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Closed loop test stand for gearboxes
Lukáš Kazda1, Gabriela Achtenová1
1 CTU in Prague, Faculty of Mechanical Engineering, Department of Automotive, Combustion Engine and Railway Engi-neering, Technická 4, 166 07 Praha 6, Česká republika
Abstract
This work introduces a closed loop test stand for gearbox testing. It was realized within a project „High-speed and lightweight reducer
of Electric Vehicle using composite materials“. The purpose of this stand is to measure noise, vibration transmission error, efficiency
of gearboxes and fatigue life of gears. The test stand is so-called closed loop test stand. It‘s using a principle of circulating power in
closed loop which allows to use less energy consuming and less complicated electronic devices because the electric motor only covers
losses.
Keywords: gearbox, test stand, measurement, data acquisition
1. Introduction
Despite advanced simulation methods it’s still necessary
to carry out gearbox tests and experiments to obtain im-
portant parameters and predict gearbox behavior. These
parameters include for example efficiency (or loss coeffi-
cient). Usual value of loss coefficient varies from 0,005 to
0,025, but precise value can be only obtained from exper-
iments. Another parameter is transmission error which
can be a significant source of noise. Tests can also deter-
mine fatigue life of gears. For satisfactory results of pa-
rameters mentioned above it’s necessary to design the ex-
periment as much alike the real operation as possible. It
requires especially proper spectra of torque and speed
ranges. [1]
Test stands can be divided in two groups according to
their construction. First one is an open-loop test stand. It
consists of electric motor, tested gearbox and dynamome-
ter. Its principle is simple. Electric motor spins the tested
gearbox and the dynamometer makes a load. Dynamome-
ters nowadays usually generate electrical power and re-
turn it back to electrical grid. The advantage of this con-
cept is that it can be easily operated, torque and speed can
be easily variated and only one gearbox is needed to per-
form a test. The main disadvantage is that such a concept
requires expensive investments in motor, dynamometer
and electronics related to it as transmitted power can reach
tens or even hundreds of kilowatts. Another disadvantage
is that space required for this test stand can be much big-
ger that an alternative one.
Second construction concept is called closed-loop test
stand. It consists of two identical gearboxes (or gearboxes
with the same gear ratio) and their inputs and outputs are
connected into closed loop (see Fig. 1). This concept uses
only one electric motor and no dynamometer. The princi-
ple is that a load (torque) can be created by relative twist-
ing of one shaft to another. When motor spins the gear-
boxes, a power circulates in the closed loop. Power of the
motor is used only to cover losses of the gearboxes. The
fact that motor with only little power relative to open-loop
one can be used is one of the main advantages of this con-
cept. Also, not needing to use dynamometer is convenient.
Both of these advantages make this concept cheaper and
less space demanding than the open-loop concept. There
are also significant disadvantages. One of them is need for
manufacturing two gearboxes. Two gearboxes also mean
more mechanical parts in tested loop that can affect a
measurement. While there is only one gearbox in open-
loop concept, there’s another one in closed-loop concept
with at least two additional couplings. In the first case,
determining losses is straightforward as it’s generally a
subtraction of motor and dynamometer power, losses of
closed-loop stand are sum of both gearboxes’ losses. Also
determining noise and vibration of tested gearbox can be
easier when there’s only one gearbox in compare to sys-
tem of couplings and gearboxes. Another disadvantage is
that if it’s required to change torque continuously, closed-
loop concept requires more complicated design, usually
using a combination of planetary and worm gearboxes.
Constant torque option doesn’t require that complicated
design, but testing has to be stopped when a change of
torque needs to be done. [2] [3]
In conclusion, closed-loop test stand is cheaper and less
energy and space demanding than open-loop. On the other
hand, it’s less flexible and more mechanically complex.
It’s recommended to use it for testing of components of
one gearbox repeatedly. For instance, comparative testing
of different gears, shafts etc.
Fig. 1: Scheme of closed-loop test stand
Studentská tvůrčí činnost 2020 | České vysoké učení technické v Praze | Fakulta strojní
2. Design of the test stand
The test stand described in this article has been built in
CTU laboratories in VTP Roztoky based on similar test
stand used for planetary gearboxes. The design is shown
in Fig. 2. It consists of two gearboxes, tested (position 1)
and input (position 2) with one gear pair. The Gear pair is
3rd gear from conventional automotive gearbox MQ200
used by Škoda Auto. Furthermore, the test stand consists
of electric motor (position 3), couplings and sensors. Spe-
cifically, encoders (position 6), torque sensor (position 7),
accelerometers and thermometers.
Fig. 2: Design of closed-loop test stand [2]
An important part in Fig. 2 is pressure coupling (position
4) that allows to disconnect the shaft (position 5) from
gearbox shaft and twist them against each other using
grooving on the shaft (5) while gearbox is braked. After
twisting the shafts, the coupling allows to connect them
again. The value of torque is controlled by the torque sen-
sor.
Fig. 3: Loading by lever
In Fig. 3 it can be seen how the gearboxes are loaded
(note: motor is hidden). A 1,019 m long lever is used.
When lever of this length is used, then each added kilo-
gram increases torque by 10 Nm. Torque value is calcu-
lated by
𝑇 = 𝑇𝐿 +𝑚𝑔𝐿 (1)
Where TL is torque generated by mass of the lever itself,
m is weight, g gravitational acceleration and L length of
the lever. When L is 1,019 m which equals to 10/g meters,
the resultant formula is
𝑇 = 𝑇𝐿 + 10𝑚 (2)
Fig. 4: Closed-loop test stand in CTU laboratory
The electric motor has maximal speed of 6000 rpm and
maximal power of 18 kW. The test stand and its critical
parts were designed for maximal load of 200 Nm. There
is also an option to connect the gearboxes to oil cool-
ing/heating circuit in case of high performance and over-
heating or in case of regulating the temperature on desired
value. Another option to reduce the temperature is to use
a fan. Self-heating of the gearboxes is described in one of
the following chapters.
Studentská tvůrčí činnost 2020 | České vysoké učení technické v Praze | Fakulta strojní
3. Measured values and used sensors
The test stand is equipped with several sensors measuring
vibrations, temperature, torque and transmission error.
These values are measured continuously during testing.
The sensors are connected to CompactDAQ 9179 device
made by National Instruments. This device is designed to
acquire analog signal from sensors, convert it to digital
format and send it to PC where the data are further pro-
cessed. On top of it, it provides precise timing and syn-
chronizing with internal timebase up to 80 MHz . For fur-
ther processing and control LabVIEW software is used.
The program for data acquisition is described in one of the
following chapters. [4]
3.1. Vibrations
Each gearbox is equipped with 2 piezoelectric uniaxial ac-
celerometers (one at each shaft). Type of accelerometer is
KS77C.10. The accelerometers are mounted by M5
screw. They are able to measure vibration up to 600 g and
their resonance frequency is 50 kHz. There’s also one ad-
ditional uniaxial accelerometer that is mounted by bond-
ing and can be placed at any place on test stand when
needed. A module that is used for acquiring and pro-
cessing signal is NI 9234. It has 4 channels and it’s able
to acquire signal with frequency of 52 100 samples per
second per channel. [5]
3.2. Temperature
Temperature is measured by platinum resistance ther-
mometers PT100. Two of them are type Jumo 902040/10
with screw, mounted on casings of the gearboxes. This
type of sensor is robust, but it takes longer to detect tem-
perature changes as there’s a lot of mass to heat up or cool
down in the sensor. On the other hand, there are two other
PT100 sensors with dimensions 1.7 x 2.4 x 1 mm and
weight of just 0.3 g that detect changes fast and can be
placed at any spot needed at the test stand. There’s again
NI module used for acquiring and processing the signal.
The type of the module is NI-9217. It has 4 channels and
can acquire 400 samples per second. There are 4 wires
needed to connect each sensor because the module has a
bridge circuit inside to compensate resistance of the wires
themselves. [6]
3.3. Torque
Torque sensor is an integral part of the closed loop which
can be seen in Fig. 2, 3 and 4. Therefore, it has to be noted
that the sensor itself can influence the measurement. The
type of the sensor is Kistler 4503A. It has voltage output
(0-10 V) and can measure torque up to 1000 Nm. There’s
also an option to measure speed but it’s not used at the
moment, as there are only 60 pulses per revolution and
speed is also read from encoders and a converter that con-
trols electric motor. The NI module used for acquiring and
processing the signal is NI 9201 with screw terminals. It’s
voltage input module with range -10 V to +10 V. It has 8
channels with sampling rate of 500 000 samples per sec-
ond. [7]
3.4. Transmission error
First it needs to be explained what transmission error is.
It’s a difference between ideal kinematic rotation of gears
and real rotation. It is influenced by stiffness of parts such
as teeth, shaft, bearings etc. Another significant factor
causing transmission error can be imperfections during
manufacturing and assembling, for example misalign-
ments and runouts. Unit of transmission error (TE) is usu-
ally µm because it’s a difference between lengths of arcs
at operating pitch diameters of each gear (dw1, dw2). TE
can be static or dynamic. Static TE is measured at very
low speed and only deformation influence the result,
whereas dynamic TE is measured at higher speed and an
influence of oscillations is added to static TE. An example
of static and dynamic TE is in Fig. 5. [8]
Fig. 5: An example of static and dynamic TE [8]
The sensors used to measure TE are rotational encoders
DFS60B-S1PL10000. There’s a pair of them attached to
both shafts of tested gearbox. The sensors have 10 000
samples per revolution and can measure at speed up to
5000 rpm (see Fig. 6). [9]
Fig. 6: Limit for speed of used encoder [9]
The signal from encoders has TTL standard. There are
four outputs from the sensor (see Fig. 7). Signal A (also
known as cos+) is the main signal used for this particular
purpose. Signal B (also known as sin+) is shifted to signal
A by 90° degrees of electrical pulse. It’s generally used
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for detection of change of direction of rotation (signal A
or B comes twice while the other one 0 times). The rota-
tion doesn’t change direction, so the signal B is used only
to check if the sensor works properly. Signal Z is trigger.
All 3 signals have their negative counterparts -A, -B and
-Z that can be used to compensate noise, but they are not
used because NI hardware doesn’t support it.
Fig. 7: Encoder signals [9]
NI module used for acquiring and processing the signal
from encoders is NI 9401. This module processes digital
data and can also operate as a counter that measures time
between two rising/falling edges with resolution of 100ns
(used in this case). If we consider maximal speed 5000
rpm and 10 000 samples per revolution, it makes minimal
period of 1 200 ns between two rising/falling edges. [10]
4. Program for data acquisition
Previous chapters described hardware that is being used
for measurement. This chapter describes a software and
code for controlling the measurement. The software used
for this purpose is LabVIEW by National Instruments. It’s
graphical programing software that works on principle of
dataflow programming. The environment has two parts, a
front panel that is used as a user interface to control meas-
urement and block diagram where the code is built. The
program itself has following features:
• Control of the electric motor
• Acquiring data from the electric motor (rpm,
torque, power etc.)
• Acquiring data from the sensors
• Saving averaged data every 1 second
• Safety features (detection of high temperature or
sudden vibration increase)
• Keeping raw data from accelerometers and
torque sensor in memory for 5 seconds
• Saving raw data after set period, on demand, dur-
ing error or safety issue
• Loading data from encoders for set time (default:
1 s) repeatedly
• Saving data from encoders after set period, on
demand, during error or safety issue
This program was conceived as a state machine and can
run independently for long time period as there is auto-
matic data acquisition and saving or safety features. It can
be also remotely controlled by another PC or smartphone
with use of graphical desktop-sharing software.
5. First test
There was a first test carried out on the test stand. The
purpose of this test was to observe a behavior of the stand,
check function of the sensors and find out if the gearboxes
need additional cooling. Constant load applied on input
shaft was 120 Nm. The sequence that was run during the
test is shown in Fig. 8. There’s speed and power of elec-
tric motor (loss power of gearboxes) shown in the figure.
Fig. 8: Sequence of the first test
After short warm-up run, the speed was gradually in-
creased from 0 rpm to 5500 rpm with increment of 250
rpm. Then the speed was decreased on level of 2500 rpm
and kept there for the rest of the test. Total time of the test
was 79 minutes. Average power of electric motor at 2500
rpm was 1700 W. Circulating power in the gearboxes was
31400 W (2500 rpm, 120 Nm). Which means that effi-
ciency of the test stand is 5,4 %.
A detail of the part of the testing sequence when the speed
was increased is shown in Fig. 9. There are vibrations
(RMS) from two accelerometers on the tested gearbox.
Studentská tvůrčí činnost 2020 | České vysoké učení technické v Praze | Fakulta strojní
Fig. 9: Vibrations
There can be seen that critical speed of the gearbox is
4000 rpm with acceleration peak of 35 g.
There was also frequency spectrum calculated at each
speed level and waterfall contour plot was made (see Fig.
10).
Fig. 10: Complete waterfall contour plot
There are two expected frequencies that proportionally
change with change in speed and can be seen in Fig. 10.
They are related to number of teeth of gears. It’s called
gear mesh frequency (GMF). There is 1st GMF (funda-
mental) 2nd GMF (2x 1st order GMF) which has lower am-
plitude in the graph. But there’s one more frequency that
is unexpected and isn’t directly related to GMF of fre-
quency of rotation of any shaft. It’s 145th multiple of 1st
order of output shaft frequency (113th multiple of input
shaft frequency). Detail of Fig. 10 focused on 1st orders
(frequencies equal to revolutions of shafts) with range of
frequencies from 0 to 100 Hz is shown in Fig. 11. There
are two 1st order frequencies in the graph as there are two
shafts with different rpm which is an expected result.
Fig. 11: 1st order frequencies
Another focus was on heat generation of gearboxes. The
question was, how fast the temperature increases and what
level it reaches. Fig. 12 shows temperature increase at
speed level of 2500 rpm and torque level of 120 Nm. Time
axis is offset to point where test sequence with constant
speed starts (650 s). The test was relatively short in order
not to damage the gears as they will be tested for fatigue
in experiments to come. The temperature curves were ex-
trapolated by eq. (3).
𝜃(𝑡) = 𝜃0 + (𝜃𝑒𝑞 − 𝜃0) (1 − 𝑒−
𝑡𝜏) (3)
Where θ is current temperature, θ0 is initial temperature,
θeq is equilibrium temperature, τ is time constant and t is
time.
Fig. 12: Self-heating of gearboxes
Resultant coefficients for both gearboxes are shown in
Tab. 1
Tab. 1: Extrapolation coefficients.
Gearbox θ0 [°C] θeq [°C] τ [s]
tested 38.6 79.7 1977
input 35.9 72.6 1669
The data show that the gearboxes aren’t overheating, and
equilibrium temperatures are in range from 70°C to 80°C.
Studentská tvůrčí činnost 2020 | České vysoké učení technické v Praze | Fakulta strojní
However, the extrapolation of the data is just approximate
and real equilibrium can be higher. Especially the temper-
ature of the tested gearbox increases more than the extrap-
olation curve at the end of the measurement. We can con-
clude that some tests can be performed without a cooling
circuit but for lower and more common temperatures (e.g.
50°C) it’s essential to use a cooling circuit or at least a
fan.
The last goal of the first test was to measure transmission
error. TE was measured at speeds of 60, 2000, 2500 and
4000 rpm. In Fig. 13 there are results of unfiltered TE.
They show big oscillations that are caused by runout of
the shafts. The argument for this is that the frequency of
the oscillations is 1 revolution. Runout causes changes in
dw, thus changes of angular velocity.
Fig. 13: Unfiltered TE
For obtaining results that neglect runout, it’s necessary to
filter the data. The results after filtration are shown in Fig.
14. The data from Fig. 13 were filtered by IIR-Bessel high
pass filter. Instead of timebase, x axis from Fig. 13 (revo-
lution of input shaft) was used. The cut-off frequency was
set at 10 Hz as it’s safely above 1 Hz (1 revolution) and
below 32 Hz (GMF – 32 teeth input gear). The amplitude
after filtration decreases to approximately 0.005 mm.
Fig. 14: Filtered TE
The graph in Fig. 15 shows frequency spectra of TE. The
Peaks of amplitudes match to GMF. (2000 rpm – 1067
Hz, 2500 rpm – 1333 Hz, 4000 rpm – 2133 Hz)
Fig. 15: Frequency spectra of TE
6. Conclusion
A closed-loop test stand for gearboxes was successfully
built in CTU laboratories. It can test gearboxes with one
pair of gears with constant torque and variable speed.
There are sensors that can measure vibrations, tempera-
ture, torque and transmission error. There was also a pro-
gram for automatic data acquisition, processing and sav-
ing and for test control made in LabVIEW environment.
A first test was carried out to observe a behavior of the
stand, check function of sensors and find out if the gear-
boxes need an additional cooling. The test shown that the
gearboxes have average efficiency of 5,4% and critical
speed of 4000 rpm. It can be furthermore found that the
gearboxes need an additional cooling if the tests are de-
signed for higher speed or higher temperature as the the-
oretical equilibrium temperature for torque of 120 Nm and
speed of 2500 rpm is 79.7°C and 74.6°C. The sensors and
data acquisition work without problems, as all the ex-
pected frequencies of vibration and transmission error
could be measured. Amplitude of unfiltered TE was ap-
prox. 0.1mm and amplitude of filtered TE (neglected
runout) was approx. 0.005 mm. Further tests will be fo-
cused on fatigue of the gears.
List of symbols
g gravitational acceleration (m/s2)
L length (m)
m mass (kg)
t time (s)
T torque (Nm)
TL torque of lever (Nm)
τ time constant (s)
θ temperature (°C)
θ0 initial temperature (°C)
θeq equilibrium temperature (°C)
Studentská tvůrčí činnost 2020 | České vysoké učení technické v Praze | Fakulta strojní
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