Paula J. Dempsey

Glenn Research Center, Cleveland, Ohio

AKM Anwarul Islam

Youngstown State University, Youngstown, Ohio

Jason Feldman and Chris Larsen

Etegent Technologies, Ltd., Cincinnati, Ohio

Investigation of Gearbox Vibration Transmission

Paths on Gear Condition Indicator Performance

NASA/TM—2013-216617

December 2013
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Paula J. Dempsey

Glenn Research Center, Cleveland, Ohio

AKM Anwarul Islam

Youngstown State University, Youngstown, Ohio

Jason Feldman and Chris Larsen

Etegent Technologies, Ltd., Cincinnati, Ohio

Investigation of Gearbox Vibration Transmission

Paths on Gear Condition Indicator Performance

NASA/TM—2013-216617

December 2013

National Aeronautics and

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Glenn Research Center

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NASA/TM22013-216617 1

Investigation of Gearbox Vibration Transmission Paths on

Gear Condition Indicator Performance

Paula J. Dempsey

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

AKM Anwarul Islam

Youngstown State University

Youngstown, Ohio 44555

Jason Feldman and Chris Larsen

Etegent Technologies, Ltd.

Cincinnati, Ohio 45212

Abstract

Helicopter health monitoring systems use vibration signatures generated from damaged components

to identify transmission faults. For damaged gears, these signatures relate to changes in dynamics due to

the meshing of the damaged tooth. These signatures, referred to as condition indicators (CI), can perform

differently when measured on different systems, such as a component test rig, or a full-scale transmission

test stand, or an aircraft. These differences can result from dissimilarities in systems design and

environment under dynamic operating conditions. The static structure can also filter the response between

the vibration source and the accelerometer, when the accelerometer is installed on the housing.

To assess the utility of static vibration transfer paths for predicting gear CI performance,

measurements were taken on the NASA Glenn Spiral Bevel Gear Fatigue Test Rig. The vibration

measurements were taken to determine the effect of torque, accelerometer location and gearbox design on

accelerometer response. Measurements were taken at the housing and compared while impacting the gear

set near mesh. These impacts were made at gear mesh to simulate gear meshing dynamics. Data measured

on a helicopter gearbox installed in a static fixture were also compared to the test rig. The behavior of the

structure under static conditions was also compared to CI values calculated under dynamic conditions.

Results indicate that static vibration transfer path measurements can provide some insight into spiral bevel

gear CI performance by identifying structural characteristics unique to each system that can affect specific

CI response.

Introduction

Helicopter transmission health is important to helicopter safety because helicopters depend on the

power train for propulsion lift and flight maneuvering. Health and Usage Monitoring Systems (HUMS)

capable of predicting impending transmission component failure for 3on-condition ́ maintenance have the

potential to decrease operating and maintenance costs, and increase safety and aircraft availability. 3Oncondition ́ maintenance refers to maintenance when HUMS 3condition indicators ́ indicate decreased

performance, instead of relying on time-based maintenance intervals. These HUMS 3condition

indicators ́ (CI) are typically vibration signatures generated from fault patterns produced when damaged

components interact with their environment. For gear CIs, these signatures relate to changes in dynamics

at the gear mesh due to tooth damage.

Condition indicators can perform differently when measured on a component test rig or a full-scale

transmission test stand or an aircraft. Damage progression tests are being performed in the Spiral Bevel

Gear Fatigue Test Rig, as shown in Figure 1, at NASA Glenn Research Center (GRC). The objective of
NASA/TM22013-216617 2

Figure 1.2Spiral bevel gear fatigue test rig at NASA GRC.

Figure 2.2Three spiral bevel geared systems.

these tests, as outlined in Reference 1, are to determine if μseeded 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. Performing these tests will also identify

limitations using seeded fault test rig data to demonstrate helicopter CI performance. For this approach,

existing in-service HUMS flight data from spiral bevel gears installed in a helicopter nose gearbox (NGB)

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 2 and 3, was fed into the development of the spiral

bevel gear rig test plan.

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

measurements were taken to characterize differences in structural dynamics between the helicopter and

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

speed, the static structure also filters the response between the vibration source and the accelerometer on

the housing. Understanding structural differences between systems may provide insight into the

difference in performance of diagnostic tools between such systems.

The approach used to assess the effectiveness of vibration transfer paths in predicting CI performance

was to compare measurements on three spiral bevel geared systems. These three systems, as shown in

Figure 2, are a helicopter NGB, an NGB fixture (an NGB removed from a helicopter and installed in a

static fixture), and a test rig (spiral bevel gear fatigue test rig). The latter two are installed at NASA GRC.
NASA/TM22013-216617 3

This comparison required taking measurements on the helicopter NGB or NGB fixture that can be

compared to future measurements on the test rig. Limited accessibility to the gear mesh within the

helicopter NGB made it impossible to simulate an impact of gear teeth at the source, directly between

meshing gear teeth. However, the NGB fixture enabled the application of impacts close to the gear mesh

with varying torques2common during aircraft operations. Results from comparisons of frequency

response functions between the helicopter NGB and NGB fixture under similar conditions found both

systems to be consistent. These results are detailed in Reference 4. To determine if transfer path

measurements under static conditions can provide insight into the gear CI performance during operation,

measurements under dynamic conditions were required.

The objective of this paper was to assess the utility of vibration transfer paths of the test rig in a static

condition for predicting its gear CI performance during its operation. The focus was on the the signal

transmission from the gear mesh inside the gear box to the accelerometer installed on the gearbox external

housing.

Measurements were taken on the static test rig to determine the effect of torque, accelerometer

location and gearbox design on the accelerometer response to impacts near the gear mesh. Impacts of the

gear set near mesh were made to simulate gear meshing dynamics. Data measured on the the NGB

fixture, per Reference 4, were also compared to those of the test rig. Inferences were made comparing

vibration measurements of the structure collected under static conditions to CI values calculated under

dynamic conditions.

Test Facility

Tests were performed in the test rig at NASA GRC. A detailed description of this test facility, as

illustrated in Figure 1, can be found in References 5 and 6. In addition to developing gear health

monitoring tools, the test facility has been used to study the effects of gear material, gear tooth design,

and lubrication on the fatigue strength of gears. Two sets of spiral bevel gears are installed in the test rig

and tested simultaneously. Facing the gearboxes per Figure 1, the left gear set (pinion/gear) is referenced

as μleft¶ and the right gear set (pinion/gear) is referenced as μright¶ within this paper.

Figure 3 shows the cross-sectional view of the test rig. The facility operates in a closed-loop

arrangement where the load is locked into the loop via a split shaft and a thrust piston on the slave side of

the rig. This forces a helical gear into mesh per Figure 3. The rotation is obtained using a drive motor

connected through v-belts to the helical gear. The spiral bevel gears on the left side operate where the

pinion drives the gear. The right side of the facility acts as a speed increaser where the gear drives the

Figure 3.2Cross-section of the test rig.
NASA/TM22013-216617 4

pinion. The concave side of the pinion is always in contact with the convex side of the gear on both the

left and right side of the gearbox. Load and speed are monitored by torque and speed sensors. The 41-

tooth gear and 19-tooth pinion gear set are typically tested at a gear speed of 3500 rpm and a pinion speed

of 7553 rpm with a gear torque of approximately 8000 in.-lb and a pinion torque of 3707 in.-lb.

Turbine engine oil that meets DOD-L-87354 specifications is used in the test rig. Both gear sets are

lubricated with oil jets pumped from an oil reservoir. The lubrication exits the gearbox, and flows through

an inductance type in-line oil debris (OD) sensor and then a magnetic chip detector. A strainer and a

three-micron filter are located downstream of the OD sensor to capture any debris before returning to the

sensor and the gearbox.

Data Acquisition and Instrumentation for Dynamic Tests

During dynamic tests, three data acquisition systems were used. Vibration, oil debris, torque and

speed data were collected once every minute with the NASA GRC data acquisition system, referred to as

the Mechanical Diagnostic System Software (MDSS). Vibration and speed data were collected from a

second set of sensors with a helicopter HUMS referred to as the Modern Signal Processing Unit (MSPU).

Operational parameters were collected with a third system referred to as the Daytronic. These operational

parameters included torque, speed, right and left gearbox oil inlet, and outlet temperatures and pressures.

A non-contact rotary transformer shaft-mounted torque sensor was used to measure torques during

testing. Thermocouples were used to measure inlet and outlet oil temperatures. The inductance type OD

sensor was used to measure the debris generated during fatigue damage to the gear teeth. Also measured

were chip indications from the chip detector, when the gap was closed with debris.

For the MDSS system, accelerometers, with a frequency range of 0.7 to 20 kHz and a resonant

frequency of 70 kHz, were installed on the right and left side of the test rig housing. These

accelerometers were referred to as high frequency (HF) accelerometers in the analysis that follows. The

MDSS HF accelerometers were mounted on the housing, radially and vertically with respect to the pinion,

as shown in Figure 4. This orientation was chosen because the calculated forces at the mesh indicated the

accelerometer would see the largest forces in this orientation. Speed is measured with optical tachometers

mounted on the left pinion shaft and left gear shaft to produce a separate once-per-rev tachometer (tach)

pulse for the pinion and gears.

For the MSPU system, accelerometers, with a frequency range of 0.5 to 5 kHz and a resonant

frequency of 26 kHz, are also installed on the right and left side of the test rig. These accelerometers are

referred to as the Dytran in the analysis that follows. A magnetic tachometer is installed on the right

pinion to measure pinion pulses per tooth pass in the MSPU system. The accelerometers were mounted on

the housing, in close proximity to the MDSS accelerometers, radially and vertically with respect to the

pinion, as shown in Figure 4.

Figure 4.2Locations of accelerometers.
NASA/TM22013-216617 5

Condition Indicator Analysis

For condition indicator calculations, vibration data were collected for the right and left pinion/gear

sets using accelerometers mounted on the right and left side of the test rig gearbox per Figure 4. Data

were collected at sample rates that provided sufficient vibration data for calculating time synchronous

averaged (TSA) data. The TSA refers to techniques for averaging vibration signals over several

revolutions of the shaft, in the time domain, to improve signal-to-noise ratio (Ref. 7). Using a once per

revolution signal, the vibration signal is interpolated into a fixed number of points per shaft revolution.

Signals synchronous with the shaft speed will intensify relative to the non-periodic signals.

Since helicopter gears generate vibration signals synchronous with speed, all helicopter gear

condition indicators are calculated from TSA data. Gear vibration condition indicators are indexes

calculated from vibration signal information. Many are based on statistical measurements of vibration

energy. Signal processing techniques used to calculate a gear CI from the TSA vibration signal are

discussed in detail in Reference 8. Some gear CI¶s are calculated directly from the time domain TSA

signal, such as the root mean square (RMS), while others are calculated from the TSA converted to the

frequency domain, such as the Sideband Index (SI).

Time synchronous averaging of the vibration data collected from the left and right accelerometer is

performed in the MDSS system for pinions via the pinion tach pulse and for gears via the gear tach pulse.

The MSPU system uses the magnetic tachometer installed at the pinion to calculate the TSA for both the

pinion and the gear. The gear ratio is used to process the pinion data at the correct speed for the gear.

Note that accelerometers installed on the left side of the test rig were used to measure vibration and

calculate CIs for the pinion and gear installed on the left side of the gearbox. Accelerometers installed on

the right side of the gearbox were used to measure vibration and calculate CIs for the pinion and gear

installed on the right side of the gearbox.

Figure 5 illustrates the information used to calculate the TSA for the right gear and pinion. Using the

sample rate of 200 kHz for one second duration and the speed of both shafts, the number of TSA averages

for each acquisition is determined. Each average consists of one revolution of the shaft. Each average is

made up of the number of linearly interpolated points rounded down to a power of two. A power of two

Figure 5.2Information used to calculate TSA.
NASA/TM22013-216617 6

data points is required to perform the Fast Fourier Transform (FFT) to convert time domain signals into

the frequency domain. According to Figure 5, the top plot displays the right accelerometer data sampled

for one second at 200 kHz. The green and blue lines are pulses from the gear and pinion 1/rev signal

measured for each shaft rotation during this one second period. Only the right accelerometer is plotted in

red in the middle plot with an expanded y-axis scale. The two lowest plots are the TSA signals calculated

from the 1/rev and vibration data for the right gear and pinion. Pulses from the 41-tooth gear and the 19-

tooth pinion can easily be seen within these two plots.

The SI methods were studied in this work for use in detecting surface fatigue damage to spiral bevel

gear teeth. These methods were selected for use in this study due to the success at detecting damage to

spiral bevel gear teeth in several helicopters (Refs. 2 and 3). The SI is a frequency domain based CI. The

CI value is an average value of sideband amplitudes about the fundamental gear mesh (GM) frequency.

The number of sidebands included in the calculation of the sideband CI can vary with different health

monitoring systems.

All gears generate a dominant GM frequency in the vibration signature due to each tooth impacting

against the gear it is driving as the teeth mesh. The gear (or pinion) mesh frequency is equal to the

number of teeth multiplied by its speed. Gear sets also produce pairs of equally spaced sidebands on

either side of the gear mesh. The sidebands are the frequencies calculated as the total number of gear teeth

plus n and minus n (where n is an integer) multiplied by the gear speed in Hz. Certain types of gear tooth

damage, such as pitting on several teeth, can affect the amplitude of sidebands. Increases in sideband

amplitudes are often used to calculate a gear condition indicator. Table 1 lists the gear frequencies and the

first order sideband frequencies for the tested pinion and gear at its operating speed.

Figure 6 illustrates the steps required to calculate RMS and SI for each reading. The RMS method

uses the interpolated TSA data per Figure 5 to calculate the RMS of the TSA. The SI method uses the

TSA data in performing the FFT. Then the peak amplitudes of the FFT data on either side of the GM are

used to calculate SI indexes. Note that the x-axis of the plot showing the FFT of the right gear is in shaft

orders or multiples of shaft speed. For example, since the gear has 41 teeth, the gear mesh frequency

(teeth x speed) shows up at 41 shaft orders.

TABLE 1.2SIDEBAND FREQUENCIES

Gear Sideband frequencies (Hz)

No. teeth Speed (rpm) Speed (Hz) 38 39 40 GM 42 43 44

41 3500 58 2217 2275 2333 2392 2450 2508 2567

Pinion Sideband frequencies (Hz)

No. teeth Speed (rpm) Speed (Hz) 16 17 18 GM 20 21 22

19 7553 126 2014 2140 2266 2392 2518 2643 2769

Figure 6.2RMS and SI calculations.
NASA/TM22013-216617 7

Data Acquisition for Transfer Path Measurements

Modal analysis is primarily concerned with resonant frequencies or natural frequencies of a structure.

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

at various locations on the structure. Frequency response functions (FRF) are used to analyze structural

dynamics under static condtions and to estimate modal parameters for the analysis of mechanical systems.

The FRF is used to measure the input-output relationship between two points on a structure as a function

of frequency. Coherence is used to measure the linear dependence between the output and input signals as

a function of frequency.

Vibration transfer path (VTP) measurements were recorded on the test rig at NASA GRC from June 3

to June 7, 2013. The objective of this effort was to perceive how an accelerometer responds to the impacts

at the gear mesh as they travel through the structure. Since the structure filters this reponse, it can impact

a CI¶s ability to detect tooth damage at the mesh. The transmission or transfer path of the test rig gearbox

was determined by applying an impact force at the mesh and measuring its response with accelerometers

installed on the gearbox housing. The same MDSS and MSPU accelerometers used for dynamic

measurements were used for VTP measurements on the test rig, as shown in Figure 4.

Since the purpose of these tests was to determine the effect of the structure on the gear CI, the FRFs

focused on the frequency ranges used for gear CI sideband index. Most of the FRF measurements were

made with an instrumented impact hammer. The hammer provides good excitation up to 6400 Hz. For

some test conditions, a commercial reaction-mass shaker in the form of a piezoelectric actuator was used.

The Kolmogorov±Smirnov test (K-S test) was used to compare the FRFs under different conditions.

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

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

empirical cumulative distribution functions (CDF) of two samples. The two-sample KS 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. 9). The Kolmogorov-Smirnov

statistic Dn,n' is defined by Equations (1) and (2).

sup F x F x Dn,n' x 1,n 2,n' (1)

n

i

n i

I X x

n

F x

1

1

 (2)

Where, is the supremum (greatest) distance between the empirical distribution functions F1,n and

F2,n' of the first and second samples, respectively, and I X x i

 is the indicator function equal to 1 if

X x i, or 0 otherwise. In K-S tests, factor Dn,n' represents the maximum vertical distance between the

CDF curves of two comparable vectors (herein FRF amplitudes for the helicopter NGB and the test rig).

KS Similarity factors between the FRF vectors were derived by subtracting Dn,n'

 from unity.
NASA/TM22013-216617 8

Results for Spiral Bevel Gear Fatigue Rig Under Static Conditions

The first part of the analysis was to characterize the test rig under static conditions. FRF

measurements were made under different conditions to compare transfer paths from the gear/pinion tooth

mesh to the accelerometers on the housing. For these tests, impacts were made at the gear mesh on the left

pinion, and the response of the MSPU and MDSS accelerometers on the right and left side of the test rig

were compared. The impacts at the gear mesh with the hammer were made on the pinion gear tooth in the

vertical direction, as shown in Figure 7. This impact orientation was selected since the largest tooth force

at the mesh was calculated for this direction.

Varying Loads

The effects of loads on the transfer path were examined by impacting the hammer on the left pinion in

the vertical direction and measuring its response with the MDSS system accelerometers. Accelerations

were measured with the HF accelerometers from 0 to 6400 Hz. The test gears were loaded by applying a

static torque in the loop. Four design loads were applied and are listed in Table 2. Similarity factors were

than calculated comparing the 29 percent design load to the other three loads and are listed in Table 2.

According to Table 2, similarity factors above 0.9 indicated the FRFs were similar under varying loads.

Representative plots of FRF, Coherence and CDF at 104 percent design load compared to 29 percent load

are shown in Figure 8.

Figure 7.2Impact on left pinion in the vertical direction.

TABLE 2.2KOLMOGOROV-SMIRNOV (KS) SIMILARITY TESTS FOR FRFS AT

3 LOADS COMPARED TO 29 PERCENT LOAD

Percent design load Gear torque,

in.-lb

Pinion torque,

in.-lb

KS similarity factor

29 2347 1088 na

53 4264 1976 0.91

78 6252 2897 0.90

104 8283 3838 0.92
NASA/TM22013-216617 9

These plots were also generated for a narrow frequency band (1800 to 3000 Hz) around the gear mesh

and its sidebands for 3500 rpm gear speed (Table 1). This expanded scale is highlighted in yellow in

Figure 8. Similarity factors calculated comparing the 29 percent design load to the other three loads are

listed in Table 3. According to Table 3, similarity factors calculated for the narrow band were lower than

the full range and decreased with an increase in load. Plots of FRF, Coherence and CDF at the three loads

compared to 29 percent design load are shown in Figure 9. These results indicate that for the most

accurate system structural characterization, loads similar to the operating loads should be applied during

transfer path measurements. Further discussion of results will focus on measurements taken at the load

closest to operating load under dynamic conditions. This load is highlighted in Table 3.

Figure 8.2FRF, Coherence and CDF at 104 percent design load compared to

29 percent load.

0 1 2 3 4 5 6 7

10-4

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left FRF comparison under load for vertical impact on left pinion

29% Load

104% Load

0 1 2 3 4 5 6 7

0

0.5

1

Frequency (kHz)

HF Accel Left Coherence comparison under load for vertical impact on left pinion

29% Load

104% Load

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF Accel Left CDF comparison under load for vertical impact on left pinion

29% Load

104% Load
NASA/TM22013-216617 10

TABLE 3.2KS SIMILARITY TESTS FOR FRFS AT 3 LOADS COMPARED

TO 29 PERCENT LOAD WITHIN A FREQUENCY BAND

Percent design load Gear torque,

in.-lb

Pinion torque,

in.-lb

KS similarity factor

29 2347 1088 na

53 4264 1976 0.74

78 6252 2897 0.71

104 8283 3838 0.70

Figure 9.2FRF, Coherence and CDF at 53, 78, and 104 percent loads compared to 29 percent load.

1.8 2 2.2 2.4 2.6 2.8 3

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left FRF comparison under load for vertical impact on left pinion

29% Load

53% Load

1.8 2 2.2 2.4 2.6 2.8 3

0

0.5

1

Frequency (kHz)

HF Accel Left Coherence comparison under load for vertical impact on left pinion

29% Load

53% Load

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF Accel Left CDF comparison under load for vertical impact on left pinion

29% Load

53% Load

1.8 2 2.2 2.4 2.6 2.8 3

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left FRF comparison under load for vertical impact on left pinion

29% Load

78% Load

1.8 2 2.2 2.4 2.6 2.8 3

0

0.5

1

Frequency (kHz)

HF Accel Left Coherence comparison under load for vertical impact on left pinion

29% Load

78% Load

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF Accel Left CDF comparison under load for vertical impact on left pinion

29% Load

78% Load

1.8 2 2.2 2.4 2.6 2.8 3

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left FRF comparison under load for vertical impact on left pinion

29% Load

104% Load

1.8 2 2.2 2.4 2.6 2.8 3

0

0.5

1

Frequency (kHz)

HF Accel Left Coherence comparison under load for vertical impact on left pinion

29% Load

104% Load

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF Accel Left CDF comparison under load for vertical impact on left pinion

29% Load

104% Load
NASA/TM22013-216617 11

Coupling Between Left and Right Pinion

The test rig was designed to test two sets of spiral bevel gears simultaneously with the right and left

pinions connected by a cross shaft. This design can make it more challenging to isolate tooth damage on

one side of the gearbox from the other side. To investigate how damage on one side can potentially affect

the other, impacts were made at the left pinion at 104 percent load and measured on the right and left side

accelerometers. Figure 10 shows plots of FRF, Coherence and CDF at 104 percent load measured with the

MDSS HF accelerometers on right and left sides of the gearbox. A KS similarity value of 0.65 was

calculated for the 0 to 6400 Hz frequency range. The FRF amplitude measured on the left side was higher

Figure 10.2FRF, Coherence and CDF at 104 percent load measured

on right and left with HF accels.

0 1 2 3 4 5 6 7

10-5

10-4

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left and Right, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right

0 1 2 3 4 5 6 7

0

0.2

0.4

0.6

0.8

1

Frequency (kHz)

HF Accel Left and Right Coherence, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF Accel Left and Right CDF, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right
NASA/TM22013-216617 12

than that of the right side due to impacts made closer to this accelerometer. The coherence for the left

accelerometer seems better than in the right one across the entire frequency range, which seems

reasonable since the location of the impact is closer to the left accelerometer. However, the right

accelerometer did respond to this impact indicating the coupling between the right and left pinion through

the shaft. The frequency bands from 2.6 to 4.0 kHz and the frequency after 5.4 kHz show big differences

in amplitudes between the left and right accelerometers. The resonant frequency appears to be at 3.2 kHz.

This is good news because it does not correlate to frequencies used for diagnostic purposes at 100 percent

operating conditions of the test rig.

Comparison Between MDSS and MSPU Accelerometers

Both the HF and Dytran accelerometers will be used during test rig failure progression tests. Dytran

accelerometers used to monitor the helicopter NGB have an integral mounting bracket. To compare both

types of sensors, impacts were made at the left pinion at 104 percent load and measured with the HF and

Dytran accelerometers installed on the left side of the test rig gearbox. Figure 11 shows plots of FRF,

Coherence and CDF at 104 percent load measured with both accelerometers. A KS similarity value of

0.94 was calculated for the 0 to 6400 Hz frequency range and 0.85 for the 1800 to 3000 Hz frequency

range. This indicates both types of accelerometers respond within the frequency of interest.

Figure 11.2FRF, Coherence and CDF at 104 percent load measured with HF and Dytran accels.

0 1 2 3 4 5 6 7

10-5

100

Frequency (kHz)

HF and Dytran Accel Left, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

Dytran Accel Left

0 1 2 3 4 5 6 7

0

0.5

1

Frequency (kHz)

HF and Dytran Accel Left Coherence, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

Dytran Accel Left

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF and Dytran Accel Left CDF, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

Dytran Accel Left

1.8 2 2.2 2.4 2.6 2.8 3

10-3

10-2

10-1

Frequency (kHz)

HF and Dytran Accel Left, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

Dytran Accel Left

1.8 2 2.2 2.4 2.6 2.8 3

0

0.5

1

Frequency (kHz)

HF and Dytran Accel Left Coherence, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

Dytran Accel Left

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

0

0.2

0.4

0.6

0.8

1

FRF Amplitude (g/lbf)

HF and Dytran Accel Left CDF, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

Dytran Accel Left
NASA/TM22013-216617 13

Dynamic Response

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

structure under static conditions can provide any insight into CI performance under dynamic conditions.

Dynamic data were collected on two different gear sets (pinion/gear), referred to as L3030R5050 and

L1515R5050, installed on the left side of the test rig. The right gear set was not changed during the tests.

Comparable oil temperatures and oil jet pressures were maintained for each test. Table 4 lists the

operating speeds and loads during the dynamic tests.

The first gear set, referred to as L3030R505, completed 100 hours of operation before measurements

were taken in support of this research. Damage occurred during the previous 100 hours of testing prior to

performing these dynamic tests. Figure 12 is a photograph of the damage observed on the gear and pinion

teeth. Figure 13 shows plots of the gear speed, gear mesh frequency and torque during the test. The gear

speed in rpm and gear mesh frequency in Hz is plotted on the left y-axis. The torque is plotted on the right

y-axis.

TABLE 4.2DYNAMIC TEST CONDITIONS

L3030R5050 L1515R5050 L1515R5050-2

RPM Hz GM(Hz) Torque RPM Hz GM(Hz) Torque RPM Hz GM(Hz) Torque

2000 33 1367 100% 2000 33 1367 100%

2500 42 1708 100% 2500 42 1708 100% 2500 42 1708 100%

3500 58 2392 100% 3500 58 2392 100% 3500 58 2392 100%

3000 50 2050 100% 3000 50 2050 100%

2000 33 1367 29%

2500 42 1708 29%

3000 50 2050 29%

3500 58 2392 29%

Figure 12.2Damage to gear and pinion teeth.
NASA/TM22013-216617 14

A snapshot of the TSA data and the corresponding spectrum data was plotted for each test condition.

The yellow triangles on the x-axis of Figure 13 indicate points where the TSA data were plotted. The

TSA time domain data were converted into the frequency domain using FFT. An example of plots of the

TSA and the spectrum data for a point on the left pinion is also shown in Figure 13. The interpolated TSA

data were averaged to one shaft revolution. The x-axis is the interpolated points of 1 revolution. The

y-axis is in volts. The spectrum data plotted is the spectrum of the TSA. The x-axis is in shaft orders. For

example, since the gear has 41 teeth, the gear mesh frequency (teeth x rpm) shows up at 41 shaft orders.

The pinion shows up at 19 shaft orders due to 19 pinion teeth. The y-axis is in G-scale.

The second gear set, referred to as L1515R5050, was installed new on the test rig. An anomaly, due

to the manufacturing process, was present at the root of the gear teeth at the start of the testing. Figure 14

shows a photograph of the anomaly observed on the gear teeth.

Figure 13.2Gear speed, gear mesh frequency and torque during L3030R5050 test.

Figure 14.2Gear teeth anomaly on the second gear set.
NASA/TM22013-216617 15

Figure 15 shows plots of the gear speed, gear mesh frequency and torque during the test. The gear

speed in rpm and gear mesh frequency in Hz is plotted on the left y-axis. The Torque is plotted on the

right y-axis. A snapshot of the TSA data and the corresponding spectrum data was plotted for each test

condition. The yellow triangles on the x-axis of Figure 15 indicate the point where the TSA data were

collected. Note that the data used for this analysis were limited to points indicated by triangles 1, 3, 7 on

the x-axis. The TSA time domain data were converted into the frequency domain using FFT.

The second gear set, referred to as L1515R5050, rotated for another 12 hr at 8000 in.-lb. Damage was

observed on one pinion tooth at test completion. Figure 16 shows a photograph of the damage observed

on the pinion teeth.

Figure 15.2Gear speed, gear mesh frequency and torque during L1515R5050 test.

Figure 16.2Damage to one pinion tooth.
NASA/TM22013-216617 16

Figure 17 shows plots of the gear speed, gear mesh frequency and torque during the test. The gear

speed in rpm and gear mesh frequency in Hz is plotted on the left y-axis. The torque is plotted on the right

y-axis. A snapshot of the TSA data and the corresponding spectrum data was plotted for each test

condition. The yellow triangles on the x-axis of Figure 17 indicate the point where the TSA data were

collected. The TSA time domain data were converted into the frequency domain by performing FFT.

The objective of this analysis was to compare the dynamic response of two different left gear sets

(L3030R5050 and L1515R5050) at comparable torques and speeds. The vibration data presented were

collected with the MDSS HF accelerometers mounted on the right and left side of the rig gearbox. The

average amplitude of the TSA data and amplitudes of the gear mesh frequencies and their harmonics were

used to compare the differences in dynamic response. In the gear mesh amplitude tables, 1H indicates the

first, 2H the second and 3H the third harmonic of the gear mesh. Note that only the left gear set was

changed. The right set remained the same for all test conditions.

Tables 5 and 6 summarize the frequency domain response of the right and left gearbox accelerometers

while Tables 7 and 8 summarize the time domain response of the accelerometers. The torque was

maintained and speed varied. For the test condition noted by an asterisk in Tables 5 and 6, the test rig was

shut down, inspected, and then data was taken again at the same condition. Tables 9 and 10 summarize

time domain and frequency domain response of the left side of the gearbox at varying speeds and low

torque on gear set (L1515R5050-2) with damage on one tooth.

Figure 17.2Gear speed, gear mesh frequency and torque during L1515R5050-2 test with damage.
NASA/TM22013-216617 17

TABLE 5.2LEFT GEAR MESH AMPLITUDES AT HIGH TORQUE AND VARYING SPEED

TABLE 6.2RIGHT GEAR MESH AMPLITUDES AT HIGH TORQUE AND VARYING SPEED

TABLE 7.2LEFT TSA AMPLITUDES AT HIGH TORQUE AND VARYING SPEED

TABLE 8.2RIGHT TSA AMPLITUDES AT HIGH TORQUE, VARYING SPEED

TABLE 9.2LEFT GEAR MESH AMPLITUDES AT

LOW TORQUE AND VARYING SPEED

TABLE 10.2LEFT TSA AMPLITUDES AT LOW TORQUE AND VARYING SPEED

RPM Torque L3030 Left L1515 Left L1515 Left L1515 2 Left

2000 8000 1H=2.75 1H=1.5

2500 8000 1H=2H=1.7 1H=1, 2H=3 1H=4

3500 8000 1H=3 1H=1.5, 2H=1 *1H=1.5 1H=3, 2H=1.5

3000 8000 1H=5 1H=3

Gear Mesh Amplitude

RPM Torque L3030 Right L1515 Right L1515 Right L1515 2 Right

2000 8000 1H=2H=1.2 1H=5.5, 2H=1.75, 4H=3

2500 8000 1H=2.5, 2H=3.5 1H=.7, 2H=4.5 1H=8

3500 8000 1H=.5 1H=5, 2H=1.5, 3H=2.5 *1H=6, 2H=2, 3H=3 1H=2.5, 2H=1

3000 8000 1H=6 1H=2H=3

Gear Mesh Amplitude

Gear Pinion Gear Pinion Gear Pinion Gear Pinion

RPM Torque L3030 Left L3030 Left L1515 Left L1515 Left L1515 Left L1515 Left L1515 2 Left L1515 2 Left

2000 8000 + 0.04 + 0.05 + 0.04 + 0.03

2500 8000 +0.04 0.05 +0.05 0.07 + 0.05 + 0.04 +0.05 0.06 +0.04 0.06

3500 8000 + 0.09 + 0.09 + 0.04 + 0.03 +0.03 0.04 + 0.03 +0.05 0.04 +0.04 0.03

3000 8000 + 0.08 +0.1 0.08 + 0.06 + 0.04

TSA Amplitude Left

Gear Pinion Gear Pinion Gear Pinion Gear Pinion

RPM Torque L3030 L3030 L1515 L1515 L1515 L1515 L1515 2 L1515 2

2000 8000 +0.04 0.02 +0.04 0.02 + 0.1 + 0.1

2500 8000 + 0.07 +0.06 0.07 +0.06 0.07 + 0.06 + 0.1 + 0.1

3500 8000 + 0.09 + 0.09 + 0.1 + 0.07 +0.12 0.1 +0.12 0.1 + 0.04 + 0.04

3000 8000 +0.09 0.1 + 0.08 +0.08 0.06 +0.07 0.04

TSA Amplitude Right

Gear Mesh Amplitude

RPM Torque L1515 2 Left L1515 2 Right

2000 2740 1H=0.5 1H=0.5

2500 2812 1H=1 1H=1

3000 2890 1H=1.5 1H=5

3500 2974 1H=1.2 1H=1.7

TSA Amplitude Gear Pinion Gear Pinion

RPM Torque L1515 2 Left L1515 2 Left L1515 2 Right L1515 2 Right

2000 2740 + 0.01 + 0.01 + 0.01 + 0.01

2500 2812 + 0.02 + 0.02 + 0.02 + 0.02

3000 2890 + 0.02 + 0.02 + 0.06 + 0.06

3500 2974 + 0.02 + 0.02 + 0.04 + 0.02
NASA/TM22013-216617 18

After review of the data, the following observations were made per the left side datasets:

1. For speeds 2000, 3000, and 3500 rpm, the first harmonic was the dominant frequency measured

by the left accelerometer for both gear sets for all conditions.

2. For the speed of 2500 rpm (1708 Hz GM), the 2nd and 3rd harmonics were almost equal for gear

set 30, and the 2nd harmonic was greater than the 1st for gear set 15. Due to the unusual dynamics

at this speed, this speed should be avoided during testing.

3. The gear set 30, with the most damage during testing, had the highest amplitude in the time

domain.

After reviewing the data, the following observations were made per the right side datasets:

1. For the speed of 3500 rpm, the first harmonic was the dominant frequency measured by the right

accelerometer for both gear sets for all conditions.

2. For the speed of 2500 rpm, the 2nd harmonic was greater than the 1st harmonic for both gear sets.

However, this changed for gear set 15 once damage occurred. Due to the unusual dynamics at this

speed, this speed should be avoided during testing.

3. For speeds of 2000 and 3000 rpm, the dynamics changed for different operating conditions,

where in two cases the 1st and 2nd harmonics were equal.

4. The highest TSA amplitude and gear mesh amplitude occurred on the right side at 3000 rpm.

Comparing torques to varying speeds, for gear set L1515R5050-2, the amplitudes of the gear mesh

increased with higher torques for all speeds. The TSA increased with higher torques for all speeds except

at 3500 rpm on the right gear. Further investigation is warranted to determine the cause of this response.

Accelerometer response changed with varying loads, speeds, gear sets and damage levels. Overall, the

right side was more sensitive to changes in speed and load. Due to the environmental conditions affecting

vibration response, isolating a relationship between structural FRF response and dynamic conditions was

challenging for these datasets. The FRFs and coherence from Figure 10 are plotted in Figures 18 and 19 at

104 and 29 percent load with expanded scales of 0 to 1000 Hz and 1000 to 2000 Hz. The purpose was to

determine if the FRFs at the frequencies tested would indicate the observed responses while the rig was

rotating. Higher amplitude resonances were observed under low load conditions at lower frequencies

possibly indicating the varying response at the lower speeds and loads. However, no unusual response

near 2500 rpm (42 Hz) that corresponds to 1708 Hz GM was noted. But according to Figure 10, the

resonant frequency appears to be at 3.2 kHz with a larger rise in amplitude between 3.4 and 3.8 kHz when

compared to the response at other frequencies. The 2nd harmonic of gear mesh at 2500 rpm is equal to

3.4 kHz. The 2nd harmonic of the gear mesh for this speed was equal to or larger than the 1st for two of the

gears tested.
NASA/TM22013-216617 19

Figure 18.2FRF, Coherence and CDF at 104 percent load measured on right and left.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

10-5

10-4

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left and Right, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (kHz)

HF Accel Left and Right Coherence, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

10-5

10-4

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left and Right, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (kHz)

HF Accel Left and Right Coherence, vert. imp. on left pin at 8283 lb-in preload

HF Accel Left

HF Accel Right
NASA/TM22013-216617 20

Figure 19.2FRF, Coherence and CDF at 29 percent load measured on right and left.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

10-4

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left and Right FRF for vertical impact on left pinion

HF Accel Left

HF Accel Right

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.2

0.4

0.6

0.8

1

Frequency (kHz)

HF Accel Left and Right Coherence for vertical impact on left pinion

HF Accel Left

HF Accel Right

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

10-4

10-3

10-2

10-1

Frequency (kHz)

HF Accel Left and Right FRF for vertical impact on left pinion

HF Accel Left

HF Accel Right

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

0.85

0.9

0.95

1

Frequency (kHz)

HF Accel Left and Right Coherence for vertical impact on left pinion

HF Accel Left

HF Accel Right
NASA/TM22013-216617 21

Comparison of the Spiral Bevel Geared Systems

One objective of making FRF measurements on the test rig was to compare them to the NGB fixture

and the helicopter NGB to determine if measuring the behavior of the structure under static conditions can

provide any insight into CI performance between the helicopter and test rig. Measurements were made in

the NGB fixture with the actuator on the ring gear and compared to measurements made with the actuator

installed on the ring gear within the test rig banded around each system¶s gear mesh frequencies at

specific torques.

FRFs and coherence were measured with 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

20 and 107 percent load conditions. These plots and the corrresponding CDF plots are shown in

Figure 20. The KS Similarity factor within this narrow frequency band between these two loads was equal

to 0.68. The coherence improved at the higher load. The shape of the FRF signature changed at the higher

load illustrating the importance of assessing the similarities of frequency response within frequencies of

interest.
NASA/TM22013-216617 22

The frequencies of interests are different between the test rig and the helicopter requiring different

methods of impact to obtain the 1.8 to 3 kHz versus the helicopter frequency band. It is important to

understand how each system structure affects the response of the CI under its operating conditions. The

most comparable measurement taken on both systems was the installation of an actuator on the ring gear

and measuring the vibration response at the housing. This type of measurement is poor at the lower

frequencies of interest for the test rig, due to the low energy of the reaction-mass shaker at low frequency.

Figure 21 is a photograph of the piezoelectric actuator installed on the test rig gear and the NGB fixture.

The vibration response on the NGB fixture was measured with a high frequency accelerometer with

specifications comparable to the test rig HF accelerometers, mounted in the horizontal position. The

vibration response on the test rig was measured with the HF accelerometers mounted in the vertical

position on the external housing. The gearbox housings are very different, as shown in Figure 2,

indicating the vibration transfer paths between the NGB fixture and the test rig would also be different.

The measurements on the NGB fixture were taken at 4 percent load, while the measurements on the

test rig were taken at 46 percent load. The 4 percent load was used for the NGB fixture because these

measurements can only be taken at that load. FRFs, coherence and the corresponding CDF plots are

shown in Figure 22. The KS Similarity factor for 0 to 50 kHz was equal to 0.25, which indicates very

different vibration transfer paths between the two structures. This is no surprise based on the design of the

two systems. One interesting observation is that the FRF amplitude is significantly higher on the

helicopter indicating the helicopter may be more responsive to gear fault signatures than the test rig. This

observation suggests that the helicopter gearbox may generate higher noise that could potentially mask

vibration amplitude changes due to faults.

Figure 21.2Actuators installed on the test rig and NGB

fixture.
NASA/TM22013-216617 23
NASA/TM22013-216617 24

Summary

Transfer path measurements taken on the test rig to assess the utility of static vibration transfer paths

in assessing dynamic gear CI performance provided some insight into gear condition indicator

performance. Varying load affected the transfer paths within specific frequency bands used for gear

condition indicators. The unique design of the test rig caused a coupling between the right and left

gearbox through the shaft indicating difficulties in isolating pinion tooth damage on one side of the

gearbox. Both the high frequency and the helicopter accelerometers responded similarly to the same

impact indicating both can be used for CI development. Measuring the dynamic behavior of the structure

in specific frequency bands under static conditions using frequency response functions (FRF) provided

limited insight into spiral bevel gear CI performance under dynamic conditions. The amplitude of the gear

mesh and TSA values increased with higher torques. A resonance near gear mesh under static conditions

caused unusual dynamic response when operated at this frequency. The comparison of the FRFs between

the helicopter NGB and the test rig was challenging since the frequencies of interest are different for both

systems and measurements were not taken under comparable loads. However, one interesting observation

was that the FRF amplitude measured on the helicopter NGB was significantly higher than that measured

on the test rig indicating the helicopter may be more responsive to gear faults. Based on these analyses,

although some useful information can be gleaned and perceived from static transfer path measurements,

the system structure, such as test rig, helicopter NGB, NGB fixture does not significantly affect the

vibration response of an accelerometer to the dynamic gear mesh signatures. It is more important to

understand the dynamic characteristics unique to each system to be used for CI development that affect

individual gear CI response for a healthy and damaged tooth.

References

1. Dempsey, P.J., Brandon, E.B., 3Validation of Helicopter Gear Condition Indicators Using Seeded

Fault Tests, ́ NASA/TM22013-217872, April 2013.

2. Antolick, L.J., Branning, J.S., Wade, D.R., and Dempsey, P.J., 3Evaluation of Gear Condition

Indicator Performance on Rotorcraft Fleet, ́ American Helicopter Society 66th Annual Forum

Proceedings, Phoenix, Arizona, May 11-13, 2010.

3. Delgado, I.R., Dempsey, P.J., Antolick, L.J., and Wade, D.R., 3Continued Evaluation of Gear

Condition Indicator Performance on Rotorcraft Fleet, ́ American Helicopter Society Condition

Based Maintenance Specialist Meeting, February 2013.

4. Islam, A., Demspey, P., Feldman, J. and Larsen, C., 3Characterization and Comparison of Vibration

Transfer Paths in a Helicopter Gearbox and a Fixture Mounted Gearbox. ́ NASA TM-216586,

September 2013.

5. Handschuh, R.F.: Thermal Behavior of Spiral Bevel Gears. NASA TM-106518, 1995.

6. Handschuh, R.F.: Testing of Face-Milled Spiral Bevel Gears at High-Speed and Load.

NASA/TM22001-210743, 2001.

7. Stewart, R.M. 1977. Some useful data analysis techniques for gearbox diagnostics. Machine Health

Monitoring Group, Institute of Sound and Vibration Research, University of Southhampton, Report

MHM/R/10/77, July 1977.

8. Zakrajsek, J.J. 1989. An investigation of gear mesh failure prediction techniques.

NASA TM±102340, AVSCOM TM 89±C-005.

9. Massey, F.J. 3The Kolmogorov-Smirnov Test for Goodness of Fit. ́ Journal of the American

Statistical Association. vol. 46, no. 253, 1951, pp. 68±78.