R. KASUBA
Professor,
Dept. of Mechanicaal Engineering
Fenn College o f Engineering,
Cleveland State University,
Cleveland, Ohio
M e m . ASME
E. I. RADZIFVIOVSKY
A Multi-Purpose Planetary Gear Testing
Machine for Studies of Gear Drive Dynamics,
Efficiency, and Lubrication
Professor,
Department o f Mechanical Engineering,
University o f Illinois at U r b a n a - C h a m p a i n ,
U r b a n a , 111.
Mem. ASME
Feasibility of a multi-purpose testing machine for research studies in gearing has been
demonstrated with construction of a unique gear testing machine with a differential
planetary gear drive. This machine was used in such interdependent studies as determination of instantaneous gear tooth engagement loads, minimum film thicknesses, and
gear efficiencies.
With minimal structural and mechanical modifications, this gear
research machine can be used for studies of surface durability, thermal distribution in
gear meshing zones, and effects of variable torques and torsional oscillations on performance of gearing.
Most of these studies could be conducted simultaneously.
Upon
selection of appropriate gear ratios, this machine was operated either with one or two
stationary gears. Presence of stationary gears simplified greatly the measurement techniques and increased the reliability of tests. This machine can accommodate spur,
helical or any special type of gearing.
Design and operational characteristics of this
machine, as well as a short summary of research projects performed on this machine, are
presented in this paper.
introduction
four-square or open ended transmission types [3, 4, 9, 10, 20, 2 3 ] . '
In some gear lubrication studies, simulated disk type machines
with or without slipping characteristics were used [6, 12, 21].
However, there are some situations where the results of combined
as well as individual parameters could be of practical importance
on overall gear performance. The reliability of such investigations would be increased if a single test rig could be used for
interdependent studies. Consequently, a unique multi-purpose
gear testing machine with a compound planetary drive has been
designed, constructed and used in the Mechanical Engineering
Department of the University of Illinois, Urbana, Illinois, for
INDICATIONS are that the presently used testing machines in the field of gear capacities, gear drive dynamics, lubrication (film thickness) and gear efficiency studies were designed primarily for a single designated task. The commonly used gear
testing machines for individual effects are usually of the closed
Contributed by the Design Engineering Division and presented at
the Mechanisms Conference and International Symposium on Gearing and Transmissions, San Francisco, Calif., October 8-12, 1972, of
T H E AMEBICAN SOCIETY or MECHANICAL ENGINEERS.
received at ASME
72-PTG-33.
Manuscript
Headquarters July 21, 1972. Paper
No.
1
Numbers in brackets designate References at end of paper.
-NomenclatureA, B, J, K =
D, H =
G =
DF =
E =
L = TH/^W'K
/ =
=
m =
gears in the drive
shafts in the drive
planetary arm
dynamic gear tooth loading factor
efficiency of planetary
gear train
gear tooth face width, in.
load parameter
speed ratio; ( + ) , (—) or
Pi
Pa
PL
JR
RF
input power, lb-in./sec
output power, lb-in./sec
power loss, lb-in./sec
pitch radius, in.
effective mesh natural
frequency/gear meshing frequency, ratio
TD = torque on input shaft in
planetary drive, Ib-in.
TH = torque on output shaft in
planetary drive, lb-in.
Vv == llinear
i n e a r vvelocity
e i o c i u y oofi ggear
ear
CO
N = number
i m u e i of
o i teeth
leei/ii
Primed superscripts reifer t o e q u i v a l e n t conventional g e a r train.
—
=
—
=
=
engagement, fpm
W = average transmitted normal force, lb/in.
M = absolute viscosity, lbsec/in. 2 (Reyns)
efficiency
of individual
V
gear pairs
V = combined mechanical efficiency of equivalent
conventional gear train
8 = normal pressure angle
angular
cu — a
n g u l a r >velocity, rad/sec
Subscripts, A , B, D, G, H, J, K, refer t o specific g e a r t r a i n elements.
Journal of Engineering for Industry
NOVEMBER
1973/
1123
Copyright © 1973 by ASME
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Fig. 1
Testing machine
studies in the areas of gear drive dynamics, efficiency of planetary
gear systems and gear lubrication. For certain speed and power
ranges, all these three studies could be conducted simultaneously.
The additional advantages of this gear testing machine over
conventional machines were the simultaneous and individual
controls of key parameters in these studies and simplicity of
measurement systems.
In the planetary drives the velocity of engagement is not equal
to the pitch line velocity and the equivalent power developed
within the system may appreciably differ from those being transmitted through the system. This machine can be operated
either as a speed reducer or increaser. With selection of proper
gear ratios it is possible to develop high transmitted gear forces
and, consequently, the high internally circulating power levels
with a relatively low magnitude of the input power. These
peculiarities were used advantageously in the design of this test
machine [1,2,7,16].
The main element in this machine is a two-stage differential
planetary gear drive which, upon selection of proper gear ratios,
can have one or two stationary gears. The fact that at least
one of the gears in the drive is fixed offers a number of advantages
over the commonly used testing machines. One of them is the
favorable and controllable condition of lubrication, since there
are no centrifugal forces in the test gear meshes whih tend to
remove liquid lubricants. In this machine the lubrication in the
gear meshes can be controlled to provide the operational situations between the fully flooded to the nearly dry conditions.
Most importantly, the fixed gears in this machine permit to use
direct, simple, and reliable systems for measuring the operational
minimum lubricating film thickness and instantaneous gear tooth
loads. These measurement systems could be easily extended
for investigating the stress and temperature distributions in gear
teeth. This machine can be used with spur, helical or any special
type of gearing [15, 18, 24] in single or both stages of the drive.
So far it has been used with spur and helical gearing. Design
and operational characteristics of this machine as well as a
short summary of test results are discussed in this presentation.
Description of Machine
This machine was designed in order to determine experimentally the interdependence between the controllable inputs (loads,
speeds and lubrication conditions) and the measurable outputs
such as instantaneous gear tooth loads, minimum lubricating
film thickness, and power losses. To meet the above situations
the multi-purpose machine with a two-stage differential planetary
gear train was designed. The basic design and other characteristics of this machine are shown in Figs. 1, 2, 3, 4, 5 and 6. The
testing machine consists of foul' principal units:
1 Input power and dynamometer unit (input platform)
2 Brake and output dynamometer unit (output platform)
3 Two-stage differential planetary gear train
4 Lubrication System. The controlled parameters were the
amount of lubricant supplied into the test mesh and temperature
of the lubricant.
Fig. 2
1124 /
Schematic representation of the testing machine
NOV EM B ER 1973
For the anticipated studies in gearing with this machine, the
main mechanical specifications were:
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Fig. 3
Planetary gear train
Fig.5
ment
~+--+- +-l-E:=l1l=1II1-
Fig. 4
Cross-sectional drawing of planetary gear train
(a) The input and output shafts must be axially aligned. For
the length of this machine it WB..') a difficult task.
(b) Planetary shaft must be parallel to the axis of rotation of
the input and output shafts
(c) Good dynamic balancing of assembled planetary carrier.
Gear counter balancing masses can be seen in Figs. 3 and 4
(d) Rigidity of machine frame
(e) Rigidity of shafts
(f) Electrical isolation of a fixed test gear from the rest of the
machine
(g) Low power losses in the bearings.
Loading device at the output shaft for inflnite spoed ratio arrange-
On the output side there is !~ similar brake-platform-dynamometer arrangement. The brake cylinder of a mechanicn.l, non
self-energizing brake was attached to the output; shaf(;. The
output platform was free to rotate whcn the output, shaft Wall
loaded. The resulting angular movements of the output platform loaded a dynamometer, which was calibrated to indicatc
the magnitudes of the outpllt torque. In the infinite I'Iltio
arrangement, the brake assembly was removed wit,houl afTect.ing
the performance of the machinll sincc the ext.ernal torque could
be applied directly to the output shaft as shown in Fig. 5.
The input and output dynamometers consisted of links aud
load rings with the strain gage,~ cementcd onto the rings. Flal,
cantilever springs were also IIsed successfully us torque dynamometers. Viscous dampers were ultaehctl to the input and
output platforms to minimize extraneous vibrutions which may
be transmitted to the strain rings. For measlII'emellbl of variable and steady torque measurements, strip recorders and strain
gage meters were used, respectively.
The heart of this machine is the differential planctaTy gear
train shown in Fig. 3. In this photograph the drivc is shown liS
it was used in some studies involving the instantaneous gllaT
tooth load and minimum film thickness Illllllsuremcnls. The
spray ring in the vicinity of the fixed gear conkols the alllount of
lubricant supplied to the instrumented area. Tn this SIlt-liP, t.he
test gears were the narrow spur gears. The ot.her gear pail'
was made up of wide face helieal gears in order to minimi7.c
extraneous excitations in the te~t geur pail'. The hasie mechanical design characteristics of the drive are shown in Fig. 1. The
length of the planetary arm is .'i.000 in. thus limit.ing t.he Slllll of
pitch diameters for any meshinl!; eombination to 10.000 in.
The input shaft D drives the planet carrier G with two planetary gears J and B. The planetary gear B is in mesh with a fixed
sun gear A. The other planetary gear meshes with the rotating
(or not!) output gear K. The velocity ratio of this system is
(1)
Items a and b were accomplished during assembly process by
using specially developed alignment cylinders. There is no limit
for desirable rigidity of shafts; however, it is believed that the
shaft deflections were within practical limits.
The input power unit was a 3/4 H.P., motor-transmission set
producing any output speed up to 1865 rpm. The motor-transmission unit was mounted on the input platform which was 'free to
rotate in the bearings around the common axis of the machine.
When the input unit supplied a certain torque, an equal and
opposite reaction acted on the platform which, in turn, loaded the
input dynamometer.
Journal of Engineering for Industry
All four gears in the train are replaceable permitting a few sets
of gears to provide a large number of positive and negative speed
ratios. If the ratio of teeth on the gears is such that (NANJ/
N BNK) = 1, the speed ratio becomes infinity, and the output
shaft will have zero angular velocity. Now this gear train will
have two stationary gears A and Ie Thus, by seleeting the
appropriate gears, this machine can be operated in two bask
types of arrangements:
Arrangement 1. Finite Positive or Negative Speed Ratio
m = (+)orm = (-)
NOV EM B E R 1973 /
1125
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Arrangement 2. Infinite Speed Ratio m = »
Both arrangements were used in a number of investigations.
In Arrangement 2, the planetary gear train becomes self-looking,
and the input power is then equal to losses in the train.
Some of t h e power, dynamics and efficiency characteristics of
this drive will be explained b y applying the concept of equivalent
gear trains, which was developed b y one of t h e co-authors for the
analyses of the planetary gear train efficiencies and dynamics
[1,2,16].
The schematic representation of the test planetary gear drive
used in this machine and the corresponding equivalent conventional gear train are shown in Pigs. 6(a) and 6(b), respectively.
Equivalent gear train is obtained b y "stopping" the planetary
carrier in the actual machine b y adding to all elements (— « D )
where an is the angular velocity of the carrier. I n the equivalent
train all axes of rotation are fixed and the relative motions of the
elements are exactly the same as in the actual machine. The
input and output torques in the planetary train are t h e same as
the torques acting on the corresponding members in its equivalent
conventional gear train. Since the equivalent train is a conventional (nonplanetary train) the conventional analyses of
forces, velocities of engagement, power transmitted by gears,
and power losses may be applied. However, in some cases the
driven elements in an actual planetary gear train m a y become
the drivers in an equivalent train. For example, referring to
Fig. 6(a), gear K, which is designated as gear K' in the equivalent
gear train becomes the driving gear in the arrangement with
positive speed ratio m = ( + ), while for m — ( —), gear K' will
remain the driven gear. Using this method the following relationships for the angular velocities of engagement can be obtained:
cox' = [COK + ( — COB)]
= OID/ITI — COB = coc(l — 1/m)
f o r m = ( + ) (2)
COK'
= [ —COK -I- ( — COB)]
COx
= —coz)(l — 1/m)
= — (OB
form = ( - )
(3)
for m = oo
(4)
where M i ' is the angular speed of engagement of gear K in both
the actual planetary and equivalent trains. I n the infinite
speed ratio arrangement, the absolute value of the angular
velocity of engagement of the stationary planetary gear K will
be equal to the absolute angular velocity of the input shaft as
shown by equation (4).
For the negative speed ratio value of uK' will be larger than
COB and in this case the planetary gear train for dynamical purposes must be treated as a speed increaser. In the limiting
case with small speed ratios, the velocity of engagement cox'
will approach a value of 2coz>.
I n this drive the maximum developed internal gear mesh
power levels are:
Pe = TBUK'/V
Pe = THOIK'
form =
(-)
for m =
<*> and m =
OUTPUT, H—7
w
a-Hs.M.1
/
f\r /
^
l (lb/in)
form = ( - )
(7)
and
WA.B
=
TH
If
Rj-qt
1
(lb/in)
for m =
(8)
RBRRCOB6_\
m = (+)
Following the same approach the average transmitted forces
can be derived for mesh J-K.
T h e first version of this machine has been designed, built and
operated a t the University of Illinois. In this version the machine has been operated in some tests with the pitch line velocities
of engagement reaching 3000 fpm. The applied average transmitted force levels characterized by equations (7) and (8) were
limited to a maximum of 1500 lb/in.
A new version of this machine is presently in the final stages of
design a t T h e Cleveland State University, This testing machine will have the nominal speed and load capacities ranging to
10,000 fpm and 3000 lb/in., respectively, with all options mentioned in this paper.
Short Summary of Research Investigations
Performed on the Gear Machine
Individual Gear Pair and Planetary Gear Train Efficiency. Following
the concept of equivalent train the theoretical efficiency E of t h e
entire planetary gear train of the type used in this test machine
with positive speed ratios can be given [1, 2, 16] as
E = Po/Pi = Po/(Po + PJ.) =
1/(1 + (m ~ 1)(1 - ii,)) for m = ( + ) (9)
with
P i = P 0 (m - 1)U - Vi)
(10)
The expressions for efficiency and power loss for this drive with
negative speed ratios are of the form
a'
i
u>a'0
0
INPUT, D—-7
:
K
l j r[
\j \J V - )
P».w„XTMH
Fig. 6(a)
\TE —
WA„
9
J'
1—
1
(+)
(5)
, .
where rj( is the mechanical efficiency of the equivalent train and
TH is t h e torque on the output shaft in the planetary gear drive.
For the cases with the finite speed ratios the output torque was
applied by the brake. In the infinite speed ratio arrangement,
torque TH was applied externally and directly to the output shaft.
The loading device for producing a constant or variable torque on
the output shaft, as used with the test machine in the infinite
speed arrangement, is shown in Fig. 5. The device consists of a
lightweight loading arm, adjustable spring, extensometer and
pneumatic vibrator. With this device, shaft torques ranging to
1000 + 350 sin cot, lb-in. with frequencies up to 25,000 cpm, were
developed and used during some tests.
The transmitted normal forces W in the gear meshes of this
test drive can be easily derived b y applying conventional analyses.
For example, the average transmitted normal force in
mesh A-B can be given as
J
Pi " T„ X W 0
Actual differential planetary gear train
1126 / NOVEMBER 1973
\JTH- TH
PH'-^HV+I
Fig. 6(b) Equivalent gear train
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E = 1]1/(1]1
+ (1
- 1]1)(1 -
m»
(11)
(- )
for m
PLANETARY
GEAR TRAIN
with
J
PL
= Po(l -
(12)
'Y/')/'Y/'
m)(l -
In the infinite ratio arrangement the planetary gem' t.rain be-
H
comes self-locking and the input power is equal t.o lm;ses in the
train. According to the cquivl1lellt, tmin con~ept, the meehllnieal losses in the planetary gear are identienl with those in the
equivalent train, therefore
= wn'I'll(I
wn'1'n
for
- 7],)
In
=
=
'Y)A.B
X
t-"'~B
A
K
D
o
(la)
00
The total mcchanielll efficienllY 7]1 aH used in equations (5)
through (13) repreHentH the combined efficiencies of the system,
which depends UpOll the losses in gearing as well us in the bearings.
In this machine the power losses in t.he gear meshes I1nd ]oHses
in the shaft supporting ball bearings eannot he separated. However, caleulat.ions and Home experimentation have indicated that
the power losses in the bearings were of secondary importance
compared to the measured power losses. Consequently, within
the load and speed ranges of this machine, we will make the approximation that
'Y)t
TRIGGERING
DEVICE
OSCIllOSCOPE
II II
BA TTERY
Fig. 9(a)
Electrical circuit for measuring minimum oil film thickness
Fig. 9(&)
Oscilloscope trace of signal at the beginning of discharge
(14)
'Y)J.rc
where 'Y)A,B and 'Y)J,rc are the effieiencies of individual pairs of
gears. In the infinite speed ratio arrangement both pairs of gears
must be identical and, thus, 'Y) = 'Y)A,B = 'Y)J,rc. By employing
equation (13) and above approximations the lower value for
efficiency of an individual gear pail' can be given as
lID
8
~
ei
IE
~
!l2
'"
III
g
IJj
~
~
l!5
. ••
!li
•
••
•
)J. - 5,~ x ro.£
•
• )J.-37.3xro.£
• J' - 51.5 x ro.£
•
A
(I'i'.!ls)
(I'i'.!ls)
(~lS)
l:l
~
III
;.
10
12
14
lfi
18
20
lOA U CHARAe TE R1ST I C. l x I a -4
Fig. 7
Experimental values of individual gear pair efficiency
100
/\
90
V
80
70
t
~
60
lIJ
.,;
50
(,) 40 ~
I\..
./
~
~
"-
V
l:i
~
!'-... k
~
ffi
...§
"
-llIDUll'JJ..UlM:
o TEST VAllIS
30
........
-
20
10
o
-80
-60
Fig. 8
-40
-20
0
20
VELOCITY RATIO, III
40
Efficiency of differential planetary drive
Journal 01 Engineering for Industry
60
80
(15)
In the accompanying tests the required torques were easily
determined. '1'H was the external torque applied directly to the
output shaft as illustrated in Fig. 5, while the required input
torque Tn was routinely indicated for various test conditions
by the input dynamometer. Fig. 7 illustrates the determined
gear pair efficiency for a typical spur gear with the testing machine in the infinite speed ratio arrangement. The represented
test spur gears had the following specifications:
Diametral pitch 12-1 in.; pitch dill, 5 in. ; pressure angle
20 deg; face width 0.375 in.; backlash 0.006 in. ; combined geometric error in mesh did not exceed 10- 4 in.; surface roughness
20-40 microin.; gear material-carbon steel, 300 BRN. Tests
were performed with three different oils supplied at 100 deg F inlet
temperature. The applied constant torque TH was varied from
25 to 200 in-lb. at 1000 rpm., which induced normal gear tooth
loads of about 27 to 215 lb/in. The experimentally determined
gear pair efficiencies for various load and speed conditions are
represented in terms of a load characteristic L where L = T / J1.Wrc'.
Efficiency 'Y) fot· considered conditions was in the range from about
90 to 99 percent [17].
For finite speed ratio arrangements the individual pail' mesh
and planetary efficiencies can be obtained from equationl' (9)
through (12). The power levels required for solution of equations
NOV EM B E R 1973 /
1127
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1
2
1
o
3
'
~:
4"
5
6
n:
Fig.l0(a)
STRAIN GAGES
Al'PLiFIER-BRIOOE LNIT
asc IlLOSCOPE
POSITIONING AND TRIGGERING CIRCUIT
0 ISPLACEM:NT STR IP
FIXED GEAR
PlANETARY DRIVE INPUT SHAFT
Electric circuit for determining instantaneous gear tooth loads
in this section were easily obtained by measuring the input and
output torques and respective speeds. No other instrumentation
was required in the efficiency test programs. The obtained single
pair mesh efficiencies as functions of speed ratios were in similar
range as shown in Fig. 7.
Typical results of the study of the efficiency of the. entire
differential planetary gear train are shown in Fig. 7. The test
results are given for the test drive operating at a constant 600
lb-in. output torque with the speed of the input shaft of 800 rpm.
The test gears had similar mechanical specifications as the previously described gear sets. The lubricating oil was SAE 50
with the inlet temperature of 80 deg F. The average single mesh
efficiency was determined to be about 98.5 percent, which was
then used for developing the theoretical curve based on equations
(9) and (11). TIlls study indicated that the planetary train
efficiencies by the equivalent train method are in good agreement
with the experimental data.
Recently this machine in the infinite speed ratio anangement
had been used to investigate the effects of cyclic torques and
torsional oscillations on the mesh and planetary train efficiencies
[25].
Fig. 10(1))
until the applied voltage produced an electrical breakdown in thc
film causing an electrical discharge. The signal from the oseilloscope at the beginning of discharge is shown in Fig. 9(1J).
The minimum film thickness for the given operational condition
was then determined from the calibration curve. The oscilloscope was triggered when gear B was entering the fully floodcd
test mesh. The time of each sweep of the oscilloscope equalled
the time of engagement of two pairs of gear teeth.
Representative data on minimum film thickness are given below
in Table 1 for a gear pair which wa.s described in detail in the
previous section. The test gears A and B were lubricated with
SAE 50 oil with the inlet temperature at 89 deg F. The data
are tabulated for the velocity of engagement of 1300 fpm.
Film Thickness Measurement
If two metallic surfaces are separated. by a thick oil film, this
film acts as an insulator. If these surfaces with the oil film be-
tween them are included now in an electrical circuit, and if the
voltage drop across the film reaches a sufficiently high value, the
applied voltage will produce an electrical breakdown in the oil
film causing an electrical discharge. This critical voltage V,.
depends upon the thickness of the oil film separating two metallic
surfaces.
This phenomenon was used for measuring the minimum oil
film thickness between the meshing gear teeth surfaces [13].
Gears A and B of the planetary drive were used as a part of the
electrical circuit shown in Fig. 9(a). The fact that one of the
test gears is fixed made the electrical isolation of this gear from
the rest of the machine simple. Both on-site and off-site calibrations were made to establish the relationship between the
minimum oil film thickness and conesponding voltage causing
the electrical breakdown in the oil film, so that the minimum film
thickness could be determined while the gears were in operation.
Before the testing machine was turned on, the mating teeth of
the test gears A and B were in contact and the electrical circuit
was grounded. Mter the motor was started, the desirable torque
was applied to the output shaft and the speed of rotation became
sufficiently high to build up the hydrodynamic pressure and to
form a film completely separating teeth surfaces so that no current
was flowing across the lubricating film. As the load at the given
speed increased, the film thickness between the teeth surfaces
of gears A and B decreased. The load was increased gradually
1128 /
NOV EM B E R
1973
Oscilloscope trace of gear tooth loading cycle
Table 1
Load capacity of the oil film
Normal
Torque on the transmitted
Voltage drop output shaft, load on gear,
across resistor
Tn lb-in.
WA.Blb/in.
0.025
0.050
0.080
0.120
0.250
166
104
74.5
49
27
Minimum film
thickness, in.
178.0
112.0
80.0
52.5
29.0
0.000012
0.000025
0.000040
0.000060
0.000110
The advantage of controlled lubrication in this type of tcst
machine was already mentioned. With oil directed from the
spray tube onto the fixed test gear mesh lubrication in the mCHh
can be varied from fully flooded to splash and dry situationH.
With the above described film thickness measurement technique
and accurate controls of lubrication and transmitted forces aB
found in this machine simultaneous studies tying in the applied
load, oil film thickness and surface fatigue durability can be
conducted. Introducing the electronic metal-to-metal contact
counting and averaging devices meaningful scoring criteria
could be developed for several types of gears and parameterH.
This approach will be attempted with the new version of this
machine presently under development.
Instantaneous Gear Tooth Load Determination
The instantaneous gear tooth loads were determined from thc
measured fixed gear tooth deflections on stresses. Specially
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1.6
ffl Y**
„ „BP
"«,
^"
OCTICW. FCSILTS
^
'
_.JL-
?2
I.I
m
PA.
33Si
I^rf
T.
wmJLmmm
SO
1.0
Fig. 11
9»
40
75D
J3
Km
2.5
1250
2
ISO
1.67
1750
Experimental and theoretical dynamic load factors
The illustrated case represents a gear pair with an error in
engagement of .0005 in., operating under a moderately heavy
load WA.B = 1200 lb/in. and below the first natural frequency of
the system which includes t h e effects of variable elasticity of
meshing gear teeth.
After having established t h e mechanical capabilities of this
machine, additional test studies are planned in which the effects
of oil damping on influence of dynamic load factors will be investigated in the vicinity of theoretically predicted resonant and
instability speed ranges.
2DO0
1.25
Summary
Feasibility of a multi-purpose testing machine for research
studies has been demonstrated with construction ,of a unique
gear testing machine with a differential planetary gear drive.
The fact t h a t at least one of the gears in the test drive is always
designed deflection strips consisting of preloaded thin brass strips
fixed offers a number of advantages over t h e commonly used
with strain gages, or the strain gages located in the gear tooth
testing machines. T h e advantages are in t h e simplicity of
roots have been used in these test studied. With a t least one of
dynamic measurement systems and controls of key parameters.
the test gears fixed, the connections to external instruments do
This testing machine was used in such interdependent studies as
not require any slip ring arrangements. The basic signal measuring system is shown in Fig. 10(a). Positioning and triggering determination of instantaneous gear tooth loads, minimum oil
devices indicated the signal for any gear mesh position for t h e film thicknesses, and gears, and gear systems efficiencies. I t is
believed t h a t with simplicity of instrumentation and control
entire length of p a t h of contact. Calibrations of signals indicatsystems as used in this machine, the reliability of tests was coning either deflections of stresses were most conveniently obtained
siderably increased. Further, the reliability of the tests can be
by applying the brake or external torque on t h e output shaft
depending on the operational arrangement and rotating t h e further increased if t h e machine will provide as it does in this
case the possibility of conducting a multitude of test programs
planetary drive a t low speeds no exceeding 150 rpm. This type
of calibration did offer some advantages over purely static cali- without removing or changing test setups. With minimal
structural and mechanical modifications, this gear research
brations since the hydrodynamic lubrication in the gear meshes
machine can be used for studies of surface durability, thermal
was improved and the frictional effects due to stickslip process
distribution in gear meshing zones, and effects of variable torques
were minimized. I n addition, this method of calibration proand torsional oscillations on performance of gearing. Most of
vided an easy and instantaneous calibration for each test run.
these studies could be conducted simultaneously.
The dynamic load factor DF for any particular point along the
At this time it can be concluded that the performance, relip a t h of contact was determined by comparing the obtained oscilability, and capabilities of this gear research machine and mealoscope traces at various speed and load levels with t h e corsurement systems have been established and found satisfactory
responding load calibration traces for the same contact point.
during various test programs.
The variables which affect the instantaneous loads, such as speed,
mass effects, average transmitted load, cyclic loads, type of lubrication, etc. were easily accommodated by this machine. Changes
in mass effects were affected by replacing individual elements or
Acknowledgment
attaching additional masses as shown in Fig. 4.
The authors wish to express their appreciation to the M e This gear testing machine was simulated for theoretical studies
chanical Engineering Department at the University of Illinois for
of transmitted forces b y means of analog and digital computers
sponsoring the construction of this machine and all test programs.
[7, 22] with accompanying test programs for establishing t h e
The authors are also indebted to M r . B . W. Kelley from t h e
accuracy of modeling techniques.
Caterpillar Tractor Company for his friendly suggestions and
One test program for determining t h e dynamic load factors help in some segments of test programs.
was conducted by using gear tooth deflection measurements with
the testing machine in the finite speed ratio arrangement [7, 8].
A typical trace of instantaneous deflection of a gear tooth for one References
cycle of engagement is shown in Fig. 10(6). This trace was used
1 Radzimovsky, E. I., "A Simplified Approach for Determining
in construction of the experimental portion of Fig. 11. Another
Power Losses and Efficiency of Planetary Gear Drives," Machine
test program for determining the dynamic load factors was based
Design, February 9, 1956, pp. 101-110.
2 Radzimovsky, E. I., "How to Find Efficiency Speed, and Power
on gear tooth bending stress measurements [22]. I n this parin Planetary Gear Drives," Machine Design, June 11, 1959, pp. 144ticular test program the gear train was in the infinite speed ratio
arrangement and was subjected to both variable and constant 153.
3 Richardson, H. H., "Static and Dynamic Load, Stress and Detorques.
flection Cycles in Spur Gearing," ScD thesis, Department of Mechanical Engineering, M.I.T., Cambridge, Mass., 1958.
The spur gear pairs which were used in the above test programs
4 Attia, A. Y., "Dynamic Loading of Spur Gear Teeth," JOURhad various geometric and manufacturing error specifications.
NAL OF ENGINEERING FOR INDUSTRY, TRANS. ASME, Series B, Vol.
With the contact ratio being one of the influential parameters on
81, No. 1, 1959, pp. 1-9.
dynamic load factors [7, 8, 9, 22], the selected gearing had the
5 Kasuba, R., "Design of a Planetary Gear Drive Testing Machine," (unpublished report), Mechanical Engineering Department,
theoretical non-loaded contact ratios in the range from 1.12 to
University of Illinois, Urbana, 111., 1959.
1.71.
6 Benedict, G. H., and Kelly, B. H., "Instantaneous Coefficient
The basic scope of these test programs is illustrated in Fig. 11 of Gear Tooth Friction," TRANS. ASME, ASLE Lubrication Conf.,
where the determined theoretical and experimental dynamic
Oct. 1960, pp. 57-70.
7 Kasuba, R., "An Analytical and Experimental Study of Dyload factors represented by
namic Loads on Spur Gear Teeth," PhD thesis, Mechanical Engineering Department, University of Illinois, Urbana, 111., 1962.
Line 1 DF = 1 (constant)
8 Brittain, T. M., "Dynamic Load Characteristics of Pairs of
1
1
Line 2 DF = l / [ 7 8 / ( 7 8 + (V) /*)] /*
Meshing Gears," (Unpublished Report), Mechanical Engineering
1 7
Line 3 DF = 1/(50/(50 + (V) - ')]
Department, University of Illinois, Urbana, 111., 1962.
Journal oi Engineering for Industry
NOVEMBER
1 9 7 3 / 1129
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9 Cloutier, L. J., "Dynamic Loads on Precision Spur Gear Teeth
According to the Theory of Variable Elasticity," Laval University,
Laboratoire d'Elements des Machines, Rapport No. EM-3, June
1962.
10 Utagawa, M., and Harada, T., "Dynamic Loads on Spur Gear
Teeth Having Pitch Errors at High Speeds," Bulletin of JSME, Vol.
5, No. 18, 1962, pp. 375-381.
11 El-Sisi, S. I., and Shawki, G. S. A., "Measurement of Oil-Film
Thickness Between Disks by Electrical Conductivity," Journal of
Basic Engineering, TRANS. ASME, Series D, Vol. 82, 1960, pp. 12-16.
12 MacConochie, I., and Cameron, A., "Measurement of OilFilm Thickness on Gear Teeth," Journal of Basic Engineering,
TRANS. ASME, Series D, Vol. 82, 1960, pp. 29-34.
13 Dareing, D. W., and Radzimovsky, E. I., "Experimental Investigation of Minimum Oil-Film Thickness in Spur Gears," Journal
of Basic Engineering, THANS. ASME, Series D, Vol. 85, 1963, p. 451.
14 Radzimovsky, E. I., Offner, D. H., and Kasuba, R., "How to
Find Efficiency of Planetary Gear Drives," Power Transmission
Design, Vol. 5, No. 11, Nov. 1963, pp. 40-44.
15 Brittain, T. M., "Involute and Non-Involute Conjugate Spur
Gears: Their Load Capacities Based on Maximum Surface Pressure, Sliding Velocity, and Condition of Lubrication," PhD thesis,
Mechanical Engineering Department, University of Illinois, Urbana,
111., 1965.
16 Radzimovsky, E. I., "Efficiency of Planetary Gear Systems,"
Mitteil. Ukrain. Techn. Wirtschaft. Inst. VIII (XI), Munich, 1965,
pp. 21-39.
17 Adkins, R. W. and Radzimovsky, E. I.,. "Lubrication Phenomena in Spur Gears: Capacity, Film Thickness Variation, and
Efficiency," Journal of Basic Engineering, TEANS. ASME, Series D,
Vol. 87, No. 3, Sept. 1965, pp. 655-665.
1130 / NOVEMBER
1973
18 Brittain, T. M. and Radzimovsky, E. I., "Load Capacity of
Involute and Non-Involute Conjugate Spur Gears," Mitteil. Ukrain.
Techn. Wirtschaft. Inst, X (XIII), Munich, 1966, pp. 11-41.
19 Cameron, R. and Gregory, R. W., "Measurement of Oil-Film
Thickness Between Rolling Disks Using a Variable Reluctance Technique," Institution of Mechanical Engineers, Tribology Convention,
1968, Proceedings 1967-68, Vol. 182, Part 3N, pp. 24-32.
20 Radzimovsky, E. I., and Mamoun, M., "Efficiency of Gear
Transmissions Subjected to Axial Vibrations," Mitteil. Ukrain.
Techn. Wirtschaft. Inst. XVI(XIX), Munich, 1968, pp. 31-54.
21 Benedict, G. H., "Correlation of Disk Machines and Gear
Tests," Lubrication Engineering, Vol. 24, No. 12, Dec. 1968, pp.
591-596.
22 Hahn, F. W., "Study of Instantaneous Load to Which Gear
Teeth Are Subjected," PhD Thesis, Mechanical Engineering Department, University of Illinois, Urbana, 111., 1969.
23 Houser, D. R., and Seireg, A., "Experimental Investigation of
Dynamic Factors for Spur and Helical Gears," Journal of Engineering
for Industry, TRANS. ASME, Vol. 92, Series B, No. 2, May 1970, pp.
495-503.
24 Lebeck, A. O., and Radzimovsky, E. I., "The Synthesis of
Tooth Profile Shapes and Spur Gears of High Load Capacity,"
Journal of Engineering for Industry, TRANS. ASME, Aug. 1970, pp.
543-553.
25 Pease, B. T. and Randolph, D. C , "Effects of Torsional Vibration in Efficiency in Planetary Gear Trains," (unpublished progress report) Mechanical Engineering Department, University of
Illinois, Urbana, 111., 1970.
26 Kasuba, R., "Dynamic Loads on Spur Gear Teeth by Analog
Computation," ASME Paper No. 71-DE-26, presented at Design
Engineering Conference, New York, New York, January 5, 1971.
Transactions of the ASME
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