Download 1. Objectives of the measurement

Measurement report on
Force and torque sensors
For the subject of sensors and transducers
Supervisor: ing. Antonín Platil
Yann KOWALCZUK
October 19th, 2006, 1800-1930
Measurement Laboratory 61
Faculty of Electrical Engineering
Czech Technical University in Prague
1. Objectives of the measurement
Learn the physical principles and function of the following position sensors:
1) Inductive transformation sensor (inductosyn) with optical incremental sensor
2) Linear variable differential transformer (LVDT)
3) Ultrasonic sensor
2. Measurement task
1) Measure the characteristic of the inductosyn sensor, i.e. the dependence of the
voltage across the coils on the moving part (“slider“) on the position, in the range of one
mechanical period of the “ruler” (approx. 2 mm).
2) Learn the principle of the LVDT. Measure its characteristic (transfer function);
estimate the resolution of the measurement. Measure the characteristic around zero
position in detail; focus also on the both end-positions of the sensor.
3) Connect the digital oscilloscope to the outputs of the sensor device and observe the
waveforms of the transmitted and received pulse. Measure the time delay between
these events, and from the known value of the sound speed in the air calculate the
respective distance. Compare the computed value to the reading displayed on the
device.
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3. Schematic diagram

Inductosyn sensor
Figure 1 - Inductosyn sensor

Linear Variable Differential Transformer (LVDT)
Figure 2 - LVDT sensor
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
Ultrasonic sensor
Figure 3 - Ultrasonic sensor
4. Theory

Inductosyn sensor: this device is set up with planar coils on a fixed part, called
ruler, while two planar coils are moving on a part called slider. It uses inductive
principles with voltage reference, which principles are well known of every student
(electronmagnetic theory). The reference value of the position is sensed by an
optical incremental sensor MS 30, connected to an intelligent indicator Modig
221. The indicator sensitivity is 1 μm / digit.

LVDT sensor: it uses electromagnetic induction principle. A magnetic flux
coupling between two coils may be altered by the movement of an object and
subsequently converted into voltage. The LVDT is basically a transformer, of
which the primary coil is driven by a sine wave with fixed amplitude. An AC signal
is induced in the secondary coils. A core made of a ferromagnetic material is
inserted coaxially into the cylindrical opening without physically touching the coils.
The two secondaries are connected in the opposed phase. When the core is
positioned in the magnetic centre of the transformer, the secondary output signals
cancels and there is no output voltage. Moving the core away from the central
position unbalances the induced magnetic flux ratio between the secondaries,
developing an output. The amplitude of the induced voltage is proportional, in the
linear operating region, to the core displacement. Consequently, voltage may be
used as a measure of a displacement. The LVDT provides the direction sensing
as well as magnitude of the displacement. The direction is determined by the
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phase angle between the primary (reference) voltage and the secondary voltage
(output). The output voltage represents how far the core is from the centre and on
which side.

Ultrasonic sensor: this sensor employs the sonar-principle, i.e. it measures the
round-trip time interval between the emitted ultrasonic pulse and received
reflected “echo”. For creating and receiving the ultrasonic pulse, only one
ultrasound transducer is used (piezoelectric device).
5. Procedure
1.) The inductosyn sensor was used to complete 30 measurements of position,
using an incremental optical sensor as a reference. Voltages of both secondary
coils were estimated with multimetres, while output signals were observed
through a digital 4 way oscilloscope. As multimetres couldn’t display the sign of
the AC waveform, a reference point was taken on the oscilloscope to determine
the sign of the voltage measured. The frequency was set at 100 kHz.
2.) The LVDT sensor was connected to a digital multimetre, while a precision
graduated rubber was used for position measurement. Position for zero voltage
was measured, and 5 measures for both sides of this region were made, using
10mm steps each time.
3.) The ultrasonic sensor was used to determine the height of the ceiling in the
lab. Then, analysis of the waveform of this sensor was performed on the digital
oscilloscope. Time between two pulses was estimated by this way, thus providing
another estimation of the ceiling of the room. Reference height was determined
by measurement with a graduated rubber.
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6. Measurement
1). Inductosyn
A zero position was first determinated with the oscilloscope: primary voltage was 0,
while secondary voltage was maximum. Then 30 measurements were made, using 10
µm position steps. The voltage value for each position is recorded in the following table:
Position x (µm)
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
U1(x) (mV)
U2(x) (mV) ArcTan(U2(x)/U1(x)) U1²(x)+U2²(x)
0,01
4,61
1,568627133
-1,37
4,37
-1,266999644
-2,52
3,74
-0,977873714
-3,45
2,89
-0,697298726
-4,27
1,41
-0,318937622
-4,49
0,01
-0,002227168
-4,32
-1,14
0,258007242
-3,56
-2,7
0,648872588
-2,66
-3,6
0,934444337
-1,15
-4,37
1,313472612
0,04
-4,49
-1,561887876
1,22
-4,29
-1,293728574
2,41
-3,71
-0,994705386
3,44
-2,77
-0,677923393
4,11
-1,54
-0,358504004
4,37
0,01
0,002288326
4,25
1,02
0,235544981
3,69
2,34
0,56514944
2,76
3,39
0,887481104
1,61
4,06
1,193266131
0,06
4,37
1,557067212
-0,99
4,22
-1,340366161
-2,28
3,68
-1,016114719
-3,52
2,86
-0,682316555
-3,95
1,73
-0,412808795
-4,34
0,02
-0,004608262
-3,91
-1,81
0,433542481
-3,32
-2,76
0,693552037
-2,65
-3,38
0,905873251
Table 1 - Inductosyn measurements
21,2522
20,9738
20,338
20,2546
20,221
20,1602
19,962
19,9636
20,0356
20,4194
20,1617
19,8925
19,5722
19,5065
19,2637
19,097
19,1029
19,0917
19,1097
19,0757
19,1005
18,7885
18,7408
20,57
18,5954
18,836
18,5642
18,64
18,4469
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The following characteristic was determined according to these values:
Output Voltage VS Position
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Voltage (mV)
2
0
0
50
100
150
200
250
300
U1(x)
U2(x)
-2
-4
-6
Position (µm)
Figure 4 - Characteristic of Output Voltage VS Position
The function ArcTan (U2/U1) was also calculated in the above table:, in order to
determine the dependence of this function with the position of the slider. This can be
seen on the following graph:
ArcTan(U2/U1) VS Position
2
1,5
1
ArcTan(U2/U1)
0,5
0
0
50
100
150
200
250
300
-0,5
-1
-1,5
-2
Position (µm)
Figure 5 - ArcTan(U2/U1) relation to position of slider
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As we can see with these two graphs, U1 and U2 are shifted by a ¼ of a mechanical
period. Furthermore, the sum U1²(x)+U2²(x) was calculated in the above table to show
that it only slightly depends on the position of the slider.
2) LVDT
The LVDT setup was used to perform several measurement, in order to obtain its
characteristic, and especially around the 0V area. The 0 value was thus a starting point,
giving the relative position associated with this value. Then, 5 measures in each
direction from this point were performed, to obtain the characteristic of this system.
The results are given in the next table:
Position
(mm)
U(x) (V)
95
1,028
96
0,82
97
0,615
98
0,402
99
0,193
100
0
101
-0,22
102
-0,419
103
-0,626
104
-0,843
105
-1,046
Table 2 - LVDT measurements
These measurements were compiled to obtain the following graph, representing the
characteristic of the LVDT. We can notice that the voltage VS position curve of the LVDT
is linear, associated with the linear scale of the precision rubber.
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Voltage VS Position
1,5
1
Voltage (V)
0,5
0
94
96
98
100
102
104
106
-0,5
-1
-1,5
Position (mm)
Figure 6 - LVDT Voltage VS Position characteristic
The resolution of the LVDT depends on the stages of the sensor processing; but as far
as we could see, this one has an infinite resolution, the minimum scaled change being
too little to be noticed.
3) Ultrasonic
The ultrasonic sensor was positioned vertically on the table, in order to measure the
height of the ceiling in the lab. It must be reminded that the wave emitter is 12 cm upper
than the base plate of the sensor. The digital oscilloscope was plugged on the output of
the device to watch the waveform of the signal. We could hear small bips when the
result was ready and displayed on the device, and some low frequency sound, when the
impulses were generated. 3 different kinds of measure were performed:

The value given by the apparatus was 8,1 feet=2,47m.

A reference measure was performed using a graduated rubber, giving a height of
2,33 m.
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
The waveform displayed was a train of impulses (outgoing and back signals), and
the result response was displayed as a big impulse on the scope. The time
measured between 2 impulses was 13,68 ms (for going and back of the signal).
Thus, with the given speed of the sound formula v(t)=331,8+0,6T, T being the
temperature of the room (measured with a scaled thermometer, T=22°C), the
result was a height of 2,36 m with this method.
The error factor to be taken in account is the unequal repartition of the temperature in
the room. Indeed, as hotter air is going in up while colder air is staying near the ground,
a gradient of temperature exists, and has actually some impact on the velocity of the
sound in air.
7. Results and conclusion
1) The inductosyn sensor was the device that took most of the time during the
measurement. We could see that a complete step was proceeded when both waveforms
completed total phase shift (i.e. 360°), for about a 2mm distance measured. The signals
from the two secondary’s coils had a ¼ phase shift. Thus, the different output voltage of
both coils can be interpreted as a position change, the distance between the units being
known. Of course, interpretation of this measure is better made after processing of the
signal output, as a direct position value for common sensing and applications. Some
electronic kits and circuitry are available to proceed such signal processing. This
requires some additional development of the device to make it practically usable in
common applications. Moreover, the system involves some mechanical parts which can
be sometimes loose or inaccurate, making it more suitable for small position changes.
As a result, the inductosyn is not a widely used sensor nowadays, usually replaced by
more common systems, but it remains an interesting contact less measurement device.
2) After looking at its principle, the LVDT sensor was used to perform several
measurements on precise position steps. We could notice that the output voltage was
really sensitive and fastly following the positions change. Around its 0 position, the
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sensor has a linear comportment, making it really suitable and easily usable for
measurement tasks. Furthermore, it was established that its resolution is virtually infinite
(of course depending of course of the signal processing of the results), the smallest
scaled change of step being unnoticeable during the lab. Specific circuitry also exists for
this device, giving extended signal processing of the measurement for applications. For
these reasons, the LVDT is a very useful device for precise position changes, even with
fast moving systems, and with outstanding results for low position changes.
3) The ultrasonic sensor gave fast and easily usable results, by indicating the distance
from the device to the obstacle. Then this position measurement could be compared to
the two others ways of measurement: the time between outgoing and incoming pulses,
and the reference rubber measurement. These two last have quite close results, giving a
good idea of the error margin of the apparatus. As an average value, the ultrasonic
sensor has about 5% margin of error. Such an error can be explained by the fact that the
display on the device has only one decimal range precision, with a US foot unit reading
(conversion in metric system introducing furthermore errors); thus, the precision of the
measurement suffers from these factors. Anyway, such an error factor is still acceptable
for most applications, making it a useful device for long range and higher positions
measurements.
Finally, we can notice along this lab that the most useful devices for position
measurements are the LVDT and the ultrasonic sensors. The first is mostly usable for
really precise measurement on small position changes, the second one giving a good
approximation of higher distances measurements. On another hand, for contact less
measurement, the inductosyn sensor should be preferred, to perform some small
position changes estimation.
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