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SAE Paper Mo. 2003-26-0014
Experimental Tooth Contact Analysis and Life Prediction
Methodology for Truck Axles Hypoid Gears
A n o o p Jain Eicher Motors Ltd., Pithampur, India
A B S T R A C T
This paper describes the methodology followed for experimental
prediction of tooth contact patterns of Truck Axle Hypoid Gear sets
in loaded state. Effort has been m a d e to establish Hypoid Gear
Life based on Duty Cycle simulation on a pair of Test Axles an
in-house developed n e w closed loop Axle Test Machine. Service
Load Data is acquired on loaded truck to establish sustained torque
levels on the Drive Axles. Loaded Tooth Contact pattern (LTCA) is
generated using Gleason Program and Deflection Test analysis is
carried out on the Four Square Axle Test Machine. Typical tooth
contact patterns at a series of loads from no load to max imum load
are generated on the axle test machine. Variation of tooth contact
patterns as a function of applied torque is compared with the
predicted L T C A . Methodology for accelerated testing has been
concluded and correlation with the service data is being
established.
I N T R O D U C T I O N
Extensive study of the performance of truck axle gears has
indicated that axle gears are more dependent on the m a x i m u m
sustained loads rather than the occasional peak loads which occur
during the anticipated life of the vehicle. The stresses resulting
from the sustained loads cannot safely exceed the endurance limit
of the gear material. On~Highway truck axle gears are sized based
on performance torque based on equivalent grade and road
conditions. Hypoid gears having pinion offset with respect to the
gear centre line permit a larger, stronger pinion with more tooth
contact area and are popular on highway truck application as
compared to spiral bevels.
According to the classic design, gear sets have three principal
types of tooth contact pattern. The type of tooth contact depends
to the highest degree on the possible flank form modifications
versus the conjugate flank form.
The intent of flank modifications is to provide a limited
contact area under no load or light load which provides
insensitivity to gear housing tolerances, inaccuracies in the gear
members and assembly, as well as deflections.
For cutting bevel gears there are three mechanisms to create
modifications known as "crowning'" that have the intent to locate
the bearing contact inside the boundaries of the teeth and
therefore, prevent edge contact.
The first element is lengthwise crowning which is a circular
modification along the face width. The second element to generate
crowning is a profile modification on the tool. The third element
of flank crowning Is flank twist from toe to heel. All real bevel
and hypoid gear application used in power transmissions use a
combination of all three types of crowning. (Refer Fig.1)
The fatigue life of bevel and hypoid gear has been known to be a
function of length, width and position of the "no load" tooth
contact pattern. Careful positioning of the tooth contact pattern
relative to the gear m e m b e r can produce dramatic increases in
bending fatigue life.
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it has been established that there is a two fold increase in
bending fatigue life obtained by positioning the tooth contact
pattern toward the toe of the gear tooth rather than at a central
toe position.
HYPOID GEAR DEVELOPMENT AND EVALUATION METHODOLOGY
Fig. 2 outlines the methodology of Gear Development process
followed.
Objective is to sign off the acceptable tooth contact pattern
and asses the acceptable range of tooth contact patterns on a
finally applied hypoid pair by making use of a variety of
theoretical analysis outputs obtained through T 9 0 0 and T 2 0 0 0
Gleason Program in consultation with gleason.
Efforts are on to establish the influence of contact patterns on
bending and contact fatigue life of truck axle hypoid gears by
conducting a series of constant duty cycle tests on a specific
ratio of hypoid gear pair on an in-house developed Axle Test
machine.
CORRELATION B E T W E E N EXPERIMENTAL A N D LOADED TCA
As torque is applied to a gear set the area of contact
between the gear and pinion teeth changes as the tooth surfaces
deform and the gear housing deflects. These changes are usually
observed as a growth in the contact pattern along with a movement
of the contact area. The exact nature of the growth and movement of
the contact pattern has a profound effect on the strength
performance of the gear set.
L O A D E D T C A T H R O U G H F E A : In order to visualize
the change in contact pattern as a function of applied torque,
Gleason program T900 was used to display the loaded TCA plots at
the no-load position and for three non zero torque loads. Four
panels are shown in Fig, 3.
The loaded T C A plot shows the growth and movement of the tooth
contact pattern as a function of applied torque. The upper left
hand panel is the bench (no -load) tooth contact pattern. The bench
tooth contact pattern corresponds to the tooth contact pattern
predicted by the Gleason T C A program and is a function of the
developed settings for the gear and pinion contained in a special
analysis file. The three non-zero torque positions shown in Fig. 3
correspond to three different percentage torques.
Program T900 uses E P . G to describe the rigid body motions of
the pinion relative to the gear as torque is
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applied to the pinion. The tooth contact patterns were
calculated using the values of E,P,G determined from the
experimental axle deflection tests as described in section
"Deflection testing".
In T900 program, gear blanks are rendered as finite element
models. Gear geometry is constructed using special analysis files
obtained by Gleason T 2000 program.
E X P E R I M E N T A L L O A D E D T O O T H C O N T A C T T E
S T A P P R O A C H A N D M E T H O D O L O G Y : This test was
performed on completely processed gears. Typical Tooth contact
check was conducted at a
series of loads from no load to maximum load; the tooth contact
photographs show how the tooth contact pattern shifts and lengthens
as the load is increased. (Refer Table - I for input torque load
simulation for carrying out the test)
Under peak torque load the contact pattern should extend to the
tooth boundaries without showing a concentration of the contact
pattern at any point on the tooth surface.
Any tooth contact pattern which shows a concentration of load
near tooth boundaries indicates
that there is either an excessive displacement of the gears in
their mounting or an unsatisfactory tooth contact pattern
development for this application.
To determine what action is required, the second phase of the
deflection test should be performed.
This test is conducted on a 4 Square Axle test machine described
below. (Refer Fig. 4)
TESTING E Q U I P M E N T , F O U R S Q U A R E A X L E T E S T
M A C H I N E : This is a back to back or closed loop type
Dynamometer where the basic arrangement includes two automotive
drive axles positioned one above the other. The output shafts of
the Axles are connected by a spur gear box at each end. Input to
Axles goes via a spur gear box which is driven by a D C Drive with
step less speed control. This in - house developed axle test
machine features a dynamic torque transducer to measure the
re-circulating torque in the system. (Refer Fig. 4) Torque is
twisted into the system to impose a load throughout, by a unique
torque mechanism, in the direction to place the load on the desired
side of the teeth, and then the entire system is rotated by the
drive motor in the direction counter to the twist (in the drive
direction). The power demand is small, being only the amount needed
to overcome the friction in the system.
Drive motor is placed at the input end of the test component to
add power here and relieve the load on the slave component. In this
set up the bottom axle is the test piece and the top one is the
slave axle.
This machine is capable of carrying out Loaded Tooth contact
test, Deflection Test, Accelerated Stress (AST) and Accelerated
Life Test (ALT) to stimulate and simulate various modes of Drive
Axle Gear failures, which include Bending Fatigue, Pitting,
Scuffing tests.
R E S U L T S A N D ANALYSIS : Variation of tooth contact
pattern for a 15.5 inch Hypoid gear design versus applied gear
torque as predicted by Finite Element model are depicted in Fig. 3.
The Four panels correspond to the
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bench contact pattern and at 25%, 50% and 100% pinion input
torque.
Corresponding tooth contact patterns obtained from the
experimental tests carried out on 4 Square Axle Test Machine on a
15.5 inch Hypoid Pair are depicted in Fig. 5.
O n comparing Fig. 3 and 5 it can be seen that there is good
agreement between the predicted and measured tooth contact patterns
as a function of applied torque. The lengths at each value of gear
torque are within five percent of each other while the shape
characteristics are in close agreement, it can be also observed
that the tooth contact spread is uniform and contained within the
tooth boundaries which suggest that the tooth contact development
is acceptable.
L O A D E D A X L E DEFLECTION T E S T A P P R O A C H A N D M E
T H O D O L O G Y
The deflection test is essential in determining the suitability
of the gear mountings. The purpose of this test is to determine the
displacements of the hypoid gear pair and their mountings under
various load conditions. This test is carried out subsequent to the
loaded tooth contact check.
The axle deflections (E,P,G) measurements are as per the Gleason
Works recommended procedure. E,P,G are the linear components of the
rigid body motions of the gear and pinion relative to the axle
housing. Drive and Coast tests are performed at 10%, 25% ,50% ,75%
and 100% of input torque in the axle.
TESTING E Q U I P M E N T : Testing was conducted with the Gear
unit installed in a device capable of applying
load in increments of 25 % of full torque up to 100%. Desirable
speed is approximately 2-3 r/min of the output shaft, to permit
accurate readings of the deflections. Experimental setup for
carrying out the deflection test is shown below in Fig. 6.
MEASUREMENT OF DISPLACEMENTS : The measurement of displacements
w a s accomplished by attaching a series of linear displacement
transducers (Dial indicators) which are appropriately located to
measure the displacement of the gears, shafts, bearings and the
differential housing itself in all the three principal directions;
along the pinion axis (P), along gear axis (G) and perpendicular to
these axis (E). Fig. 7 shows a typical placement of the indicators
on the Axle housing to measure the displacements. O n c e the
indicators were mounted, the displacements were recorded at various
input torque levels as indicated in the Input torque simulation
matrix (Table - I)
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DEFLECTION S U M M A R Y A N D ANALYSIS : Dial indicator
readings were recorded for further
analysis. A completed Indicator / Displacement diagram (refer
Fig. 8) was prepared where the maximum readings were posted at each
indicator position.
Using dial indicator readings, calculations were made along each
of the three principal axis E,P,G and also the relative
displacements were calculated. (Refer Table - I!)
Although the combination of deflections exceeded the recommended
limits as specified below, these deflections are tolerable as
contact behavior was found satisfactory. (Refer Table - III)
E N D U R A N C E TESTING
The Endurance testing is frequently identified as the
"acceptance" test because it establishes the working life of the
product and thus its acceptability. The purpose of endurance test
is to determine the life of a gear design under actual or simulated
conditions of test operation. The endurance tests include : Bending
Fatigue (Tooth root fillet breakage) a Contact Fatigue (Pitting and
Case crushing) Scoring Wear Repetitive shock loading breakage
And the test procedures include : Field Testing in Normal
service Field Testing under controlled conditions Laboratory
Testing, using a closed-loop Axle test
Dynamometer.
At E M L , Various Endurance tests are being conducted on a 4
Square Axle Test machine.
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SERVICE LOADING AND ENDURANCE TEST PRINCIPLE : Reproduction of
realistic driveline loading warrants the need for multi-channel,
phase related, recorded road load data. This has been achieved by
carrying out Dynamic Service load data acquisition of strain,
angular velocities and gear shift pattern on a truck operating at
rated G V W using Q X -3 data gate system with a sampling rate of
205 samples on roads and under various events viz. highway, rough
road, hilly section and on standard grade. Refer Fig. 9 for
illustration of a sample data recorded on test vehicle.
TEST APPROACH and METHODOLOGY : Most automobile gear teeth are
subjected to
repeated, one way bending for the major part of their lives. O n
road vehicle gears are loaded in reverse which represents only 0.1
% to 1 % of their service life. So, in general, it is considered
appropriate to test automobile gears in one way bending
fatigue.
Bending fatigue tests are performed at loads that correspond to
a life factor between 2.00 to 2.67 thus yielding an expected test
life of between 20,000 and 1,000,000 pinion cycles (Fig. 10).
This is constant amplitude testing with increased frequency of
cyclic loading (Accelerated test)
Test torque should produce a stress on the Gear and Pinion at s
o m e value above the endurance limit to avoid a test that could
continue indefinitely.
5 samples of each Gear pair of different type are being tested
for bending fatigue in accordance to the Accelerated Test
Simulation Matrix (refer Table - IV) at a life factor of 1.8, which
yields an estimated Pinion life of 200,000 cycles or 18h
approximately (Fig. 10).
S - N Curves are to be generated by approximating the Life
scatter data as available from the test rig.
Failure m o d e s are to be recorded and analyzed.
LIFE C Y C L E S E V A L U A T I O N : Life cycle computation
for the pair is done based on the Gleason method is briefly
described below :
Life Factor, KL , is defined as the numerical ratio of the
calculated tensile bending stress, St to the allowed tensile
bending stress, Sat.
Equivalent Life cycles for pinion
Infinite life is assumed to be greater than 6 x 106 cycles for
Pinion. Based on the calculated life cycles, equivalent test torque
is computed for simulating the rupture cycles is determined using
Gleason Dimension sheet of the
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particular Gear design under Bending fatigue test. This is
summarized in a form of a test Simulation matrix (Table - IV).
ACCELERATED TEST PROGRESS SUMMARY : Currently, Bending fatigue
tests are being conducted on a particular Drive Axle Hypoid pair.
Fatigue data for two samples have been recorded.
Efforts are on to establish experimental procedures which
closely correlate the theoretical model which will cut short the
future development cycle for establishing and proving a n e w
pair.
Refer failure photographs in Fig. 11 and 12 of two failed
samples where teeth uprooting took place after 36 and 2 8 h of
Accelerated test respectively.
F U T U R E W O R K O N HYPOID G E A R LIFE PREDICTION
Correlation of field life data on proven designs with data
obtained on Axle test machine.
To perform Weibull analysis of the fatigue data associated with
the gear design. Weibull slopes and mean life for the gear design
to be compared with
a second set of data for a different gear design. Weibull
analysis calculates the slope and shape parameter for a given
confidence value (usually 90%) and displays the upper limit
estimates of the 50 percent mean life curve on the S-N curve for
the gear design being analyzed.
To draw updated S-N Curve displaying the upper and lower
confidence limits of the estimated mean life curve based on
confidence limits along with gear and pinion failures plot.
Axle test machine will be upgraded to simulate the actual RLDA
cycles by replacing the manual mechanical torque mechanism with a
magnetic torque valve coupled with an Epicyclic Gear Box. Post
Upgradation, variable dynamic torque loads can be simulated in the
Axle test machine loop which will be controlled by a
microprocessor.
S E L E C T E D B IBL IOGRAPHY
1. "Design and Manufacture of Spiral Bevel and Hypoid Gears for
Heavy Duty Drive Axles", Gleason Works Publication
2. Theodore, J. K., "Tooth Contact Analysis of Spiral Bevel and
Hypoid Gears under Load", S A E Paper No . 810688
3. "Understanding Tooth Contact Analysis", Gleason Works
Publication, SD3139A, January 1978.
4. Lehrmann, J. R., "Development of Contact Patterns on Tractor
Spiral and Hypoid Gears", S A E Paper No. 841091
5. Wilcox, L., "Analyzing Gear Tooth Stress as a Function of
Tooth Contact Pattern Shape and Position", Gleason Works
Publication
6. Wicox, L., "Improved Finite Element Model For Calculating
Stresses in Bevel and Hypoid Gear Teeth", A G M A Paper, 1997
7. "Application Testing of Bevel and Hypoid Gears", Gleason
Publication
8. "Bending and Contact Stresses in Hypoid Gear Teeth", Gleason
Publication
C O N T A C T
Mr. Anoop Jain Manager, Product Design & Development Eicher
Motors Limited Indore, India E-mail : [email protected]
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