—O— Baseline set #1

—O— Baseline set #2

—O— High-strength set #1
—O— High-strength set #2

—A— Low-noise set #1

° —A— Low-noise set #2

—~&— Low-noise mod #1(0.050" TOPREM)
—~&— Low-noise mod #2 (0.090" TOPREM)
—&— Low-noise mod #3 (0.120" TOPREM)
—@— Low-noise, improved-bearing-contact pinion

12 a) Acc #1, input bevel hsg, 45° V-T 2 20 pe) Acc #5, top hsg, 45°L-T
oO <= ~
9 15
tof

o
a

Time averaged acceleration, g's
°

Time averaged acceleration, o's

°
°

3 o 21 f) Acc #6, top hsg, -45° L-T
A be ee
: i
8 i
2
3 }
8 H
a
: g
E =
4
§
H
3
8
&
|
A
&
=

Time averaged acceleration, g's | Time averaged acceleration, g's

Time averaged acceleration, o's

i
50 75 100 125

Transmission input torque, % of maximum ‘Transmission input torque, % of maximum
Fig. 11. Vibration results.

NASA/TM—2003-212353 15



Table I. Comparison of low-noise, improved-bearing-contact design
static strain test results to previously tested results, 100% torque.

a) Pinion fillet gages, Max Stress Change Min Stress Change Alt Stress Change
(ksi) (%) (ksi) (%) (ksi) (%)
Baseline design 126 -38 157
High-strength design 92 27.2% = 462.3% = 136 -13.3%
Low-noise design 89 294% = 356.1% =A -27.6%
Low-noise, improved-bearing-contact design 96 244% 26 30.6% 16 ——-25.9%
b) Gear fillet gages. Max Stress Change Min Stress Change “Alt Stress Change
(ksi) (0) ksi) (%) ksi), ——(%)
Baseline design 88 35 ug
High-strength design TT 124% =— 29 --15.1% = 101 -14.4%
Low-noise design Tl 19.0% = 21 384% «=—87 26.3%
Low-noise, improved-bearing-contact design 36 -36.0% 29 16.5% —82_——-30.4%
©) Pinion root gages. Max Stress Change Min Stress Change Alt Stress Change
(ksi) (%)_ ksi) (0) ksi) (%)
Baseline design 33 40 2
High-strength design 4 247% 769.2% =D 52.3%
Low-noise design 41 242% = TL 775% = 051.3%
. Low-noise, improved-bearing-contact design $7 742% 54 35.9% AM ——52.7%
4) Gear root gages. Max Stress Change Min Stress Change Alt Stress Change
(ksi) (ksi) (%)——ksiy),——(%)
Baseline design 30 67 92
High-strength design 39° 315% = -74_— 4% = 107 16.5%
Low-noise design 30-15% = -75 10.9% = 9S 3.1%
Low-noise, improved-bearing-contact design 30 0.0%  -74 103% 97 5.7%

NASA/TM—2003-212353



Q
3

——Baseline set #2

—Hligh-strength set #2

—Low-noise set #2

~—Low-noise, improved-
bearing-contact-
pinion

°

a
s

Stress, ksi

a8

°

Stress, ksi

Stress, ksi

c) Gages 5 and 24

Stress, ksi
°

a
3

d) Gages 6 and 25

as
88

Stress, ksi
8 6

e) Gages 7 and 26

3

40 20 2 10 0 1 2 3 40
Pinion shatt position, deg

Fig. 15. Results from static strain tests, gear root gages, 100% torque (refer to Fig. 7 for strain gage locations).

NASA/TM—2003-212353 19



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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
June 2003 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Evaluation of Low-Noise, Improved-Bearing-Contact Spiral Bevel Gears

WBS-22-708-90-01
‘6. AUTHOR(S) 1L162211A47A

David G. Lewicki and Ron L. Wood

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

REPORT NUMBER
National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

E-13041
Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING
National Aeronautics and Space Administration AGENCY REPORT NUMBER
Washi 1. DC 20546-0001
od NASA TM—2003-212353
U.S. Army Research Laboratory ARL-TR-2970

Adelphi, Maryland 20783~1145

11. SUPPLEMENTARY NOTES.

Prepared for the 59th Annual Forum and Technology Display sponsored by the American Helicopter Society, Phoenix,
Arizona, May 6-8, 2003. David G. Lewicki, U.S. Army Research Laboratory, NASA Glenn Research Center; Ron L.
Woods, Bell Helicopter Textron, Inc., Fort Worth, Texas 76101. Responsible person, David G. Lewicki, organization
code 5950, 216-433-3970.

‘12a. DISTRIBUTION/AVAILABILITY STATEMENT 712b. DISTRIBUTION CODE.
Unclassified - Unlimited
Subject Category: 37 Distribution: Nonstandard

Available electronically at hitp://gltrs. gre. nasa.gov
This publication is available from the NASA Center for AeroSpace Information, 301-621-0390.

13. ABSTRACT (Maximum 200 words)

Studies to evaluate low-noise, improved-bearing-contact spiral-bevel gears were performed. Experimental tests were
performed on the OH-58D helicopter main-rotor transmission in the NASA Glenn 500-hp Helicopter Transmission Test
Stand, Low-noise, improved-bearing-contact spiral-bevel gears were compared to the baseline OH-S8D spiral-bevel gear
design, a high-strength design, and previously tested low-noise designs. Noise, vibration, and tooth strain tests were
performed. The low-noise, improved-bearing-contact spiral-bevel design showed a decrease in noise compared to the
baseline OH-58D design, but not as much reduction as previous tested low-noise designs. The low-noise, improved-
bearing-contact spiral-bevel design gave the same benefit in reduced vibration compared to the baseline OH-58D design
as that of the previously tested low-noise designs. The pinion tooth stresses for the low-noise, improved-bearing-contact
spiral-bevel design showed a decrease compared to the baseline OH-58D design, but not quite as much as the previous
tested high-strength and low-noise designs. For the low-noise, improved-bearing-contact design, the maximum stresses
shifted toward the heel, compared to the center of the face width for the baseline, high-strength, and previously tested
low-noise designs. Lastly, no hardline condition was found on the pinion tooth flank for the low-noise, improved-
bearing-contact design.

14. SUBJECT TERMS: 15. NUMBER OF PAGES

28
Strain gages; Vibration; Noise reduction; Spiral bevel gears; Bevel gears 16. PRICE CODE

17. SECURITY CLASSIFICATION |18. SECURITY CLASSIFICATION | 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT
OF REPORT OF THIS PAGE OF ABSTRACT

\ Unclassified Unclassified Unclassified

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. 239-18
298-102



38a
88

Stress, ksi
°o &

Stress, ksi Stress, ksi
8886888 $4838 8 8

Stress, ksi
°o &

8388

Stress, ksi

Stress, ksi

Stress, ksi

a) Gages 4 and 11

b) Gages 5 and 12

c) Gages 6 and 13

d) Gages 7 and 14

~——Baseline set #2

—High-strength set #2

—Low-noise set #2

——Low-noise, improved-
bearing-contact-
pinion

e) Gages 8 and 15
f) Gages 9 and 16
g) Gages 10 and 17
LOSES
~40 30 -20 -10 0 10 20 30 40

Pinion shaft position, deg

Fig. 12. Results from static strain tests, pinion fillet gages, 100% torque (refer to Fig. 6 for strain gage locations).

NASA/TM—2003-212353

16



Fig. 18. Spiral-bevel pinion tooth contact, low-noise, improved-bearing-contact design.

Fig. 19. Spiral-bevel gear tooth contact, low-noise, improved-bearing-contact design.

NASA/TM-—2003-212353 22



3
8

. a) Gages 1 and 18 ——Baseline set #2
B 50 —High-strength set #2
goo ——Low-noise set #2
£ 50 —Low-noise, improved-
GH + bearing-contact-

“400 pinion

100

b) Gages 2 and 19

a 50
2
go ~
2
6 50

100

100 r.

c) Gages 3 and 20

3 50
g
g 0
g
o 50

-100

20 40 0 10 2 30 40 50 60
Pinion shaft position, deg

Results from static strain tests, pinion root gages, 100% torque (refer to Fig. 6 for strain gage locations),

NASA/TM—2003-212353 18


Fig. 7. Strain gage locations on spiral bevel gear.

Fig. 6. Strain gage locations on spiral bevel pinion.

Fig. 8. Static strain test setup. Fig. 9. Dynamic strain test setup..

NASA/TM—2003-212353 13



Tooth fillet and root gages were placed on successive
teeth to determine loading consistency. The grid length
of the gages was 0.381 mm (0.015 in.) and the nominal
resistance was 120 Q. The gages were connected to
conditioners using a Wheatstone bridge circuitry and
using a quarter-bridge arrangement.

Static: strain tests were performed on both the spiral-
bevel pinions and gears. A crank was installed on the
transmission input shaft to manually rotate the shaft to
the desired position. A sensor was installed on the
transmission output shaft to measure shaft position. At
the start of a test, the transmission was completely
unloaded and the strain gage conditioners were zeroed.
Conditioner spans were then determined using shunt
calibrations. The transmission was loaded (using the
facility closed-loop system) to the desired torque, the
shaft was positioned, and the strain readings along with
shaft positions were obtained using a computer. This
was done for a variety of positions to get strain as a
function of shaft position for the different gages. At the
end of a test, the transmission was again completely
unloaded and the conditioner zeroes were checked for
drift. A photograph of the static strain setup is shown
in Fig. 8.

Dynamic strain tests were performed only on the spiral-
bevel pinions. The pinion gages were connected to slip
tings mounted on the input shaft. A slip ring assembly
for the spiral-bevel gear was unavailable, and thus, dy-
namic strain tests of the gear were not performed. The
test procedure was basically the same as the noise and
vibration tests, except that the transmission was not run
as long in order to maximize strain gage life. A photo-
graph of the dynamic strain setup is shown in Fig. 9.
The dynamic strain data were recorded on tape and
processed off-line. The dynamic strain data were later
digitized into a computer and time-averaged in a manner
similar to the vibration data. This procedure was used
to remove random slip ring noise.

RESULTS AND DISCUSSION
Noise Tests

Fig. 10 gives sound power as a function of torque. The
depicted sound power is the sum of the sound power at
the spiral-bevel meshing frequency (1905 Hz) and its
first harmonic (3810 Hz). In inspecting the frequency
content of the data, the sound power at the meshing fre-
quency was dominant. As interpreted from the figure,
the data is divided into three groups. The first group is
the circles and squares, which are the baseline and in-
creased strength designs. The sound power (i.e., noise
from the bevel gear mesh) for these designs show a

NASA/TM—2003-212353

slight increase with torque. They give about the same
trend with approximately 5 dB of scatter. This is ex-
pected since the bevel pinion and gear tooth geometries
for this group were identical except for the fillet region.

The second group is the triangles, which are the original
low-noise designs, with and without TOPREM. These
data show a significant decrease in noise, especially at
the. 100% torque condition (about 16 dB). They give
about the same trend with approximately 2 to 8. dB of
scatter. The third group is the solid diamonds, which
are the data from the low-noise, improved-bearing-
contact design. The sound power from this design is
nearly constant with torque. It shows a decrease in.
noise from the baseline design (about 7dB at 100%
torque), but not as much reduction as the previous low-
noise designs.

Vibration Tests

Fig. 1.1 gives the results from the vibration tests. Shown.
is acceleration as a function of torque for the eight ac-
celerometers mounted on the OH-58 transmission hous-
ing. Again, the acceleration was time-averaged with
respect to the input shaft to remove all non-synchronous
vibration. -In inspecting the frequency content of the
data, the majority of the time-averaged vibration was
from the spiral-bevel mesh. The data points in the fig-
ure are the root-mean-square (rms) values of the time-
averaged vibration time traces. In general, each figure
can be divided in two groups: 1) baseline and high-
strength designs (circles and squares), and 2) low noise
designs (triangles and diamonds). As with the noise
results, there was a significant reduction in vibration for
the low-noise designs compared to the baseline. For
accelerometers 1, 3, 4, 5, 6, and 8, the vibration for all
the low-noise designs are basically lumped together
with a scatter of about 3 g's. The low-noise, improved-
bearing-contact design gave the same benefit in reduced
vibration as that of the previously tested low-noise de-
signs. As with the noise test results, the vibration for
the low-noise, improved-bearing-contact design was
pretty much constant with torque. Note that cases
where data are missing from the figure (low-noise,
improved-bearing-contact pinion design for accelerome-
ter #5, Fig. 1le, as an example) were due to faulty
instrumentation.

Strain Tests

Set #2 (pinion and gear) of the baseline design, set #2 of
the high-strength design, set #2 of the original low-noise
design, and the low-noise, improved-bearing-contact
pinion were instrumented with strain gages. The low-
noise, improved-bearing-contact pinion meshed with the
gear member of the high-strength design. Results of the



fatigue, excessive wear, or scoring, and should be
avoided in a proper gear design. Thus, subsequent
analyses were performed to improve the gear tooth con-
tact (eliminate the hard line) while maintaining low
noise, vibration, and fillet stress [12]. These studies
again used a pre-designed low level of parabolic trans-
mission error constrained to have the bearing: contact
that avoids hardline conditions under design load.

The objective of this report is to describe the results of
the experiments to evaluate the low-noise, improved-
bearing-contact spiral-bevel gear design. Experimental
tests were performed on the OH-58D helicopter main-
rotor transmission in the NASA Glenn 500-hp Helicop-
ter Transmission Test Stand. The low-noise, improved-
bearing-contact spiral-bevel gear design was compared
to the baseline OH-58D spiral-bevel gear design, a high-
strength design, and the previous low-noise designs.
Noise, vibration, and tooth strain test results are pre-
sented.

APPARATUS
OH-58D Main-Rotor Transmission

The OH-58 Kiowa is an Army single-engine, light, ob-
servation helicopter. The OH-58D is an advanced ver-
sion developed under the Army Helicopter Improve-
ment Program (AHIP). The OH-58D main-rotor trans-
mission is shown in Fig.1. It is currently rated at
maximum continuous power of 410 kW (550 hp) at
6016 rpm input speed, with the capability of 10 sec
torque transients to 475 kW (637 hp), occurring once
per hour, maximum. The main-rotor transmission is a
two-stage reduction gearbox with an overall reduction
ratio of 15.23:1. The first stage is a spiral-bevel gear set
with a 19-tooth pinion that meshes with a 62-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. Both pinion and
gear are straddle mounted.

A planetary mesh provides the second reduction stage.
The bevel-gear shaft is splined 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
splined to the transmission housing. Power is taken out
through the planet carrier splined to the output mast
shaft. The output shaft is supported on top by a split-
inner-race ball bearing and on the bottom by a roller
bearing. The 62-tooth bevel gear also drives a 27-tooth
accessory gear. The accessory gear runs an oil pump,
which supplies lubrication through jets and passageways

NASA/TM—2003-212353

located in the transmission housing, as well as a hydrau-
lic pump for aircraft controls.

Spiral-Bevel Test Gears

Four different spiral-bevel pinion and gear designs were
compared. The first design was the baseline and used
the current geometry of the OH-58D design. Table 1
lists basic design parameters. The reduction ratio of the
bevel set is 3.26:1. All gears were made using standard
aerospace practices where the surfaces were carburized
and ground. The material used for all test gears was
X-53 (AMS 6308). Two sets of the baseline design
were tested.

The second spiral-bevel design was an increased
strength design. The configuration was identical to the
baseline except that the tooth fillet radius of the pinion
was increased by a factor of approximately two. Also,
the tooth fillet radius of the gear was slightly increased
(approximately 1.16 times the baseline) and made full
fillet. Tooth fillet radii larger than those on conven-
tional gears were made possible by advances in spiral-
bevel gear grinding technology. Advanced gear grind-
ing was achieved through redesign of a current gear
grinder and the addition of computer numerical con-
trol [13]. Two sets of the increased-strength design
were tested.

The third spiral-bevel design was a previous low-noise
design. The low-noise design was identical to the in-
creased-strength design except the pinion teeth were
slightly altered to reduce transmission error. The gear
member was the same as in the increased-strength de-
sign. The low-noise design was based on the idea of
local synthesis that provided at the mean contact point
the following conditions of meshing and contact [4]:
a) the required gear ratio and its derivative, b) the de-
sired direction of the tangent to the contact path, and
c) the desired orientation and size of the major axis of
the instantaneous contact ellipse. The local synthesis
was complemented with a tooth contact analysis [4].
Using this approach, the machine tool settings for re-
duced noise were determined. As with the high-strength
design, precise control of the manufactured tooth sur-
faces was made possible by advances in the final grind-
ing operation machine tool [13]. Further information on
the previous low-noise design can be found in refer-
ences [7-8]. In summary, the effect of the topological
change in the low-noise design was a reduction in over-
all crowning of the tooth, leading to an increase in con-
tact ratio and reduced transmission error.

Two sets of a first attempt of a low-noise design were
tested. This included two low-noise pinions and two


Evaluation of Low-Noise, Improved-Bearing-Contact Spiral Bevel Gears

David G. Lewicki
U.S. Army Research Laboratory
National Aeronautics and Space Administration
Glenn Research Center
Cleveland, Ohio 44135

Ron L. Woods
Bell Helicopter Textron, Inc.
Fort Worth, Texas 76101

ABSTRACT—Studies to evaluate low-noise, improved-bearing-contact spiral-bevel gears were performed. Ex-
perimental tests were performed on the OH-58D helicopter main-rotor transmission in the NASA Glenn 500-hp
Helicopter Transmission Test Stand. Low-noise, improved-bearing-contact spiral-bevel gears were compared to the
baseline OH-S8D spiral-bevel gear design, a high-strength design, and previously tested low-noise designs. Noise,
vibration, and tooth strain tests were performed. The low-noise, improved-bearing-contact spiral-bevel design
showed a decrease in noise compared to the baseline OH-58D design, but not as much reduction as previous tested
low-noise designs. The low-noise, improved-bearing-contact spiral-bevel design gave the same benefit in reduced
vibration compared to the baseline OH-58D design as that of the previously tested low-noise designs. The pinion
tooth stresses for the low-noise, improved-bearing-contact spiral-bevel design showed a decrease compared to the
baseline OH-58D design, but not quite as much as the previous tested high-strength and low-noise designs. For the
low-noise, improved-bearing-contact design, the maximum stresses shifted toward the heel, compared to the center
of the face width for the baseline, high-strength, and previously tested low-noise designs. Lastly, no hardline condi-
tion was found on the pinion tooth flank for the low-noise, improved-bearing-contact design.

INTRODUCTION misaligned mode to compensate for housing deflections.
Over compensation for this type of operation, however,
leads to large transmission error and higher noise and

vibration levels.

Spiral-bevel gears are used extensively in rotorcraft
applications to transfer power and motion through non-
parallel shafts. In helicopter applications, spiral-bevel
gears are used in main-rotor and tail-rotor gearboxes to
drive the rotors. In tilt-rotor applications, they are used
in interconnecting drive systems to provide mechanical
connection between two prop-rotors in case one engine
becomes inoperable. Even though spiral-bevel gears
have had considerable success in these applications,
they are a main source of vibration in gearboxes, and
thus, a main source of noise in cabin interiors [1-2]. In
addition, higher strength and lower weight are required
to meet the needs of future aircraft [3].

In previous. studies, gears with tooth fillet and root
modifications to increase strength were manufactured
and tested [7-8]. In addition, these previous studies
tested gears with tooth surfaces designed for reduced
transmission errors. The teeth were designed using the
methods of Litvin and Zhang [9] to exhibit a parabolic
function of transmission error at 4 controlled low level
(8 to 10 arc sec). The low level of transmission error
reduces the vibration and noise caused by the mesh.
The new tooth geometries for this design were achieved
through slight modification of the machine tool settings
used in the manufacturing process. The design analyses
addressed tooth generation, tooth contact analysis,
transmission error prediction, and effects of misalign-
ment [9-11]. The results. from these tests showed a sig-
nificant decrease in spiral-bevel gear noise, vibration,
and tooth fillet stress. However, a hardline condition
(concentrated wear lines) was present on the pinion

Various investigators have studied spiral-bevel gears
and their influence on vibration and noise [4-6]. Most
studies show that transmission error is directly related to
undesirable vibration and noise. Transmission error is
the difference of the actual rotation of the output gear
minus the theoretical amount of rotation (equal to the
rotation of the input pinion multiplied by the pinion to

gear tooth ratio). A common practice is to modify spi-
ral-bevel gear surface topology to permit operation in a

NASA/TM—2003-212353

tooth flank area. A hardline condition could possibly
lead to premature failure such as early pitting/surface



95

85

80+

75

Sound Power, dB (re 1 pW)

_o-
oe
a
a
a

—s-
-e

Baseline set #1

Baseline set #2

High-strength set #1

High-strength set #2

Low-noise set #1

Low-noise set #2

Low-noise mod #1 (0.050" TOPREM)
Low-noise mod #2 (0.090" TOPREM)
Low-noise mod #3 (0.120" TOPREM)
Low-noise, improved-bearing-contact pinion

65

NASA/TM—2003-212353

50

75 100 125

Transmission input torque, % of maximum

Fig. 10. Sound power at spiral-bevel mesh frequencies.

14


improved-bearing-contact design pinion was manufac-
tured and tested. This pinion meshed with one of the
gear members of the high-strength set for all of its tests.

Noise and vibration tests were performed on all pinions
and gears manufactured. One set of the baseline design,
one set of the high-strength design, one set of the previ-
ous low-noise design, and the low-noise, improved-
bearing-contact design pinion were all instrumented
with strain gages and strain tests were performed on
these. Again, the low-noise, improved-bearing-contact
design pinion meshed with the instrumented gear mem-
ber of the high-strength set for its strain tests. A de-
scription of the instrumentation, test procedure, and data
reduction procedure is as follows.

Noise Tests

Acoustic intensity measurements were performed using
the two-microphone technique. The microphones used
had a flat response (+2 dB) up to 5000 Hz and a nomi-
nal sensitivity of 50 mV/Pa. The microphones were
connected to a spectrum analyzer which computed the
acoustic intensity from the imaginary part of the cross-
power spectrum, Near the input region of the OH-58D
transmission, a grid was installed which divided the
region into 16 areas (Fig. 3). For each test, the acoustic
intensity was measured at the center of each of the
16 areas. Only positive acoustic intensities (noise flow-
ing out of the areas) were considered. The acoustic in-
tensities were then added together and multiplied by the
total area of the grids to obtain sound power of the
transmission input region.

At the start of each test, the test transmission ‘oil was
heated using an external heater and pumping system.
For all the tests, the oil used conformed to a DOD-L-—
85734 specification. Once the oil was heated, the
transmission input speed was increased to 3000 rpm, a
nominal amount of torque was applied, and mast lift
load was applied to align the input shaft (18 310 N,
4120 Ib). The transmission input speed and torque were
then increased to the desired conditions. The tests were
performed at 100-percent transmission input speed
(6016 rpm) and torques of 50, 75, 100, and 125-percent
of maximum design. The transmission oil inlet tem-
perature was set at 99 °C (210 °F). After the transmis-
sion oil outlet stabilized (which usually required about
20 min), the acoustic intensity measurements were
taken. The time to obtain the acoustic intensity meas-
urements of the 16 grid points at a given test condition
was about 30 min.. For each acoustic intensity spectrum
at a grid point, 100 frequency-domain averages were
taken. This data was collected by a computer. The
computer also computed the sound power spectrum of
the grids after all the measurements were taken.

NASA/TM—2003-212353

Vibration Tests

Eight piezoelectric accelerometers were mounted at
various locations on the OH-S8D transmission hous-
ing (Fig. 4). The accelerometers were located near the
input spiral-bevel area (accelerometers land 2, measur-
ing radially to the input shaft), the rirtg gear area (accel-
erometers 3 and 4, measuring radially to the planetary),
and on the top cover (accelerometers 5 to 8, measuring
vertically). All accelerometers had a 1 to 25 000-Hz
(+3 dB) response, 4 mV/g sensitivity, and integral elec-
tronics. Fig. 5 shows a photograph of the noise and
vibration test setup.

The vibration tests were performed in conjunction with
the noise tests. After collecting the acoustic intensity
data for a given test, the vibration data were recorded on
tape and processed off-line. The vibration data were
later analyzed using time averaging. Here, the vibration
data recorded on tape were input to a signal analyzer
along with a tach pulse from the transmission input
shaft. The signal analyzer was triggered from the tach
pulse to read the vibration data when the transmission
input shaft was at the same position. The vibration sig-
nal was then averaged in the time domain using
100 averages. This technique removed all the vibration
which was not synchronous to the input shaft. Before
averaging, the major tones in the vibration spectrum of
the OH-S8D baseline design were the spiral-bevel and
planetary gear fundamental frequencies and harmonics.
Time averaging removed the planetary contribution,
leaving the spiral-bevel contribution for comparing the
different design configurations.

Strain Tests

Twenty strain gages were mounted on the spiral-bevel
pinions for one set of each of the four designs (Fig. 6).
Twenty-six gages were mounted on the spiral-bevel
gears (Fig. 7). Gages were positioned across the tooth
face widths with some in the fillet area and some in the
root area of the teeth. The fillet gages were placed on
the drive side of two adjacent teeth. The fillet gages
were also positioned at a point on the tooth cross-
section where a line at a 45° angle with respect to the
tooth centerline intersects the tooth profile. The fillet
gages were placed there to measure maximum tooth
bending stress. (Previous studies on spur gears showed
that the maximum stresses were at a line 30° to the tooth
centerline [14]. Forty-five degrees was chosen for the
current tests to minimize the possibility of the gages
being destroyed due to tooth contact.) In addition to
maximum tensile stresses, root stresses can become
significant in lightweight, thin-rimmed aerospace gear
applications [15]. Thus, root gages were centered be-
tween teeth in the root to measure gear rim stress.


Fig. 16. Comparison of dynamic and static stresses, low-noise, improved-bearing-contact design:

NASA/TM—2003-212353

Stress, ksi

Stress, ksi

Stress, ksi

eee

100 -

t | tli

20 c) Gage 16

60+ Static (bold)
40+
20F

Dynamic

207 a) Gage 12
40 Fe ee es

Static (bold)
60+
40-
207 = Dymamie

ea

-20F b) Gage 14
-40 1

Static (bold)

4 1 1 1 1 1 1 1

-40
-180 -135 -90 45 0 45 90 135 180

Pinion shaft position, deg

pinion fillet gages, 100% torque.

20


NASA/TM—2003-212353 ARL-TR-2970

RESEARCH LABORATORY

Evaluation of Low-Noise,
Improved-Bearing-Contact
Spiral Bevel Gears

David G. Lewicki

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

Ron L. Woods
Bell Helicopter Textron, Inc.; Fort Worth, Texas

DISTRIBUTION STATEMEN
Approved for Public Release A
Distribution Unlimited

20030905. 125.

June 2003



designs increased about the same amount compared to
the baseline. The maximum tensile stress in the gear
root significantly increased for the high-strength design
compared to the baseline, but stayed the same for the
original: low-noise design and low-noise, _improved-
bearing-contact design (Table Id).

Figure 16 compares the dynamic and static stresses for
the pinion fillet gages at 100% torque for the low-noise,
improved-bearing-contact design. For the three gages
shown (gages 12, 14, and 16), there was no apparent
change in stresses due to dynamic effects. There was no
change in shape of the stress-position traces and the
maximum and minimum values were similar. This was
typical for all the fillet gages (Table Ila and IIIb). The
same observation were found for the pinion root gages
(Fig. 17, Tables IIc and Id).

Bevel Tooth Contact Patterns

As previously reported, the original low-noise designs
showed a significant decrease in spiral-bevel gear noise,
vibration, and tooth fillet stress [7-8]. However, a hard-
line condition (concentrated wear lines) was present on
the pinion tooth flank area for these designs. Figures 18
and 19 show close-up photographs of the pinion and
gear, respectively, for the low-noise, improved-bearing-
contact design after completion of all tests. No hardline
condition was found on the pinion tooth flank.

SUMMARY OF RESULTS

Studies to evaluate low-noise, improved-bearing-contact
spiral-bevel gears were performed. Experimental tests
were performed on the OH-58D helicopter main-rotor
transmission in the NASA Glenn 500-hp Helicopter

. Transmission Test Stand. | Low-noise, improved-
bearing-contact spiral-bevel gears were compared to the
baseline OH-58D spiral-bevel gear design, a high-
strength design, and previously tested low-noise de-
signs. Noise, vibration, and tooth strain tests were per-
formed. The following results were obtained:

1) The low-noise, improved-bearing-contact spiral-
bevel design showed a decrease in noise compared to
the baseline OH-58D design (about 7 dB at 100%
torque), but not as much reduction as previous tested
low-noise designs design (about 16 dB at 100% torque).
The bevel mesh sound power for the low-noise, im-
proved-bearing-contact spiral-bevel design was nearly
constant with torque.

2) The low-noise, improved-bearing-contact spiral-

bevel design gave the same benefit in reduced vibration
compared to the baseline OH-58D design as that of the

NASA/TM—2003-212353

previously tested low-noise designs. As with the noise
test results, the vibration for the low-noise, improved-
bearing-contact design was nearly constant with torque.

3) The spiral-bevel pinion’ tooth stresses for the low-
noise, improved-bearing-contact spiral-bevel design
showed a significant decrease compared to the baseline
OH-58D design, but not quite as much as the previous
tested high-strength and low-noise designs. The gear
stresses, however, showed a significant decrease com-
pared to the baseline OH-58D design, even more than
the previous tested high-strength and low-noise designs.
For the low-noise, improved-bearing-contact design, the
maximum stresses shifted toward the heel; compared to
the center of the face width for the baseline, high-
strength, and previously tested low-noise designs.
There was no apparent change in stresses due to dy-
namic effects for the low-noise, improved-bearing-
contact design.

4) No hardline condition was found on the pinion tooth
flank for the low-noise, - improved-bearing-contact
design.

REFERENCES

1. Lewicki, D.G., and Coy, J.J., Vibration Characteristics
of OH-58A Helicopter Main Rotor Transmission,
1987, NASA TP-2705, AVSCOM TR-86-C-42.

2. Mitchell, A.M., Oswald, F.B., and Coe, H.H., Test-
ing of UH-60A Helicopter Transmission in NASA-
Lewis’ 2240-kW (3000-hp) Facility, 1986, NASA
TP-2626. .

3. Vialle, M., “Tiger MGB-, High Reliability-. Low
Weight," Proceedings of the 47th American Heli-
copter Society Annual Forum Proceedings, Vol. 2,
AHS, Alexandria, VA, 1991, pp. 1249-1258.

4. Litvin, F.L., and Zhang. Y., Local Synthesis and
Tooth Contact Analysis of Face-Milled Spiral
Bevel Gears, 1991, NASA CR-4342, AVSCOM
TR-90-C--28.

5. Gosselin, C., Cloutier, L., and Brousseau, J., Tooth
Contact Analysis of High Conformity Spiral Bevel
Gears, Proceedings of the International Conference
on Motion and Power Transmissions, 1991,
pp. 725-730.

6. Fong, Z.H., and Tsay, C.B., Kinematic Optimiza-
tion of Spiral Bevel Gears, Journal of Mechanical
Design, 1992, Vol. 114. No. 3, pp. 498-506.

7. Lewicki, D.G., Handschuh, R.F., Henry, Z.S., and
Litvin, F.L., “Improvements in Spiral-Bevel Gears
to Reduce Noise and Increase Strength," Proceed-
ings of the 1994 International Gearing Conference,
Sep. 1994, pp. 341-346.



strain measurements will be presented both as plots of
stresses as functions of shaft positions and tables of val-
ues summarizing the peak values.

First, results of the static strain tests at 100% torque for
the pinion fillet gages are shown in Fig. 12. Shown is
stress versus pinion shaft position for all the pinion fillet
gages of the baseline, high-strength, original low-noise,
and low-noise, improved-bearing-contact designs.
Since the strain in the tooth fillet is mostly uniaxial and
in the tangential direction of the tooth face [16], the
stress was calculated by multiplying the measured strain
by the modulus of elasticity (30 x 10° psi for steel), The
figure depicts results from fillet gages on adjacent gear
teeth (gages 4 and 11, 5 and 12, 6 and 13, ...) for the
seven positions along the gear tooth face width. Gages
4 and 11 correspond to positions at the heel of the pin-
ion and gages 10 and 17 correspond to positions at the
toe of the pinion. The gages show typical results of a
driving pinion member rolling through mesh. As a driv-
ing pinion rolls through mesh, it first sees a small
amount of compression in the fillet when the tooth
ahead of the strain-gaged tooth is in contact with the
driven gear. As the pinion rolls further through mesh,
the strain-gaged tooth is in contact with the driver and
the fillet region sees tensile stress. At the maximum
stress, the strain-gaged tooth is loaded in single tooth
contact. Note that cases where data are missing from
the figure (baseline design gages 4, 5, 8, 9, and 10, as
examples) were due to faulty gages.

For the pinion fillet gages at 100% torque, the maxi-
mum tensile stress occurred at the middle of the tooth
face width for the baseline and high-strength designs
(gage 6, 7, 13, and 14 regions; it should be noted that
gages 6-8 and 13-15 were located as close to each other,
respectively, as possible). The minimum stress (maxi-
mum compression) occurred slightly to the heel side of
the middle of the tooth face width. The maximum al-
ternating stress. occurred at the same location of the
maximum tensile stress, where the alternating stress is
defined as the maximum stress minus the minimum
stress for a given gage position. For the previously
tested low-noise design, maximum values of the stresses
(tensile, compressive, alternating) shifted slightly to-
ward the toe compared to the baseline design. For the
low-noise, improved-bearing-contact design, maximum
values of the stresses (tensile, compressive, alternating)
shifted significantly toward the heel compared to the
baseline design. Table II lists the values of the maxi-
mum, minimum, and alternating stresses of the various
designs tested at 100% torque. It should be noted that
the values listed in the table were the average of the two
row of the corresponding gages. In all cases the Change
column compares the stress to the baseline design.
From Table Ila, there was a significant reduction in

NASA/TM—2003-212353

pinion fillet maximum tensile stress of the high-strength
design compared to the baseline. There was an even
greater reduction for the original low-noise design.
There was less of a reduction for the low-noise, im-
proved-bearing-contact design, but it was still signifi-
cant. There was a reduction in the absolute value of the
minimum (compressive) stress for the low-noise, im-
proved-bearing-contact design compared to the baseline,
which led to a significant reduction in alternating stress
compared to the baseline.

Figure 13 gives the results of the static strain tests at
100% torque for the gear fillet gages. The shapes of the
stress-position traces look similar to that of the pinion
except the fillet compression occurs after the tension.
This is because the tooth ahead of the strain-gage tooth
sees contact with the driver member after the strain-
gaged tooth is in contact. For the baseline design, high-
strength design, and original low-noise design, the
maximum tensile stresses occurred at the middle of the
tooth face width. For the low-noise, improved-bearing-
contact design, the maximum tensile stress shifted to-
ward the heel. From Table IIb, there was a significant
reduction in gear fillet maximum tensile stress for the
high-strength, low-noise, and low-noise, improved-
bearing-contact designs compared to the baseline. The
greatest benefit was from the low-noise, improved-
bearing-contact design. Also, note that the magnitude
of gear fillet tensile stresses was significantly lower than
that of pinion. Lastly, cases where data are missing
from the figure (low-noise, improved-bearing-contact
pinion design gages 9 and 16) were due to faulty gages.

Figure 14 gives the results of the static strain tests at
100% torque for the pinion root gages. Although the
root gages were physically located three teeth apart
(Fig. 6), they are plotted as if they were on adjacent
teeth. The stress-position traces were different than the
fillet gages in that the maximum compression was
nearly twice as great as the maximum tension. How-
ever, the magnitude of the maximum tension is signifi-
cantly less than that in the fillet. As with the fillet
gages, the maximum stresses (tensile and alternating)
occurred at the middle of the tooth face width for the
baseline design, high-strength design, and original low-
noise design, and shifted toward to heel for the low-
noise, improved-bearing-contact design. The same trend
was observed for the gear root gages (Fig. 15). The
maximum tensile stress in the pinion root significantly
increased for the high-strength design, and original low-
noise design compared to the baseline (Table IIc). The
maximum tensile stress in the pinion root drastically
increased for the low-noise, improved-bearing-contact
design compared to the baseline. The alternating
stresses in the pinion root of the high-strength, original
low-noise, and low-noise, improved-bearing-contact


gear members where the gear members were the same
as the increased-strength design. In addition, one low-
noise pinion with 0.050" TOPREM, one low-noise pin-
ion with 0.090" TOPREM, and one low-noise pinion
with 0.120" TOPREM, were tested. TOPREM is the
decrease in the pressure angle at the tip of the grinding
wheel used on the pinion during final machining. This
decrease in pressure angle causes more stock to be re-
moved in flank portion of the tooth to prevent interfer-
ence-with the top of the gear member during operation.
The 0.050, 0.090, and 0.120" designations refer to the
depth of modification along the blade cutting edge.

Lastly, the fourth spiral-bevel design was a new low-
noise, improved-bearing-contact design. This new de-
sign was in general based on the principles of the previ-
ous low-noise design, but included an improved itera-
tive approach balancing low transmission errors for re-
duced noise and tooth contact analysis to avoid adverse
contact and concentrated wear conditions [12]. In addi-
tion, modified roll was used in the pinion generation,
and finite element analysis was used to evaluate stress
and contact conditions. One. low-noise, improved-
bearing-contact design pinion was tested.

NASA Glenn 500-HP Helicopter Transmission Test
Stand

The OH-58D transmission was tested in the NASA
Glenn 500-hp helicopter transmission test stand (Fig. 2).
The test stand operates on the closed-loop or torque-
regenerative principle. Mechanical power recirculates
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 differen-
tial gearbox. The output of the differential attaches to
the hollow shaft in the closing-end gearbox. The output
of the closing-end gearbox connects to the speed in-
creaser gearbox. The output of the speed increaser
gearbox attaches to the input of the test transmission,
thereby closing the loop.

A 149-kW (200-hp) variable-speed direct-current (d.c.)
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. An
11-kW (15-hp) d.c. 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 re-
ducer 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

NASA/TM—2003-212353

respect to the gear connected to the input shaft of the
closing-end gearbox. ‘This is done within the differen-
tial gearbox through use of a compound planetary sys-
tem where the planet carrier attaches to the sprocket
housing. The magnitude of torque in the loop is ad-
justed 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-58D transmission output
mast shaft. The OH-58D transmission output mast shaft
connects to a loading yoke. Two vertical load cylinders
connected to the yoke produce lift loads. A 14,000-kPa
(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.
Note that in the OH-58D design, the transmission at no-
load is misaligned with respect to the input shaft. At
18,309 N (4116 Ib) mast lift load, the elastomeric corer
mounts of the OH-5S8D transmission housing deflect
such that the transmission ‘is properly aligned with the
input shaft (In the actual helicopter, this design serves to
isolate the airframe from the rotor vibration).

The test transmission input and output shafts have speed
sensors, torquemeters, and slip rings. Both load cylin-
ders on the mast yoke are mounted to load cells. The
149-kW (200-hp) motor has a speed sensor and a
torquemeter. The magnetic particle clutch has speed
sensors on the input and output shafts and thermocou-
ples. An external oil-water heat exchanger cools the test
transmission oil. A facility oil-pumping and cooling
system lubricates the differential, closing-end, speed
increaser, and bevel gearboxes. The facility gearboxes
have accelerometers, thermocouples, and chip detectors
for health and condition monitoring.

TEST PROCEDURE

From the previous studies, two sets of the baseline de-
sign (a set consisted of a pinion and a gear), two sets of
the high-strength design, and two sets of the previous
low-noise design were manufactured and tested. Note
that the gear members for the high-strength set and pre-
vious low-noise set were the same design. There were,
however, four of these gear members manufactured, two
for the high-strength set and two for the low-noise set.
Again, these gears differed from the gear member of the
baseline set (two if these manufactured and tested) due
to the increased fillet radius and full fillet. Also from
the previous studies, three additional low-noise design
Pinions with TOPREM modifications were manufac-
tured and tested. These pinions meshed with one of the
gear members of the previous low-noise set for all of
their tests. For the current study, one low-noise,



100

50

Stress, ksi Stress, ksi

Stress, ksi

Stress, ksi Stress, ksi
688 o 8 B88 2 8B

Stress, ksi

°

Stress, ksi

50

a) Gages 8 and 15 ——Baseline set #2
—High-strength set #2
\ ——Low-noise set #2
——Low-noise, improved-
bearing-contact-
pinion

b) Gages 9 and 16

©) Gages 10 and 17

[ d) Gages 11 and 18

f) Gages 13 and 20°

g) Gages 14 and 21

Ss

40 -30 20-10 ti) 10 20 30 40

Pinion shatt position, deg

Fig. 13. Results from static strain tests, gear fillet gages, 100% torque (refer to Fig. 7 for strain gage locations),

NASA/TM—2003-212353

17



The Propulsion and Power Program at
NASA Glenn Research Center sponsored this work.

Available from
NASA Center for Aerospace Information National Technical Information Service
7121 Standard Drive 5285 Port Royal Road
Hanover, MD 21076 Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov


Table TH.

(n/w = gage not working)

Comparison of static and dynamic stresses, low-noise, improved-bearing-contact design, 100% torque.

a) Pinion fillet gages 4, 5, 6, 7, 8,9, 10.
Static Tests

Gage 4 Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10
Max stress (ksi) 87 96 88 85 83 64 40
Min stress (ksi) 27 +16 15 -12 9 7 5
Alt stress (ksi) 14 112 102 97 93 7 44
Dynamic Tests
Gage 4 Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10
Max stress (ksi) 82 95 89 ww nw 66 40
Min stress (ksi) -27 “17 -I5 nlw niw 9 5
Alt stress (ksi) 109 2 105 nw niw 75 46
Difference
Gage 4 Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10
Max stress (ksi), 6.0% 1.0% 2.2% nw nw 2.3% 1.5%
Min stress (ksi) 18% 7.9% 23% nw nlw 34.7% 16.8%
Alt stress (ksi) 4.2% 0.3% 2.3% nw, niw 54% 3.0%
b) Pinion fillet gages 11, 12, 13, 14, 15, 16, 17.
Static Tests
Gage 11 Gage 12 Gage 13 Gage 14 Gage 15 Gage 16 Gage 17
Max stress (ksi) 95 90 86 85 77 63 39
Min stress (ksi) 23 28 2 -20 7 8 5
Alt stress (ksi) 19 6 107 105 94 i 44
Dynamic Tests .
Gage 11 Gage 12 Gage 13 Gage 14 Gage 15 Gage 16 Gage 17.
Max stress (ksi) nw 86 84 85 nw 67 40
Min stress (ksi) nw -26 21 -20 nlw ll 6
Alt stress (ksi) nw, t12 105 105 niw 7B 47
Difference
Gage 1 Gage 12 Gage 13 Gage 14 Gage 15 Gage 16 Gage 17
Max stress (ksi) nw ATM% 2.1% 0.0% niw 6.4% 3.8%
Min stress (ksi) niw 1.6% 0.6% 1.9% niw 29.1% 33.2%
Alt stress (ksi) niw 3.4% 18% 0.4% niw 9.0% FARO
) Pinion root gages 1, 2, 3. 4) Pinion root gages 18, 19, 20.
Static Tests Static Tests
Gage] _Gage2__ Gage 3 Gage 18 Gage 19 Gage 20
60 59 37 Max stress (ksi) 53 55 4
Min stress (ksi) 49 42 17 ‘Min stress (ksi) 60 4 13
Alt stress (ksi) 109 101 54 Alt stress (ksi) 13. 96. 55
Dynamic Tests Dynamic Tests
Gage | Gage 2 Gage 3 Gage [8 Gage 19 Gage 20
Max stress (ksi), niw niw 38 Max stress (ksi) 50 54 47
Min stress (ksi) iw nlw -17 Min stress (ksi) 65 43 -15S
Alt stress (ksi) nw niw, 55 Alt stress (ksi) Hs 97 61
Difference Difference
Gage 1 Gage 2 Gage 3 Gage 18 Gage 19 Gage 20,
Max stress (ksi) niw nw 3.3% Max stress (ksi) 5.5% 2.5% 12.5%
Min stress (ksi) niw nw 3.2% Min stress (ksi) 8.2% 6.3% 9.8%
Alt stress (ksi) nw nw 1.2% Alt stress (ksi) 1.8% 1.2% 11.8%

NASA/TM—2003-212353



Test transmission

5 6
Output shaft 57 68
‘Sound intensity probe 4 3
4
1,2
Computer
b

analyzer 5

= 7 8
Input shaft a) Top view b) Side view
Fig. 3. Sound intensity measurement system. Fig. 4. Accelerometer locations on OH-58D transmission.

Fig. 5. Noise/vibration test setup.

NASA/TM—2003-212353 12


NASA/TM—2003-212353

U.S. ARMY

RESEARCH LABORATORY

Evaluation of Low-Noise,
Improved-Bearing-Contact
Spiral Bevel Gears

David G. Lewicki
U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Ron L. Woods
Bell Helicopter Textron, Inc., Fort Worth, Texas

Prepared for the

59th Annual Forum and Technology Display
sponsored by the American Helicopter Society
Phoenix, Arizona, May 6-8, 2003

National Aeronautics and
Space Administration

Glenn Research Center

ARL-TR-2970

June 2003



Stress, ksi

Stress, ksi

Stress, ksi

[ c) Gage 20
naa

-80
180 -135 -90 45 0 45 90 135 180

Pinion shaft position, deg

Fig. 17. Comparison of dynamic and static stresses, low-noise, improved-bearing-contact design;
pinion root gages, 100% torque.

NASA/TM—2003-212353 21



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12.

Lewicki, D.G., Handschuh, R.F., Henry, Z.S., and
Litvin, F.L., "Low-Noise, High-Strength, Spiral-
Bevel Gears for Helicopter Transmissions,” AIAA
Journal of Propulsion and Power, Vol. 10, No. 3,
May-Jun. 1994, pp. 356-361.

Litvin, F.L., and Zhang, Y., “Local Synthesis and
Tooth Contact Analysis of Face-Milled Spiral
Bevel Gears," NASA CR-4342, 1991.

). Litvin, F.L., Zhang, Y., and Chen, J., “User's Man-

ual for Tooth Contact Analysis of Face-Milled Spi-
ral Bevel Gears With Given Machine-Tool Set-
tings," NASA CR-189093, 1991.

« Litvin, F.L., Kuan, C., and Zhang, Y., “Determina-

tion of Real Machine-Tool Settings and Minimiza-
tion of Real Surface Deviation by Computer In-
spection,” NASA CR-4383, 1991.

Fuentes, A., Litvin, F.L., Mullins, B.R., Woods, R.,
Handschuh, R.F., and Lewicki, D.G., "Design and
Stress Analysis of Low-Noise Adjusted-Bearing-
Contact Spiral Bevel Gears," Proceedings of the In-
ternational Conference on Gears, Munich, Ger-
many, Vol. 1, Mar. 2002, pp. 327-340.

13.

Scott, H.W., Computer Numerical Control Grinding
of Spiral Bevel Gears, 1991, NASA CR-187175,
AVSCOM TR-90-F-6.

. Hirt, M.C.O., Stress in Spur Gear Teeth and Their

Strength as Influenced by Fillet Radius, Ph.D. Dis-
sertation, Technische Universitat Munchen, 1976,
translated by the American Gear Manufacturers
Association.

. Drago, R.J., Design Guidelines for High-Capacity

Bevel Gear Systems, AE-15 Gear Design, Manu-
facturing and Inspection Manual, Society of Auto-
motive Engineers, 1990, pp. 105-121.

. Winter, H., and Paul, M., Influence of Relative

Displacements Between Pinion and Gear on Tooth
Root Stresses of Spiral Bevel Gears, 1985, Journal
of Mechanisms Transmissions and Automation in
Design, Vol. 107, pp. 43-48.

Table 1. Baseline spiral-bevel gear parameters
of the OH-S8D main-rotor transmission.

Number of tecth,
pinion
gea

Module, mm (diametral pitct

Pressure angle. deg,
Mean spiral angle, deg
Shaft angle, deg...
Face width, mm (

36.83 (1.450)

NASA/TM—2003-212353


Output

Planet gear H

Ring gear

Sun gear

Spiral bevel gear

Input

$f ‘Spiral bevel pinion

Fig. 1. OH-58D helicopter main-rotor transmission.

15-hp de motor
Magnetic particle clutch

Fig. 2. NASA Glenn 500-hp helicopter transmission test facility.

NASA/TM—2003-212353 1