The document discusses different types of instruments used to measure acceleration, vibration, and density. It describes LVDT, piezoelectric, and strain gauge accelerometers. It also discusses vibration sensors, including accelerometers, strain gauges, velocity sensors, and gyroscopes. Finally, it covers various densitometers for measuring liquid and gas density, including displacement, float, and ultrasonic densitometers.

1. UNIT-II
MEASUREMENT OF
ACCELERATION,
VIBRATION AND
DENSITY

2. MEASUREMENT OF ACCELERATION, VIBRATION
AND DENSITY
Accelerometers: LVDT, Piezoelectric, Strain gauge and Variable reluctance type
accelerometers - Mechanical type vibration instruments - Seismic instruments as
accelerometer – Vibration sensor - Calibration of vibration pickups - Units of density and
specific gravity – Baume scale and API scale – Densitometers: Pressure type densitometers,
Float type densitometers, Ultrasonic densitometer and gas densitometer.

3. LVDT

4. WORKING
A type of accelerometer takes advantage of the natural linear displacement measurement of the
LVDT to measure mass displacement.
LVDT is Linear Variable differential transducer which works on magnetic principle. In these
instruments, the LVDT core itself is the seismic mass.
Displacements of the core are converted directly into a linearly proportional ac voltage.
These accelerometers generally have a natural frequency less than 80 Hz and are commonly
used for steady-state and low-frequency vibration.
Fig. shows the basic structure of such an accelerometer.

7. EXPLANATION
The LVDT accelerometer consists of one primary and two secondary windings which are
placed on either side of central core.
The two ends of the core are connected with spring steel but these are already placed in a
casing.
If a core is exactly placed at the center, the voltage produced between primary and
secondary windings will be exactly equal; this voltage is called as static field voltage.
If any vibration occurs on the casings of the LVDT accelerometer, the core will either
move upward or downward.
Owing to this, the voltage is induced in the secondary coil according to the movement of
the core.
Now the difference in voltage arises in the output terminal.
This output voltage is directly proportional to the vibration or acceleration.

8. LVDT ACCELEROMETER
The linear Variable Differential Transformer (LVDT) described in pressure measurement section
offers another convenient means for measurement of the relatives displacement between the
seismic mass and accelerometer housing.
Such devices have somewhat higher natural frequencies than potentiometer devices (270 to 300
Hz) but are still restricted to applications with lower frequency response requirments.
The LVDT however has a much lower resistance to motion than the potentiometer and is capable
of much better resolution.
In addition, the seismic accelerometer using an LVDT can be considerably lighter in construction
than one with a potentiometer.

10. ELECTRICAL RESISTANCE STRAIN GAUGE
The electrical resistance strain gauge discussed in earlier chapters may also be used for
displacement sensing in a seismic instrument.
Consider the schematic in fig. the seismic mass is mounted on a cantilever beam.
On each side of the beam a resistance strain gauge is mounted to sense the strain in the beam
resulting from the vibrational displacement of the mass.
Damping for the system is provided by the viscous liquid, which fulls the housing.
The outputs of the strain gauges are connected to an appropriate bridge circuit, which is used
to indicate the relative displacement between the mass and the housing frame.
The natural frequencies of such systems are fairly low and roughly comparable to that of the
LVDT systems.

11. Unbonded-strain-gauge accelerometers use the strain wires as the spring element
and as the motion tranducer.
They are useful for general-purpose motion measurement and for vibration up to
relatively high frequencies (17 to 800 hz)

13. Bonded-strain gauge accelerometers generally use a mass supported by thin flexure beam,
wit strain gauges cemented to the beam so as to achieve maximum sensitivity, temperature
compensation, and insensitivity to cross-axis and angular acceleration.
Silicon-oil damping is widely used.
Semiconductor strain gauges (Piezoresistive sensors) are widely used as strain gauge
sensors in cantilever-beam/ mass types of accelerometers.
The semiconductor strain gauge type consists of semiconductors bonded to a mass whose
deformation under acceleration forces is reflected as a change of resistance.
The resistance measurement is made by means of a wheatstone bridge with the elements

15. PIEZOELECTRIC
ACCELEROMETER

16. The induced charge on the crystal is proportional to the impressed force and it is given by,
Q=dF
Where, Q=charge in coulombs
d = Piezoelectric constant
F = Force in Newtons
The output voltage of the crystal is given by E = gtp
Where
t = crystal thickness in meters
P = impressed pressure in Newtons/m2.
g=voltage sensitivity (g=d/ε)

17. VARIABLE- RELUCTANCE
ACCELEROMETER

19. The primary coils set up a flux dependent on the reluctance of the magnetic path. The main
reluctance is the air gap. When the core is in the neutral position, the flux is same for both
halves of the secondary coil; and since they are connected in series opposition, the net output
voltage is zero.
A motion of the core increases the reluctance (air gap) on one side and decreases it on the other,
causing more voltage to be induced into one half of the secondary coil than the other and thus a
net output voltage.
Motion in the other direction causes the reverse action, with a 180° phase shift occurring at
null. The output voltage is half wave, non-phase sensitive rectified (demodulated) and filtered
to produce an output of the same form as the acceleration input. If the 2.5 V output for zero-
acceleration is objectionable, it can be bucked out with a 2.5 V battery of opposite polarity
connected externally to the accelerometer.
The actual full-scale motion of the mass in this particular instrument is just a few thousandths
of 1m, which gives a displacement sensitivity for the variable-reluctance element of almost 500
V/cm.

20. EDDY CURRENT PROXIMITY
SENSOR AS VIBRATION PICK
UP
As the proximity detectors measure the distance between objects, they can be used to measure
frequencies and amplitude of vibrations.
To detect the proximity of conducting materials, an eddy current probe can be used.
The schematic arrangement of such a probe is shown in fig.
Two identical coils are wound on the probe, and these, together with the resistances, complete a
bridge circuit.
With no conducting surface near the probe, the bridge is in balance.
When a conducting object is brought near the probe, the bridge becomes unbalanced and the
output signal is in proportion to the proximity of the object.

22. The excitation is a high frequency signal which induces eddy currents in the test
object.
The excitation is a high frequency signal which induces eddy currents in the test
object.
These currents produce losses in the bridge circuit in such a way that bridge
imbalance is related to the proximity of the object.
The output signal amplitude is related to the vibration or displacement amplitude,
and the frequency of vibration.

23. VIBRATION SENSOR
At present in the industry like research and development, the ability of monitoring,
measuring as well as analyzing the vibration is very important.
Unfortunately, the suitable techniques for making a measurement system for
vibration with precise & repeatable are not always clear to researchers with the
shades of test tools & analysis of vibration.
There are some challenges related while measuring the vibration which includes a
selection of suitable component, the configuration of the system, signal conditioning,
analysis of waveform and setup.
This article discusses what is a vibration sensor, working principle, types, and
applications

24. WHAT IS A VIBRATION SENSOR?
The vibration sensor is also called a piezoelectric sensor. These sensors are flexible
devices which are used for measuring various processes.
This sensor uses the piezoelectric effects while measuring the changes within
acceleration, pressure, temperature, force otherwise strain by changing to an
electrical charge.
This sensor is also used for deciding fragrances within the air by immediately
measuring capacitance as well as quality.

25. VIBRATION SENSOR WORKING
PRINCIPLE
The working principle of vibration sensor is a sensor which operates based on different
optical otherwise mechanical principles for detecting observed system vibrations.
The sensitivity of these sensors normally ranges from 10 mV/g to 100 mV/g, and there
are lower and higher sensitivities are also accessible. The sensitivity of the sensor can
be selected based on the application.
So it is essential to know the levels of vibration amplitude range to which the sensor will
be exposed throughout measurements.

26. VIBRATION SENSOR TYPES
The types of vibration sensors include the following.
Accelerometer Sensor
Strain Gauge Sensor
Velocity Sensor
Gyroscope Sensor
Pressure or Microphone Sensor
Laser Displacement Sensor
Capacitive Displacement or Eddy Current
Vibration Meter
Vibration Data Logger

27.  The applications of vibration sensors include different industries for measuring the vibration. The exclusive
industrial characteristics will decide sensor characteristics.
 For instance, this sensor is used in industries like wind power and mining for slow rotation of turbines with 1 Hz
or less frequency response.
 In disparity, the industries like gas and oil need high frequency ranges from 10 Hz to 10 kHz uses these
sensors to handle with the speed rotation of gears and turbines.
 The industries which use the vibration sensor mainly include food & beverage, mining, metalworking, gas & oil,
paper, wind power, power generation, etc.
 Thus, this is all about vibration sensor. From the above information, finally, we can conclude that vibration is a
difficult measurement which includes different parameters. Based on the goals of vibration measurement, the
measurement technologies have benefits and drawbacks. These sensors are mainly used for measuring,
analyzing, displaying, proximity, acceleration, displacement, etc.
Applications

28. DENSITY
•Measurement of density becomes necessary in most industrial applications. Density measure
ments are done for all the three states of matter namely solids, liquids and gases.
•By measur ing the density of a process steam, one can determine its concentration composition,
or, in the case of fuels, its calorific value. Density measurements is also necessary to convert
volumetric flow measurements into mass flow information.
•For measuring the mass flow of gases, direct density measurement can be simpler and more
accurate than the indirect calculation which must consider pressure, temperature, super
compressibility, and humidity.
•The density of solids involves the weighing of a fixed volume. Density measurements are done
for slurry, viscous or clean process materials. Depending on the nature of the process media
(slurry, viscous, clean, solid, liquid, or gas etc.) densitometers are to be properly selected.

29. UNITS OF DENSITY, SPECIFIC
GRAVITY AND VISCOSITY
Density is defined as the quantity of matter per unit volume. Kg per cubic meter of any
object can be called as specific weight or 'weight density' of that object.
A second term known simply as 'density' is used to indicate the mass per cubic meter.
Though they refer to two entirely different things, in metric system of units, both are
interchangeably used as the weight of one kg mass is taken as one kgf. Kg is used as a unit
on many occasions for both mass and weight (or force), though Newton is the unit of
weight or force in metric units. (one kgf = 9.8 Newtons.)

30. RELATIVE DENSITY
Relative density, or specific gravity, is defined as the ratio between
the density of a process material to that of water or air at specified
conditions. Being a ratio, specific gravity has no units associated with
it. Water is used as reference for solid and liquid medias because of
its common occurrence.

31. Materials having specific gravities less than one are lighter than water, where as those having
specific gravities greater than one are heavier than water.
Both density and specific gravity characterise the same physical property of the process
media, and they are meaningful only if defined at stated temperatures.
In the case of specific gravity, the temperatures might be different for the process and the
reference fluid, which is acceptable, but must be clearly stated.
For example, a specific gravity table might list a process fluid as having 0.980/40 specific
gravity, which means that this liquid at 80°F will have a density of 0.9 times that of water at
40°F.

32. For Gases, the specific gravity is based on air at standard conditions (i.e, at STP-Stand ard temperature of 0°C and
pressure of 760 mmHg).
For ideal gases, the ratio of molecular weights equals specific gravity.Various Industrial Specific Gravity Scales.
The more common materials and liquids all have had their specific gravities determined entirely on the basis of
the ratio of their weights to the weight of an equal volume of water. (Similarly for gases with reference air).
But several specific gravity scales depart from this basis, and their values are not based on these simple ratios.
Some of the commonly used spe cific gravity units are defined below.

36. DENSITOMETER

37. DISPLACEMENT AND FLOAT TYPE DENSITOMETERS
(FOR LIQUID DENSITY)
When an object of a fixed volume and a known density is submerged in a process fluid, the
resulting buoyant force can be detected as an indication of process density.
If the submerged float is lighter than the process fluid, the buoyant force will try to lift out
of the fluid and a force will be needed to keep the float submerged.
If the displacer is heavier than the process fluid, it will have a tendancy to sink and a force
will be required to hold it in position.
As the density of the process fluid increases, the apparent weight of the displacer will drop

38. CONVENTIONAL DISPLACER- TYPE
DENSITOMETER
Archimedes principle states that a body wholly or partially immersed in a fluid is buoyed up by a force
equal to the weight of the fluid displaced.
The sample fluid enters around the center section of the cage, through a piezometer ring which
eliminates the velocity effects of the flowing fluid.
For less velocity(<0.6 m/minutes) the piezometer ring is not essential.
The sample fluid leaves the case through the top and bottom connections.
It is recommended to keep these flows constant by the use of purgemeters.
The above system applies when the density measurement is made in a sample bypass of the process
piping.
If the density is to be measured in tanks or vessels, the flange mounted dsplacer illustrated below

39. TORQUE DISPLACER TUBE

40. DISPLACER DENSITY
SENSOR

41. SIDE MOUNTED DISPLACER
The sizing of the displacer has to be done taking the standard
force range of the displacer and the maximum and minimum
values of the density of process fluid into account.

42. CHAIN – BALANCED FLOAT
DENSITOMETER
The submerged float and chain assembly
displaces a fixed fluid volume.
Float buoyancy is a function of liquid density and
therefore an increase in density causes the float to
rise.
As it rises it will support a larger portion of the
calibrated chain, the weight of which cancels out
the increase in buoyancy so that a new equilibrium
condition is achieved.
The new float position is an indication of fluid
density.

43. FORCE BALANCE,
DIAPHRAGM SEATED
DISPLACEMENT DETECTOR

44. ANGULAR POSITION
DENSITOMETER

45. The process fluid sample flows continuously through the detector at a constant rate. The
gauge chamber contains three displacer floats, each of different density and volume.
The solid displacers are spaced 90 to 100 degrees apart and assembled to a common shaft.
Each fluid density sample positions the shaft and displaces at a precise angular position.
The assembly rotation is a function of float position and buoyant force.
By having the three displacers moments in balance, the assembly is in equilibrium always.
The angular position of the assembly is transmitted to the electrical components through
magnetic coupling.
The output signal to remote readout devices is available in either analog or digital form.

46. HYDROMETERS
The hydrometer element consists of a weighted float with a small-diameter indicator stem
attachment at the top as shown in Fig. 4.33.
The stem is graduated in any of the density its discussed earlier.
According to Archimedes principle, when a body is immersed in a fluid it loses its weight equal
to the weight of the liquid which is displaced.
The hydrometer element is a constant-weight body which, if immersed in fluid with differing
densites, will displace differing volumes of fluid.
Therefore, the degree of stem scale submersion is an indication of fluid density.
Readings are made at the point where the stem emerges from the liquid.
One of the simplest in-line density indicators is illustrated in Fig. 4.34.
It consists of a transparent glass tee with a hydrometer element. The process fluid enters from
bottom and overflows to maintain constant level in the tee.
A thermometer is added for temperature correction purpose.

47. HYDROMETERS