Linear and Rotational Displacement Measurement

7/31/2019 Linear and Rotational Displacement Measurement

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Linear & Rotational

Displacement measurement


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Translational displacement transducers are

instruments that measure the motion of a body in a

straight line between two points.

Apart from their use as a primary transducermeasuring the motion of a body, translational

displacement transducers are also widely used as a

secondary component in measurement systems,

where some other physical quantity such as

pressure, force, acceleration or temperature is

translated into a translational motion by the primary

measurement transducer.

Linear Displacement Transducers


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Many different types of translational

displacement transducer exist and these, along

with their relative merits and characteristics, are

discussed in the following sections .

Displacement transducers


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The resistive potentiometer is perhaps the best-known displacement-measuring device.

It consists of a resistance element with a movable

contact as shown in Figure (Voltage sensitive

circuit.) A voltage Vs is applied across the two ends

A and B of the resistance element and an output

voltage V0 is measured between the point of contact

C of the sliding element and the end of theresistance element A.

A) The resistive potentiometer

Voltage Sensitive

input circuit


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A linear relationship exists between the output

voltage V0 and the distance AC, which can be

expressed by:


The body whose motion is being measured is

connected to the sliding element of thepotentiometer, so that translational motion of the

body causes a motion of equal magnitude of the

slider along the resistance element and a

corresponding change in the output voltage V0.


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Fig shows the schematics of a current sensitive

circuit. A change in the physical variable

(measurand) moves the slider across the resistor and

brings about a change in the resistance of the circuit.

The resistance change is then indicated by a change

in the current flow in the circuit.


Current Sensitive

input circuit


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The current flow is given by,


where Vsis the supply or input voltage,Rb is the

resistance of the system outside the transducer,

and R is the resistance of the transducer thatvaries with measurand.


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Linear differential Variable transformer

LVDT is inductive transducer .Translates liner

motion into electrical signals

The device has one primary and two secondary

windings with the magnetic core free to move inside

the coils. The core is attached to the moving part on which

the displacement measurements are to be made.

When a.c. current is supplied to the primarywinding, the magnetic flux generated by this coil is

disturbed by the armature so that voltages are

induced in the secondary coil.


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The secondary windings are symmetrically placed,

are identical and are connected in phase oppositionso that emf induced in them are opposite to each

other. The net output from the transformer is then

the difference between the voltages of the two

secondary windings.

The position of the magnetic core determines the

flux linkages with each winding, When the core isplaced centrally, equal but opposite emfs are

induced in the secondary windings and zero output

is recorded. This is termed as the balance point or

null position.


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A variation in the position of the core from itsnull position produces an unbalance in the

resistance of Secondary windings to the

primary windings. The voltage induced in the

secondary winding towards which the core isdisplaced increases. A simultaneous decreased

induced voltage results from the other secondary

coil.


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Thus, upon displacement of the armature, the

resultant will be a voltage rise in one secondary

and a decrease in the other. The asymmetry in the

core position thus produce a differential voltage

E0 which varies linearly with change in the core

position .

Change in Voltage is proportional to displacement


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Linear range

Central Core Position

Displacement


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Advantages

High range (from 1.25mm to 500 mm)

Low power consumption (


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Disadvantages

Large displacement required for small o/p

Sensitive to stray magnet Performance affected by temperature

Limited dynamic response


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Applications

Primary transducer converts

displacement directly to voltage.

Secondary transducer for measuring

pressure, force, weight etc.


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Rotational displacement transducers

Rotational displacement transducers measure theangular motion of a body about some rotation axis.

They are important not only for measuring the

rotation of bodies such as shafts, but also as part of

systems that measure translational displacement by

converting the translational motion to a rotary

form.

The various devices available for measuring

rotational displacements are presented below,


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Rotational displacement

Rotational displacement transducers measure theangular motion of a body about some rotation axis.

They are important not only for measuring the

rotation of bodies such as shafts, but also as part of

systems that measure translational displacement by

converting the translational motion to a rotary

form.

The various devices available for measuring

rotational displacements are presented below,


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Angular measurements are made with a device

called tachometer. The dictionary definitions of atachometers are :

*"an instrument used to measure angular velocity

as of shaft, either by registering the number ofrotations during the period of contact, or by

indicating directly the number of rotations per

minute.

*"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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Tachometers are broadly classified into twocategories,

Mechanical tachometers

Electrical tachometers

Selection of type of tachometer based on cost,need

of portability, accuracy desired , magnitude of

speed measured and size of the rotating element


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Revolution counter and timer

The revolution counter, sometimes called a speedcounter, consists of a worm gear which is also the

shaft attachment and is drives by the speed source.

The worm drives the spur gear which in turn

actuates the pointer on a calibrated dial.

The pointer indicates the number of revolutions

turned by the input shaft in a certain length of time.The unit requires a separate timer to measure the

time interval. The revolution counter, thus, gives

an average rotational speed rather than an

instantaneous rotational speed.


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Revolution counter and timer

Such speed counters are limited to low speedengines which permit reading the counter at

definite time intervals. A properly deigned and

manufactured revolution counter would give a

satisfactory speed measure ment upto 2000-3000

rpm.


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Slipping clutch tachometer

The rotating shaft drives an indicating shaft

through a slipping clutch.

A pointer attached to the indicator shaft moves

over a calibrated scale against the torque of aspring.

The pointer position gives a measure of the shaft

speed.


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Slipping clutch tachometer

The rotating shaft drives an indicating shaft

through a slipping clutch.

A pointer attached to the indicator shaft moves

over a calibrated scale against the torque of aspring.

The pointer position gives a measure of the shaft

speed.


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Drag Cup tachometer

The drag-cup tachometer, also known as an eddy-

current tachometer, has a central spindle carryinga permanent magnet that rotates inside a non-

magnetic drag-cup consisting of a cylindrical

sleeve of electrically conductive material, as

shown in Figure.

D C h


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Drag Cup tachometer

As the spindle and magnet rotate, a voltage is

induced which causes circulating eddy currents in

the cup. These currents interact with the magnetic

field from the permanent magnet and produce a

torque.

In response, the drag-cup turns until the induced

torque is balanced by the torque due to the

restraining springs connected to the cup.


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Drag Cup tachometer

When equilibrium is reached, the angular

displacement of the cup is proportional to therotational velocity of the central spindle. The

instrument has a typical measurement inaccuracy

of 0.5% and is commonly used in the

speedometers of motor vehicles and as a speedindicator for aero-engines. It is capable of

measuring velocities up to 15 000 rpm.

O ti l t h t


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Optical tachometer

Optical pulses can be

generated by one of thetwo alternative

photoelectric techniques

illustrated in Figure.

In Figure (a), the pulses

are produced as the

windows in a slotted discpass in sequence between a

light source and a detector.

Photoelectric pulse generation techniques.

pt ca tac ometer


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pt ca tac ometer The alternative form, Figure

(b), has both light source and

detector mounted on the same

side of a reflective disc which

has black sectors painted onto

it at regular angular intervals.

Light sources are normallyeither lasers or LEDs, with

photodiodes and

phototransistors being used as

detectors.

Optical tachometers yield better accuracy than

other forms of digital tachometer but are not as

reliable because dust and dirt can block light paths


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Magnetic (Hall-effect) sensing

The rotating element in Hall-effect ormagnetostrictive tachometers has a very simple

design in the form of a toothed metal gearwheel.

The sensor is a solid-state, Hall-effect device that

is placed between the gear wheel and a permanentmagnet.


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Magnetic (Hall-effect) sensing

When an inter tooth gap on the gear wheel is

adjacent to the sensor, the full magnetic field from

the magnet passes through it.

Later, as a tooth approaches the sensor, the toothdiverts some of the magnetic field, and so the field

through the sensor is reduced. This causes the

sensor to produce an output voltage that is

proportional to the rotational speed of the gear

wheel.

n uct ve c p


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n uct ve c p

Variable reluctance velocity transducers, also known asinduction tachometers, are a form of digital tachometer that

use inductive sensing. A more sophisticated version shown

in Figure has a rotating disc that is constructed from a

bonded-fibre material into which soft iron poles are insertedat regular intervals around its periphery. The sensor consists

of a permanent magnet with a shaped pole piece, which

carries a wound coil.

The distance between the pick-up and the outer perimeter of

the disc is around 0.5 mm.


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Inductive Pick Up

As the disc rotates, the soft iron inserts on the

disc move in turn past the pick-up unit. As each

iron insert moves towards the pole piece, the

reluctance of the magnetic circuit increases and

hence the flux in the pole piece also increases.

Similarly, the flux in the pole piece decreases as

each iron insert moves away from the sensor. The

changing magnetic flux inside the pick-up coil

causes a voltage to be induced in the coil whose

magnitude is proportional to the rate of change of

flux.

I d ti Pi k U


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Inductive Pick Up

This voltage is positive whilst the flux isincreasing and negative whilst it is decreasing.

Thus, the output is a sequence of positive and

negative pulses whose frequency is proportional

to the rotational velocity of the disc. The

maximum angular velocity that the instrument

can measure is limited to about 10000 rpmbecause of the finite width of the induced pulses.

d i i k


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Inductive Pick Up

As the velocity increases, the distance between

the pulses is reduced, and at a certain velocity,

the pulses start to overlap. At this point, the pulse

counter ceases to be able to distinguish the

separate pulses. The optical tachometer hassignificant advantages in this respect, since the

pulse width is much narrower, allowing

measurement of higher velocities.

S b


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Stroboscope

The stroboscopic technique of rotational velocity

measurement operates on a similar physical

principle to digital tachometers except that the

pulses involved consist of flashes of light

generated electronically and whose frequency isadjustable so that it can be matched with the

frequency of occurrence of some feature on the

rotating body being measured.


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This feature can either be some naturallyoccurring one such as gear teeth or the spokes of

a wheel, or it can be an artificially created pattern

of black and white stripes. In either case, the

rotating body appears stationary when the

frequencies of the light pulses and body features

are in synchronism.

Stroboscope

S b


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Flashing rates available in commercial

stroboscopes vary from 110 up to 150 000 per

minute according to the range of velocity

measurement required, and typical measurement

inaccuracy is +/-1% of the reading. The

instrument is usually in the form of a hand-helddevice that is pointed towards the rotating body.

It must be noted that measurement of the flashing

rate at which the rotating body appears stationary

does not automatically indicate the rotational

velocity, because synchronism also occurs when

the flashing rate is some integral sub-multiple of

the rotational speed.

Stroboscope

S b


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The practical procedure followed is therefore toadjust the flashing rate until synchronism is

obtained at the largest flashing rate possible, R1.

The flashing rate is then carefully decreased until

synchronism is again achieved at the next lowerflashing rate, R2. The rotational velocity is then

given by:

Stroboscope

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Linear and Rotational Displacement Measurement