Lab 7 Transducers

8/10/2019 Lab 7 Transducers

1/14

Transducer sensitivity and linearity

Introduction

In this experiment, we will use three types of transducers: photonic, inductive proximity, and capacitive

proximity. These transducers function to measure small linear displacements. Each type is explainedbelow.

Photonic transducer:

This transducer emits a steady light source through optical fibers, which will hit the object. This light

will reflect off the object and come back to be received by a photocell detector. The longer it takes for

light to bounce back off the object, the larger the linear displacement between the object and the

transducer. The graph below shows the voltage output as a function of displacement. At very close

distances, the receiving fibres can capture most of the reflected light, and therefore the sensitivity is

highest (the slope of the graph is largest). This linearity only lasts for a certain range; after a certain

displacement, the voltage output decreases dramatically due to the inverse square law. Reflected light

intensity also depends on the surface material of the object.

Inductive proximity sensor:

An important property of this device relies on the reluctance Rm of a magnetic circuit. This reluctance

determines how much flux is produced for a given current in a coil. Therefore, this transducer uses an E-

shaped piece with a coil wrapped around, as seen in the following diagram. With an AC source, the coil

produces an alternating magnetic flux, which permeates through the air gap and the plate which is to be

moved. When this plate does move, the magnetic flux will change and therefore the current will change

(since the reluctance remains constant). The change in current is outputted as a voltage by a control box.


2/14

Given the following formula:

=

I(t) = L Imax cos ( t) and =2

N= number of turns of wire

Capacitive proximity sensor:

The capacitance of a capacitor depends on d, the separation of the plates; A the overlapping area; and

the dielectric constant Ke . To measure small linear displacements between the plates, A and K are kept

constant.

As the capacitance changes with displacement, a simple circuit can be set up to output voltages that

depend on C.

Objectives:

In the first part, we will calibrate the voltage outputs simultaneously for each transducer for many small

displacements. Once our data is recorded, we will graph our results and analyze the response curves.From these graphs we can identify the three transducers respective linear ranges, their corresponding

linearity, and the sensitivity which they produce. We will then compare these values for each transducer

to determine which is most suitable for a particular measurement range. Knowing this is essential for

any future experiments requiring the most accurate measurements for small linear displacements.


3/14

Equipment and procedure

- One X-Y sliding table equipped with micrometers. A flatplateis mountedon it.

- One capacitive displacement transducerBC10-G30-Y0X

- One inductivedisplacementtransducerBI10-G30-Y1- One Photonicsystem. Please be aware the fiber opticmustnot be bent.

- All transducersare mountedon a fixed support.

- Power supply.

- One DVM

- Three signal conditioners (Photonic: 3B11-01, Capacitive: 3B31-03, Inductive: 3B41-03).

- LabVIEW virtual digital voltmeters.

Procedure

1. First check the lab setup. Make sure that the transducers are properly connected to their

respectivecontrolboxes and power supplies. Record the model and gain of each signal

conditionerused to amplify the signal of each transducer.

2. Use LabVIEW to record the measurements. The program has already been created for you

and is available on WebCT. Copy the file Lab7.vi to your desktop. Also download the excel file

named Lab7.xls. This excel file containsthe tableyou will use to record the data.

3. Turn on thepower supply and thephotoniccontroller(the switch is on the back of thebox).

Use the digital voltmeter to measure and record the supply voltage. You will need this value to

calculatethe static sensitivity of the Inductive and Capacitive transducers.

4. The LabVIEW program allows you to record three voltage signals simultaneously. Specify

the minimum and maximum limits as -1 and +10 respectively, and the channel numbers

corresponding to the connections of your transducers (drop the arrow, click Browse, press the

CTRL key and click on the 3 channels in the following order: 10,12,14). After this, you should

see in the Physical channels box display DEV1/ai10, DEV1/ai12, DEV1/ai14. If you dont

see that repeattheprevious step.

5. Using the X-axis micrometer, adjust the flatplate position until the micrometer reads zero.

This plate position should be close to, but not touching,the transducers.

6. Move away from theplatein incrementscorresponding to the values given in the Lab 7 spread-sheet. The resolution of the micrometer is 0.01 mm. At each displacement, run the LabVIEW

program once and record the voltage readings in your table. You will take approximately 70

readings. The number of readings is the minimum needed to fully resolve the response curves of

each transducer.

7. When you finish collecting the data turn off the power supply, the photoniccontroller and the

backplane.


4/14

Results and Discussion:

Inductive: 3B41-03 Photonic: 3B11-01 Capacitive: 3B31-03 Gain=1.0 for all three transducers, supply voltage = 5.0446 V

Figure 1. Response curve of three transducers; photonic, capacitive, and inductive sensor

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 2.0 4.0 6.0 8.0 10.0

output(volts)

displacement (mm)

Response Curve of Three Transducers

Photonic

Capacitive

Inductive


5/14

1) Photonic Sensor

Table 1. Range of readings with high sensitivity and an approximate linear response

Figure 2. Calibration plot for photonic readings with linear best fit line (Sensitivity = 9.947)

Displacement

(mm)

Photonic reading

(volts)0.2 0.942383

0.225 1.235352

0.25 1.28418

0.275 1.713867

0.3 1.972656

0.325 2.006836

0.35 2.485352

0.375 2.807617

0.4 2.856445

0.475 3.520508

0.55 4.560547

0.625 5.253906

0.7 5.776367

V = 9.947*d - 1.0628

R = 0.9949

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Output(volts)

Displacement (mm)

Calibration Plot for Photonic Reading


6/14

Displacement(mm)

Points on the lineof best fit (volts)

Residual(volts)

0.2 0.9266 0.015783

0.225 1.175275 0.060077

0.25 1.42395 -0.13977

0.275 1.672625 0.041242

0.3 1.9213 0.051356

0.325 2.169975 -0.163139

0.35 2.41865 0.066702

0.375 2.667325 0.140292

0.4 2.916 -0.059555

0.475 3.662025 -0.141517

0.55 4.40805 0.152497

0.625 5.154075 0.099831

0.7 5.9001 -0.123733

Table 2. Points on the line of best fit and residual values of photonic readings

Residual values for corresponding displacements can be identified through two ways. 1) By

subtracting points on the line of best fit from photonic reading 2) Using data analysis on excel

Figure 3. Residual data for photonic readings with straight line connecting terminal points

Displacement(mm)

Residual(volts)

0.2 0.015783

0.225 0.060077

0.25 -0.13977

0.275 0.041242

0.3 0.051356

0.325 -0.163139

0.35 0.066702

0.375 0.140292

0.4 -0.059555

0.475 -0.141517

0.55 0.152497

0.625 0.099831

0.7 -0.123733

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.2 0.3 0.4 0.5 0.6 0.7

Deviation(volts)

Displacement (mm)

Residual Data for Photonic Reading


7/14

The lower and upper accuracy limits of the response curve are -0.163139 volts and 0.152497

volts, respectively, or -2.82% and 2.64% full scale. The full scale value of the response curve is

taken at 0.7mm, therefore full scale value is 5.776367 volts.

Equation of the line is V= -0.279032*d +0.0715894 (linear line of residual plot)

Displacement (mm)Point on the line

(volts)Residual

(volts) q

0.2 0.015783 0.015783 1.11022E-16

0.225 0.0088072 0.060077 0.0512698

0.25 0.0018314 -0.13977 0.1416014

0.275 -0.0051444 0.041242 0.0463864

0.3 -0.0121202 0.051356 0.0634762

0.325 -0.019096 -0.16314 0.144043

0.35 -0.0260718 0.066702 0.0927738

0.375 -0.0330476 0.140292 0.17333960.4 -0.0400234 -0.05955 0.0195316

0.475 -0.0609508 -0.14152 0.0805662

0.55 -0.0818782 0.152497 0.2343752

0.625 -0.1028056 0.099831 0.2026366

0.7 -0.123733 -0.12373 3.33067E-16

Table 3. Points on the line of residual plot, residual and q values

|

|

= 0.2343752

=1 || 100% =10.2343752

5.776367100% = 95.94%


8/14

2) Capacitive Sensor

Table 4. Range of capacitive readings with high sensitivity and an approximate linear response

Figure 4. Calibration plot for capacitive readings with linear best fit line (Sensitivity = -0.3332)

Displacement(mm)

Capacitivereading (vol ts)

2.90 0.86426

3.05 0.82520

3.20 0.78125

3.35 0.75195

3.50 0.67871

3.65 0.59082

3.80 0.54688

3.95 0.54199

4.10 0.47852

4.25 0.41016

4.40 0.35645

4.55 0.31250

4.70 0.27344

4.85 0.24902

V = -0.3332*d+ 1.8383R = 0.9924

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2.5 3.0 3.5 4.0 4.5 5.0

Output(volts)

Displacement (mm)

Calibration Plot for Capacitive Reading


9/14

Displacement(mm)

Point on the line ofbest fit (volts)

Residual(volts)

2.90 0.87202 -0.00776

3.05 0.82204 0.00315

3.20 0.77206 0.00919

3.35 0.72208 0.02987

3.50 0.6721 0.00661

3.65 0.62212 -0.03130

3.80 0.57214 -0.02527

3.95 0.52216 0.01983

4.10 0.47218 0.00634

4.25 0.4222 -0.01204

4.40 0.37222 -0.01578

4.55 0.32224 -0.00974

4.70 0.27226 0.00118

4.85 0.22228 0.02674

Table 5. Points on the line of best fit and residual values of capacitive readings

Figure 5. Residual data for capacitive readings with straight line connecting terminal points

Displacement(mm) Residual (volts)

2.90 -0.00776

3.05 0.003155

3.20 0.00919

3.35 0.029873

3.50 0.006611

3.65 -0.0313

3.80 -0.02527

3.95 0.019832

4.10 0.006336

4.25 -0.01204

4.40 -0.01578

4.55 -0.00974

4.70 0.001177

4.85 0.026743

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7

Deviation(volts)

Displacement (mm)

Residual Data for Capacitive Reading


10/14

The lower and upper accuracy limits of the response curve are -0.0313 volts and 0.029873 volts,

respectively, or -3.62% and 3.46% full scale. The full scale value of the response curve is taken

at 2.9mm, therefore full scale value is 0.864258 volts.

Equation of the line is V=0.017693846*d 0.059072153 (linear line of residual plot)

Displacement(mm)

Point on the line(volts)

Residual(volts) q

2.90 -0.00776 -0.00776 2.0004E-06

3.05 -0.005105923 0.003155 0.008260923

3.20 -0.002451846 0.00919 0.011641846

3.35 0.000202231 0.029873 0.029670769

3.50 0.002856308 0.006611 0.003754692

3.65 0.005510385 -0.0313 0.036810385

3.80 0.008164462 -0.02527 0.033429462

3.95 0.010818539 0.019832 0.009013461

4.10 0.013472616 0.006336 0.007136616

4.25 0.016126693 -0.01204 0.028170693

4.40 0.018780769 -0.01578 0.034555769

4.55 0.021434846 -0.00974 0.031174846

4.70 0.024088923 0.001177 0.022911923

4.85 0.026743 0.026743 1E-10


|| = 0.036810385 =1 || 100% =1

0.036810385

0.864258 100% = 95.74%


11/14

3) Inductive Sensor

Displacement

(mm)

Inductive reading

(volts)5.45 1.01563

5.60 1.25488

5.75 1.53809

5.90 1.85059

6.00 2.06055

6.50 2.92481

Table 7. Range of inductive readings with high sensitivity and an approximate linear response

Figure 6. Calibration plot for inductive readings with linear best fit line (Sensitivity = 1.845)

V = 1.845*d - 9.0501

R = 0.9985

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6

Output(volts)

Displacement (mm)

Calibration Plot for Inductive Reading


12/14

Displacement(mm)

Point on the line ofbest fit (volts)

Residual(volts)

5.45 1.00515 0.01047

5.60 1.2819 -0.02702

5.75 1.55865 -0.02056

5.90 1.8354 0.01519

6.00 2.0199 0.04065

6.50 2.9424 -0.01759

Table 8. Points on the line of best fit and residual values of inductive readings

Figure 7. Residual data for inductive readings with straight line connecting terminal points

The lower and upper accuracy limits of the response curve are -0.027017 volts and 0.040647

volts, respectively, or -0.92% and 1.39% full scale. The full scale value of the response curve is

taken at 6.5mm, therefore full scale value is 2.92481 volts.

Equation of the line is V=0.017693846*d 0.059072153 (linear line of residual plot)

Displacement (mm)Residual

(volts)

5.45 0.010475

5.60 -0.027017

5.75 -0.020564

5.90 0.015186

6.00 0.0406476.50 -0.017595

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

5.45 5.65 5.85 6.05 6.25 6.45Deviation(volts)

Displacement (mm)

Residual Data for Inductive Reading


13/14

Displacement (mm) Point on the line (volts) Residual (volts) q

5.45 0.010475001 0.010475 1.15E-09

5.60 0.006465001 -0.02702 0.033482

5.75 0.002455001 -0.02056 0.023019

5.90 -0.001554999 0.015186 0.016741

6.00 -0.004228332 0.040647 0.044875

6.50 -0.017594999 -0.01759 1.5E-09


|| = 0.044875 =1 || 100% =1

0.044875

2.92481100% = 98.47%

From the readings generated from each transducer, usable range for the transducers which has a

high sensitivity and an approximately linear response are identified. From the linear best fit line

superimposed on the calibration plot of each transducer, the sensitivity of each transducer was

identified. Sensitivity of photonic, capacitive, inductive transducer is 9.947, -0.3332, and 1.845

V/mm, respectively. Therefore, it can be seen that inductive transducer has the highest

sensitivity. Therefore, inductive transducer is most responsive to small changes in displacement

as the equation for the sensitivity is, = = .Linearity of each transducer was identified using the equation:

=1 || 100%, whereas ||were found by observing Table 3, Table 6,andTable 9. Linearity of photonic, capacitive, and inductive transducer is 95.94%, 95.74%, and

98.47% respectively.

Usable range of photonic, capacitive, and inductive transducer is 0.2mm to 0.7mm, 2.9mm to

4.85mm, and 5.45mm to 6.50mm respectively. This means there are number of gaps in the range

of the displacement given by the micrometer that are not within usable ranges of the transducers.

These are: 0 to 0.2mm, 0.7mm to 2.9mm, 4.85mm to 5.45mm, and 6.50mm to 10mm

To account for these gaps and have accurate measurements, there is one method I can think of.

We introduce a new reference point from which to measure; it can be a metal plate at an arbitrary

point. However this reference point must be within an existing usable range of one of the

devices. Therefore we can measure its distance relative to the transducer. Then we measure the

distance from the object to the transducer (object must be within usable range). Finally, we


14/14

subtract these two distance values to determine the displacement of the object from the new

reference plate. Thickness of the reference plate must be known.

For all three transducers, our results showed very high linearity over their usable ranges.

Although each device had its own unique usable range, we are confident they will output

accurate measurements over that range. When it comes to high sensitivity and high linearity overtheir usable range, the inductive sensor was superior to the other two. However, the capacitive

sensor had a larger usable range by 186% compared to that of the inductive sensor, with only a

linearity of 3% lower. Therefore, determining which transducer is the best depends on the

measurement range of the experiment, and the small changes in displacement that need to be

measured (the resolution), which relies on the sensitivity.

Conclusion

There are three main objectives we have learned from this lab. The first is how each of the three

types of transducers work. The second is how to perform a static calibration using a micrometer

and setting up the virtual instruments in LabView. The third is how to do a statistical analysis of

the response curves obtained from the calibration. In other words, how to determine linear range;

calculate sensitivity and linearity from a residual plot using Microsoft Excel. Once weve

obtained these values for each transducer, we can appropriately and effectively use these devices

for future experiments. Knowing this information is essential for future experiments, where we

must decide which transducer is most suitable for a particular displacement range. The most

suitable choice of transducer will have the largest linear range over which we are measuring, the

highest percentage linearity, and the highest sensitivity within that range. From our results, we

can conclude that the inductive sensor has the highest sensitivity and linearity over its usable

range. But most importantly, if we are measuring displacements outside its usable range, then

another transducer, such as capacitive or photonic, would be much more accurate.

Reference:

Wheeler, Anthony J., and A. R. Ganji.Introduction to Engineering Experimentation. Upper

Saddle River: Pearson/Prentice Hall, 2004. Print.

Lab 7 Transducers

Documents