* Contact: lukas.kazda@fs.cvut.cz

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

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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.

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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.

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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.

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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)

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