ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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Fig. 7 Weibull analysis with RCF test data
Single-Tooth Fatigue (STF) Test
The STF test is used to generate a statistically significant quantity of bending fatigue data at a comparatively
low price. Teeth are tested one at a time with a fixed loading point, allowing the generation of bending fatigue
data at comparatively high cycles without risk of losing tests to other modes of failure. Another cost-saving
measure is that four or more tests can be conducted with each gear specimen.
Test Equipment. A gear is placed in a fixture so that one tooth at a time can be loaded while another tooth
supports the reaction. The test is usually done in an electrohydraulic, servocontrolled universal test machine.
The primary object of this test is to determine fatigue properties in bending. However, the same setup can be
used to determine single overload properties (ultimate bending strength) as well. Frequently, enough teeth are
tested to develop a stress-cycles diagram to define the bending fatigue characteristics of the material system.
Several arrangements for loading can be considered. One fixture arrangement is shown in Fig. 8. This
illustration shows the Boeing flexural design, which appears to have found favor with the aerospace sector. This
fixture is designed for a 32 tooth, 5.333 diametral pitch (DP), 8 mm ( in.) face width spur gear with several
teeth removed to provide access to test and reaction teeth. The gear is rigidly supported on a shaft. Load is
applied through a carbide block contacting the test tooth at the highest point of single-tooth contact. The
loading block is held in the specified orientation to the gear by a flexural loading arm. This flexural design
ensures accurate loading of the gear tooth with minimal migration of the point of loading. Reaction is carried
through a block contacting the reaction tooth at the lowest point of single-tooth contact. Load is cycled from the
specified test load to a minimum load high enough to keep the slack in the system taken up (usually 10% of the
test load). While most testing is conducted at 20 Hz, other frequencies also are possible. The fatigue test
machine is instrumented to monitor instantaneous loads and tooth deflections. Changes in compliance can be
used for monitoring crack initiation and propagation in the root fillet region. In addition, a crack wire can be
incorporated to monitor catastrophic tooth failure. Typical fatigue load capacity of such types of equipment is
in the range of 10 to 20 kips, although higher loads, up to 110 kips, can be used for single overload tests.
Fig. 8 Flexure arm single-tooth fatigue (STF) test fixture
A second fixture arrangement (Fig. 9) appears to have found favor with many other industry segments. This
fixture utilizes a 34 tooth, 6 DP, 25 mm (1 in.) face width spur gear and is derived directly from the Society of
Automotive Engineers (SAE) Division 33 STF fixture. Fatigue test loads up to about 15 kips are feasible with
this fixture, and single overload tests up to about 50 kips can be accommodated. These STF fixtures are
compact enough to be immersed in heated fluid; thus, fatigue testing can be conducted at elevated temperatures
(up to 400 °F).
Fig. 9 SAE division 33 single-tooth fatigue (STF) test fixture
Test Procedure. Special concern must be taken with regard to safety in conducting the STF test (in addition to
general lab safety procedures). Setting up the test requires moving the hydraulic load ram while lining up the
fixture, bypassing safety features, such as a light curtain to stop the machine, and so on, and considerable
caution needs to be exercised during setup. Periodic calibration of the test fixture is important because there are
many closely fitted parts that can wear and change the bending stress in specimen gears. A calibration gear is
made from a standard specimen with strain gages fit at key points in the root fillets. This calibration gear is
installed in the fixture and loaded to set loads periodically to ensure consistent loading. If specimens for a
specific test program differ from the standard design established for the fixture, one of these specimens should
also be fitted with strain gages, and calibrations should be conducted with both gears. Typical calibration
intervals are from every six to every thirty tests, or any time the fixture is cleaned and repaired.
Other set-up items that can affect test results are mounting of the fixture on the universal test stand, tuning of
the test-stand controller, and test frequency. If the SAE type fixture is used, it is important to ensure that the
fixture floats freely on an oil film before starting each test. Other fixture designs can be bolted to the machine
base, provided proper alignment between the load ram and loading point on the load arm is maintained. The
feedback control should be tuned to suit test fixture and specimen compliance. Some systems do this
automatically each time the machine is turned on; with others, this tuning may have to be done manually. At a
minimum, tuning should be verified as often as fixture calibration. Some systems provide a feature to
automatically adjust tuning as compliance changes. This feature should be turned off when running STF tests—
a significant change in compliance is proof of failure. The maximum frequency for STF testing is limited by the
capacity of the system to maintain a satisfactory load waveform. An inability to maintain peaks on the unload
side of the wave at the specified value is a sign of testing at too high a frequency. All of the tests for a given
project should be conducted at the same frequency, which is usually set at slightly less than the maximum for
the highest anticipated load.
The other procedural item that can affect test results is the method used to detect failure and stop the test (and
stop counting cycles). All systems can be set up to stop if the load goes out of the specified range. This
deviation will happen when compliance changes, usually as a result of a crack in the root fillet. Many systems
incorporate a linear variable differential transformer and can be set up to stop if the load ram moves beyond the
specified range (also an indication of tooth failure). A limit switch can be set to trip when the load ram moves
too far. Other failure detection devices, such as a crack wire bonded near the root fillet so that it will break
when the tooth cracks, or an ultrasonic system to detect cracking, can be used to stop the test. At least two of
these methods should be employed to ensure that the machine stops cycling load when the tooth breaks. If a
computer is used to control loading during tests, one of the failure detection systems should be connected
directly to the universal test-stand controller to guarantee that the machine stops if the computer crashes.
Specimen Results. Table 2 summarizes results from a typical set of STF tests. Testing was conducted in three
phases. Initial searching tests were conducted to establish loads that would result in failure in reasonable time.
A “modified staircase sequence” of tests was conducted to develop data at a series of loads representing zero to
100% failure. Further tests were conducted to fill in the stress cycles relationship. Searching tests are started at
a high load to ensure starting with a failure, then stepped down until the tooth survives the specified number of
cycles (here, 5 million cycles has been selected as a run-out limit). The modified staircase sequence is
conducted by testing three specimen gears in sequence. If the tested tooth breaks before the specified limit, the
next test is conducted one load step lower. If it does not break by the specified limit, the next test is conducted
one load step higher. After the modified staircase sequence is completed, additional tests are conducted to
ensure that all the specimen gears are tested at the lowest load. More tests are conducted to develop enough data
for Weibull analysis at two loads resulting in 100% failure.
Table 2 Results from a typical set of gear single-tooth fatigue tests showing overall testing sequence,
including modified staircase (“up and down”) tests
Legend: X, failure; O, runout. Specimen serial numbers 2, 4, and 6. Specimens cut from bar stock, hobbed
roots. R, loading; R = 0.1. Frequency, 25 Hz
Gear
/
tooth
Life,
cycle
× 10
6
2/1 0.
263
4/1 0.152 6/1 0.324 2/2
0.270
4/2
0.918
6/2 R
un out
Run
out
4/3
Run
out
6/3
0.521
2/4
0.461
4/4
Run
out
6/4
Ru
n
out
Run
out
0.55
7
6/5
0.299
2/6
Run
out
4/6
0.220
Load 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17
10,00
0 lb
9,500
lb
9,000
lb
X
8,500
lb
X X
8,000
lb
X X O X X
7,500
lb
X O X O O
7,000
lb
X O O
6,500
lb
O
6,000
lb
Load 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17
Searchi
ng
tests
Modified
staircase
test
sequence
Finite life
and
confirmatio
n tests
The load-cycles diagram shown in Fig. 10 was developed from the data in Table 2. Results at 9000 and 8500 lb
were analyzed via Weibull statistical analyses (similar to that shown in Fig. 7) to determine lives to 10, 50, and
90% failure. The failure rates at 5 million cycles for loads from 6500 to 8500 lb were analyzed using normal
probability concepts to determine 10, 50, and 90% failure loads. The curves labeled G10, G50, and G90 were
then fit visually using the results of these analyses as a guide. Results are reported in terms of load versus
cycles, and load can be converted to stress using the method discussed previously. Comparisons can be made
between groups of gears with the same geometry on a load-cycles basis or between gears with differing
geometry on a stress-cycles basis. When converting to stress for comparison with running gear data,
consideration must be given to the different stress ranges applied to STF gears and running gears. Also,
consideration must be given to the statistical difference between four, eight, or more data points from a single
STF specimen gear compared with one data point from a running gear specimen set.
Fig. 10 Load cycles diagram constructed from STF data. See Table 2 for load-cycles relationship for
data
Single-Tooth Single-Overload and Impact Testing
The single-tooth impact test is used to investigate impact strength of gear steels. Impact strength is an important
property for steels to be used in high-speed gear drives or transmissions for off-highway equipment, which can
be subjected to significant shock loading. It has been suggested that fatigue strength can be related to impact
strength; however, results of tests to support this suggestion have been mixed.
Single overload tests are used to investigate the ultimate strength of gear materials. The results are useful in
selecting loads for fatigue tests and in constructing allowable stress-range diagrams (e.g., for use in comparing
STF results with bending fatigue data developed from running gear tests).
Test Equipment. Figure 11 shows a closeup of the test area of a 4.5 m (15 ft) drop tower for single-tooth impact
testing. A single-tooth fatigue test fixture, without loading block, load arm, and so on, is placed on a load cell
and arranged so that the striking surface of the drop weight hits the load point on the test gear tooth. Stops are
provided to prevent the forces required to stop the drop weight after the test tooth fractures passing through the
load cell. A high-speed digital oscilloscope captures the signal from the load cell.
Fig. 11 Test area of an impact test tower
Single-tooth, single-overload tests are accomplished with the same equipment used in STF testing. The only
change is that a high-speed digital oscilloscope captures the signal from the single event.
Test Procedure. The single-tooth fatigue test fixture, without loading block, loading arm, and so on, is placed on
a load cell and installed under the drop weight. The striking surface on the drop weight is adjusted to the correct
angle to strike the test tooth at the load point. This point is verified by coating the tooth with a thin layer of
layout blue and allowing the drop weight assembly to contact the tooth statically. The digital oscilloscope is set
up to record a single event using a change in signal as a trigger. Usually three to six tests per variant are
conducted.
For single-overload tests, the STF fixture is installed in the universal test stand as for fatigue testing, and a
preload is applied. For the SAE fixture, 1800 kg (4000 lb) is used, and for other fixtures the load should be high
enough to take the slack out of the system. The function generator is set up to ramp up the load to break the
tooth in approximately 30 s for slow bend tests and in approximately 0.050 s for fast bend tests. One slow bend
and three fast bend tests usually are conducted per variant.
Specimen Results. A load deflection trace for a single-tooth impact test is shown in Fig. 12. Results from fast
and slow bend tests are similar. This trace shows load increasing linearly with deflection up to 5900 kg (13,000
lb), then increasing at a slower rate until tooth breakage at 9000 kg (20,000 lb). This result is typical for many
materials and is possibly related to the onset of plastic flow prior to fracture. Based on this, the stress
corresponding to the change in slope of the load deflection (or load time) trace corresponds to the ultimate
bending strength of the material at the critical point in the case. Maximum load, or energy required to break the
tooth, represents the strength of the core rather than the strength of the case.
Fig. 12 Load deflection trace from single-tooth impact test
Mechanical Testing of Gears
Douglas R. McPherson and Suren B. Rao, Applied Research Laboratory, The Pennsylvania State University
Gear Power-Circulating (PC), or Four-Square, Tests
A gear failure map is shown in Fig. 13. This map indicates that by varying load and speed, failure by any of
several different modes can be induced. Thus, PC gear tests can be used to evaluate bending fatigue strength,
surface durability with regard to pitting, or scoring resistance. A limiting factor is that tests targeted at one of
the failure modes may have to be terminated because of failure by another mode. For example, bending fatigue
tests conducted at a comparatively low load, targeting failure in several million cycles, may have to be
terminated due to pitting failure. Consequently, PC gear testing is more expensive than the tests simulating gear
action previously discussed. It is, however, less expensive than bench testing, and several standard specimen
designs are available to allow tests targeted at particular failure modes.
Fig. 13 Gear failure map
Test Equipment. A test and a torque-reversing gear set are mounted at opposite ends of the test bed. One shaft
connects the test and torque-reversion pinions, and another connects the torque-reversing and test gears. One
gearbox is loaded against the other by twisting the shafts to lock in torque. This rig is known as a power (re-)
circulating, or four-square, test rig and is schematically illustrated in Fig. 14. The locked-in torque, which is
fixed at various values to create the required tooth load, can be generated mechanically or hydraulically. The
entire loaded arrangement is driven by an electric motor at the required speed, and the motor need only supply
the friction losses. Significant transmitted power can be simulated in this system with comparatively little
power input. Data from these tests can be directly translated for design use.
Fig. 14 Schematic of a power (re-) circulating (PC) test rig
In a four-square test rig, the tooth accuracy of the torque-reversing gears, and their transmission error, has a
significant impact on the dynamic loads on the test-gear pair. These dynamic loads due to torque reversing gear
inaccuracy can be further amplified or attenuated by the longitudinal and torsional frequency response
characteristics of the four-square-test rig. This intensification is of particular significance in high-speed testing
where operating frequencies will be close to or at torsional and/or longitudinal natural frequencies of the four-
square system. However, high-accuracy torque-reversing gears are expensive. Consequently, the PC test rigs
can be classified into two categories. The first category of PC test rigs have low power, operate at low speeds,
and generally have AGMA quality class Q9 or Q10 gears in the torque-reversing gearbox that are quite
adequate for many industry segments. The second category of PC test rigs operate at high power, high speed,
and incorporate high-accuracy torque-reversing gears that are essential for gear testing in certain industry
segments, such as the aerospace industry. Testing costs associated with each of the two categories of test rigs
are significantly different.
The low-speed PC test rigs illustrated in Fig. 15 nominally operate at 900 rpm but can be adapted to operate at
1500 rpm. The standard center distance is 100 mm (4 in.), which can be modified if necessary, although there
are some costs associated with doing so. These test rigs can simulate the transmission of up to 100 hp when
driven with a 3 hp motor. Load is applied via a mechanical loading arm and locked in with a special coupling
that can be set at any angle. Thus, load cannot be varied as the rig is running. Depending on specimen design,
contact stresses of up to 450 ksi at the lowest point of single-tooth contact and bending stresses up to 160 ksi
can be generated. Splash lubrication is standard, and spray lubrication to either side of the mesh can be
provided. These rigs can be adapted to conduct scoring tests.
Fig. 15 Low-speed (4 in. center distance) PC test rig
Figure 16 shows a PC test rig with a 155 mm (6 in.) center distance that can operate up to 8000 rpm and
simulate the transmission of up to 1400 hp. This test rig has two test gearboxes so that two pairs of gears can be
tested simultaneously. In programs to evaluate materials for aerospace gearing, runout can be set as high as 400
million cycles for surface durability tests, making the project a lengthy exercise. In this case, obtaining two data
points in one run can be a significant benefit. Figure 17 shows another PC test rig with a 90 mm (3.5 in.) center
distance, capable of operating at 10,000 rpm and simulating transmission of up to 700 hp. Torque-reversing
gears in these high-power rigs are in AGMA quality class Q13 and Q14. Load is applied via a servocontrolled
hydraulic system and can be varied as required during tests. Torque is monitored continuously by a noncontact
torque cell. This monitoring permits interpretation of test results in light of the actual load signature. Based on
input lubricating oil temperature and load, surface durability (pitting), bending, and scoring tests can be
conducted on these PC test rigs. Spray lubrication, to either side of the mesh, is standard; oil-mist lubrication
can be provided.
Fig. 16 High-speed (6 in. center distance) PC test rig