1. The document discusses various methods for measuring linear and angular velocity, including electromagnetic, seismic, and digital transducers as well as using the Doppler effect. 2. Electromagnetic transducers are the most commonly used for linear velocity and work by inducing a voltage in a coil from the motion of a magnet. Moving magnet and moving coil types are described. 3. Angular velocity can be measured with a tachometer, which can be mechanical and count revolutions or electrical and generate a voltage proportional to speed.

1. VELOCITY MEASUREMENTS
AKHIL KRISHNAN G
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2. MEASUREMENT OF LINEAR VELOCITY
• Velocity is the first derivative of displacement.
• Linear velocity is defined as the rate of change
of the position vector with time at an instant in
time.
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3. • The methods used for measurement of linear velocity utilize the following
type of transducers.
1. Electro-magnetic transducers.
2. Seismic transducers.
3. Linear velocity transducer.
4. Digital transducers.
5. Transducers using Doppler effect.
Moving magnet type
Moving Coil Type
6. Velocity measurement using displacement and acceleration sensors
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4. 1.ELECTROMAGNETIC TRANSDUCERS
• The most commonly used transducer for measurement of
linear velocities .
• This transducer utilizes the voltage produced in a coil on
account of change in flux linkages resulting from change in
reluctance.
• They are classified into two types
A)Moving magnet type
B)Moving coil type
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5. A)MOVING MAGNET TYPE TRANSDUCER
• The sensing element is a rod type permanent magnet that is
rigidly coupled to the device whose velocity is being
measured .
• There is a coil surrounding the
permanent magnet.
• The motion of the magnet induces
a voltage in the coil and the amplitude
of the voltage is directly proportional
to the velocity.
• The polarity of the output voltage determines the direction of
motion 5

6. • For a coil placed in magnetic field the voltage generated is:
e0= BANv
= Kv
K=BAN= a constant
B=flux density ; Wb/m2 ,
A= area of coil; m2
N= Number of turns of coil,
v=relative velocity of magnet with respect to coil
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7. ADVANTAGES
1. The maintenance requirements of these transducers are
negligible , because there are no mechanical surfaces or
contacts.
2. The output voltage is linearly proportional to velocity.
DISADVANTAGES
1. The performance of these transducers is adversely affected
by stray magnetic fields. These fields can cause noise.
2. The frequency response is usually limited and is stated.
3. These transducers are not very useful for measurement of
vibrations because their calibration deteriorates as contact
with steel tools etc. leads to progressive demagnetization.
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8. B)MOVING COIL TYPE VELOCITY TRANSDUCER
 It operates essentially through the action of a coil moving
in a magnetic field.
 A voltage is generated in the coil which is proportional to
the velocity of the coil.
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9. • The coil is mounted on a pivoted arm.
• There is a mass attached at the end of the arm.
• The velocity to be measured is applied to the arm and therefore
the coil moves in the field of permanent magnet.
• A voltage is generated on account of motion of the coil in the
magnetic field.
• The output voltage is proportional to the velocity.
ADVANTAGES
1. This is a more satisfactory arrangement as the system now
forms a closed magnetic circuit with a constant air gap, and the
whole device is contained in an antimagnetic case which
reduces the effects of stray magnetic fields.
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10. 2.SEISMIC TYPE VELOCITY TRANSDUCER
• A permanent magnet is supported between two springs and fitted with low
friction bearing rings. It act as a seismic mass.
• The frame is rigidly attached to the object whose velocity is being
measured.
• The object is vibrating at a frequency in excess of the low natural
frequency of the transducer.
• The self resonant frequencies of seismic mass are typically 10 Hz to 15 Hz.
• If the operation at frequencies above 20 Hz occurs the mass is relatively
stationary, and the case and coil moving in the magnetic field has a large
voltage induced in it which is proportional to the velocity.
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11. • The seismic transducer have a good frequency response.
• Both moving coil and seismic transducers have the disadvantage that
connections must be made on the moving part.
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12. 3.LINEAR VELOCITY TRANSDUCER (LVT)
• A linear velocity transducer (LVT) is an inductive device which
utilizes the link between electricity and magnetism as found by
H. A. Lorentz, if a magnetic field moves near an electrical wire,
current flows through the wire.
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13. • An LVT consists of a rod called the core (a permanent magnet), and
two electrical coils
• The core slides inside a hollow cylindrical tube called a bobbin and A
DC voltage is generated when the core moves.
• Since the two coils are wrapped with opposite polarity, and since the
magnet also has two poles (north and south), the south pole induces a
voltage primarily in coil 1, and the north pole primarily in core 2.
• It turns out that the net voltage is proportional to the speed of the core.
• Although the range is limited, LVTs are used in some types of
machinery, like milling machines.
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14. 4.DIGITAL TRANSDUCERS
• Velocity is the rate of change of displacement with respect to time.
• If a number of evenly spaced marks are placed on the moving object
ant the number of these marks is n, passing at a given time t s, the
velocity is
• v=nd/t
• d=distance between the marks
• The marks can be made photo electrically or there may be
protrusions which are detected by inductive or capacitative
techniques.
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15. 5.TRANSDUCERS USING DOPPLER EFFECT
• The doppler effect is an effective and accurate method of
measuring linear velocity.
• If a narrow radio beam or ultrasonic beam is aimed at an
object, the beam will be reflected back to the source.
• However ,if the object is moving ,the frequency of the signals
received back differs from that of the transmitted signal.
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16. A radar-Doppler velocimeter
• Radio waves of wavelength λ are transmitted (incident waves)
towards a moving object.
• The object moves with velocity V at angle θ relative to the radar
unit, as sketched
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17. • The radio waves reflect off the moving object, and are sensed
by a radio wave detector (receiver), that is also mounted on
the radar unit.
• The detector measures the frequency of the reflected radar
beam, and the unit compares the frequency of the transmitted
and reflected beams.
• Doppler radar units are used by police to measure the speed of
automobiles, and they are also used in professional sports to
measure the speed of baseballs, etc.
• Laser light can be used in place of radio waves. Then, the
device is called a laser Doppler velocimeter
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18. 6.VELOCITY MEASUREMENT USING DISPLACEMENT
AND ACCELERATION SENSORS
 Displacement sensors
• velocity is the time derivative of displacement
• V (t) ₌ dx(t) / dt.
• We could calculate velocity by taking the time derivative of
displacement measurements from a displacement
sensor(potentiometer, LVDT, laser displacement meter, etc.)
• This technique is often used for measuring the velocity of very
fast-moving objects like bullets.
• Disadvantage: the process of differentiation of a signal amplifies
the noise in the system.
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19. • Acceleration sensors
• velocity is the time integral of acceleration.
• V (t) =V ₀ + ∫a (t) dt
• Unlike differentiation, the process of integration
decreases the noise in the system.
• Thus, velocity measurement by integration of
acceleration data is generally a wise choice.
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20. MEASUREMENT OF ANGULAR VELOCITY
• The measurement of angular velocity may be made with a tachometer.
• The tachometer may be defined as:
i. An instrument used for measure of angular velocity , as of shaft , either
by registering the total number of revolutions during the period of
contact, or by indicating directly the number of revolutions per minute.
ii. An instrument which either continuously indicates the value of rotary
speed or continuously displays a reading of average speed over rapidly
operated short intervals of time.
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21. • The tachometers are classified as:
1. Mechanical tachometers
2. Electrical tachometers
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22. 1.MECHANICAL TACHOMETERS
Hand speed tachometers.
• It has a spindle which can be attached to this to be measured. The spindle is
connected to mechanical counters which display the count. This indicator
has an inbuilt stop watch and a mechanical counter with automatic
disconnect.
• The hand speed indicators can be used to speeds
of 20,000 to 30,000 rpm with an accuracy of 1 %.
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23. Disadvantages of Mechanical Tachometers.
• Mechanical tachometers impose a load on the shafts to which they are
connected and hence absorb power. So they cannot be used for
applications involving small powers since the attachment of tachometer to
the shaft will decrease the speed. Therefore mechanical tachometers are
only useful for heavy machinery.
• On account of inertia of mechanical parts, the mechanical tachometers
are not able to follow the variations in the speed. Therefore they indicate
only the average speed over a particular interval of time. They cannot be
used in applications where instantaneous indication of speed is desired.
• The mechanical tachometers normally use an arrangement wherein a
counter is used for counting the number of events and a stop watch for
measurement of time. The speed is calculated from the reading of two.
This involves large errors especially when the stop watch is operated
manually.
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24. 2.ELECTRICAL TACHOMETERS
• D.C. Tachometer Generators
• They consist of a small armature which is coupled to the machine whose
speed is to be measured. This armature revolves in a field of permanent
magnet. The emf generated is proportional to the product of flux and
speed.
• Since the flux of the permanent magnet is constant, the voltage generated
is proportional to speed. The polarity of output voltage indicates the
direction of rotation. This emf is measured with the help of a moving coil
voltmeter having a uniform scale and calibrated directly in terms of speed.
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25. • A series resistance is used in the circuit for the purpose of
limiting the current from the generator in the event of a short
circuit on the output side.
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26. Advantages
i. The direction of rotation is directly indicated by the polarity of the output
voltage.
ii. The output voltage is typically 10mv/rpm and can be measured with conventional
type d.c. voltmeters.
Disadvantages
i. Brushes of small tachometer generators often produce maintenance problems, as
their contact resistance may vary and produce appreciable error. Thus the
commutator and the brushes require periodic maintenance.
ii. The input resistance of meter should be very high as compared with output
resistance of generator. This is required to limit the armature current to small
value. If the armature current is large, the field of the permanent magnet is
distorted giving rise to non-linearity
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