Tooth Temperature Measurements

7/23/2019 Tooth Temperature Measurements

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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 delineation 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

36 gearsolutions.com


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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.

315

AUGUST 2009


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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.

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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.

AUGUST 2009


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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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Tooth Temperature Measurements

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