MMM Force Torque Strain Final
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Transcript of 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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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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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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