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Much can be learned from measuring the
temperature of gears under load. The following
paper describes an experimental technique
developed specifically for this purpose.
By Suren B. Rao and Douglas R. McPherson
Gear TooThTemperaTureMeasureMents
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This paper presents the technique developed to measure the tem-
perature on various active portions of a gear operating under load,at high speeds, and the results obtained. Comparison of the mea-
sured temperatures to computed temperatures utilizing standard
AGMA methods is also presented. This experimental technique was
developed as a part of a larger project to establish design stress
allowables on aircraft gear steels at elevated temperatures. This
required that the ability to control the temperature of the gear tooth
material at the mesh be demonstrated. The results of this success-
ful effort are described in this paper as a matter of interest to the
gear community.
BACKGROUNDIn order to provide extended operation of gears in a loss of lubri-cant situation in high performance gearboxes, special steels have
been introduced for aircraft gears. However, further benefits, such
as increasing aircraft payload by decreasing the size and capac-
ity of the lubrication system, could be derived if the gearbox were
designed to operate at higher temperatures. This design change
requires that the fatigue performance of these special steels be
characterized at elevated temperatures.
In an effort to establish a program to determine the bending and
contact fatigue characteristics of gear steels, it was necessary to
demonstrate that power re-circulating (PC) bending and contact
fatigue tests could be conducted at controlled elevated tempera-
tures. Key to conducting PC experiments at elevated temperatures
is demonstrating the ability to control the temperature in the rel-
evant regions of the gear tooth, utilizing the only variable that can be
easily controlled in such experiments, which is the inlet temperature
of the lubricant.
A schematic of a PC test rig is shown in figure 1. It consists of a
four-square, kinematic loop including a test gearbox with a pair of
meshing gears and a slave, or reversing gearbox, consisting of
another pair of gears. The load on the gears is applied by generating
and locking a torque within the kinematic loop, by the torque applier.
The motor driving the test rig has to only supply the losses in the
mechanism. The gears in the reversing gearbox usually have a much
wider face width than the test gears so that they will not fail as they
experience significantly lower contact and bending stresses for thesame applied torque than the test gears.
While this type of a test rig has traditionally been utilized for
gear surface fatigue testing, as described in reference 1, it has
also being extensively utilized for conducting gear bending fatigue
testing2. This is particularly true when experiments are designedto establish bending stress design allowables for various gea
materials or for analyzing the impact of various manufacturing pro
cesses on bending strength. The details of the 0.25 inch face width
test gears utilized in the PC test rig are described in table 1.
The lubrication arrangement in the test gearbox is illustrated in
figure 2. This shows a single nozzle providing oil into the mesh
Fig. 1: Schematic of a four-square test rig.
Fig. 2: Lubrication nozzle arrangement in test gearbox.
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(gear rotational direction shown on left hand side shaft) and two
nozzles providing the cooling oil into the out of mesh side of the
engagement.
Thermal Regions of Gear Teeth: In order to conduct gear mate-
rial characterization at elevated temperatures, it is necessary todelineate the various thermal regions of an operating gear that are
relevant to the failure mechanisms under consideration. One pro-
posed thermal de-lineation is illustrated in figure 3. The gear blank
temperature, measured close to the root area of the gear tooth, is
considered relevant to bending fatigue, the maximum gear tobulk temperature measured very close to the involute surfa
of the tooth is considered relevant to surface durability, and t
maximum contact temperature at the tooth surface is conside
relevant to scoring resistance. If this de- lineation is acceptable, th
Fig. 3:Thermal regions in a loaded gear tooth.
Table 1: Details of the test and mate gears.
Number of Teeth 28
Diametral Pitch 8
Module 3.175
Pressure Angle 20 degrees
Helix Angle 0 degree
Root Diameter 3.185-3.190
Base Diameter 3.288924
Form Diameter 3.3305SAP Diameter 3.3405
Pitch Diameter 3.50000
EAP Dameter 3.729-3.741
Tip Diameter 3.749-3.751
Circular Tooth Thickness at PD 0.1915-0.1935
Measurement over 0.2160 pins 3.9893-3.7942
Minimum root fillet radius 0.0665
615
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the experimental effort distills down to measuring the gear blank
and gear tooth bulk temperature in order to characterize the bending
fatigue and contact fatigue properties of the material, demonstrating
that they can be held to a defined value with accuracy and precision
by controlling the oil input temperature.
EXPERIMENTAL EFFORTThere have been a few efforts to measure temperature in a gear
tooth in operation. Prominent among them is3 where five thermo-
couples were inserted through a test gear, made in two halves, to
be positioned along the flank of the tooth. While it is unclear how
the two half gears were assembled for the actual experiments,
data on the temperature and temperature distribution was obtained
along the tooth flank at speeds of 1000 revs/minute and at differ-
ent contact pressures. In this study, however, the thermocouples
were distributed in the relevant thermal regions as discussed in the
earlier section.
Instrumentation Setup: The instrumentation effort was conducted
in two distinct phases. In the first phase a thermocouple was sur-
face mounted in the root area of the gear tooth to measure the blank
temperature in the area of maximum bending stresses. This is shown
in figure 4. In the second phase three thermocouples were inserted
angularly from the face of the gear tooth (figure 5), with one thermo-couple breaking through the flank surface to measure contact tem-
perature and the second and third thermocouple angularly inserted
from the face of the gear but stopping short of the flank surface by
0.008 inch and 0.018 inch to measure the tooth bulk temperature.
While the output of the contact temperature thermocouple w
recorded in the experiments conducted, it is no longer discussed
the paper, based on the delineation of the thermal regions releva
to the failure mechanisms of interest in this study, discussed
the earlier section. The thermocouples are, in all cases, at the loest point of single tooth contact (LPSTC), but spaced 120 degre
apart (figure 6) in order to ensure balanced mounting, as the ge
was anticipated to operate at speeds in excess of 5,000 revs/m
Thermally conducting epoxy, recommended by the thermocou
Fig. 4:Thermocouple for gear blank temperaturemeasurement.
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manufacturer, was used in locating the sensors in their respect
locations. In both of these measurement phases the thermocoup
were connected to amplifiers and the amplified outputs brought o
through slip rings to voltage measurement devices, to record t
temperatures at the thermocouples. A picture of the entire setup
the test box on a high speed (up to 10,000 revs/min) PC test rig
shown in figure 7.Experimental Results:The plot of the gear blank temperature m
surement as a function of inlet oil temperature (lubricant is DO
PRF-23699), speed (4250 and 6600 revs/min), and torque (14
and 1800 inch. lbs) is shown in figure 8. The nature of the measu
Fig. 6:Angulardisposition ofthe thermocou-ples for bulktooth tempera-ture.
Fig. 7:Experimental setup for temperature measuremen
Fig. 5:Ther-mocoupleinsertion forbulk toothtemperature.
1233
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gear blank temperatures appears logical as it is directly proportional
to the oil inlet temperature, speed, and torque. When gear blank
temperature was monitored during actual Scoring Resistance tests,
the initiation of scoring failure was easily detected by the sudden
increase in the gear blank temperature.
Figure 9 shows the measured gear tooth bulk temperature (aver-age of the measurement from the thermocouples at 0.008 and
0.018 inch away from the flank surface) as a function of the same
three variables, inlet oil temperature, speed, and torque. The nature
of the measurements again appear logical, and repeat measure-
ments indicated very good repeatability, provided sufficient time w
permitted between and during the measurements for the tempe
tures to stabilize.
COMPARISON OF EXPERIMENTAL
VS. ANALYTICALThis comparison was conducted to further establish the credib
of the temperature measurements. As discussed earlier, only t
gear blank temperature and the gear tooth bulk temperature
considered relevant in this paper, and of these two temperatu
only the gear tooth bulk temperature is computed 4and compa
to the experimentally obtained values. The relationships used for t
computation are as follows:
where
tM=bulk temperature (steady state)
toil
=oil inlet temperature in oF
tflmax
=maximum flash temperature in oF, and
Fig. 8:Gear blank temperature measurement in degrees F.
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where
K is 0.80, numerical factor valid for a semi-elliptic (Hertzian)
distribution of frictional heat over the instantaneous width, 2 bH,
of the rectangular contact band;
m
is the mean coefficient of friction
X is load sharing factor
wNr is normal unit load
vr1 is rolling velocity of the pinion
vr2 is rolling velocity of the gear
BMis thermal contact coefficient
bHis semi-width of Hertzian contact band
The maximum flash temperature is obtained by computing t
flash temperature at a sufficient number of points on the line
action. Figure 10 illustrates the ratio of measured temperature
computed temperature as a function of the oil inlet temperature
different speeds and torques. While the authors believe that t
measurement of the temperatures was conducted with great ca
Fig. 9:Gear bulk tooth temperature measurementin degrees F.
Fig. 10:Ratio of measured to computed gear tooth bulktemperature.
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and precision, it appears that the computed
values are well correlated to the measured
values, only at oil inlet temperatures around
175 F. The measured values are higher
when oil inlet temperatures are below 175
F and the computed values are higher
when oil inlet temperatures are higher than
175 F.
The discrepancy is most likely the result
of the thermal response of the test rig. The
equation for bulk temperature4
is an empiri-cal equation that gives a first approxima-
tion for typical operating conditions. The
thermodynamic response of the test rig
approximates typical operating conditions
most closely at 175F oil inlet temperature.
For higher oil inlet temperature the rig dis-
sipates heat generated in the gear mesh
more effectively than typical operating con-
ditions and for lower inlet temperatures it
dissipates heat less effectively.
CONCLUSIONSAn experimental technique to measure thetemperature of relevant regions of a gear in
mesh and under load was demonstrated.
The relevant regions were defined as the
gear blank temperature and the gear tooth
bulk temperature for characterizing the
bending fatigue and contact fatigue proper-
ties, respectively. The ability to control the
temperature of the relevant regions of the
gear by varying the oil inlet temperature
was also demonstrated. The measured gear
tooth bulk temperature was compared to
computed values, utilizing standard AGMA
methods. While it is believed that the mea-
sured values are more precise than the
computed values, a good degree of correla-
tion between the two further establishes
the credibility of the measurement.
REFERENCES:1) McPherson, D. R. and Rao, S. B.,
Mechanical Testing of Gears, Mechanical
Testing and Evaluation, ASM Handbook,
vol. 8, 2000.
2) S. B. Rao and D. R. McPherson,
Experimental Characterization of
Bending Fatigue Strength in Gear Teeth,
Gear Technology, January/Februar y 2003,
pp. 25-32.
3) J. Yi and P. D. Quinonez, Gear Surface
Temperature Monitoring, Proce.
ImechE, vol. 219 Park J:J. Engineering
Technology.
4) ANSI/AGMA 2001-C95 Annex A
About the Authors:
Suren B. Rao and Douglas R. McPherson are with the Applied Research
Laboratory at The Pennsylvania State University. Contact Rao at [email protected]
and McPherson at [email protected]. The authors wish to acknowledge the support
of the Aerospace Bloc of the Gear Research Institute for conducting the effort
described in this paper. To learn more go to www.gearresearch.org.
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