mmm force torque strain final

8/10/2019 MMM Force Torque Strain Final

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Force Torque Strain

Measurements


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Force Measurements


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Applications

Force/Stress measurement:Weighing of an object

Dynamics of vehicles

Control applications such as deployment of air bag in a vehicle

Study of behavior of materials under different types of loads

Vibration studies

Seismology or monitoring of earthquakes

Torque measurement:Measurement of brake power of an engine

Measurement of torque produced by an electric motorStudies on a structural member under torsion

Power measurement:Measurement of brake horse power of an engine

Measurement of power produced by an electric generator


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Contd..

Methods :

Direct methods

Analytical balance

Platform balance

Elastic Members(Indirect methods)

Load cells

Cantilever beamsProving rings


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Force Measurement

1. Platform balance


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Contd..

2. Force to displacement conversion:

A spring balance is an example where a forcemay be converted to a displacement based on

the spring constant. For a spring element (it need not actually be a

spring in the form of a coil of wire) the

relationship between force F anddisplacement x is linear and given by,

F = K x


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Contd..

2. Force to displacement conversion:

The spring is fixed at one end and

at the other end hangs a pan. The

object to be weighed is placed inthe pan and the position of the

needle along the graduated scale

gives the weight of the object.

For a coiled spring like the one

shown in the illustration, the spring

constant is given by,


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Contd..

An elastic element

may be used toconvert a force to a

displacement.

Any elastic material

follows Hookes law

within its elastic limit

and hence is a

potential spring

element.


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Contd..

3. Conversion of force to hydraulic pressure:

A piston cylinder arrangement in which the

pressure is converted to hydraulic pressure.

If the piston area is accurately known, thepressure in the hydraulic liquid developed by

the force acting on the piston may bemeasured by a pressure transducer.

This pressure when multiplied by the pistonarea gives the force.


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4. Piezoelectric force transducer: The prefix piezo is a Greek word meaning to

squeeze.

Materials that produce an electric charge when a

force is applied to them exhibit what is known as the

piezoelectric effect..


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What is a Piezoelectric Transducer?

A transducer converts one form of energy into another

In the case of a piezoelectric transducer thetransduction is from mechanical energy to electricalenergy

This signal is proportional to the force acting on thematerial.

Many piezoelectric materials are known to exist Quartz, tourmaline, ceramic (PZT), GAPO4 and

many others


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Example

A cantilever beam made of spring steel (Youngsmodulus 200 GPa) 25 mm long has a width of 2 mmand thickness of 0.8 mm. Determine the springconstant. If all the lengths are subject to measurement

uncertainties of 0.5% determine the percentuncertainty in the estimated spring constant.

What is the force if the deflection of the free end ofthe cantilever beam under a force acting there is 3

mm? What is the uncertainty in the estimated force ifthe deflection itself is measured with an uncertainty of0.5%? Sketch below describes the situation.


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Contd..


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Contd..


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Contd..


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Contd..


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Force Measurement: Load cell

1 24

3

The diagram

represents what

might happen if a

strip of metal were

fitted with fourgauges.

An downward bend

stretches the gauges

on the top and

compresses those on

the bottom.

A load cell may

contain several similar

strain gauges

elements.


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Contd..Proving Ring

P

LVDT

This Load incorporates ring as the elastic element. Thering element can be designed to cover wide range

loads by:

radius,

The thickness, t,

The depth w.

Strain Gauge or LVDT could be employed to measure

displacement related to Force applied. In case of LVDT

compression of the ring ,the relationship between

displacement and Load Pand is given by:

= 1.79 PR3/(Ewt3) = K .P

Where E is modulus of Elasticity of material;

K for given ring is constant = 1.79 R3/(Ewt3)

Out put Volts = Vo= S Vs and S is sensitivity of LVDT

t

R

w

3

3

3

3

1.79

0.56

o s

o

s

SPRv v

Ewt

EwtP v

SR v

=

=


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LVDT


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Measurement of Torque and Power

Torque and power are important quantitiesinvolved in power transmission in rotatingmachines like engines, turbines, compressors,

motors and so on. Torque and power measurements are made

by the use of a dynamometer.

In a dynamometer the torque and rotationalspeed are independently measured and theproduct of these gives the power.


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Torque Measurement: Brake Arrangement

Construction:

A rope or belt is wrapped around the brake drum attached to

the shaft. The two ends of the rope or belt are attached to

rigid supports with two spring balances as shown. The loading

screw may be tightened to increase or loosened to decrease

the frictional torque applied on the drum.

Figure: Schematic of a brake drum dynamometer


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Working:

When the shaft rotates the tension on the two sides will be

different. The difference is just the frictional force applied at

the periphery of the brake drum. The product of this

difference multiplied by the radius of the drum gives the

torque.

Figure: Schematic of a brake drum dynamometer

Torque Measurement: Brake Arrangement


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Contd

The device consists of a magnet which is rotated by the drive

shaft. A speed cup made of aluminum is mounted close to the

rotating magnet with an air gap as indicated.

Figure: Speedometer or tachometer


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Contd..

The speed cup is restrained by a

hair spring and has a pointer

attached to its own shaft that

moves over a dial.

When the magnet rotates due to

the rotation of its own shaft the

speed cup tends to be dragged

along by the moving magnet and

hence experiences a torque andtends to rotate along with it. Figure: Speedometer or tachometer


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Contd..

The speed cup moves and takes up

a position in which the rotating

magnet induced torque is

balanced by the restraining torque

provided by the spring.

Knowing the drive gear speed ratio

one may calibrate the angular

position on the dial in terms of the

rotational speed in rpm. Figure: Speedometer or tachometer


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Tachometer: Centrifugal Action


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Measurement of rotational speed:

Non contact optical rpm meter

This is a non contact method of

rotational speed of a shaft.

However it requires a wheel with

openings to be mounted on the

rotating shaft.

The frequency of interruption of

the beam is directly proportional

to the rpm of the wheel, that is

usually the same as the rpm of theshaft to be measured and the

number of holes provided along

the periphery of the wheel.

Figure: Optical rpm measurement


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mmm force torque strain final

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