Mechanical measurements

SUDHEER NANDI
MECHANICAL MEASUREMENTS
19MET12

Topic covered –II
Measurement of speed:
 Mechanical Tachometers
 Electrical Tachometers
 Stroboscope
 Non contact type of Tachometers.
Stress & strain Measurements:
 Various types- Electrical Strain Gauge.
 Gauge factor
 Method of usage of resistance strain gauge for bending compressive & Tensile strains
 Usage for Measuring torque.
 Strain gauge Rosettes.

What is “Tachometer”?
•Tachometer is used for measuring rotational speed, can be used to measure speed of a rotating shaft.
•Can also be used to measure flow of liquid by attaching a wheel with inclined vanes.
What Are the Different Types of Tachometers?
•Tachometers can be classified on the basis of data acquisition contact or non contact types
•They can also be classified on the basis of the measurement technique time based or frequency
based technique of measurement
•They can also be classified as analog or digital type.
Analog Tachometer
•Has a needle and dial type of interface
•No provision for storage of readings
•Cannot compute average, deviation, etc
Digital Tachometer
•Has a LCD or LED readout
•Memory is provided for storage
•Can perform statistical functions like averaging, etc

Classification Based on Data Acquisition Technique
•Contact type The wheel of the tachometer needs to be brought into contact with the rotating object
•Non Contact type The measurement can be made without having to attach the tachometer to the rotating
object.
Contact Type
•The tachometer has to be in physical contact with the rotating shaft
•Preferred where the tachometer is generally fixed to the machine
•Generally, optical encoder / magnetic sensor is attached to shaft of tachometer
Non Contact Type
•The tachometer does not need to be in physical contact with the rotating shaft
•Preferred where the tachometer needs to be mobile
•Generally, laser is used or an optical disk id attached to rotating shaft and read by a IR beam or laser

Measurement of speed: Mechanical Tachometers
Revolution counter
• Revolution counter is used to measure an average of rational speed instead of instantaneous rotational
speed.
• It consists of a worm gear that is usually attached to a spindle. It has two dials, an inner one and an
outer one.
• The inner dials represent one revolution of the outer dials and the outer dials represent on revolution
of the spindle.
• The tachometer has a stopwatch attached to the revolution counter and is used to indicated time.
• These are limited to low speed engines and measure satisfactory upto 2000-3000r.p.m.
What is Worm Gear and how its go to operate .

Hand speed indicator
• Hand Speed Indicator has an integral stopwatch and counter with automatic disconnect.
• The spindle operates when brought in contact with shaft.
• Counter does not function until start and wind button is pressed to start watch and engage the clutch.
• The instrument indicates average speed over short interval in r.p.m .

Tachoscope
• Tachoscope consists of revolution counter for timing device.
• The two components are integrally mounted and start simultaneously when contact point is pressed
against rotating shaft.
• The rotational speed is computed from reading of counter and timer.
• Tachometer can be used to measure speeds up to 5000r.p.m.

Centrifugal tachometer
•Centrifugal Tachometer operates on principle that centrifugal force is proportional to speed of rotation.
• It consists two balls arranged about spindle.Centrifugal force developed by these balls compress
spring as function of speed positions pointer.
• They are suitable for 4000r.p.m.
w = angular speed, 1 = shaft,
2 and 3 = masses, 4 = displacement-sensitive element.
Technical LEGO: Centrifugal tachometer - Bing video
Centrifugal Tachometer - YouTube

Resonance (vibrating reed) tachometer
• In Vibrating Read Tachometers a series of consecutively timed steel rods are used to determine speed
on basis of vibrations created by machine.
•One end of rod is fixed to a base which is kept in contact with any non-moving part of machine and
other is attached to calibrated scale.
• These can be used in speed range of 600-10000 rpm
Vibrating reed tachometer - Bing vide
How To Use a Tachometer - Bing vid

Measurement of speed: Electrical Tachometers
Eddy current or drag cup tachometer
•An eddy-current tachometer uses the interaction of the magnetic fields generated by a permanent
magnet and a rotor, whose speed of rotation is proportional to the eddy currents generated.
• The currents tend to deflect a disk, which is mounted on the shaft and restrained by a spring,
through a certain angle.
• The deflection of the disk, which is rigidly connected to a pointer, is indicated on a dial.
ANUNIVERSE 22 - EDDY CURRENT OR DRAG CUP
TACHOMETER WORKING - Bing video

D.C. Tachogenerator
• In a D.C. generator the e.m.f generated depends upon the following two factors:
(i) Field excitation
(ii) Speed
• If for the field system permanent magnet pole pieces are used, then the generated voltage depends
only on the speed. Hence the speed can be computed by measuring the generated e.m.f.
• The shaft whose speed is to be measured is coupled to the armature.
• A moving coil voltmeter is connected across the brushes to measure the generated voltage. The
variable resistance R is incorporated to limit the current through the voltmeter.
• Since voltage is proportional to speed, the voltmeter may be calibrated in terms of speed (r.p.m.).

A.C. Tachogenerator
The inherent demerits associated with D.C. tachometer generator, due to the provision of commuter
and brushes,are eliminated in A.C. tachometer generator.
 It consists of, like an alternator, a stationary armature (stator) and a rotating field system (rotor).
Owing to the generation of e.m.f in a stationary coil on a stator, commutation problems no longer exist.
 The alternating e.m.f. induced in the stationary coil is rectified, and the output D.C. voltage is
measured with the help of a moving coil voltmeter (V).
 The ripple content of the rectified voltage is smoothened by the capacitor filter (C).
•As the speed depends on both the amplitude of
the voltage and frequency, anyone of them can
be used as a measure of the speed.
•In an A.C. tachometer, it is the induced voltage
that is considered as the required
•parameter.

Magnetic pickup tachometer
•A coil wounded on permanent magnet not on iron core, this configuration enable us to measure
rotational speed of the systems.
• In the construction of variable reluctance sensor, we use ferromagnetic gearwheel. As the gearwheel
rotates, change in magnetic flux take place in the pickup coil which further induces voltage. This
change in magnitude is proportional to the voltage induced in the sensor.
N
S

Pickup tachometer
•Various pick-up devices can be used in conjunction with a digital counter to give a direct reading of
speed.
• An inductive pick-up tachometer is shown in Figure (a).
• As the individual teeth pass the coil they induce an e.m.f. pulse which is appropriately modified and
then fed to a digital counter.
• A capacitive pick-up tachometer is shown in Figure (b). As the rotating vane passes between the plates
a capacitance change occurs in the form of a pulse.
• This is modified and then fed to the digital counter.
https://www.youtube.com/watch?v=37oJtcUTpL8

Photo-electric tachometer
• It consists of a opaque disc mounted on the shaft whose speed is to be measured. The disc has a
number of equivalent holes around the periphery. On one side of the disc there is a source of light (L)
while on the other side there is a light sensor (may be a photosensitive device or photo-tube) in line
with it (light-source).
• On the rotation of the disc, holes and opaque portions of the disc come alternatory in between the light
source and the light sensor. When a hole comes in between the two, light passes through the holes and
falls on the light sensor, with the result that an output pulse is generated. But when the opaque portion
of the disc comes in between, the light from the source is blocked and hence there is no pulse output.
• Thus whenever a hole comes in line with the light source and sensor, a pulse is generated. These
pulses are counted/measured through an electronic counter.

• The number of pulses generated depends upon the following factors:
i. The number of holes in the disc; ii. The shaft speed.
• Since the number of holes are fixed, therefore, the number of pulses generated depends on the speed
of the shaft only. The electronic counter may therefore be calibrated in terms of speed (r.p.m.).
Computer mouse
https://www.youtube.com/watch?v=HksPmdwazT0

Measurement of speed:Stroboscope
•The instrument operates on the principle that if a repeating event is only viewed when at one particular
point in it’s cycle it appears to be stationary. A mark is made on rotating shaft, and a flashing light is
subjected on the shaft. The frequency of the flashing is one very short flash per revolution.
• To determine the shaft speed we increases the frequency of flashing gradually from small value until
the rotating shaft appears to be stationary, then note the frequency. The frequency then doubled, if there
is still one apparent stationary image, the frequency is again doubled. This continued until two images
appear 180 degrees apart. When first appear for these two images the flash frequency is twice the speed
of rotation.
•Stroboscopes are used to measure angular speed between 600 to 20000 rpm .
• It’s advantage is that it doesn’t need to make contact with the rotating shaft.
https://youtu.be/6eQQNeqidD4

Comparison Between Analog and Digital Tachometers
Analog Tachometer Digital Tachometer
Has a needle and dial type of interface Has a LCD or LED readout
No provision for storage of readings Memory is provided for storage
Cannot compute average, deviation, etc Can perform statistical functions like averaging, etc
Classification Based on Data Acquisition Technique
• Contact type – The wheel of the tachometer needs to be brought into contact with the rotating object
• Non Contact type – The measurement can be made without having to attach the tachometer to the
•rotating object
Classification Based on Measurement Technique
• Time Measurement – The tachometer calculates speed by measuring the time interval between the
incoming pulses
•Frequency Measurement – The tachometer calculates speed by measuring the frequency of the incoming
pulses

Comparison Between Contact and Non Contact Tachometers
Contact Type Non Contact Type
The tachometer has to be in physical contact
with the rotating shaft
The tachometer does not need to be in physical
contact with the rotating shaft
Preferred where the tachometer is generally
fixed to the machine
Preferred where the tachometer needs to be
mobile
Generally, optical encoder / magnetic sensor is
attached to shaft of tachometer
Generally, laser is used or an optical disk id
attached to rotating shaft and read by a IR
beam or laser
Calibration
Why calibrate?
• Wrong calibration = Wrong readings
• Calibration compensates for ageing, wear and tear and other degrading effects
How to calibrate?
• Calibration is done by comparing the reading from tachometer to a standard speed
• Necessary changes are made so that the actual reading matches the desired reading

Comparison Between Time and Frequency Based Measurement
Time Based Frequency based
 The tachometer calculates speed by
measuring the time interval between pulses
 The tachometer calculates speed by
measuring the frequency of pulses
 More accurate for low speed measurement  More accurate for high speed measurement
 Time to take a reading is dependant on the
speed and increases with decrease in speed
 Time to take a reading is independent of
speed of rotation
 The resolution of the tachometer is
independent of the speed of the
measurement
 The resolution of the tachometer depends on
the speed of the rotating shaft

Stress & strain Measurements:Various types- Electrical Strain Gauge.
STRESS : pressure or tension exerted on a material object.
STRAIN : A force tending to pull or stretch something to an extreme or damaging degree

What is a Strain Gauge
A strain gauge is a resistor used to measure strain on an object. When an external force is applied on an
object, due to which there is a deformation occurs in the shape of the object. This deformation in the
shape is both compressive or tensile is called strain, and it is measured by the strain gauge. When an
object deforms within the limit of elasticity, either it becomes narrower and longer or it become shorter
and broadens. As a result of it, there is a change in resistance end-to-end.
The strain gauge is sensitive to that small changes occur in the geometry of an object. By measuring the
change in resistance of an object, the amount of induced stress can be calculated.
Stress & strain Measurements: Various types- Electrical Strain Gauge.
Use of Strain Gauge
In the field of mechanical engineering development.
To measure the stress generated by machinery.
In the field of component testing of aircraft like; linkages, structural damage etc.

Various types- Electrical Strain Gauge.
• The Electrical strain gauge is a passive, resistive transducer which converts the mechanical
elongation and compression into a resistance change.
• This change in resistance takes place due to variation in length and cross sectional area of the gauge
wire, when an external force acts on it.
The Various types- Electrical Strain Gauge
1. Wire gauge
a) Unbounded
b) Bonded
c) Foil type
2. Semiconductor gauge

Electrical Strain Gauge.
• A strain gauge is a thin, wafer-like device that can be attached to a variety of materials to measure
applied strain.
Working on Wheatstone Bridge
l
l
R
R
K




2
1

K
The sensitivity of a strain gauge is described in terms of a characteristic called the
gauge factor, defined as unit change in resistance per unit change in length
[OR]
Gauge factor is related to Poisson's ratio μ

Stress & strain Measurements: Electrical Strain Gauge.

.
K
R
R


Resistance =R(Ω)
Changed resistance
=∆R(Ω)
Strain=€ ;Gage Factor=K

Stress & strain Measurements:Electrical Strain Gauge.
UNBONDED STRAIN GAUGE
• An unbounded meter strain gauge is shown in fig
• This gauge consist of a wire stretched between two point in an insulating medium such as air. The wires
may be made of various copper, nickel, crome nickle or nickle iron alloys.
• In fig the element is connected via a rod to diaphragm which is used for sensing the pressure. The wire
are tensioned to avoid buckling when they experience the compressive force.
• The unbounded meter wire gauges used almost exclusively in transducer application employ preloaded
resistance wire connected in Wheatstone bridge as shown in fig.
• At initial preload the strain and resistance of the four arms are nominally equal with the result the output
voltage of the bridge is equal to zero.
Application of pressure produces a small displacement , the displacement increases a tension in two wire
and decreases it in the other two thereby increase the resistance of two wire which are in tension and
decreasing the resistance of the remaining two wire .
• This causes an unbalance of the bridge producing an output voltage which is proportional to the input
displacement and hence to the applied pressure .

UNBONDED STRAIN GAUGE

BONDED STRAIN GAUGE
• The bonded metal wire strain gauge are used for both stress analysis and for construction of
transducer. A resistance wire strain gauge consist of a grid of fine
• resistance wire. The grid is cemented to carrier which may be a thin sheet of paper Bakelite or Teflon.
• The wire is covered on top with a thin sheet of material so as to prevent it from any mechanical
damage.
• The carrier is bonded with an adhesive material to the specimen which permit a good transfer of
strain from carrier to grid of wires.

METAL FOIL STRAIN GUAGE
silicon and germanium for their construction
± 0.01~0.002 precision

STRAIN GAUGE MEASUREMENT: SPECIAL APPLICATIONS
1.High temperature applications
•tie rods for the steel industry
2.Applications on special material (composite materials, stone, etc.)
•carbon fiber paddle handle
•rear rotor helicopter blade
•marble columns
•specimens stone (marble and tuff)
•Human tooth
5.Installation on pressurized components
•dryer cylinder for paper industry
•manifold prototype
•diesel engine common rail
•centrifugal compressor casing
•moist-heat industrial sterilizers for food industry
•CNG tanks for bus
6.Transducers (load cells, etc.)
7.Installations submerged
•centrifugal compressor casing
•centrifugal pump
8.Thermal characterization of strain gauge installations
•specimen tie rod for steel industry
•steel specimens for thermal characterization
•natural ventilation laboratory oven
3.Miniaturized application
•Metering rod for internal-combustion
engine
•Needle for dental use
4.Installations on rotating components
•couplings (for torque measurements)
•centrifugal compressor impellers
•spindle coupling metal rolling mill

STRAIN GAUGE MEASUREMENT: APPLICATION FIELDS
The strain gage through the SG is a method for points suitable for the measurement of elastic and
plastic strain on any material. The typical resolution is 1 μm/m, while the measurement range is
typically between 5000 and 50000 μm/m (up to 200,000 μm/m with special SG). The method is
suitable for the strain measurements even at low and high temperatures and in hostile environment.
This technique is widely used in many fields, among which:
1. stress experimental analysis
2. residual stress analysis
3. torque and tensional vibration measurements
RELATIONSHIP BETWEEN ELECTRICAL RESISTANCE AND STRAIN
Ro
R
K


1

where:
K gauge factor of the SG( Strain Gauge)
ΔR change in resistance of the installed
SG
R0 initial resistance of the installed SG.
 experimental modal analysis
• stresses dynamic analysis
• pressure vessels

Stress & strain Measurements: Gauge factor
Gauge factor G:
The sensitivity of the strain gauge is expressed in the terms of a characteristic called the Gauge
factor.
Strain wire Gauge factor G is the ratio between relative change in resistance due to the change in
relative length.
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
G
L
L
R
R
L
L
R
R
L
L
R
R
L
L
R
R












where:
G gauge factor of the SG( Strain Gauge)
ΔR change in resistance of the installed SG
R initial resistance of the installed SG.
ΔL change in length of the installed SG
L change in length of the installed SG

Stress & strain Measurements: Gauge factor
L
L
R
R



G

Stress & strain Measurements: Method of usage of resistance strain gauge for
bending compressive & Tensile strains

Stress & strain Measurements: Usage for Measuring torque

Bonded and Unbounded Strain Gauges
Working Principle:
The strain gauge working principle is based on the fact that the electrical resistance of
materials varies with deformation. A strain gauge is an example of a passive transducer that
converts the mechanical displacement into electrical quantity.
The resistance of the conductor depends on the length and cross-sectional area.
L = length of the conductor or semiconductor element.
A = Cross sectional area.
ρ = Resistivity.
A
ρL
R 

Bonded strain gauge :
Bonded strain gauges are so-called because they are attached to the elastic element surface. The most
commonly used are bonded resistance type strain gauges. They are primarily used for strain analysis.
In bonded resistance wire strain gauges resistance element is cemented to the base which may be a
thin sheet of paper or a thin sheet of bakelite or Teflon. The bonded strain gauge is connected to the
Wheatstone bridge circuit.
WIRE STRAIN GAUGE:
The resistance element is in the form of wire foil or film of
the material.
In a metal bonded strain gauge a fine wire element, about
0.025 mm or less in diameter is looped back and forth on
the base carrier or mounting plate. The base is cemented to
the member subjected to the stress.
The grid fine wire is cemented on a carrier which may be a
thin sheet of paper bakelite or Teflon.

METAL FOIL :
The strain is detected by using a metal foil. The metal foil is pasted on one side of the plastic The leads
are soldered to the metal foil for connecting the Wheatstone bridge.
The metal and alloys used for the foil or wire are Constantan(Cu-Ni), Nichrome V(Ni-Cr),
Isoelastic(Fe-Ni-Cr-Mn-Mo), Platinum-Tungsten(Pt-W). Metal Foil strain gauges exhibit a higher
gauge factor than wire foil strain gauges.
ROSETTE STRAIN GAUGES:

Stress & strain Measurements: Strain gauge Rosettes.
A strain gage rosette is, by definition, an arrangement of two or more closely positioned gage grids,
separately oriented to measure the normal strains along different directions in the underlying surface of
the test part. Rosettes are designed to perform a very practical and important function in experimental
stress analysis
To increase the accuracy of a strain rosette, large angles are used. A common rosette of three gages is
where the gages are separated by 45 o, or θa = 0 o, or θb = 45 o, or θc = 90 o. The three equations can
then be simplify to

A wire strain gage can effectively measure strain in only one direction. To determine the three
independent components of plane strain, three linearly independent strain measures are needed, i.e.,
three strain gages positioned in a rosette-like layout.
Consider a strain rosette attached on the surface with an angle a from the x-axis. The rosette itself
contains three strain gages with the internal angles b and g, as illustrated on the right.
Suppose that the strain measured from these three strain gages are ea, eb, and ec, respectively.
The following coordinate transformation equation is used to convert the longitudinal strain from each
strain gage into strain expressed in the x-y coordinates,
These equations are then used to solve for the three unknowns, ex, ey, and exy.

The formulas use the strain measure εxy as opposed to the engineering shear strain γxy, . To use γxy,
the above equations should be adjusted accordingly.
The free surface on which the strain rosette is attached is actually in a state of plane stress, while
the formulas used above are for plane strain. However, the normal direction of the free surface is
indeed a principal axis for strain. Therefore, the strain transform in the free surface plane can be
applied.
Case 1: 45º strain rosette aligned with the x-y axes, i.e., a = 0º, b = g = 45º.

Case 2: 60º strain rosette, the middle of which is aligned with the y-axis, i.e., a = 30º, b = g = 60º

REFERENCES
1. Experimental Methods for Engineers / Holman/McGraw Hill.
2. Mechanical Measurements / Sirohi and Radhakrishna / New Age.
3. Instrumentation & Mech. Measurements /A.K. Tayal /Galgotia Publications.
4. Instrumentation and Control systems! S.Bhaskar/Anuradha Agencies.
5. Instrumentation, measurement & analysis IB.C.Nakra & K.K.Choudhary/
TMH.
6. Principles of Industrial Instrumentation and Control Systems Chennakesava R
Alavala/ Cengage Learning.
7. Measurement systems: Application and design, Doeblin Earnest. O. Adaptation
by Manik and Dhanesh/ TMH.
8. Mechanical and Industrial Measurements / R.K. Jain/ Khanna Publishers.
9. Mechanical Measurements / BeckWith, Marangoni,Linehard, PHI / PE.

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