Design of Transducer to measure comparative rotation in 3D using LVDT

1. Electronics
National
Measurements
UNDER THE GUIDANCE OF
DR. CHANDRAJIT CHOUDHURY
DEPT OF ELECTRONICS AND COMMUNICATION
NIT SILCHAR
1
Department of
Electronics and Communication Engineering
ational Institute of Technology
2020
Measurements and Instrumentation
Mini Project
Submitted By:
Group – 28
RanSher (1814110)
HOUDHURY SIR
COMMUNICATION ENGINEERING,
Engineering
Technology, Silchar
Instrumentation

2. 2
Design of Transducer to measure
comparative rotation in 3D using LVDT
Ran Sher
Department of Electronics and Communiction Engineering
National Institute of Technology, Silchar
ABSTRACT
Transducers are excellent devices in converting the one form of energy to another. LVDTs are one of
the famous transducer and well known for their ability to measure the linear displacement with high
accuracy and precision. In this project we have designed a transducer device with the help of group of
LVDTs to measure the comparative rotation in three dimensions. Three LVDTs situated on three
perpendicular axes can measure the displacements produced by each, when rotated in specific
direction. These displacements produced in each of the LVDT can be used to calculate the angle of
rotation from any of the axes.
TABLE OF CONTENTS
Introduction…………………………………….2
Transducers……………………………….…....3
LVDTs……………………………..…………..3
Applications of LVDTs…..………………..….4
Design of Transducer……..………………..…. 5
Working of Transducer…………………….......5
Solutions for challenges in implementation……8
Results and discussion…………………………9
Conclusions…………………………………….9
Acknowledgement……………………………..9
References……………………………………...9
1. INTRODUCTION
A transducer is an electronic device that converts energy from one form to another. Common
examples include microphones, loudspeakers, thermometers, position and pressure sensors, and
antenna. LVDT is a class of transducer, which works principle of mutual induction and can
measure the linear displacement by determining difference in voltages. 3 LVDTs can be to design a
transducer which can measure comparative rotation in 3D, by binding it to 3 perpendicular axes x,
y and z with its centres kept at near origin. Rotating the designed transducer to some angles causes
displacement in core of LVDTs, hence these displacements measured can be utilised to determine

3. 3
the angle of rotation about any axes using cosine formula discussed earlier. There are many
challenges in physical implementations which can be solved by using suitable conditions and
favourable precautions.
2. TRANSDUCERS
Transducers are the electronic devices which can convert one form of energy to another. This
ability of transducers can be utilized in measurements and instrumentation purposes in better
manner.
The word “Transducer” is the collective term used for both Sensors which can be used to sense a
wide range of different energy forms such as movement, electrical signals, radiant energy, thermal
or magnetic energy etc, and Actuators which can be used to switch voltages or currents.
There are many different types of sensors and transducers, both analogue and digital and input
and output available to choose from. The type of input or output transducer being used, really
depends upon the type of signal or process being “Sensed” or “Controlled” but we can define a
sensor and transducers as devices that converts one physical quantity into another.
Devices which perform an “Input” function are commonly called Sensors because they “sense” a
physical change in some characteristic that changes in response to some excitation, for example
heat or force and covert that into an electrical signal. Devices which perform an “Output” function
are generally called Actuators and are used to control some external device, for example
movement or sound.
Transducers can be classified as:
 On the basis of transduction form used.
 As primary and secondary transducers.
 As passive and active transducers.
 As analog and digital transducers
3. LVDTs
The linear variable differential transformer (LVDT) is a type of electrical transformer used for
measuring displacement.
Working Principle:
LVDT works under the principle of mutual induction, and the displacement which is an on
electrical energy is converted into an electrical energy. And the way how the energy is getting
converted is described in working of LVDT in a detailed manner.
It consists of a cylindrical former where it is surrounded by one primary winding in the centre of
the former and the two secondary windings at the sides. The number of turns in both the
secondary windings are equal, but they are opposite to each other, i.e., if the left secondary
windings is in the clockwise direction, the right secondary windings will be in the anti-clockwise
direction, hence the net output voltages will be the difference in voltages between the two
secondary coil.

4. 4
Case 1: On applying an external force which is the displacement, if the core reminds in the null
position itself without providing any movement then the voltage induced in both the secondary
windings are equal which results in net output is equal to zero.
Case 2: Due to external force if the steel iron core moves in the right hand side direction then the
voltage induced in the secondary coil 2 is greater when compared to the voltage induced in the
secondary coil 1.
Case 3: Due to external force if the steel iron core moves in the left hand side direction then the
voltage induced in the secondary coil 1 is greater when compared to the emf voltage induced in
the secondary coil 2.
Advantages and Disadvantages of LVDTs
Advantages of LVDT
 LVDT has High Range.
 LVDT is a frictionless device.
 LVDT has low hysteresis.
Disadvantages of LVDT
 Sensitive to a stray magnetic field.
 Performance is affected by vibrations.
 Temperature affects the performance.
4. APPLICATIONS OF LVDTs
In applications where both accuracy and reliability are key; an LVDT is well suited and
recommended. Some benefits to choosing LVDTs are:
Friction Free – they are non-contacting and therefore friction free meaning they offer long life.
Fast Response – the fast response time of the LVDT means that time can be managed effectively
during use.
Robust – being robust means that LVDTs can be used in extreme applications and environments.
Versatile – different configurations are available to suit different applications. Contact Ixthus to
find the right LVDT for your application.
 Used in applications where displacements ranging from fraction of mm to few cm are to be
measured.
 Acts as the secondary transducers.
 Power turbines
 Hydraulics
 Aircrafts
 Satellites
 Nuclear reactors
 Factory automation
 Servo mechanisms

5. 5
 Weight sensitive applications
 General industrial applications
 Process and control
5. DESIGN OF TRANSDUCER
 Three similar LVDT, numbered with LVDT1, LVDT2 and LVDT3 are kept at x-axis, y-axis and z-
axis respectively.
 They are attached in such a way that middle portion of each LVDT lies at the origin ideally.
 LVDTs can freely rotate in any direction about origin.
 Initially, LVDT 3, which lies on z-axis has maximum displacement of core (let say L) and LVDT
1 and LVDT 2 has zero displacement of core.
 Any rotation about origin will tend to decrease the value of L (displacement of core of LVDT 3)
and tend to increase the value of core displacement of LVDT 1 and LVDT 2.
6. WORKING OF TRANSDUCER
 According to principle of LVDT, when core of LVDT is displaced from the centre machanically,
the voltage difference of two secondary coils becomes non-zero and hence displaced position
of core can be measured easily.
 Weight of the core is responsible for its displacement from the centre. When LVDT is vertical,
it has maximum core displacement whereas when it is horizontal, it has minimum
displacement.
 Let’s displacement along x-axis, y-axis and z-axis is denoted by 𝑑 , 𝑑 and 𝑑 .
State 1: LVDT 3(z-axis) is fixed and LVDT1(x-axis) and LVDT 2(y-axis) is rotated x-y plane.

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Here, 𝑑 = 0
𝑑 = 0 , 𝑑 = L (let)
Therefore, if 𝛼 is the angle with x,
Then,
cos 𝛼 = , i.e., 𝛼 = 90
State 2: LVDT 2 (y-axiz) is fixed Motion in x-z plane
OR
LVDT 1 (x-axis) is fixed, Motion in y-z plane.
Due to rotation in x-z plane, there will be increase in 𝑑
and decrease 𝑑 while 𝑑 remains constant.
𝑑 = L’ (let)
𝑑 = 0
𝑑 = L – L’ {since increase displacement of LVDT 1 will be same as decrease in LVDT 3 }

7. 7
cos 𝛼 =
=
( )
hence, 𝛼 = cos−1(
( )
)
State 3: All LVDTs are rotated by angle 𝛼 .
Let say L’ is increase in displacement of LVDT1 and LVDT2 and it is known that there is same
decrease in LVDT 3, hence
𝑑 = L’ (let)
𝑑 = L’
𝑑 = L – L’ {since increase displacement of LVDT 1 will be same as decrease in LVDT 3 }
cos 𝛼 = =
=
( )
hence, 𝛼 = cos−1(
( )
)
State 4: LVDT 1 , LVDT 2 and LVDT 3 are rotated by angle α, β and γ respectively from x, y ,z
axes .

8. 8
Let say Lx’ and Ly’ are increase in displacement of LVDT1 and LVDT2 and Lz’ is decrease in
LVDT 3, hence
𝑑 = Lx’ (let)
𝑑 = Ly’
𝑑 = L – Lz’ {since increase displacement of LVDT 1 will be same as decrease in
LVDT 3 }
cos 𝛼 =
=
( )
hence, 𝛼 =cos−1(
( )
)
Similarly β = cos−1(
( )
)
and γ = cos−1(
( )
)
Next Step
Three dampers is added at the centre of the designed LVDT ,in such a way that when LVDT at any
time starts moving away from the central point in uncontrolled
acceleration, then damper comes into effect to start damping force to stop or
to oppose the LVDT in opposite direction of its motion.

9. 9
7. SOLUTIONS FOR CHALLENGES IN IMPLEMENTATION
 Centres of all three LVDTs should lie on origin initially, which is not possible in real senario.
 Solution: Although it is not possible, but it can be achieved to near ideal value by reducing the
thickness of LVDTs to minimum value.
 During rotation, centrifugal force comes into effect which causes vary in actual displacement in
cores of LVDTs.
 Solution: Measurement readings should be taken during equilibrium condition, which can
reduce this error.
 Accuracy can be hampered by Temperature and Hysteresis.
 Solution: Temperature must be kept constant by cooling and soft iron core can be used for
reduction in losses due to hysteresis.
8. RESULT AND DISCUSSION
A transducer designed with the help of LVDTs is found to be theoretically satisfactory and
working according to the principles of LVDT. The linear displacement produced by the LVDTs
was used to calculate the angle of rotation using the cosine formula which is given as
cos 𝛼 = where 𝛼 is the angle of rotation
Various challenges are there in the practical implementation of the device is discussed earlier
and it was found that device can work efficiently.
9. CONCLUSIONS
After studying transducers and their properties in view of LVDTs, we can conclude that LVDTs
are excellent devices to measure the linear displacement and these linear displacements can be
used to measure the angular rotation in three dimensions. The design of above transducer can
have some practical challenges which can be solved by following some ideal situations
10. ACKNOWLEDGEMENT
The author is thankful to Dr. Chandrajit Choudhury, Assistant Professor, National Institute of
Technology Silchar for his guide, advise and motivation throughout the completion of this
report.
Author would also like to express his gratitude to his college, National Institute of Technology,
Silchar for providing him with such a strong platform and enabling him to harness his talents.
Lastly, he would like to express his appreciation to his parents for providing him moral
support and encouragement.

10. 10
11. REFERENCES
[1] AK SAWHNEY A Course In Electronics & Electrical Measurements And Instrumentation.pdf
[2] Electronic Instrumentation And Measurements by Cooper.pdf
[3] https://www.slideshare.net
[4] https://www.electronics-tutorials.ws/io/io_1.html
[5] https://en.wikibooks.org
[6] https://en.wikipedia.org