VELOCITY MEASUREMENTS

AKHIL KRISHNAN G

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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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• 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.

6. Velocity measurement using displacement and acceleration sensors

Moving magnet type

Moving Coil Type

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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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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

• 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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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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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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• 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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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.10

• 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.11

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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• 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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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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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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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 sketched16

• 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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6.VELOCITY MEASUREMENT USING DISPLACEMENTAND 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.18

• 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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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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• The tachometers are classified as:

1. Mechanical tachometers

2. Electrical tachometers

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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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Disadvantages of Mechanical Tachometers.

• Mechanical tachometers impose a load on the shafts to which they areconnected and hence absorb power. So they cannot be used forapplications involving small powers since the attachment of tachometer tothe shaft will decrease the speed. Therefore mechanical tachometers areonly useful for heavy machinery.

• On account of inertia of mechanical parts, the mechanical tachometersare not able to follow the variations in the speed. Therefore they indicateonly the average speed over a particular interval of time. They cannot beused in applications where instantaneous indication of speed is desired.

• The mechanical tachometers normally use an arrangement wherein acounter is used for counting the number of events and a stop watch formeasurement 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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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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• 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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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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