both the MEMS sensors and stationary sensors, the fault detection time was not 

much sooner than the actual tooth fracture time. The MEMS sensor spectrum data showed large first 

order shaft frequency sidebands due to the measurement rotating frame of reference. The method of 

constructing a pseudo tach signal from periodic characteristics of the vibration data was successful in 

deriving a TSA signal without an actual tach and proved as an effective way to improve fault detection for 

the MEMS. 

Introduction 

Gears are used extensively in rotorcraft drive systems. Effective gear fault detection is crucial to 

ensure flight safety. In addition, tremendous economic benefits can result from condition based 

maintenance practices, for which gear fault detection plays an important role. Much work has been 

devoted to the development of health and usage monitoring systems for rotorcraft gearbox and drivetrain 

components. Samuel and Pines give a comprehensive review of the state-of-the-art in vibration-based 

helicopter transmission diagnostics (Ref. 1). Fault detection has been documented using advanced signal 

processing techniques of vibration from accelerometers mounted on the transmission housing. However, 

for complex systems or for components buried deep in the transmission with poor signal transfer paths, 

alternate methods are needed to detect failures, such as embedded sensors and MEMS (Refs. 2 to 7). 

To improve diagnostic technology, the NASA Glenn Research Center (GRC) awarded multiple Small 

Business Innovation Research (SBIR) contracts to Ridgetop Group Inc. The goal was to develop 

prototype MEMS-based vibration sensors embedded on rotating components in a helicopter transmission. 

One such implementation was accelerometers embedded on a spiral-bevel pinion gear in an OH-58 

helicopter main-rotor transmission. Subsequent tests were performed at GRC to evaluate fault detection 

capabilities. 

 
NASA/TM—2015-218722 2 

The objective of the current study is to report the results of these tests. The diagnostics capabilities of 

MEMS-based, rotating accelerometer sensors in detecting gear tooth crack failures in helicopter mainrotor transmissions were evaluated and compared to those using conventional accelerometers mounted on 

the transmission housing. Experiments were performed on an OH-58C helicopter main-rotor transmission 

in the NASA GRC 500-hp helicopter transmission test facility. MEMS sensors were installed on the 

OH-58C spiral-bevel pinion gear. A notch was fabricated on the gear to promote gear tooth bending 

fatigue failure. Endurance tests were performed and the gear was run to tooth fracture failure. Results 

from the MEMS sensor were compared to conventional accelerometers mounted on the transmission 

housing. 

Apparatus 

Test Facility 

The tests were performed in the NASA GRC 500-hp helicopter transmission test facility (Fig. 1). The 

test stand operates on the closed-loop or torque-regenerative principle. Mechanical power re-circulates 

through a closed loop of gears and shafting, part of which is the test transmission. The output of the test 

transmission attaches to the bevel gearbox. The output shaft of the bevel gearbox passes through a hollow 

shaft in the closing-end gearbox and connects to the differential gearbox. The output of the differential 

attaches to the hollow shaft in the closing-end gearbox. The output of the closing-end gearbox attaches to 

the input of the test transmission, thereby closing the loop. 

A 200-hp variable-speed direct-current (DC) motor powers the test stand and controls the speed. The 

motor output attaches to the closing-end gearbox. The motor replenishes losses due to friction in the loop. 

A 15-hp DC motor provides the torque in the closed loop. This motor drives a magnetic particle clutch. 

The clutch output does not turn but exerts a torque. This torque is transferred through a speed reducer 

gearbox and a chain drive to a large sprocket on the differential gearbox. The torque on the sprocket 

applies torque in the closed loop by displacing the gear attached to the output shaft of the bevel gearbox 

with respect to the gear connected to the input shaft of the closing-end gearbox. This is done within the 

Figure 1.—NASA GRC 500-hp helicopter transmission test facility.
NASA/TM—2015-218722 3 

differential gearbox through use of a compound planetary system where the planet carrier attaches to the 

sprocket housing. The magnitude of torque in the loop is adjusted by changing the electric field strength 

of the magnetic particle clutch. 

A mast shaft loading system in the test stand simulates rotor loads imposed on the OH-58C 

transmission output mast shaft. The OH-58C transmission output mast shaft connects to a loading yoke. 

Two vertical load cylinders connected to the yoke produce lift loads. A single horizontal load cylinder 

connected to the yoke produces a bending load. A 2000-psig nitrogen gas system powers the cylinders. 

Pressure regulators connected to the nitrogen supply of each of the load cylinders adjust the magnitude of 

lift and bending. 

OH-58C Test Transmission 

Tests were performed using an OH-58C helicopter main-rotor transmission (Fig. 2). The OH-58C 

transmission is rated at maximum continuous power of 335 hp at 6180 rpm input speed. The main-rotor 

transmission is a two-stage reduction gearbox with an overall reduction ratio of 17.44:1. The first stage is 

a spiral-bevel gear set with a 19-tooth pinion that meshes with a 71-tooth gear. Triplex ball bearings and 

one roller bearing support the bevel-pinion shaft. Duplex ball bearings and one roller bearing support the 

bevel-gear shaft. The pinion is straddle mounted and the gear is overhung. A planetary mesh provides the 

second reduction stage. The bevel-gear shaft is connected through a spline to a sun gear shaft. The 

27-tooth sun gear meshes with four 35-tooth planet gears, each supported with cylindrical roller bearings. 

The planet gears mesh with a 99-tooth fixed ring gear. The ring gear is connected to the transmission 

housing through a spline on its outer diameter. Power is taken out through the planet carrier which is 

connected to the output mast shaft through a spline. The output shaft is supported on top by a 

split-inner-race ball bearing and on the bottom by a roller bearing. 

The OH-58C transmission is lubricated and cooled with a dedicated lubrication system. The 71-tooth 

bevel gear of the first reduction stage drives a 27-tooth accessory gear. The accessory gear runs an 

internal oil pump, which supplies pressurized oil. After passing through the standard OH-58C 10-micron 

filter, the oil is ported to an external facility heater and heat exchanger, allowing precise control of oil 

inlet temperature. The oil is then routed back in the OH-58C transmission, providing lubrication for the 

gears and bearing through jets and passageways located in the transmission housing. The lubricant used in 

the OH-58C transmission was a synthetic base helicopter transmission oil conforming to the DOD-L85734 specification. The nominal oil outlet pressure was 80 psig and the oil inlet pressure was 45 psig. 

The oil inlet temperature was 180 F. 

Figure 2.—OH-58C helicopter main-rotor transmission.

 
NASA/TM—2015-218722 4 

Figure 3.—Fabricated notches on OH-58C spiral-bevel pinion gear teeth. 

The test article for this study was the spiral-bevel pinion gear. At the start of the test, a 0.01-in. long 

by 0.03-in. deep by 0.005-in. wide notch was fabricated in the fillet region (loaded side) of one pinion 

tooth using the electric discharge machining (EDM) process. The purpose of the notch was to introduce a 

stress concentration in the tooth fillet and promote a bending fatigue failure of the gear tooth during 

prolonged running. The desired location of the notch was on the fillet radius of the tooth where a large 

tensile bending stress occurs during gear tooth engagement. The actual location of the notch (Fig. 3(a)) 

was a little lower than desired, biased toward the root of the gear. After 51.86 hr of run time (described 

later in the paper), the gear tooth did not initiate bending fatigue and the original notch was extended to 

0.5-in. long by 0.045-in. deep by 0.005-in. wide (Fig. 3(b)). This notch, however, was slightly misaligned 
NASA/TM—2015-218722 5 

to the tooth fillet and the ends of the notch were not located at the high stress regions. After 106.11 

cumulative hours of run time, the gear tooth did not initiate bending fatigue and an additional notch, 

0.5-in. long by 0.045-in. deep by 0.005-in. wide, was fabricated using EDM on a second tooth (Fig. 3(c)). 

This notch was oriented in the high stress fillet region as desired, and bending fatigue occurred after 

112.36 cumulative hours run time. 

MEMS Instrumentation 

A schematic of the MEMS instrumentation setup is given in Figure 4. For the rotating components, 

the accelerometer board, micro-controller board, and battery were mounted in a canister pressed into the 

inner bore of the OH-58C spiral-bevel pinion gear. Three MEMS accelerometers and analog-to-digital 

modules were installed on the accelerometer board. The micro-controller and memory chips were 

installed on the micro-controller board. The micro-controller transmitted and received data wirelessly to 

and from the stationary receiver through the transmitter antenna. The receiver transmitted data to and 

from the controlling laptop through use of a USB connection. 

Figure 4.—MEMS instrumentation setup. 

 
NASA/TM—2015-218722 6 

Figure 5.—MEMS sensing package and installation in OH-58C transmission. 

Figure 5 shows an exploded view of the rotating MEMS instrumentation setup. As seen in the top of 

the figure, the accelerometer board and micro-controller board straddled the battery and were contained 

within the canister mounted in the spiral-bevel pinion gear. The transmitter antenna was mounted on an 

existing spacer ring connected to the end of the spiral-bevel pinion flange. Figure 6 shows the MEMS 

receiving station. The wireless receiver was mounted close to the rotating transmitter antenna. 

Figure 7 shows a close up of the accelerometer board. Three commercially-available MEMS 

accelerometers were mounted on the board with specific placement and orientation. One radial 

accelerometer, R, was positioned at the center of the board (and center of pinion gear axis of rotation) to 

measure the radial (or lateral) acceleration of the pinion. Two tangential accelerometers, T1 and T2, were 

oriented with sensitive axes perpendicular to line T1-R-T2 to measure torsional acceleration of the pinion 

as well as radial acceleration. The accelerometers had a dynamic range of 250 g peak acceleration, a 

sensitivity of 4.4 mV/g, a resonance frequency of 22 kHz, and were linear in response up to 10 kHz. The 

accelerometer outputs passed through a passive resistor-capacitor anti-aliasing filter circuit with an 
NASA/TM—2015-218722 7 

approximate cutoff frequency of approximately 15 kHz, then to commercially-available analog-to-digital 

converters (ADC), one for each accelerometer. The ADC's were 16-bit resolution and data were 

simultaneously acquired at approximately 43 kHz sample rate for one second duration. The battery 

chosen for the system was a 3.6-Volt DC lithium-thionyl chloride cell designed for high temperature and 

high power capacity. The battery life was estimated to power the MEMS system and transfer data from 

pinion gear to laptop at once per minute for eight hours a day for roughly one month. 

Figure 6.—MEMS receiving station. 

Figure 7.—MEMS accelerometer board. 

Wireless

receiver

OH-58C

transmission

MEMS

transmitter

antenna
NASA/TM—2015-218722 8 

Facility Instrumentation 

The test facility used a commercially available data acquisition system to collect and store test facility 

parameters. The test facility parameters were speeds, torques, oil flow rates, oil pressures, broadband 

vibration levels, mast loads, cycle counts, and various component temperatures. The values for each 

parameter were acquired, time-stamped, and stored once every second. 

The NASA-developed Mechanical Diagnostics System Software (MDSS) fault detection system was 

used to compare with the MEMS system. The MDSS consisted of high-frequency accelerometers, shaft 

tachometers, and customized software equipped with gear and shaft fault detection algorithms developed 

throughout the years (Ref. 8). Four piezoelectric accelerometers were installed on the top-cover housing 

of the OH-58C transmission (Fig. 8). Two accelerometers (A1 and A2) were mounted at the input spiralbevel pinion gear region. One (A1) was mounted in the vertical direction and the other (A2) in the 

Figure 8.—Accelerometer locations on OH-58C 

transmission top cover housing. 
NASA/TM—2015-218722 9 

Figure 9.—Oil debris monitoring setup. 

horizontal direction, both to measure radial motion of the pinion shaft. Two additional accelerometers, A3 

and A4, were mounted adjacent to the planetary ring gear, primarily mounted to measure ring gear radial 

motion. The accelerometers were commercially available and had a flat high-frequency response up to 

about 40 kHz and a resonant frequency of about 90 kHz. A coaxial fiber optic reflective scanner was 

mounted on the OH-58C transmission input shaft to produce a once-per-revolution tachometer pulse of 

the shaft. The outputs of the accelerometers and tachometer pulses were routed to anti-aliasing filters with 

a 50 kHz cut-off frequency, then to a PC-based data acquisition system. The data were acquired at 

125 kHz sampling rate for one second duration. 

A commercially available oil debris monitor (ODM) was also used for the tests. Pre-filtered OH-58C 

transmission outlet oil was routed to the ODM unit using a specially designed filter adapter block (Fig. 9). 

The oil was then routed back to the transmission, where it passed through the filter, and exited the 

transmission to the facility external heater and heat exchanger (cooler) as previously described. The 

output of the ODM sensor was continuously polled by the unit's conditioning box which also calculated 

cumulative mass of the debris as well as classifying the debris by size in predefined bin sizes. The data 

was routed to the MDSS monitoring PC data collection system and collected and time-stamped with the 

 
NASA/TM—2015-218722 10 

MDSS vibration data. In addition to the ODM, the standard OH-58 transmission magnetic chip detection 

was used. This device collects ferrous debris generated in the transmission. When excessive debris is 

generated, a gap in the sensor is bridged which closes an electric circuit and illuminates a warning light in 

the control room. 

Lastly, a proximity probe was installed inside the OH-58C transmission near the spiral-bevel pinion 

gear using a special bracket. The probe was attached near the pinion teeth. The output of the probe 

conditioner was sent to an oscilloscope. This produced a sinusoidal display of the pinion teeth during 

rotation to visually indicate excessive movement or fracture of a tooth during test. 

Test Procedure 

Endurance tests were performed on the OH-58C transmission spiral-bevel pinion gear. The objective 

was to produce a bending fatigue tooth crack on the pinion gear. Thus, the OH-58C transmission was run 

at constant speed and relatively high torque for many days until failure occurred. At the start of each days 

run, the OH-58C transmission oil was externally heated to 180 F. Once stabilized, the transmission input 

speed was set to 6180 rpm and the transmission input torque was set to either 4339 or 4649 in.-lb, 

depending on the test. Once steady state was reached, the MDSS and MEMS systems were started. The 

clocks on the MDSS, MEMS, and facility data computers were all synchronized at the start of each day 

such that all time-stamped data were comparable to each other. The MDSS system acquired one second of 

data every minute. For each acquisition, the raw vibration time signals were stored as well as calculated 

fault condition indicators at that point in time. The MEMS system acquired one second of data 

continuously. At each acquisition, the raw vibration time signals for each accelerometer were transferred 

to the receiving station and saved on the laptop. The data transfer time from the MEMS micro-controller 

to the receiving station and to the laptop was dependent on receiver signal strength and slightly varied 

from approximately 45 to 55 sec throughout the test. On the average, the MEMS system acquired one 

second of data every 51 sec. Additional post processing of the MEMS data occurred after the tests. 

Results and Discussion 

Test Summary 

Figure 10 shows the timeline of the OH-58C endurance tests, displaying the transmission input torque 

versus run time for the entire test. All tests were run at full input speed of 6180 rpm. The entire test lasted 

112.36 hr spanning 24 days. As previously mentioned, a 0.01-in. long by 0.03-in. deep by 0.005-in. wide 

notch was fabricated in the fillet region (loaded side) of one pinion tooth at the start of the test. This 

condition was run for 24.59 hr at 4339 in.-lb input torque (127 percent design). At no sign of failure, the 

torque was increased to 4649 in.-lb (136 percent design). During this time, a crack occurred on the OH58C top cover housing at 37.84 cumulative hours. This failure had no bearing on the pinion endurance 

tests, and a replacement cover was installed on the transmission and testing resumed. At 51.86 cumulative 

hours, no failure of the pinion occurred. Upon inspection, the actual location of the notch was a little 

lower than desired, biased toward the root of the gear. Due to this, the stress concentration on the notched 

pinion tooth was less than desired and no failure occurred. The original notch was extended to 0.5-in. long 

by 0.045-in. deep by 0.005-in. wide. Testing resumed at 4339 in.-lb input torque. At 72.51 cumulative 

hours, no failure occurred and the torque was increased to 4649 in.-lb. During this period, indication of 

chips and debris were observed and testing was stopped at 106.11 cumulative hours. The transmission 

was disassembled, inspected, and a fatigue spall failure was discovered on the spiral-bevel gear roller 

bearing inner race. A replacement bearing was installed. 

 
NASA/TM—2015-218722 11 

Figure 10.—Timeline of spiral-bevel pinion endurance tests. 

Figure 11.—Fractured spiral-bevel pinion tooth after 

112.36 hr run time. 

It was observed that the widened notch on the pinion was slightly misaligned to the tooth fillet and 

the ends of the notch were not located at the high stress regions. Thus, an additional notch, 0.5-in. long by 

0.045-in. deep by 0.005-in. wide, was fabricated on a second tooth. Testing resumed at 4339 in.-lb input 

torque and increased to 4649 in.-lb at 110.17 cumulative hours. At 112.30 hr, a fractured spiral-bevel 

pinion tooth was observed from the proximity probe data. The endurance tests concluded at 112.36 

cumulative hours. The transmission was disassembled and the fractured pinion tooth occurred at the 

second notch location (Fig. 11), which was correctly oriented in the high fillet stress region. 
NASA/TM—2015-218722 12 

MDSS Results 

Figure 12 depicts the root-mean-square (RMS) of the raw vibration for the four MDSS 

accelerometers for the entire test. The RMS indicates the general overall vibration levels of the 

transmission housing. The discontinuities in the data correspond to the start and stop times for the 

different run days. Significant discontinuities occurred at the time of the top cover replacement (37.84 hr) 

and at the time of the rebuild after the spiral-bevel gear roller bearing failure (106.11 hr). The RMS did 

vary from day to day and, in general, was a poor indicator of gear tooth failure when considering data 

from the entire test. Figure 13 shows the RMS for only the last 30 min of the last day of testing. Here, an 

upward trend of vibration levels can be seen at end of the test when tooth fracture occurred. 

Figure 12.—RMS of MDSS raw vibration for entire test. (a) Accelerometer A1, bevel pinion 

vertical. (b) Accelerometer A2, bevel pinion horizontal. (c) Accelerometer A3, ring gear. 

(d) Accelerometer A4, ring gear.

Vibration, g rms

12

14

16

18

20

22

Vibration, g rms

12

14

16

18

20

Vibration, g rms

8

10

12

14

Run time, hrs

0 20 40 60 80 100 120

Vibration, g rms

8

10

12
NASA/TM—2015-218722 13 

Figure 13.—RMS of MDSS raw vibration for last 30 min of test. (a) Accelerometer A1, bevel 

pinion vertical. (b) Accelerometer A2, bevel pinion horizontal. (c) Accelerometer A3, ring gear. 

(d) Accelerometer A4, ring gear.

To further quantify the capabilities of the gear fault detection condition indicators (CI’s) described in 

this paper, statistical methods will be employed. Here, the run time CI values will be compared to a 

running mean plus three-standard-deviation average. The CI will be defined as “fully detecting failure” if 

above the running average (mean plus three-standard-deviation) at the time of gear tooth failure and 

below the running average for the vast majority of time before failure (no false alarms). The CI will be 

defined as “marginally detecting failure” if above the running average at the time of gear tooth failure and 

below the running average for most of time before failure (some false alarms). In addition, the running 

mean plus three-standard-deviation average will be computed for two cases: (1) for the entire test, and (2) 

for only the last day of the test. Vibration, g rms

18.0

18.5

19.0

19.5

Vibration, g rms

14.5

15.0

15.5

Vibration, g rms

11.0

11.5

12.0

Run time, hrs

111.86 111.96 112.06 112.16 112.26 112.36

Vibration, g rms

9.0

9.5

10.0

a)

b)

c)

d)

Fractured tooth
NASA/TM—2015-218722 14 

Figure 14 shows a sample analysis using the raw RMS CI. The left column (Figs. 14(a) to (c)) is for 

accelerometer A1, bevel pinion vertical. Figure 14(a) shows the RMS data for the entire test along with a 

running mean plus three-standard-deviation average. Here, the RMS is below the running average, thus 

giving no indication of gear failure. Figure 14(b) shows the same data for the last 30 min of testing, again 

showing no indication of failure. Figure 14(c) shows the same RMS as in Figure 14(b), but with the mean 

plus three-standard-deviation average calculated only for the last day of testing. Since the RMS was 

significantly lower the last day, the running average was also lower. However, the RMS was still lower 

than this running average, and thus, gave no indication of gear failure. 

The right column (Figs. 14(d) to (e)) is for accelerometer A3, ring gear. Figure 14(d) shows the RMS 

data for the entire test along with a running mean plus three-standard-deviation average. Here, most of the 

RMS values were above the running average for tests after the bearing failure at 106.11 hr, thus indicating 

false alarms for the majority of this data. This is further seen in Figure 14(e). The data in Figure 14(f), 

however, is based on a mean plus three-standard-deviation average for only the last day of testing. Here, 

the RMS does give an indication of gear failure at the end of the test. In summary and based on this 

analysis, none of the MDSS accelerometers gave an indication of gear failure using the raw RMS and a 

running average for the entire test. Accelerometers A2 and A3 did fully detected failure and A4 

marginally detected failure when using a running average for the last day only. 

Figure 14.—Evaluation of fault detection capability, RMS of MDSS raw vibration. (a) Accelerometer A1, entire test. 

(b) Accelerometer A1, last 30 min of test. (c) Accelerometer A1, last 30 min of test, mean and standard deviation 

evaluated for last day of test only. (d) Accelerometer A3, entire test. (e) Accelerometer A3, last 30 min of test. 

(f) Accelerometer A3, last 30 min of test, mean and standard deviation evaluated for last day of test only. 

 
NASA/TM—2015-218722 15 

Figure 15 depicts six specific gear fault detection CI’s from the MDSS system as a function of run 

time for the entire test. A complete definition of these CI’s is given in Appendix A. The CI’s were 

calculated from the time synchronous average (TSA) of the raw vibration data. The TSA method removes 

noisy data and allows the vibration signature of the gear under study to be separated from other gears or 

noise sources in the transmission that are non-synchronous with that gear (Ref. 9). For the OH-58C 

Figure 15.—MDSS fault detection condition indicators for entire test.
NASA/TM—2015-218722 16 

spiral-bevel pinion gear, the TSA was derived using the once-per-revolution tach pulse of the pinion gear 

shaft. The tach pulse was used to group vibration data in one shaft revolution increments. The groups 

were then resampled and time averaged to remove noise. The period of the TSA signal was one revolution 

of the pinion gear shaft. 

RMS, sideband index (SI1), and input shaft 3/rev of the TSA signals are shown in Figures 15(a), (d), 

and (f), respectively. FM4 and M8A of the difference signals are shown in Figures 15(b) and (e), 

respectively. The difference signal is the TSA signal minus the vibration at the gear mesh frequencies and 

first order shaft sidebands. NA4 of the residual signals is shown in Figure 15(c). The residual signal is the 

TSA signal minus the vibration at the gear mesh frequencies. From Figure 15, significant discontinuities 

existed for RMS and SI1, and somewhat less for NA4. Again, the discontinuities correspond to the start 

and stop times for the different run days. M8A was the most sensitive CI, reacting most to damage but 

exhibiting the most noise. 

Figure 16 shows the same CI’s as in Figure 15, but for only the last 30 min of run time. As stated 

above, pinion tooth fracture was observed at time 112.30 hr, indicated by dashed vertical lines in the 

figure. RMS for accelerometers A2 and A3 were fairly constant throughout the test, then increased in 

value at tooth fracture. This is not extremely obvious in Figure 16(a) due to wide vertical-axis scaling 

range in order to fit the plots for all four accelerometers. Based on the statistical definitions above, the 

TSA RMS for A2 and A3 fully detected failure using a running average for the last day only, and 

marginally detected failure using a running average for the entire test (due to false alarms). 

FM4 for accelerometer A3 significantly increased at the end of the test (Fig. 16(b)) and fully detected 

failure. FM4 for accelerometer A4 fully detected failure for the running average for the last day only, and 

marginally detected failure for the running average of the entire test. NA4 for all four accelerometers 

significantly increased at the end of test, fully detecting failure, and performed the best of all CI’s 

(Fig. 16(c)). SI1 for accelerometers A2 and A3 significantly increased at failure (fully detected failure), 

and accelerometers A1 and A4 somewhat increased at failure (Fig. 16(d)). M8A for accelerometer A3 

significantly increased at failure (fully detected failure, Fig. 16(e)). Input shaft 3/rev for accelerometer A2 

(Fig. 16(f)) increased at failure and fully detected failure using the running average of only the last day 

and marginally detected failure using the running average for the entire test. 

Tables I and II summarize the gear fault detection capabilities for the MDSS indicators. Table I uses 

the running mean plus three-standard-deviation average for the entire test while Table II uses the running 

average for the last day only. Fault detection capability was not consistent for the four accelerometers and 

the seven indicators. Accelerometer A3 performed the best and all indicators gave some fault detection 

(fully or marginal) with it. Accelerometer A1 performed the worst. Condition indicator NA4 performed 

the best and fully detected failure for all accelerometers. The fault detection capability was different when 

using the running average for the entire test (Table I) compared to only the last day of test (Table II). For 

the entire test, the standard deviation of the indicators was greater than using that for just the last day due 

to the increased scatter of the indicators. Thus, the criteria for fully detecting failure was more strict. As a 

final observation, the response from the best indicators did not react much sooner than the actual tooth 

fracture time (Fig. 16). 

To gain insight of the MDSS vibration data, Figure 17 shows spectra plots at two run times toward the 

end of the test. The first run time was at 110.50 hr (left column, Figs. 14(a) to (d)). This was at the start of 

the last day of testing. The second time was at 112.35 hr (right column, Figs. 14(e) to (h)) and was the last 

data point taken for the test, which occurred after pinion tooth fracture. All data were at 6180 rpm 

transmission input speed and 4649 in.-lb input torque. For the test before tooth failure (left column), the 

majority of the vibration energy occurred at the spiral-bevel and planetary mesh fundamental and harmonic 

frequencies (triangles and crosses in the figures). After tooth fracture (right column), the overall energy at 

the spiral-bevel and planetary mesh fundamental and harmonic frequencies was similar (same vertical scale 

in figures between left and right columns). However, increased energy occurred at sidebands of the spiralbevel mesh fundamental and harmonic frequencies in multiples of the transmission input shaft frequency 

(103 Hz). This energy is what was picked up by CI’s RMS, FM4, NA4, SI1, and M8A. 

 
NASA/TM—2015-218722 17 

Figure 16.—MDSS fault detection condition indicators for last 30 min of test. 

 
NASA/TM—2015-218722 18 

TABLE I.—GEAR TOOTH FAULT DETECTION CAPABILITY, MDSS DATA 

(Mean plus three-standard deviation running average based on entire test). 

 Accelerometer 

Condition indicator A1 A2 A3 A4 

RMS (raw) 

RMS (TSA) m m 

FM4 m Y m 

NA4 Y Y Y Y 

SI1, g Y Y 

M8A m Y m 

Input Shaft 3/rev, g m 

 Y, Failure fully detected 

 m, Failure marginally detected 

TABLE II.—GEAR TOOTH FAULT DETECTION CAPABILITY, MDSS DATA 

(Mean plus three-standard deviation running average based on last day of test). 

 Accelerometer 

Condition indicator A1 A2 A3 A4 

RMS (raw) Y Y m 

RMS (TSA) Y Y Y Y 

FM4 m Y Y 

NA4 Y Y Y Y 

SI1, g m Y Y Y 

M8A Y Y 

Input Shaft 3/rev, g m Y 
NASA/TM—2015-218722 19 

Figure 17.—MDSS sample spectrums. (a) Accelerometer A1 at run time 110.50 hr. (b) Accelerometer A2 at run time 

110.50 hr. (c) Accelerometer A3 at run time 110.50 hr. (d) Accelerometer A4 at run time 110.50 hr. (e) Accelerometer 

A1 at run time 112.35 hr. (f) Accelerometer A2 at run time 112.35 hr. (g) Accelerometer A3 at run time 112.35 hr. (h) 

Accelerometer A4 at run time 112.35 hr. 

MEMS Results 

Figure 18 shows the RMS of the raw broadband vibration for the MEMS sensors as a function of run 

time for the entire endurance test. This data was post-processed after completion of the tests. The RMS 

values for each of the three MEMS sensors were calculated for each one-second broadband time 

acquisition with DC offsets removed. Figure 18(a) gives the radial accelerometer, R, Figure 18(b) gives 

the tangential accelerometer, T1, and Figure 18(c) gives the tangential accelerometer, T2 (refer to Fig. 7) 

plotted versus cumulative run time. The radial accelerometer measured radial or lateral motion of the 

pinion gear shaft. The tangential accelerometers measured radial motion as well as tangential or rotational 

acceleration of the gear shaft. Adding the signals of the tangential accelerometers (T1+T2, Fig. 18(d)) 

results in purely torsional motion since the T1 and T2 accelerometers are positioned at opposite polarity 

(Fig. 7). Subtracting the signals of the tangential accelerometers (T1-T2, Fig. 18(e)) results in just radial 

motion and is similar to the radial accelerometer, R. 
NASA/TM—2015-218722 20 

Figure 18.—RMS of MEMS raw vibration for entire test. (a) Radial accelerometer, R. (b) Tangential 

accelerometer, T1. (c) Tangential accelerometer, T2. (d) T1+T2, torsional acceleration. (e) T1-T2, 

radial acceleration.
NASA/TM—2015-218722 21 

Overall, the MEMS system performed well and lasted the entire 112.36-hr test. At 11.50 hr 

cumulative run time, the MEMS battery, accelerometer board, and transmitter board were replaced with 

spare units. This was due to difficulties encountered with the sleep portion of the controlling software, 

which would reduce battery power during non-run time. At 51.86 hr run time, the battery and transmitter 

board were replaced with additional spare units. This was due to a long period of inactivity in which an 

additional notch was being fabricated on the test pinion gear. 

Figure 19 shows the same data as Figure 18, but expanded for only the last 30 min of test. From the 

RMS, all three accelerometers (R, T1, and T2) gave an indication of failure at the end of the test 

(Figs. 19(a) to (c)). Based on the statistical definition previously defines, accelerometers R and T2 fully 

detected failure and accelerometer marginally detected failure using the running average for the entire test 

and all accelerometers fully detected failure using the running average of only the last day. As with the 

MDSS data, the MEMS sensors did not respond much sooner than the actual tooth fracture time. 

To gain insight of the MEMS vibration data, Figure 20 shows spectra plots at two run times toward 

the end of the test. The first run time was at 110.49 hr (left column, Figs. 20(a) to (e)). This was at the 

start of the last day of testing. The second time was at 112.35 hr (right column, Figs. 20(f) to (j)) and was 

the last data point taken for the test, which occurred after pinion tooth fracture. All data were at 6180 rpm 

transmission input speed and 4649 in.-lb input torque. 

For the radial accelerometer, only radial or lateral motion is measured. The measurement direction of 

the sensor rotates in a sinusoidal manor with the pinion gear shaft. Thus, the measured response from the 

radial accelerometer is the product of a sinusoidal function of the pinion shaft frequency and a sinusoidal 

function of the radial motion, such as from the gear mesh frequencies. The product of trigonometric 

functions is given by (Ref. 10) 

cos A cos B  0.5cos A B cosA B (1) 

sin A sin B  0.5cos A B cos A B (2) 

Thus, the vibration for the spiral-bevel gear mesh will not occur at the mesh frequencies, fm, but at the 

sideband frequencies fm+fs and fm-fs, where fs is the shaft frequency. The spectrum for the radial 

accelerometer in Figure 20(a) illustrates this phenomenon. Vibration did not occur at the spiral-bevel mesh 

frequencies, 1957 (meshing frequency), 3914 (1st harmonic), and 5871 (2nd harmonic) Hz. They occurred 

at 1957103 = 1854 and 2060 Hz (meshing frequencies), 3914103 = 3811 and 4017 Hz (1st harmonic), 

and 5871103 = 5768 and 5974 Hz (2nd harmonic), where the shaft frequency was 103 Hz. 

For the tangential accelerometers, radial motion and tangential motion are measured. The torsional 

motion will cause vibration directly at the gear meshing frequencies since this motion follows the rotating 

measurement position. The radial motion will cause the sidebands as described above. Figures 20(b) and 

(c) show this where vibration spikes occur at 3811, 3914, 4017, 5768, 5871, and 5974 Hz for the spiralbevel mesh second and third harmonic frequencies. It is interesting to note that there is no torsional 

vibration at the spiral-bevel meshing frequency of 1957 Hz. Accelerometers T1 and T2 gave very similar 

responses. Figure 20(d) depicts the vibration from T1+T2, which is the torsional acceleration. Here, the 

radial/lateral portion is cancelled out, and thus, vibration occurred at the gear meshing frequencies and not 

the sidebands as in R, T1, and T2. Figure 20(e) shows the vibration from T1-T2. Here, the torsional 

portion is cancelled out and the response is similar to the radial accelerometer from Figure 20(a). 

For the data before tooth failure (Fig. 20 left column), the majority of the vibration energy occurred at 

the spiral-bevel mesh, harmonic, and sideband frequencies (triangles in the figures). Only a small amount of 

energy occurred at the planetary mesh frequencies (cross in figures) since the MEMS sensing package was 

installed directly on the rotating spiral-bevel pinion gear shaft. After tooth fracture (right column), the 

overall energy at the spiral-bevel and planetary mesh fundamental and harmonic frequencies was similar 

(same vertical scale in figures between left and right columns). However, much increased energy occurred 

through the complete spectrum, with an emphasis on sidebands at multiples of the bevel gear shaft 

frequency. This was the reason the RMS indicator on the overall broadband signal did detect tooth failure. 
NASA/TM—2015-218722 22 

Figure 19.—RMS of MEMS raw vibration for last 30 min of test. (a) Radial accelerometer, R. 

(b) Tangential accelerometer, T1. (c) Tangential accelerometer, T2. (d) T1+T2, torsional 

acceleration. (e) T1-T2, radial acceleration. 
NASA/TM—2015-218722 23 

Figure 20.—MEMS sample spectrums. (a) Radial accelerometer, R, at run time 110.49 hr. (b) Tangential 

accelerometer, T1, at run time 110.49 hr. (c) Tangential accelerometer, T2, at run time 110.49 hr. (d) T1+T2 at run 

time 110.49 hr. (e) T1-T2 at run time 110.49 hr. (f) R at run time 112.35 hr. (g) T1 at run time 112.35 hr. (h) T2 at 

run time 112.35 hr. (i) T1+T2 at run time 112.35 hr. (j) T1-T2 at run time 112.35 hr. 

 
NASA/TM—2015-218722 24 

It was desired to apply time synchronous averaging to the MEMS data to investigate if it improved 

fault detectability. There was, however, no tach pulse associated with the saved MEMS data. The method 

of Bechhoefer (Ref. 11) was used to construct a pseudo tach signal from the periodic characteristics of the 

vibration data. From this method, the vibration time signal was filtered around a strong periodic signal 

with high signal-to-noise ratio, such as a gear mesh fundamental or harmonic frequency, using a narrow 

band pass filter. The filtered signal was fed to a zero-crossings algorithm which calculated the time and 

index when the signal crossed zero in a positive sense. The resulting indexes were used to determine the 

gear shaft period. As an example, every 319 = 57 indexes from the zero-crossings routine would indicate 

one rotation of the gear shaft if the 3rd harmonic frequency of a 19-tooth gear was used for the pass band 

frequency. 

First, this method was applied to MDSS data to compare the TSA calculated from the pseudo tach 

signal to that calculated from the actual tach signal. Figure 21(a) shows a sample spectrum from MDSS 

accelerometer A2 at run time 110.50 hr (same data as in Fig. 17(b)). The black data is the spectrum from 

the raw time signal and the red data is the spectrum from the filtered signal used for the pseudo tach 

calculation. The red data was filtered around 5872 Hz, which was the 3rd harmonic of the spiral-bevel 

mesh. Figure 21(b) shows the calculated pseudo tach from the zero-crossings routine. The mean 

Figure 21.—Sample pseudo tach calculation results using MDSS 

data at run time 110.50 hr. (a) Spectrum from accelerometer 

A2. (b) Calculated pseudo tach. (c) Time synchronous 

averages (black: MDSS tach, red: Pseudo tach). 
NASA/TM—2015-218722 25 

calculated speed from the pseudo tach data was 6182 rpm, which correlated exactly with that from the 

facility data acquisition speed sensor. Figure 21(c) compares the TSA’s. The black data is the MDSScalculated TSA using the measured tach signal. The red data is the TSA using the pseudo tach signal. As 

seen in the figure, good correlation between the TSA using the measured tach signal to that using the 

pseudo tach signal is seen. 

Figure 22 shows a sample TSA from the MEMS data at run time 110.49 hr. Tangential accelerometer 

T1 was used to extract the pseudo tach signal and Figure 22(a) shows the spectrum. The filtered data 

around 3915 Hz (spiral-bevel mesh 2nd harmonic frequency) was used because it was the cleanest gear 

harmonic. Figure 22(b) to (d) depict the TSA’s for accelerometers R, T1, and T2, respectively. 

Figure 22(e) to (g) shows the spectrums of the TSA’s. For this example, a relatively large once-perrevolution oscillation occurred. The period of the TSA signal was one gear shaft rotation. A total of 512 

interpolated point were used for the TSA. This gave a bandwidth of one shaft order (103 Hz) in the 

frequency domain. As expected, energy is seen around the spiral-bevel gear mesh fundamental and 

Figure 22.—Sample time synchronous average calculation results using MEMS data at run time 110.49 hr. 

(a) Spectrum from accelerometer T1, used for pseudo tach calculation. (b) TSA, radial accelerometer, R. (c) TSA, 

tangential accelerometer, T1. (d) TSA, tangential accelerometer, T2. (e) FFT of TSA, radial accelerometer, R. 

(f) FFT of TSA, tangential accelerometer, T1. (g) FFT of TSA, tangential accelerometer, T2. 
NASA/TM—2015-218722 26 

harmonics frequencies, with higher activity at the 2nd and 3rd harmonics. Similar results were obtained 

when accelerometer T2 was used to extract the pseudo tach signal. Radial accelerometer R could not be 

used to extract the pseudo tach signal since it did not exhibit strong energy directly at any gear mesh 

harmonic frequency. 

Figure 23 shows six gear fault detection CI’s calculated from the pseudo tach TSA signals of the 

MEMS data. The CI’s are shown as a function of run time for the entire test. These CI’s can be compared 

to those from the MDSS (Fig. 15). Note that SI3 performed better than SI1 for the MEMS data and is 

shown in the results. In general, the MEMS CI’s were a little noisier than those from the MDSS, but all 

exhibited an increase in value at gear tooth failure at the end of the test. Figure 24 shows the MEMS CI’s 

for the last 30 min of the testing. Again, gear tooth failure occurred at 112.30 hr. Tables III and IV 

summarize the gear fault detection capabilities for the MEMS indicators. Table III uses the running mean 

plus three-standard-deviation average for the entire test while Table IV uses the running average for the 

last day only. All CI’s for all accelerometers give an indication of failure when using the running average 

of only the last day (Table IV). Raw RMS, TSA RMS, NA4, and SI3 fully detected failure for all 

accelerometers. Accelerometer T1 performed the best where all CI’s fully detected failure. This was 

probably due to accelerometer T1 being physically closest to the fractured gear tooth (Fig. 7). The method 

of constructing a pseudo tach signal from periodic characteristics of the vibration data was successful in 

deriving a TSA signal without an actual tach and proved as an effective way to improve fault detection. 

As with the MDSS results, the fault detection capability was rated lower when the running average used 

data from the entire test (Table III) due to increased scatter. The MEMS CI’s reacted to the gear failure at 

a similar time as that from the MDSS data, again, not much sooner than the actual tooth fracture. In 

comparing the gear fault detection capability of the MDSS to the MEMS (comparing Tables I to IV), the 

MEMS systems performed as well, if not better, than the MDSS. 

Bearing Failure Detection 

As previously mentioned, a fatigue spall failure was discovered on the spiral-bevel gear roller bearing 

inner race at 106.11 hr run time. Figure 25(a) shows the cumulative mass of the oil debris sensor as a 

function of run time for the entire test. From 0 to 9 hr, the debris increased from 0 to 29 mg, exhibiting a 

common “cleaning” condition. From the 29 to 58 hr, discrete increases in debris were measured. At 58 hr, 

the measured debris rapidly increased with time, giving a pronounced indication of component failure. At 

59 hr, the OH-58 transmission flight hardware chip detector started to give indication of debris also. The 

transmission was disassembled and inspected at 106.11 hr run time, and the spalled spiral-bevel gear 

roller bearing inner race was discovered. 

Figure 25(b) shows the processed vibration data from MDSS accelerometer A3. This data used a 

common method for rolling element bearing fault detection in which the raw data was band pass filtered 

and enveloped (Ref. 12). Shown in the figure are the magnitudes of the inner race bearing frequency of 

filtered and enveloped data. Some disturbance is shown at about 70 hr, but significant response to the 

fault is shown at about 86 hr. This analysis used band pass frequencies from 30 to 50 kHz. Fault detection 

was possibly in this range since high-frequency energy from the bearing was measured using the MDSS 

high-frequency accelerometers while low-frequency noise from the gear mesh was filtered and removed. 

Subsequent analysis was performed using lower band pass frequencies. Bearing failure was not detected, 

however, for lower limit band pass frequencies less than 30 kHz. 

The MEMS vibration data did not give any indication of the bearing failure. This was most likely due 

to the limited frequency content of the sensors. The system was designed to detect spiral-bevel pinion 

gear failure, and was limited to around 44 kHz sampling rate, and thus, 22 kHz maximum usable 

frequency. As stated above, the MDSS needed 30 to 50 kHz band pass filters to detect bearing failure. 

 
NASA/TM—2015-218722 27 

Figure 23.—MEMS fault detection condition indicators for entire test. 
NASA/TM—2015-218722 28 

Figure 24.—MEMS TSA condition indicators for last 30 min of test. 
NASA/TM—2015-218722 29 

TABLE III.—GEAR TOOTH FAULT DETECTION CAPABILITY, MEMS DATA 

(Mean plus three-standard deviation running average based on entire test). 

 Accelerometer 

Condition indicator R T1 T2 

RMS (raw) Y m Y 

RMS (TSA) Y m m 

FM4 m m 

NA4 m m m 

SI3, g Y 

M8A m m 

Input Shaft 3/rev, g m m m 

TABLE IV.—GEAR TOOTH FAULT DETECTION CAPABILITY, MEMS DATA 

(Mean plus three-standard deviation running average based on last day of test). 

 Accelerometer 

Condition indicator R T1 T2 

RMS (raw) Y Y Y 

RMS (TSA) Y Y Y 

FM4 m Y m 

NA4 Y Y Y 

SI3, g Y Y Y 

M8A m Y m 

Input Shaft 3/rev, g Y Y m 

Figure 25.—Bearing fault detection condition indicators from MDSS data. (a) Oil debris monitor (ODM) 

cumulative mass. (b) Accelerometer A3 bearing inner race condition indicator. 
NASA/TM—2015-218722 30 

Conclusions 

The diagnostics capability of MEMS-based, rotating accelerometer sensors in detecting gear tooth 

crack failures in helicopter main-rotor transmissions was evaluated. MEMS sensors were installed on a 

pre-notched spiral-bevel pinion gear inside the OH-58C helicopter main-rotor transmission. Endurance 

tests were performed and the gear was run to tooth fracture failure. Results from the MEMS sensor were 

compared to conventional accelerometers mounted on the transmission housing. The following results 

were obtained: 

1. The MEMS system performed well and lasted the entire 112.36-hour test, providing both rotational 

vibration and speed measurement data. 

2. All three MEMS accelerometers mounted inside the gear box gave an indication of failure at the end 

of the test. 

3. Most of the four stationary accelerometers mounted on the gear box housing and most of the CI’s 

used gave indications of failure at the end of the test. 

4. The MEMS systems performed as well, if not better, than the stationary accelerometers mounted on 

the gear box housing with regards to gear tooth fault detection. 

5. For both the MEMS sensors and stationary sensors, the fault detection time was not much sooner than 

the actual tooth fracture time. 

6. The MEMS sensor spectrum data showed large first order shaft frequency sidebands due to the 

measurement rotating frame of reference. 

7. The method of constructing a pseudo tach signal from periodic characteristics of the vibration data 

was successful in deriving a TSA signal without an actual tach and proved as an effective way to 

improve fault detection for the MEMS data. 
NASA/TM—2015-218722 31 

Appendix A—Condition Indicator (CI) Definitions 

Root Mean Square 

The root mean square (RMS) is defined as the square root of the average of the sum of the squares of 

the TSA vibration signal (Eq. (3)). For a simple sine wave vibration trace, the RMS value is 

approximately 0.707 times the amplitude of the signal. 















  



N

i

Si N 1

1 2 RMS (3) 

where 

S time-synchronous-averaged (TSA) vibration trace 

i data point number in vibration trace 

N total number of data points in vibration trace 

FM4 

The FM4 parameter (Eq. (4)) was developed to detect changes in vibration pattern resulting from 

damage to a single gear tooth (Ref. 9). The metric is calculated by dividing the fourth statistical moment 

(kurtosis) of the difference signal by the square of the variance of the difference signal. The difference 

signal is defined as the time-averaged vibration trace, S, minus the vibration at the gear mesh frequencies 

and first order shaft sidebands. The metric is non-dimensional with a nominal value of three for Gaussian 

noise (assumed for a healthy component). 

 

 

2

1

2

4 1

FM4



  

 







N

i i

N

i i

d d

N d d

 (4) 

where 

d difference signal 

݀̅ mean value of difference signal 

i data point number in difference signal 

N total number of data points in difference signal 

NA4 

The NA4 metric (Eq. (5)) was developed to overcome a shortcoming of the FM4 metric (Ref. 13). As 

the occurrences of damage progresses in both number and severity, FM4 becomes less sensitive to the 

new damage. Two changes were made to the FM4 metric to develop the NA4 metric as one that is more 

sensitive to progressing damage. One change is that FM4 is calculated from the difference signal while 

NA4 is calculated from the residual signal. The residual signal includes the first order gear sidebands that 

were removed from the difference signal. The second change is that trending was incorporated into the 

NA4 metric. While FM4 is calculated as the ratio of the kurtosis of the data record divided by the square 

of the variance of the same data record, NA4 is calculated as the ratio of the kurtosis of the data record 

divided by the square of the average variance. The average variance is the mean value of the variance of 

all previous data records in the run ensemble. These two changes make the NA4 metric a more sensitive 

and robust metric. The NA4 metric is calculated by 
NASA/TM—2015-218722 32 

 

 

2

1 1

2

1

4

1

4





 



 

 

 



 



M

j

N

i ij

N

i i

rr

M

rrN

NA (5) 

where 

r residual signal 

ݎ̅ mean value of residual signal 

i data point number in residual signal 

N total number of points in residual signal 

j time record number in run ensemble 

M current time record in run ensemble 

M8A 

The parameter M8A (Eq. (6)) was proposed by Martin (Ref. 14) and was designed to be more 

sensitive than FM4 or NA4 to peaks in the difference signal. M8A uses the eight moment normalized by 

the variance to the fourth power and is given as 

 

  4

1

2

1

3 8

8



  

 









N

i i

N

i i

dd

ddN

AM (6) 

SI 

The sideband index, SI1 (Eq. (7)), is a measure of local gear faults and is defined as the average of the 

first shaft order sidebands of the gear mesh fundamental frequency (Ref. 15). An increase in magnitude of 

the sidebands drives this CI and indicates a local fault, and is given by 

2

SI 11

1

   yy (7) 

where 

y-1 magnitude of TSA spectrum at frequency (fm -fs), where fm = gear mesh fundamental frequency 

and fs = gear shaft frequency 

y+1 magnitude of TSA spectrum at frequency (fm +fs) 

A slight deviation of this parameter, SI3 (Eq. (8)), is to use the first three sideband about the gear mesh 

frequency where 

6

SI 321123

3

       yyyyyy (8) 

where 

y±i magnitude of TSA spectrum at frequency (fm ±ifs, i = 1 to 3) 
NASA/TM—2015-218722 33 

Input Shaft 3/Rev 

The input shaft 3/rev parameter is the magnitude of the TSA spectrum at a frequency of three time the 

shaft speed. From previous gear endurance tests (Ref. 16), it was shown that a gear fault disturbed the 

simply once per revolution periodicity of the TSA signal. The magnitude at two to ten shaft orders were 

increased for a local gear fault. Trending the three per revolution magnitude was effective in detecting 

gear tooth local failures. 

References 

1. Samuel, P.D., and Pines, D.J., “A Review of Vibration-Based Techniques for Helicopter 

Transmission Diagnostics,” Journal of Sound and Vibration, Vol. 282, No. 1-2, pp. 475-508, 2005. 

2. Suryavanashi, A., Wang, S., Gao, R., Danai, K., and Lewicki, D., “Condition Monitoring of 

Helicopter Gearboxes by Embedding Sensing,” Proceedings of American Helicopter Society 58th 

Annual Forum, Montreal, Quebec, Canada, Jun 11-13, 2002. 

3. Ghoshal, A., Welsh, G.S., Gurvich, M.R., Butler, S.L., Winston, H., Costiner, S., Attridge, P., 

Urban, M.R., and Bordick, N., “Smart Embedded Sensors in Rotorcraft Composite Components for 

Condition Based Maintenance,” Proceedings of the American Helicopter Society 66th Annual 

Forum, Phoenix, AZ, May 11-13, 2010. 

4. Baldwin, C.S., Kiddy, J.S., and Samuel, P.D., “Towards Development of a Fiber Optic-Based 

Transmission Monitoring System,” Proceedings of SPIE Vol. 8026 Photonic Applications for 

Aerospace, Transportation, and Harsh Environment II, Orlando, FL, May 25, 2011. 

5. Berdy, D., Adams, D., Jang, J.H., Jung, B., Peroulis, D., Sadeghi, F., and Scott, S., “Self-Powered 

Helicopter Health Monitoring Sensor,” Proceedings of the American Helicopter Society 66th Annual 

Forum, Phoenix, AZ, May 11-13, 2010. 

6. Scott, S.; Kovacs, A.; Gupta, L.; Katz, J.; Sadeghi, F.; Peroulis, D., “Wireless Temperature 

Microsensors Integrated on Bearings for Health Monitoring Applications,” Proceedings of the 24th 

IEEE International Conference on Micro Electro Mechanical Systems, Jan. 23-27, 2011. 

7. Qin, G. Hu, N., “Design of Embedded Wireless Sensor and Its Soft Encapsulation for Embedded 

Monitoring of Helicopter Planetary Gear Set,” Proceedings of the 25th International Congress on 

Condition Monitoring and Diagnostic Engineering, Journal of Physics: Conference Series 364, 2012. 

8. Dempsey, P.J., “Data Fusion Tool for Spiral Bevel Gear Condition Indicator Data,” Proceedings of 

the Society for Machinery Failure Prevention Technology for the Society’s 68th Conference, May 

20-22, 2014. 

9. Stewart, R.M., “Some Useful Data Analysis Techniques for Gearbox Diagnostics,” Report 

MHM/R/10/77, Machine Health Monitoring Group, Institute of Sound and Vibration Research, 

University of Southampton, Jul. 1977. 

10. Spiegel, M.R., “Mathematical Handbook, Schaum’s Outline Series,” McGraw-Hill Book Company, 

1968. 

11. Bechhoefer, E., and Kingsley, M., “A Review of Time Synchronous Average Algorithms,” 

Proceedings of the Annual Conference of the Prognostics and Health Management Society, 

San Diego, CA, Sep. 27–Oct. 1, 2009. 

12. Randall, R.B., Antoni, J., “Rolling Element Bearing Diagnostics - A Tutorial,” Mechanical Systems 

and Signal Processing, Vol. 25, pp. 485–520, 2011. 

13. Zakrajsek, J.J., Townsend, D.P., and Decker, H.J., “An Analysis of Gear Fault Detection Methods as 

Applied to Pitting Fatigue Failure Data,” Proceedings of the Machinery Failure Prevention 

Technology for the Society’s 47th Conference, Apr. 13-15, 1993. 

14. Martin, H.R., “Statistical Moment Analysis as a Means of Surface Damage Detection,” Proceedings 

of the Seventh International Modal Analysis Conference, Society for Experimental Mechanics, 

Schenectady, NY, 1989, pp. 1016–1021. 
NASA/TM—2015-218722 34 

15. Antolick, L.J, Branning, J.S., Wade, D.R., and Dempsey, P.J., “Evaluation of Gear Condition 

Indicator Performance on Rotorcraft Fleet,” Proceedings of the American Helicopter Society 66th 

Annual Forum, Phoenix, AZ, May 11-13, 2010. 

16. Lewicki, D.G., Heath, G.F., Filler, R.R., Slaughter, S.C., and Fetty, J., “Face-Gear Surface 

Durability Investigations,” Journal of the American Helicopter Society, Vol. 53, No. 3, pp. 282-289, 

Jul. 2008.