Anwarul Islam

Youngstown State University, Youngstown, Ohio

Paula Dempsey

Glenn Research Center, Cleveland, Ohio

Jason Feldman and Chris Larsen

Etegent Technologies, Ltd., Cincinnati, Ohio 

Characterization and Comparison of Vibration 

Transfer Paths in a Helicopter Gearbox 

and a Fixture Mounted Gearbox

NASA/TM—2013-216586

September 2013
	
	
	








	



	

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Anwarul Islam

Youngstown State University, Youngstown, Ohio

Paula Dempsey

Glenn Research Center, Cleveland, Ohio

Jason Feldman and Chris Larsen

Etegent Technologies, Ltd., Cincinnati, Ohio 

Characterization and Comparison of Vibration 

Transfer Paths in a Helicopter Gearbox 

and a Fixture Mounted Gearbox

NASA/TM—2013-216586

September 2013


	



	


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NASA/TM—2013-216586 1 

Characterization and Comparison of Vibration Transfer Paths in a 

Helicopter Gearbox and a Fixture Mounted Gearbox 

Anwarul Islam 

Youngstown State University 

Youngstown, Ohio 44555 

Paula Dempsey 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Jason Feldman and Chris Larsen 

Etegent Technologies, Ltd. 

Cincinnati, Ohio 45212 

Abstract 

Health monitoring of rotorcraft components, currently being performed by Health and Usage 

Monitoring Systems through analyses of vibration signatures of dynamic mechanical components, is very 

important for their safe and economic operation. HUMS analyze vibration signatures associated with 

faults and quantify them as condition indicators to predict component behavior. Vibration transfer paths 

are characterized by frequency response functions derived from the input/output relationship between 

applied force and dynamic response through a structure as a function of frequency. With an objective to 

investigate the differences in transfer paths, transfer path measurements were recorded under similar 

conditions in the left and right nose gearboxes of an AH-64 helicopter and in an isolated left nose gearbox 

in a test fixture at NASA Glenn Research Center. The test fixture enabled the application of measured 

torques—common during an actual operation. An impact hammer as well as commercial and lab piezo 

shakers, were used in conjunction with two types of commercially available accelerometers to collect the 

vibration response under various test conditions. The frequency response functions measured under 

comparable conditions of both systems were found to be consistent. Measurements made on the fixture 

indicated certain real-world installation and maintenance issues, such as sensor alignments, accelerometer 

locations and installation torques, had minimal effect. However, gear vibration transfer path dynamics 

appeared to be somewhat dependent on the presence of oil, and the transfer path dynamics were notably 

different if the force input was on the internal ring gear rather than on the external gearbox case.

Introduction 

The integrity of the helicopter transmission system is critical to helicopter safety because helicopters 

depend on the powertrain for propulsion, lift and maneuvering (Ref. 1). A study of 1,168 helicopter 

accidents from 1990 to 1996 found that accidents due to various system and structural failures were 

second in importance only to failures due to human causes (Ref. ). In 1999, 28 out of 192 turbine 

powered helicopter accidents in the world were directly caused by mechanical failures in the drive 

train of the propulsion system (Ref. ). In order to reduce the occurrence of such accidents, the study in 

Reference recommended the design of Health and Usage Monitoring System (HUMS) capable of 

predicting impending equipment failure for on-condition maintenance, and more advanced systems 

capable of warning pilots of imminent equipment failure. 
NASA/TM—2013-216586 2 

Time in operation

Life consumption

Time-based service

Mild usage without monitoring

Severe usage

Current service life

Design life of

component

Potential safety risk

without monitoring

Gain in service life

due to monitoring

Figure 1.—Economic and safety benefits of health monitoring systems (Ref. ). 

Figure 1 shows the potential safety and economic benefit of diagnostic and prognostic maintenance of 

critical components in a mechanical system (Ref. ). If the damage and wear due to usage is more severe than 

what is expected from the predicted service life of a component, health and usage monitoring would provide 

a safety benefit. Conversely, the service life could be extended if actual usage is less severe than predicted. 

HUMS use algorithms referred to as condition indicators (CIs), which are generated from fault 

patterns produced in vibration signatures when damaged components interact with their environment. 

Understanding structural differences between systems may provide insight into the difference in 

performance of diagnostic tools between such systems. 

Damage progression tests of spiral bevel gears, that consist of a ring gear and pinion set, are being 

performed in the Spiral Bevel Gear Fatigue test rig at the at NASA Glenn Research Center (GRC). The 

objective of these tests, as outlined in Reference , are to determine if ‘seeded or accelerated fault’ tests, 

in which a component is tested with a known fault, can be used as evidence that a HUMS condition 

indicator will reliably detect tooth damage when installed on a helicopter. For this approach, existing inservice HUMS flight data from helicopter nose gearbox (NGB) spiral bevel gears will be compared to test 

rig spiral bevel gear failure progression data. The field data analysis of spiral bevel gears condition 

indicators determined the CIs that performed the best in the field. The information learned from this 

analysis, documented in References  and , was fed into development of the spiral bevel gear rig tests. 

Performing these tests will also be used to identify the limitations of seeded fault data sets for 

demonstrating helicopter CI performance. 

In addition to performing dynamic tests of the gears with varying levels of damage to the gear teeth, 

measurements will be made to characterize differences in the structural dynamics between the helicopter 

and test rig systems. Although the transfer path can change under dynamic conditions due to load and 

speed, the static structure can also filter the response between the vibration source and the accelerometer 

on the housing. Understanding how the response of the gear set, at gear mesh due to damage, travels 

through the structure may answer some questions as to why diagnostic tools perform differently on 

different systems. 
NASA/TM—2013-216586 3 

Figure 2.—Three spiral bevel geared systems 

The approach used to assess the usefulness of vibration transfer paths in assessing CI performance 

was to take measurements on three spiral bevel geared systems for comparison. These three systems were 

the helicopter NGB, a NGB removed from a helicopter and installed in a static fixture, and the spiral 

bevel gear fatigue rig as shown in Figure 2. This comparison requires taking measurements on the 

helicopter or fixture that can be compared to future measurements on the test rig. The helicopter nose 

gearbox transfer path measurements were taken for selecting enveloping/demodulation frequency bands 

for bearing monitoring (Ref. ). Since the purpose of measurements made for this analysis was to 

determine if transfer path measurements under static gear conditions could provide insight into gear CI 

performance, additional measurements were required (Ref. 	). Limited accessibility to the gear mesh 

within the NGB installed on the helicopter made it impossible to simulate an impact of the gear teeth at 

the source. That is, the ideal force input location for this measurement would be directly between meshing 

gear teeth, but this is not physically possible. However, external measurements made on the helicopter 

could be repeated on the fixture to verify both had similar response, then additional measurements could 

be made on the fixture under conditions that could be later compared to the test rig. 

The objectives of this research were to compare frequency response functions for a nose gearbox 

installed on an AH-64 helicopter to those of a left NGB installed in a fixture at GRC for testing and 

research. The NGB test fixture enabled the application of measured torques—common during an actual 

operation and the simulation of other environmental conditions experienced in the field that could not be 

made on the helicopter. Measurements were taken under varying operational conditions and compared on 

the NGB fixture. This approach first required the comparison of external measurements made on the 

helicopter to external measurements made on the fixture under the same conditions. Next, measurements 

taken with the fixture NGB under load and other varying operational conditions were compared. Third, 

measurements were taken and compared while impacting the gear set near mesh to simulate gear meshing 

dynamics. 

Test Procedure 

Modal analysis is generally done to identify the resonance frequencies or natural frequencies of a 

structure. It is typically performed by exciting a structure with a known force and measuring the vibration 

response, such as acceleration, at various locations on the structure. Frequency response functions (FRF) 

are used to analyze structural dynamics under static conditions and to estimate modal parameters for 

analysis of mechanical systems. An FRF is measured response normalized by measured input. Presence of 

damage in a dynamic mechanical system is usually reflected in its dynamic vibration signatures. The 

effect the static structure has on the response can be further analyzed using FRFs. Therefore, vibration 

transfer path (VTP) characteristics in a NGB might be useful in determining the difference in structural 

dynamics between the Spiral Bevel Gear Test Rig and a helicopter. In this research, vibration response of 

left and right NGBs in an AH-64 helicopter and the left NGB in the test fixture at GRC were collected 

under similar boundary conditions to determine the characteristics of their vibration transfer paths using 
NASA/TM—2013-216586 4 

FRFs. The similarity between the FRFs of the NGBs in the helicopter and the test fixture were quantified 

using Kolmogorov-Smirnov tests. Vibration transfer path measurements were recorded on the left and 

right NGBs of an AH-64 helicopter during the week of April 11 through April 15, 2011, at Fort 

Campbell, Kentucky (Ref. ). These measurements were made from 0 to 50 kHz. Since the reaction-mass 

shaker only provides good excitation from about 3 kHz and up, impact testing was done to measure the 

low frequency response. These measurements were put together to produce a complete FRF from 0 to 

50 kHz; stitching the FRFs together provides a further check that measurements from two different input 

sources agree. There were six excitation locations in both the left and right NGBs, as shown in Figure 3. 

These locations were kept as identical as possible in the right NGBs in the helicopter and the left NGB in 

the test fixture. 

Vibration transfer path measurements were also recorded on an isolated left NGB at GRC test facility 

from April 18 to 20, 2012. The transfer paths were recorded from 0 to 50 kHz. Locations of 

accelerometers were kept the same on the lab fixture as they were on the helicopter. For comparison, it 

was important to use the same equipment and locations that were used during the helicopter data 

collections. Although the measurements in the field were taken with no load on the gear set, the test 

fixture enabled the application of torque to the input side of the NGB comparable to the torques applied 

by their engine (Ref. 
). 

Figure 3.—Shaker locations 1 through 6 on left and right NGBs in AH-64 helicopter.

Location 5 

Location 2 

Location 6 

Location 3 

Location 4 

Location 1 Location 1 

Location 2 

Location 6 

Location 3 

Location 4 

Location 5 

Left NGB 

Left NGB 

Right NGB 

Right NGB 
NASA/TM—2013-216586 5 

The basic component of these tests was a 60-sec data set recorded with two shakers one at a time 

stepping from 0 to 50 kHz in a 5 sec chirp. In this way, each FRF was computed by averaging 12 sweeps. 

Table I shows the types of shaker and accelerometer, shaker locations and load on gearboxes for each test. 

However, Test 4 was discarded because the shaker did not function properly. The Commercial Shaker is a 

piezoelectric actuator and the Lab Piezo Shaker is a custom shaker made from two miniature multilayer 

Piezo stack actuators and a similarly sized tungsten cube (for reaction mass), which can be seen along 

with the PCB (Ref. 1
) Hammer in Figure 4. While the Commercial Shaker was mounted on the outside 

of the gearbox, the Lab Piezo Shaker was attached to the ring gear of the NGB close to the gear mesh, 

since the Commercial Shaker would not fit inside the closed gearbox. For low frequency measurements, a 

general purpose impact hammer was used since the shakers do not generate much energy below 5 kHz. 

The left NGB at GRC was also subjected to various ranges of loads, as shown in Table II, to determine if 

load causes any difference in VTP. Pictures of shaker locations, ring gear, left NGB fixture and the torque 

application are shown in Figure 5. 

TABLE I.—DESCRIPTIONS OF TESTS WITH SHAKER AND ACCELEROMETER TYPES 

Test Shaker type Accelerometer 

type 

Shaker 

location 

Loads on gearbox/comments 

Test 1 Commercial Dytran Location 1 Gearbox under range of loads 

Test 2 Hammer Dytran Location 1 Low frequency component of Test 1 

Test 3 Commercial Dytran All locations Gearbox at 4 percent load 

Test 4 Lab Dytran Ring gear Shaker faulty, test not used 

Test 5a Lab Dytran Ring gear Range of loads, HUMS acc. clocked 

Test 6 Lab PCB HF Ring gear Gearbox with oil under range of loads 

Test 7 Commercial and Lab PCB HF Ring gear Two additional acc. on ring gear

Test 8 Lab Dytran Ring gear Gearbox under range of loads; no oil 

Test 9 Lab PCB HF Ring gear Gearbox under range of loads; no oil a

 First two tests to compare between gearbox with and without oil, rests are without oil. 

Figure 4.—Two shakers and a hammer used in the tests. 

 

Commercial 

Shaker 

Lab Piezo 

Shaker 

PCB 

Hammer 
NASA/TM—2013-216586 6 

TABLE II.—RANGE OF LOADS APPLIED ON 

GEARBOX DURING TESTS (REF.
) 

Horsepower, 

% 

Torque, 

in*lb 

4 188 

9 421 

20 939 

50 2346 

70 3285 

100 4693 

107 5020 

114 5348 

Figure 5.—Shaker locations 1 through 6 in NGB fixture and torque application. 

Location 2 

Location 1 

Location 3 

Location 4 Location 5 

Location 6 

Ring Gear Left NGB 

Torque 

Application 
NASA/TM—2013-216586 7 

 Unfiltered data Filtered data 

Figure 6.—FRFs before and after filtering. 

Results and Discussions 

In order to make the FRF plots easier to analyze and compare, a smoothing process was applied to the 

FRF data. Rather than displaying every ‘blip’ in the measured FRFs, smoothing allows easier viewing and 

comparison of general vibration transfer path trends. Smoothing preserves the general shape, simplifies 

the graphs, and makes trend comparisons easier. Figure 6 shows an example of a set of as-measured FRFs 

as well as the smoothed FRFs from measurements taken on the NGB test fixture (Ref. 	). The results and 

observations from the measured FRFs are discussed below. 

Vibration Transfer Path Consistency 

The investigation of similarities/differences and characterization of on-aircraft NGB transfer path 

dynamics and test-rig dynamics requires that the measured FRFs on the NGB in the lab are comparable to 

those recorded on the aircraft. The first part of this testing was to demonstrate the similarity/difference 

between NGB FRFs measured in the lab and those measured on the aircraft. Figure 7 shows the filtered 

FRFs of the response of the HUMS Dytran accelerometers for all six shaker locations in both NGBs in 

the helicopter and the left NGB on the test fixture (at 4 percent load). 

Across all six test locations, the FRFs compare very well, especially at lower frequency up to 25 kHz, 

as shown in Figure 7. At the higher frequency, the FRF amplitudes tend to vary between gearboxes 

sometimes by more than an order of magnitude, and Location 6 especially shows very substantial 

differences in amplitudes at frequencies over 25 kHz. For the purpose of selecting frequency bands for 

enveloping/demodulation, these FRF amplitudes overall seem very much similar under frequency of 

25 kHz. Table III shows a similarity matrix of Kolmogorov-Smirnov (K-S) tests between FRF amplitude 

curves for left NGB in the helicopter and test fixture (at 4 percent load). 

0 5 10 15 20 25 30 35 40 45 50 10-10

10-8

10-6

10-4

10-2

100

102

Frequency (kHz)

Amplitude (g/lbf)

Location 1, 9% Load, Unfiltered

HUMS Dytran

Vertical Dytran

Horizontal Dytran

0 5 10 15 20 25 30 35 40 45 50 10-4

10-3

10-2

10-1

100

101

102

Frequency (kHz)

Amplitude (g/lbf)

Location 1, 9% Load, Filtered

HUMS Dytran

Vertical Dytran

Horizontal Dytran
NASA/TM—2013-216586 8 

TABLE III.—K-S SIMILARITY TESTS 

FOR FRFS AT ALL SIX LOCATIONS 

Location K-S 

similarity factor 

1 0.88 

2 0.84 

3 0.77 

4 0.81 

5 0.84 

6 0.56 

The K-S test is a nonparametric test for the equality of continuous, one-dimensional probability 

distributions that can be used to compare two samples. The K-S statistic quantifies a distance between the 

empirical cumulative distribution functions (CDF) of two samples. The two-sample K-S test is one of the 

most useful and general nonparametric methods for comparing two samples, as it is sensitive to 

differences in both location and shape of the CDF of the two samples (Ref. 1). The K-S statistic, D, is 

defined by Equations (1) and (2). 

D, = |	,(
)  ,(
) (1) 

(
) = 

	


 [  
] 

	 (2) 

Where,  is the supremum (greatest) distance between the empirical distribution functions 	,and 

, of the first and second samples, respectively, and [  
] is the indicator function equal to 1 if 

  
, or 0 otherwise. In K-S tests, factor D, represents the maximum vertical distance between the 

CDF curves of two comparable vectors (herein FRF amplitudes for helicopter and test fixture). K-S 

Similarity Factors between the FRF vectors in Table III were derived by subtracting D, from the unity. 

Figure 8 shows CDF plots of FRF amplitudes for shaker Location 1 to 6 in left NGB in helicopter and test 

fixture. According to Table III, FRF curves for Locations 1 to 5 show 77 to 88 percent similarity while 

that in Location 6 has only 56 percent similarity with a difference in amplitudes of approximately 

10 g/lbf. 

Since no internal measurements were made on the helicopter at gear mesh, a comparison of external 

measurements within a frequency band known to contain gear mesh dynamics was made. Figure 9 shows 

FRF comparison with coherence and CDF plots for K-S test results within the frequency band that 

contains ±3 sidebands around the gear mesh for Commercial Shaker at Location 1 of left NGBs in NASA 

and on the helicopter under minimal load conditions. Coherence is the linear dependence between the 

output and input signals as a function of frequency. The comparison shows a 66 percent similarity 

between the FRFs of left NGBs in NASA and helicopter within this frequency band of interest. However, 

gear CIs are measured under load conditions and the effect of load on response will be discussed in two 

following sections. The plot also indicates the helicopter values are greater for the cumulative fraction. 

Overall, it can be concluded that vibration transfer paths are consistent in NGBs between the helicopter 

and test fixture. 

 
NASA/TM—2013-216586 9 

Figure 7.—FRFs and Coherence comparisons at six locations of NGBs in test fixture and helicopter. 
NASA/TM—2013-216586 10 

Figure 8.—CDF plots for Com. Shaker at six locations of NGBs in test fixture and helicopter. 

0 0.5 1 1.5 2 2.5 3 3.5 0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

Cumulative probability

CDF plots for NASA (4% load) and Helicopter FRFs at Location 1 

NASA

Helicopter

0 0.5 1 1.5 2 2.5 3 3.5 4 0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

Cumulative probability

CDF plots for NASA (4% load) and Helicopter FRFs at Location 2 

NASA

Helicopter

0 2 4 6 8 10 12 0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

Cumulative probability

CDF plots for NASA (4% load) and Helicopter FRFs at Location 3 

NASA

Helicopter

-1 0 1 2 3 4 5 6 7 0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

Cumulative probability

CDF plots for NASA (4% load) and Helicopter FRFs at Location 4 

NASA

Helicopter

0 1 2 3 4 5 6 7 8 0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

Cumulative probability

CDF plots for NASA (4% load) and Helicopter FRFs at Location 5 

NASA

Helicopter

0 5 10 15 20 25 0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

Cumulative probability

CDF plots for NASA (4% load) and Helicopter FRFs at Location 6 

NASA

Helicopter
NASA/TM—2013-216586 11 

Figure 9.—FRFs, coherence and CDF plots for Commercial Shaker at Location 1 of 

NGBs in test fixture helicopter. 
NASA/TM—2013-216586 12 

Figure 10.—FRFs for Com. Shaker at Location 1 of NGB fixture under various loads. 

Bearings Under Varying Loads 

A helicopter gearbox is subjected to widely varying loads in normal operation; therefore, it is 

important to understand the gearbox’s transfer path characteristics in such cases. Substantial changes in 

transfer path with load may indicate that the regime recognition is critical for reliable health monitoring. 

The vibration transfer path was measured in the lab NGB with the shaker at Location 1 and the gearbox 

under a range of torques indicated by a percent of the gearbox’s maximum torque rating. In total, the 

gearbox was tested under these conditions at eight different torque percentages shown in Table II; 

however, in the interest of clarity, only four are shown in Figure 10. The pictured FRFs match each other 

very well through the first 30 kHz frequency and are still easily comparable beyond that. This test 

illustrates that the surface-measured vibration transfer path measured under static conditions in the NGB 

subjected to considerably variable torque under operating conditions will not change significantly. 

Additionally, this type of measurement was also made previously on an AH-64 intermediate gearbox 

(IGB) with a specialized bearing transducer and produced similar results (Ref. ). Therefore, it appears 

that the bearing vibration transfer paths measured on the external NGB surface, under static conditions, 

are not much affected by variations in gearbox loads. 

Gears Under Varying Loads 

While the bearing vibration transfer path changes very little under variable loading conditions, the 

gear vibration transfer path changes more with loads, as shown in Figure 11. The figure shows FRFs 

under 4 and 107 percent torque loads from excitation with the lab piezoshaker at the ring gear. Table IV 

shows a similarity matrix of K-S tests between FRF amplitude curves for the test fixture between 

4 percent load and six other loads from 0 to 50 KHz. The K-S Similarity factor decreases as the load 

increases. 
NASA/TM—2013-216586 13 

This fact suggests that the contact stress at the gear mesh plays a significant role. As larger torque is 

applied to the input shaft of the gearbox, the contact area between the gear and pinion teeth in mesh 

increases slightly changing the vibration transfer path. The likely reason that the surface or bearing 

transfer paths do not change much with load is that the transfer path for bearings is through the outer race, 

the housing, and then to the sensor, and not dependent on stress due to change in contact area in the gear 

mesh. With gears, however, the energy must pass through the bearings and the gear teeth before being 

transmitted to the case. It seems likely that small changes in contact area and contact stress in the gear 

mesh would affect the vibration transfer path more noticeably. By extension, it seems likely that the 

vibration transfer path for a bearing fixed race defect may also be load-dependent since it is directly 

connected to the gear. It is important to note that while the gear transfer paths are more load dependent, 

they do no differ much more than those seen on different gearboxes. As a result, the same frequency band 

would likely be chosen for health monitoring for all load cases; however, certain condition indicator 

amplitudes at some frequencies may change significantly. This effect suggests that regime recognition 

may be important for reliable condition indicators of gear health. Therefore, a separate future study of 

different gear CIs measured during rotating conditions is required to determine their response to torque 

changes. However, a brief discussion of the similarity within a narrow band of interest will be discussed 

in a following section. 

TABLE IV.—K-S SIMILARITY TESTS FOR FRFS AT 

SIX LOADS COMPARED TO 4 PERCENT LOAD 

Horsepower, 

% 

Torque, 

in*lb 

K-S 

similarity factor 

9 421 0.95 

20 939 0.91 

50 2346 0.89 

70 3285 0.88 

100 4693 0.87 

107 5020 0.86 

Figure 11.—HUMS FRFs with Lab Piezo Shaker on ring gear under various loads. 

0 5 10 15 20 25 30 35 40 45 50

10-2

10-1

100

101

102

Frequency (kHz)

Amplitude (g/lbf)

Gear Transfer Path Load Extremes

4% Load

107% Load
NASA/TM—2013-216586 14 

Figure 12.—FRFs with Lab Piezo Shaker on ring gear for gearbox with and without oil. 

Presence of Lube Oil 

While the helicopter NGB is operating, the oil pump will be engaged in circulating oil within the 

gearbox. It is impossible to exactly replicate these circumstances in the lab without the means of 

controlling the pump; therefore, as a compromise, vibration transfer path measurements were recorded in 

the two extreme conditions: the gearbox full of oil and the gearbox without oil. The reason for taking such 

measurements under these two extreme conditions is the initial perception that the vibration transfer path 

of the gearbox in operation will be somewhere between these two extreme situations. In fact, the 

measurements taken on the helicopter were recorded with the gearbox full of oil; though they were 

external measurements and not likely to be strongly affected by the presence of oil. 

Figure 12 shows that the addition of oil into the gearbox quite significantly increases the amplitude of 

FRFs from the Lab Piezo Shaker on the ring gear to the accelerometers mounted on the outside of the 

gearbox. This might be due to the oil resting at the bottom of the gearbox acted as an additional medium 

for the transfer of vibrational energy. This does not happen if there is no oil present at the bottom of the 

gearbox. However, despite the transfer path improvement due to oil at the bottom of the gearbox, it is 

realistic to assume that the ‘gearbox without oil’ condition more closely resembles the gearbox under 

actual operating conditions since most of the oil in the gearbox would be circulated by the oil pump rather 

than resting at the bottom. 

Sensor Orientation and Removal/Replacement 

While HUMS is a sophisticated system, its components undergo real world maintenance treatments 

that may not be ideal. During these tests, some of these real world conditions were recreated in the lab to 

investigate if they have any detrimental effects on the system performance. These varying maintenance 

conditions include skewing or clocking the accelerometer by changing its angle relative to the gearbox, as 

well as removing and reattaching it. 
NASA/TM—2013-216586 15 

(a) (b) 

Figure 13.—Commercial shaker at Location 3 of NGB fixture with varying maintenance conditions. 

For this comparison, the test with the gearbox under 4 percent load and the shaker at Location 3 were 

used as a baseline. The nut holding the HUMS accelerometer in place was loosened and the accelerometer 

was rotated clockwise so that the angle between its direction of sensitivity and the gearbox’s horizontal 

was approximately 30°, which can be seen in Figure 13(a). The condition of removal and reattachment of 

accelerometer was also tested by completely removing the nut and the accelerometer, and then reattaching 

them with a combination wrench, tightening the nut to an unknown torque. This condition was worth 

testing because the HUMS Dytran accelerometer documentation specifies that the sensor should be held 

in place with a nut under a specific torque. Figure 13(b) clearly shows that the varying some maintenance 

conditions of the HUMS Dytran accelerometer do not detrimentally affect the accelerometer performance. 

Alternate Accelerometer Locations 

The existing helicopter HUMS uses a single Dytran accelerometer mounted on a stud forward on the 

gearbox. It is not known exactly why this location was chosen. Therefore, two other Dytran 

accelerometers were mounted on the gearbox in different locations to explore the possibility of other 

accelerometer locations being more suitable/effective for detecting defects. The two additional locations, 

‘Vertical’ and ‘Horizontal’ at approximately right angles to each other and the original HUMS location 

are shown in Figure 14(a). The ‘Vertical’ accelerometer location was chosen because it may measure 

response that is orthogonal to the HUMS accelerometer’s direction, and thus in the direction of gear 

mesh. The ‘Horizontal’ accelerometer location was chosen because it was closer to the input bearing, and 

much closer to the gear mesh of the gearbox than the HUMS accelerometer, thus it may be able to better 

capture defect signals from those locations. 

Figure 14(b) shows the FRFs from all three Dytran accelerometer locations under 4 percent load. 

Clearly, there is very little difference in FRFs measured from these three locations. Though not expected, 

it appears that the transfer path from the gear-mounted shaker to the studs on the outer casing does not 

significantly change between studs. In order to understand this, the somewhat radially symmetric nature 

of the gearbox needs to be taken into account. When examined closely, it became evident that the shortest 

path from the outer circumference of the gear to any point on the outer circumference of the gearbox 

access cover is always at the center of the gear through the output shaft to the center of the access cover, 

and then out to the circumference of the cover. This is likely to be the reason for the FRF similarity 

between different accelerometer locations. 

Accelerometer clocked 
NASA/TM—2013-216586 16 

(a) (b) 

Figure 14.—Sensor locations comparison at 4 percent load with Lab Piezo Shaker on ring gear. 

Lightly-Damped Steel Gear 

The VTPs measured for bearings are through the cast aluminum alloy gearbox cases, and this material 

is generally highly damped. When the case was struck with a hammer, the sound was a thud and decayed 

very quickly. On the other hand, the steel gear rings more like a bell when struck. This audible difference 

is a macroscopic indication of one of the physical characteristics of gears that may impede gear health 

monitoring. This characteristic was investigated by measuring the transfer path from a point on the ring 

gear to another point on the gear, and to the standard acceleration location. The test setup with upper and 

lower accelerometers on the ring gear is shown in Figure 15(a). The notable trait of the FRFs measured 

with the Lab Piezo Shaker mounted directly on the ring gear is the sharp resonances seen in Figure 15(b). 

These FRFs were measured with the cover off and the blue trace is generated from the response of the 

accelerometers mounted directly on the ring gear, and the green trace is produced from the HUMS 

accelerometer mounted on the stud. The blue trace, which shows the direct FRFs of the ring gear, 

indicates a lightly-damped structure. FRFs measured on this type of structure tend to have much sharper 

and closer resonances and anti-resonances, while the green trace which shows the VTP to the HUMS 

accelerometer shows the characteristics of a structure which has high damping, and the FRFs tend to have 

softer, more spread-out resonances and anti-resonances. However many of the sharp peaks seen in the 

blue trace are still visible in the green indicating that the dynamics of the gear itself play a significant role 

in determining the gear mesh transfer path. For health monitoring, the broad, highly-damped peaks 

provide more consistent energy transmission through a frequency range, while the sharp, lightly-damped 

peaks provide high amplification, but over a very short frequency range. These lightly-damped peaks 

have some implications for health monitoring—relatively small changes in frequency may produce large 

changes in amplitude, which will affect the gear CIs response. While helicopter drivetrains are run at a 

constant speed, the frequencies at these peaks will likely vary between gearboxes and may produce large 

amplitude differences between helicopters. This further highlights the need to run a test rig at varying 

conditions to assess CI performance. 

HUMS 

location 

Vertical 

location 

Horizontal 

location 
NASA/TM—2013-216586 17 

(a) (b) 

Figure 15.—FRFs comparison between accelerometers mounted on ring gear and housing. 

Sensor Dynamics 

The Dytran accelerometers used to monitor the helicopter NGB have an integral mounting bracket. 

While the sensor itself is supposed to provide flat response to 5 kHz with its first resonance at 26 kHz, the 

mounting bracket has structural modes beginning at 3 kHz. High-frequency monitoring including 

enveloping or demodulation is performed above 5 kHz; therefore, the bracket dynamics play a part in the 

measured response. To separate the bracket dynamics from the sensor dynamics, the Dytran 

accelerometers were replaced with high frequency PCB accelerometers attached to mounting brackets, 

which were made to emulate the Dytran brackets. Although the Dytran accelerometers used on the HUMS 

systems are not likely to be replaced anytime in the near future, the Spiral Bevel Gear Test rig has Dytran 

accelerometers as well as lab-grade sensors, and therefore, this data may be useful in creating a more 

meaningful comparison of vibration transfer paths between Spiral Bevel Gear Test Rig and the helicopter. 

Figure 16 shows these unfiltered FRFs with the corresponding coherence graph. In general, the FRFs 

are similar, but the PCB accelerometers appear to provide better-quality measurements, as evidenced by 

the cleaner FRFs and superior coherence. The primary difference in these sensors can be seen in the 42 to 

50 kHz region, where the Dytran accelerometer’s response is an order of magnitude higher than that of 

the PCB accelerometer. This seems to suggest that the Dytran accelerometer is receiving additional 

amplification in this region, perhaps from a bending mode of the mounting bracket or a sensing element 

resonance. 

Future Comparison to the Spiral Bevel Gear Fatigue Test Rig 

One underlying objective of the FRF measurements is to determine if measuring the behavior of the 

structure under static conditions can provide any insight into CI performance across three spiral bevel 

geared systems: the helicopter NGB, NGB fixture and Spiral Bevel Gear Fatigue Test Rig. This requires 

first making measurements on the helicopter or fixture that can be compared to future measurements on 

the test rig. Limited accessibility to the gear mesh within the NGB installed on the helicopter made it 

impossible to simulate an impact of the gear teeth at the source. However, measurements made with the 

actuator on the ring gear banded at gear mesh frequencies at specific torques could be compared to the 

response of the actuator installed on the ring gear within the test rig banded around its gear mesh 

frequencies at specific torques. 

FRFs and coherence were measured by the Dytran accelerometer with the shaker on the ring gear, at a 

frequency band that contains ±3 sidebands around the gear mesh. These measurements were taken at six 

loads and compared to the 4 percent load conditions. These plots and the corresponding CDF plots for the 

Lower 

acceleration 

Lab Piezo 

Shaker 

Commercial 

Shaker 

Upper 

acceleration 
NASA/TM—2013-216586 18 

six loads are shown in Figure 17 and Figure 18. Table V shows a similarity matrix of K-S tests between 

FRF amplitude curves for the test fixture between 4 percent load and six other loads within this frequency 

band. The K-S Similarity factor within this narrow frequency band improves at the higher loads. The 

coherence also improves with higher loads. The shape of the signature also changes at higher loads. This 

illustrates the importance of assessing the similarities of frequency response within frequencies of 

interest. Measurements will be made in the Spiral Bevel Gear Fatigue Test Rig under comparable 

conditions in future studies and then compared to dynamic conditions for the helicopter and test rig to 

determine how CI performance is related to VTP amplitude with the rig at static conditions. 

Figure 16.—Sensor type comparison at 4 percent load with Lab Piezo Shaker on ring gear. 

TABLE V.—K-S SIMILARITY TESTS FOR FRFS AT SIX LOADS 

COMPARED TO 4 PERCENT LOAD WITHIN A FREQUENCY BAND 

Horsepower, 

% 

Torque, 

in*lb 

K-S 

similarity factor 

9 421 0.83 

20 939 0.68 

50 2346 0.74 

70 3285 0.88 

100 4693 0.87 

107 5020 0.87 
NASA/TM—2013-216586 19 

Figure 17.—HUMS FRFs, Coherence and CDF at 9, 20 and 50 percent loads compared to 4 percent. 

 
NASA/TM—2013-216586 20 

Figure 18.—HUMS FRFs, Coherence and CDF at 70, 100 and 107 percent loads compared to 4 percent. 
NASA/TM—2013-216586 21 

Summary and Conclusions 

The measurements taken on the test fixture nose gearbox at GRC were shown to be consistent with 

those taken on similar gearboxes mounted in an AH-64 helicopter. It was also shown that certain real 

world installation and maintenance issues, such as sensor alignment and installation torque, do not 

significantly affect the performance of HUMS. It has been shown that the presence of oil increased the 

amplitude of FRFs at some frequencies through acting as an additional medium for vibrational energy 

transfer. However, the no-oil condition is closer to real world conditions in a running aircraft, since the oil 

would be circulated by the oil pump rather than resting at the bottom. In fact, oil only affects the gear 

VTP, not the bearing VTP. It was also found that neither of the alternative accelerometer locations 

showed any marked improvement in vibration energy transmissibility from the ring gear. 

Gear vibration transfer path dynamics are found to be load dependent to some extent and depends on 

the frequency of interest. The replacement of Dytran accelerometers with PCB high frequency sensors 

provided cleaner data. The lightly-damped ring gear produced sharp and closer transfer path resonances 

and anti-resonances, and these may lead to substantially different condition indicator amplitudes with 

changing operating conditions, or even between gear boxes with different serial numbers. Ultimately, the 

test diagnostician must understand these differences and make every attempt to develop algorithms, which 

are robust to the actual conditions found on the aircraft. The key to improving CI performance across 

systems (helicopter, fixture, test rig) is to understand dynamic characteristics unique to each system that 

affect individual gear CI response for a healthy and damaged tooth. Therefore, the vibration transfer path 

characterization and consistencies found in this research might be useful in characterizing differences/ 

similarities in structural dynamics between a test rig and a helicopter, and their effects on gear CI 

performance. 

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