UXDE dot Net Wordpress Themes

# Posts Selected From the Category "Transducers"

Strain Gauge is a passive transducer that converts a mechanical elongation or displacement produced due to a force into its corresponding change in resistance R, inductance L, or capacitance C. A strain gauge is basically used to measure the strain in a work piece. If a metal piece is subjected to a tensile stress, the metal length will increase and thus will increase the electrical resistance of the material. Similarly, if the metal is subjected to compressive stress, the length will decrease, but the breadth will increase. This will also change the electrical resistance of the conductor. If both these stresses are limited within its elastic limit (the maximum limit beyond which the body fails to regain its elasticity), the metal conductor can be used to measure the amount of force given to produce the stress, through its change in resistance.

#### Strain Gauge Transducer

The device finds its wide application as a strain gauge transducer/sensor as it is very accurate in measuring the change in displacement occurred and converting it into its corresponding value of resistance, inductance or capacitance. It must be noted that the metal conductor which is subjected to an unknown force should be of finite length.

#### Types

Strain gauge transducers are broadly classified into two. They are

1. #### Electrical Resistance Type Strain Gauge

In an electrical resistance strain gauge, the device consists of a thin wire placed on a flexible paper tissue and is attached to a variety of materials to measure the strain of the material. In application, the strain gauge will be attached to a structural member with the help of special cement. The gauge position will be in such a manner that the gauge wires are aligned across the direction of the strain to be measured. The wire used for the purpose will have a diameter between 0.009 to 0.0025 centimeters. When a force is applied on the wire, there occurs a strain (consider tensile, within the elastic limit) that increases the length and decreases its area. Thus, the resistance of the wire changes. This change in resistance is proportional to the strain and is measured using a Wheatstone bridge.

A simple Wheatstone bridge circuit is shown in the figure below. It can be set in three different ways such as – full bridge, half bridge or quarter bridge. A full bridge will have all four of its gauges active. The half bridge will have two of its gauges active and thus uses two precise value resistors. The quarter bridge will have only one gauge and the rest of the resistors will be precise in value.

Wheatstone Bridge

A full bridge circuit is used in applications where complimentary pair of strain gauges is to be bounded to the test specimen. In practice, a half bridge and full bridge circuit has more sensitivity than the quarter bridge circuit. But since, the bonding is difficult, a quarter bridge circuits are mostly used for strain gauge measurements. A full bridge circuit is said to be more linear than other circuits.

An external supply is given to the bridge as shown in the diagram. Initially, when there is no application of strain, the output measurement will be zero. Thus, the bridge is said to be balanced. With the application of a stress to the device, the bridge will become unbalanced and produces an output voltage that is proportional to the input stress.

The application of a full bridge and quarter bridge strain gauge circuit is shown in the figure below.

Quarter And Full Bridge Strain Gauge Circuit

A quarter bridge output corresponding to the application of a force is shown below. Initially, the circuit will be balanced without the application of any force. When a downward force is applied, the length of the strain gauge increases and thus a change in resistance occurs. Thus an output is produced in the bridge corresponding to the strain.

Quarter Bridge Strain Gauge Circuit-Working

The wire strain gauge can be further divided into two. They are bonded and unbonded strain gauge.

As shown in the figure below, an unbounded strain gauge has a resistance wire stretched between two frames. The rigid pins of the two frames are insulated. When the wire is stretched due to an applied force, there occurs a relative motion between the two frames and thus a strain is produced, causing a change in resistance value. This change of resistance value will be equal to the strain input.

Unbonded Strain Gauge

A bonded strain gauge will be either a wire type or a foil type as shown in the figure below. It is connected to a paper or a thick plastic film support. The measuring leads are soldered or welded to the gauge wire. The bonded strain gauge with the paper backing is connected to the elastic member whose strain is to be measured.

Bonded Type Strain Gauges

According to the strain to be measured, the gauges can be classified as the following.

• Uniaxial/Wire Strain Gauge

The figure of such a strain gauge is shown above. It mostly uses long and narrow sensing elements so as to maximize the length of the strain sensing material in the desired direction. Gauge length is chosen according to the strain to be calculated.

Gauge Configurations

• Biaxial Strain Gauges

When the measurement of strain is to be done in two directions (mostly at right angles), this method is used. The basic structure for this is the two element 90 planar rosette or the 90 planar shear/stacked foil rosette. The gauges are wired in a Wheatstone bridge circuit to provide maximum output. For stress analysis, the axial and transfers elements have different resistances which can be selected that the combined output is proportional to the stress while the output of the axial element alone is proportional to the strain. The figure is given below.

• Three Element Rosettes

It is divided into two types – three element 60delta rosette strain gauge and three element 45planar rectangular rosette. They are used in applications where both the magnitude and direction of the applied strains are to be found out. Both the figures are shown below. The 60 rosette is used when the direction of the principal strain is unknown. The 45 rosette is used to determine a high angular resolution, and when the principal strains are known.

2.   Semiconductor Strain Gauge

This is the most commonly used strain gauge as a sensor, although the bonded type may also be used in stress analysis purposes. The bonded type is usually made in wafers of about 0.02 centimeters in thickness with length and resistance values nearly equal to the wire gauge. It uses either germanium or silicon base materials to be made available in both n-type or p-type. The p-type gauges have a positive gauge factor while the n-type gauges have a negative gauge factor. Temperature dependence of gauge factor is governed by the resistivity of the material. The large value of the gauge factor in semiconductor gauges is attributed to the piezoresistance effect in such materials.

#### Variable Inductance Type Strain Gauge

The basic arrangement of a variable inductance strain gauge is shown below. This type of strain gauge is very sensitive and can be used to measure small changes in length – as small as 1 millionth of an inch. Thus, it is highly applicable as a displacement transducer. The member whose strain is to be measured is connected to one end of a moveable iron armature. The long part of the armature is placed between the two cores with wires coiled in between. If the strain produced makes the armature move towards the left core (core 1), it increases the inductance of the left hand coil, that is, coil 1 and decreases the inductance of coil 2. These two coils produce the impedance Z1 and Z2 in the bridge circuit. This produces an output voltage E, which is proportional to the input displacement and hence proportional to the strain. This type of strain gauge is more accurate and sensitive than a resistive strain gauge. But, it is difficult to install the device as it is bulky and complex in construction.

Variable Inductance Type Strain Gauge

#### Errors in Strain Gauge

Some of the main causes for errors and inaccuracy in the device reading are given below.

• Temperature Variation – This can be one of the major causes of error in a strain gauge. It can easily change the gauge resistance and cause differential expansion between the gauge and the test piece, causing variation in the measurable strain.
• Humidity – Humidity can affect the accuracy by the breakdown of insulation between the gauge and the ground point. It also causes electro-chemical corrosion of gauge wire due to electrolysis.
• Small errors could be caused due to thermoelectric effect.
• The gauge will be erroneous even due to small factors like zero drift, hysteresis effect and so on.
• Magnetostrictive effect can also cause errors in strain gauges of ferromagnetic materials. It produces a small voltage fluctuation of almost 2 mill volts.

#### What is an Accelerometer?

An accelerometer is a transducer that is used to measure the physical or measurable acceleration that is made by an object. Co-ordinate acceleration cannot be measured using this device. (Refer: Acceleration Transducer)

Accelerometer

An accelerometer is an electro-mechanical device that is used to measure the specific force of an object, a force obtained due to the phenomenon of weight exerted by an object that is kept in the frame of reference of the accelerometer.

In the case of static acceleration, the device is mainly used to find the degrees at which an object is tilted with respect to the ground. In dynamic acceleration, the movement of the object can be foreseen.

#### Working

The most commonly used device is the piezoelectric accelerometer. As the name suggests, it uses the principle of piezoelectric effect. The device consists of a piezoelectric quartz crystal on which an accelerative force, whose value is to be measured, is applied.

Due to the special self-generating property, the crystal produces a voltage that is proportional to the accelerative force. The working and the basic arrangement is shown in the figure below.

Piezoelectric Accelerometer

As the device finds its application as a highly accurate vibration measuring device, it is also called a vibrating sensor. Vibration sensors are used for the measurement of vibration in bearings of heavy equipment and pressure lines. The piezoelectric accelerometer can be classified into two. They are high impedance output accelerometer and low impedance accelerometer.

In the case of high impedance device, the output voltage generated in proportion to the acceleration is given as the input to other measuring instruments. The instrumentation process and signal conditioning of the output is considered high and thus a low impedance device cannot be of any use for this application. This device is used at temperatures greater than 120 degree Celsius.

The low impedance accelerometer produces a current due to the output voltage generated and this charge is given to a FET transistor so as to convert the charge into a low impedance output. This type of accelerometers is most commonly used in industrial applications.

#### Types

In industrial applications, the most commonly used components to convert the mechanical action into its corresponding electrical output signal are piezoelectric, piezoresistive and capacitive in nature. Piezoelectric devices are more preferred in cases where it is to be used in very high temperatures, easy mounting and also high frequency rang e up to 100 kilohertz. Piezoresistive devices are used in sudden and extreme vibrating applications. Capacitive accelerometers are preferred in applications such as a silicon-micro machined sensor material and can operate in frequencies up to 1 kilohertz. All these devices are known to have very high stability and linearity.

Nowadays, a new type of accelerometer called the Micro Electro-Mechanical System (MEMS) Accelerometer is being used as it is simple, reliable and highly cost effective. It consists of a cantilever beam along with a seismic mass which deflects due to an applied acceleration. This deflection is measured using analog or digital techniques and will be a measure of the acceleration applied.

#### Accelerometer Specifications

1. Frequency Response – This parameter can be found out by analyzing the properties of the quartz crystal used and also the resonance frequency of the device.
2. Accelerometer Grounding – Grounding can be in two modes. One is called the Case Grounded Accelerometer which has the low side of the signal connected to their core. This device is susceptible to ground noise. Ground Isolation Accelerometer refers to the electrical device kept away from the case. Such a device is prone to ground produced noise.
3. Resonant Frequency – It should be noted that the resonant frequency should be always higher the the frequency response.
4. Temperature of Operation – An accelerometer has a temperature range between -50 degree Celsius to 120 degree Celsius. This range can be obtained only by accurate installment of the device.
5. Sensitivity – The device must be designed in such a way that it has higher sensitivity. That is, even for a small accelerative force, the electrical output signal should be very high. Thus a high signal can be measured easily and is sure to be accurate.
6. Axis – Most of the industrial applications requires only a 2-axis accelerometer. But if you want to go for 3D positioning, a 3-axis accelerometer will be needed.
7. Analog/Digital Output – You must take special care in choosing the type of output for the device. Analog output will be in the form of small changing voltages and digital output will be in PWM mode.

#### Device Selection

Selection of the device depends on the following factors.

1. Selection depends on the range of frequency you need.
2. Depends on the size and shape of the object whose acceleration is to be measured.
3. Whether the measurement environment is dirty or clean.
4. Depends on the range of vibration that is to be measured.
5. Depends on the range of temperature in which the device will have to work.
6. Depends on whether the device is to be case grounded or grounded isolated.

#### Applications

1. Machine monitoring.
2. Used to measure earthquake activity and aftershocks.
3. Used in measuring the depth of CPR chest compression.
4. Used in Internal Navigation System (INS). That is, measuring the position, orientation, and velocity of an object in motion without the use of any external reference.
5. Used in airbag shooting in cars and vehicle stability control.
6. Used in video games like PlayStation 3, so as to make the steering more controlled, natural and real.
7. Used in camcorder to make images stable.

#### Eddy Currents

Eddy currents, also known as “Focault Currents”, are currents induced in a conductor due to the magnetic field produced by the active coil. The conductor is placed in a changing magnetic field and the current is produced according to the change of magnetic field with time. The amount of eddy current produced will be more if the field strength is greater. When there is high field strength, the conductivity of the metal conductor increases, causing faster reversals of the field and hence more flow of eddy currents. Eddy currents will be produced in both conditions where either the conductor moves through a magnetic field or a magnetic field changes around a stationary conductor.  Even a small amount of the current will be produced in cases where a small change in magnetic field intensity is experienced on a conductor.

Like other currents in a conductor, eddy currents can also generate heat, EMF, and all types of losses. Its biggest disadvantage can be seen in a transformer, where power loss due to this, affects the device’s efficiency. This can be reduced by reducing the area of the conductor, or by laminating it. Since the insulator in the lamination area stops the electrons from moving forward, they will not be able to flow on wide arcs. Thus, they accumulate at the insulated ends and resist further accumulation of charges. This, in turn will reduce the flow of eddy currents. The amount of currents produced can also be reduced by using conductors having less electrical conductivity.

#### Eddy Current Transducer

This type of transducer is comparatively low in the measurement field and depends mostly on the quality of a high alternating source which is fed to a set of coils. One coil is called the active coil and the other provides temperature compensation (Compensating coil) by being the adjacent arm of a bridge circuit. A conducting material is kept close to the active coil so as to make it influenced by its absence or presence, or, by being any closer or away. Magnetic flux is induced in the active coil and is passed through the conductor producing eddy currents. The density of this current will be maximum at the surface and will lessen as the depth increases. This penetration depth can be calculated using the equation given below.

δ=1/fπμσ
δ-Penetration Depth (m)
f-Frequency (Hz)
μ-Magnetci Permeability
σ-Electrical Conductivity (S/m)

The circuit diagram of an eddy current transducer/sensor is shown below.

Eddy Current Transducer

#### Working

The active coil is kept closer to the conducting material and both of them are placed inside a probe. The compensating coil is kept further away from the conducting material. The high frequency source acts as the bridge circuit and feeds the coil across the two capacitors. The amount of eddy current produced becomes more as the distance between the conducting material and the active coil becomes less. This causes a change in the impedance of the active coil and thus unbalances the bridge circuit. The bridge circuit produces an output proportional to the amount of closeness between the conducting material and the active coil. The output of the bridge circuit is given to a low pass filter (LPF) and then its dc output is calculated. The high frequency allows a thin target to be used and also with this, the frequency response becomes good up to a target frequency 1/10th the supply frequency.

It should be noted that the diameter of the conducting material should be larger or at least same as that of a probe. If not, the output is prone to reduce linearity. If shafts are used as conducting materials, they should have a bigger diameter so that their curved surfaces effectively behaves as flat surfaces.

#### Applications

Since it is a non-contact device, it is suitable for higher resolution measurement applications. The device is used for finding out the position of an object that is conductive in nature.

• Position Measurement

Since the output of an eddy current transducer represents the size of the distance between the probe and the conductor, the device can be calibrated to measure the position or displacement of the target. Thus, it can be applicable in monitoring or sensing the precise location of an object such as a machine tool. It can also be used to locate the final position of precise equipments such as a disk drive.

• Vibrating Motion Measurement

The device is also suitable for finding the alternate positions of a vibrating conductor. Since a contact device is impracticable for this application, a non-contact device such as eddy current transducer is highly recommended. Thus, it can be applicable in measuring the distance of a shaft from a reference point or the to-and-fro movement of vibrating instruments.

1. Measurement of distance can be carried out even in rough or mixed environments.
2. Cost-effective.
3. The device is insensitive to material in the gap between the probe and the conductor.
4. The device is less expensive and has higher frequency response than a capacitive transducer.

1. The result will be precise only if the gap between the probe and the conductor is small.
2. The device cannot be used for finding the position of non-conductive materials. Another way is to connect a thick conductor onto the non-conductive material.
3. There always occurs a non-linear relationship between the distance and impedance of the active coil of the device. This problem can be overcome only by calibrating the device at fixed intervals.
4. The device is highly temperature sensitive. This can be overcome by adding a suitable balance coil to the circuit.

Magnetostriction

Magnetostriction can be explained as the corresponding change in length per unit length produced as a result of magnetization. The material should be magnetostrictive in nature. This phenomenon is known as Magnetostrictive Effect.  The same effect can be reversed in the sense that, if an external force is applied on a magnetostrictive material, there will be a proportional change in the magnetic state of the material. This property was first discovered by James Prescott Joule by noticing the change in length of the material according to the change in magnetization. He called the phenomenon as Joule effect. The reverse process is called Villari Effect or Magnetostrictive effect. This effect explains the change in magnetization of a material due to the force applied. Joule effect is commonly applied in magnetostrictive actuators and Villari effect is applied in magnetostrictive sensors.

This process is highly applicable as a transducer as the magnetostriction property of a material does not degrade with time.

Magnetostriction Transducers

A magnetostriction transducer is a device that is used to convert mechanical energy into magnetic energy and vice versa. Such a device can be used as a sensor and also for actuation as the transducer characteristics is very high due to the bi-directional coupling between mechanical and magnetic states of the material.

This device can also be called as an electro-magneto mechanical device as the electrical conversion to its appropriate mechanical energy is done by the device itself. In other devices, this operation is carried out by passing a current into a wire conductor so as to produce a magnetic field or measuring current induced by a magnetic field to sense the magnetic field strength.

Working

The figure below describes the exact working of a magnetostrictive transducer. The different figures explain the amount of strain produced from null magnetization to full magnetization. The device is divided into discrete mechanical and magnetic attributes that are coupled in their effect on the magnetostrictive core strain and magnetic induction.

Magnetostrictive Transducers

First, considering the case where no magnetic field is applied to the material. This is shown in fig.c. Thus, the change in length will also be null along with the magnetic induction produced. The amount of the magnetic field (H) is increased to its saturation limits (±Hsat). This causes an increase in the axial strain to “esat”. Also, there will be an increase in the value of the magnetization to the value +Bsat (fig.e) or decreases to –Bsat (fig.a). The maximum strain saturation and magnetic induction is obtained at the point when the value of Hs is at its maximum. At this point, even if we try to increase the value of field, it will not bring any change in the value of magnetization or field to the device. Thus, when the field value hits saturation, the values of strain and magnetic induction will increase moving from the center figure outward.

Let us consider another instance, where the value of Hs is kept fixed. At the same time, if we increase the amount of force on the magnetostrictive material, the compressive stress in the material will increase on to the opposite side along with a reduction in the values of axial strain and axial magnetization.

In fig.c, there are no flux lines present due to null magnetization. Fig.b and fig.d has magnetic flux lines in a much lesser magnitude, but according to the alignment of the magnetic domains in the magnetostrictive driver. Fig.a also has flux lines in the same design, but its flow will be in the opposite direction. Fig.f shows the flux lines according to the applied field Hs and the placing of the magnetic domains. These flux fields produced are measured using the principle of Hall Effect or by calculating the voltage produced in a conductor kept in right angle to the flux produced. This value will be proportional to the input strain or force.

Applications

The applications of this device can be divided into two modes. That is, one implying Joule Effect and the other are Villari Effect.

• In the case where magnetic energy is converted to mechanical energy it can be used for producing force in the case of actuators and can be used for detecting magnetic field in the case of sensors.
• If mechanical energy is converted to magnetic energy it can be used for detecting force or motion.
• In early days, this device was used in applications like torque meters, sonar scanning devices, hydrophones, telephone receivers, and so on. Nowadays, with the invent of “giant” magnetostrictive alloys, it is being used in making devices like high force linear motors, positioners for adaptive optics, active vibration or noise control systems, medical and industrial ultrasonic, pumps, and so on. Ultrasonic magnetostrictive transducers have also been developed for making surgical tools, underwater sonar, and chemical and material processing.

A piezoelectric crystal transducer/sensor is an active sensor and it does not need the help of an external power as it is self-generating. It is important to know the basics of a piezoelectric quartz crystal and piezoelectric effect before going into details about the transducer.

#### Piezoelectric Quartz Crystal

A quartz crystal is a piezoelectric material that can generate a voltage proportional to the stress applied upon it. For the application, a natural quartz crystal has to be cut in the shape of a thin plate of rectangular or oval shape of uniform thickness.  Each crystal has three sets of axes – Optical axes, three electrical axes OX1, OX2, and OX3 with 120 degree with each other, and three mechanical axes OY1,OY2 and OY3 also at 120 degree with each other. The mechanical axes will be at right angles to the electrical axes. Some of the parameters that decide the nature of the crystal for the application are

• Angle at which the wafer is cut from natural quartz crystal
• Plate thickness
• Dimension of the plate
• Means of mounting

#### Piezoelectric Effect

The X-Y axis of a piezoelectric crystal and its cutting technique is shown in the figure below.

X-Y Axes of a Piezoelectric Crystal

The direction, perpendicular to the largest face, is the cut axis referred to.

If an electric stress is applied in the directions of an electric axis (X-axis), a mechanical strain is produced in the direction of the Y-axis, which is perpendicular to the relevant X-axis. Similarly, if a mechanical strain is given along the Y-axis, electrical charges will be produced on the faces of the crystal, perpendicular to the X-axis which is at right angles to the Y-axis.

Some of the materials that inherit piezo-electric effect are quartz crystal, Rochelle salt, barium titanate, and so on. The main advantages of these crystals are that they have high mechanical and thermal state capability, capability of withstanding high order of strain, low leakage, and good frequency response, and so on.

A piezoelectric transducer may be operated in one of the several modes as shown in the figure below.

Piezoelectric Crystal

#### Piezoelectric Transducer

The main principle of a piezoelectric transducer is that a force, when applied on the quartz crystal, produces electric charges on the crystal surface.  The charge thus produced can be called as piezoelectricity. Piezo electricity can be defined as the electrical polarization produced by mechanical strain on certain class of crystals. The rate of charge produced will be proportional to the rate of change of force applied as input. As the charge produced is very small, a charge amplifier is needed so as to produce an output voltage big enough to be measured. The device is also known to be mechanically stiff. For example, if a force of 15 kiloN is given to the transducer, it may only deflect to a maximum of 0.002mm. But the output response may be as high as 100KiloHz.This proves that the device is best applicable for dynamic measurement.

The figure shows a conventional piezoelectric transducer with a piezoelectric crystal inserted between a solid base and the force summing member. If a force is applied on the pressure port, the same force will fall on the force summing member. Thus a potential difference will be generated on the crystal due to its property. The voltage produced will be proportional to the magnitude of the applied force.

Piezoelectric Transducer

#### Applications

1. Due to its excellent frequency response, it is normally used as an accelerometer, where the output is in the order of (1-30) mV per gravity of acceleration.
2. The device is usually designed for use as a pre-tensional bolt so that both tensional and compression force measurements can be made.
3. Can be used for measuring force, pressure and displacement in terms of voltage.

1. Very high frequency response.
2. Self generating, so no need of external source.
3. Simple to use as they have small dimensions and large measuring range.
4. Barium titanate and quartz can be made in any desired shape and form. It also has a large dielectric constant. The crystal axis is selectable by orienting the direction of orientation.

1. It is not suitable for measurement in static condition.
2. Since the device operates with the small electric charge, they need high impedance cable for electrical interface.
3. The output may vary according to the temperature variation of the crystal.
4. The relative humidity rises above 85% or falls below 35%, its output will be affected. If so, it has to be coated with wax or polymer material.

The basic principle behind the measurement of force is – when a force is applied on an object, the object gets displaced. The amount of displacement occurred can be calculated using the various displacement transducers, and thus force measurement can be done. This is an indirect method for calculating force. Some of the direct methods for measuring force are given below.

#### Force Measurement Using Pressure

Force measurement through pressure can be done with two types of load cells. They are explained below.

As shown in the figure given below, the inside chamber of the device is filled with oil which has a pre-load pressure. The force is applied on the upper portion and this increases the pressure of the fluid inside the chamber. This pressure change is measured using a pressure transducer or is displayed on a pressure gauge dial using a Bourdon Tube.

When a pressure transducer is used for measuring the value, the load cell is known to be very stiff. Even at a fully forced condition, it will only deflect up to 0.05mm. Thus, this device is usually used for calculating forces whose value lies between 500N and 200KiloN. The force monitoring device can be placed at a distance far away from the device with the help of a fluid-filled hose. Sometimes there will be need of multiple load cells. If so, a totaliser unit has to be designed for the purpose.

The biggest advantage of such a device is that it is completely mechanical. There is no need of any electrical assistance for the device. They can also be used for calculating both tensile and compressive forces. The error percentage does not exceed more than 0.25% if the device is designed correctly.

The device will have to be calibrated according to the temperature in which it is used as it is temperature sensitive.

The working of a pneumatic load cell is almost same to that of a hydraulic load cell. The force, whose value is to be measured, is applied on one side of a piston and this is balanced by pneumatic pressure on the other side. The pressure thus obtained will be equal to the input force applied. The value is measured using a bourdon tube.

The pneumatic load cell has an inside chamber which is closed with a cap. An air pressure is built up inside the chamber until its value equals the force on the cap. If the pressure is increased further, the air inside the chamber will forcefully open the cap and the process will continue until both the pressures are equal. At this point, the reading of the pressure in the chamber is taken using a pressure transducer and it will be equal to the input force.

#### Other Force Measuring Systems

1. Elastic Devices

The strain gauge can be replaced with a Linear Voltage Differential Transformer (LVDT) inside a load cell to know the displacement of an elastic element. The device is best suitable for dynamic measurements as it has good features like high resolution and hysteresis.

Another device most suitable for the measurement of force in an elastic element is the capacitive load cell. With the device, the displacement can be calculated by measuring the capacitance. The sensor has two parallel plates with a small gap in between. According to the force applied on the device, there will be a change in length of the spring member, which in turn changes the gap distance between the plates and produces a proportional capacitance. This measured capacitance value will be proportional to the force applied.

Optical fibers can also be used to design an optical strain gauge to measure force. When a force is applied on the force summing member, it causes a change in length of the optical fibers that are bonded to the strain gauge. If the level of strain is different for two optical fiber strain gauges, then the phase difference between the monochromatic beams that strike the optical gauges will be proportional to the value of force applied.

For obtaining a displacement value of high resolution, a device called interference-optical load cell can be used. A Michelson Interferometer is used to measure the amount of force that has caused the change in shape of the fork-shaped spring. The highest amount of elastic deformation and along with it, the strain of the material need not be as large as in the case of the strain gauge load cell. The spring is made of quartz with very little temperature dependence.

2. Vibrating Elements

The principle of resonance is used in the force transducer of vibrating elements. If a tuning fork load cell is used, the transducer will have two parallel band plates connected at both ends and will be made to vibrate in opposite directions. The change in resonance thus caused will be proportional to the force applied. The transmission and reception of the signals are carried by two piezo-electric elements kept very close to the fork.

Displacement is a basic variable whose value is measured and involved in many other physical parameters such as velocity, force, acceleration, torque and so on. The transducer used for the measurement of displacement can be classified in many ways. One of the most common classification is given below.

• Mechanical
• Pneumatic
• Electrical
• Optical

In order to obtain an electrical output, a mixture of two or more methods is also used. For example, optical methods using photo-detectors present the output as an electrical quantity like voltage, current and so on. Thus, the combined mechanical and optical method is desired.

Measurements can be made in the direct and indirect way. In direct method, the displacement is measured directly. But indirect methods are mostly used as the associated variables like force, acceleration, torque, velocity and so on can be obtained.

In electrical conversion method, the displacement is converted to an electrical quantity like voltage or current. This value is then recorded or displayed on a screen.

A basic displacement scheme is shown in the figure below.

Displacement Transducer

Some of the most commonly used methods are listed and explained below. Though some of these methods can be used for the measurement of other physical quantities, the electrical signals derived from such transducers always depend on a displacement parameter.

#### Photo-Electric Transducers

Before explaining about the different photo-electric transducers, it is important to know the basics of photo-electric effect.
Photo-Electric Effect – It can be explained as the electric current produced when a light of certain intensity strikes on a piece of metal. The energy contained in the light is transferred to the surface of the metal and thus produce a movement of electrons. This movement produces a current. This effect cannot be produced by all colors in the spectrum. A
bright red colored light will not produce a current flow in the metal. But, a dim blue light can cause current flow. Thus, the only way to decide the colors producing the photo-electric effect is through the concept of photons. The idea was brought forward by Albert Einstein, and according to him, light is made up of small packets of energy that had the behavior of particles. These packets of energy were named photons. A red light does not move the electrons, as their individual photons does not have much energy. But a blue light can move electrons as their individual photons have more energy than that of red light. The electrons thus emitted in this manner are called photo electrons.

Some of the most commonly used displacement transducers through the application of photo-electric effect are explained below.

1. Vacuum Photo-Tube as Transducer

A schematic of the vacuum photo-tube transducer is shown in the figure below.

Vaccum Photo-Tube Transducer

A displacement produced will modulate or change the intensity of the light intensity of the light incident on the photo-cathode. This changes the amount of voltage and thus, the proportional anode current is given to the resistor R. This changes the output voltage. The output voltage produced will be proportional to the amount of displacement given as input. This transducer is appropriate when there is an availability of a stable light source or an ac modulated light.

• Efficiency is fairly high.
• Can take both static and dynamic measurements.

• Stability is achieved only for a short period.
• If the light variations are subjected to high temperatures, there will be very little response.
• Only suitable for applications having large displacements.

2. Photo-Diode as Transducer

The circuit for a photo-diode transducer is shown below.

Photo-Diode Transducer

The arrangement is almost same as a photo-tube transducer except that the photo-tube has been replaced by a photo-diode and the lens has been replaced to make the light strike on the junction of the photo-diode. When a displacement is produced, it provides a force on the summing member and thus changes the quantum of light intensity incident on the photo-diode junction. The proportional change in anode voltage produces a current in the resistor R. Thus, an output voltage is produced which will be proportional to the displacement given as input.

3. Photo-Conductor as Transducer

The circuit is the same as a vacuum photo-tube arrangement except that the photo-conductor is placed instead of a photo-tube. The displacement causes a unique light intensity incident on the photo-conductor and causes a variation in current through resistor R. Hence the output voltage produced will be a linear function of the displacement produced. This device is not used much as the sensitivity produced remains stable only at the beginning and becomes poor at high frequencies.

4. Photo-Voltage Cell as Transducer

This device has great applications in electronic instrumentation and control circuits as it is an active transducer and needs no associated energy source. According to the light intensity striking on the photo-voltage cell, it illuminates and produces a small proportional voltage. The circuit diagram is the same as that given above except that the photo-tube is replaced by photo-voltaic cell and the source for voltage is taken away. The working is also the same as that explained above and it can be calibrated according to the amount of displacement produced.

To learn about a capacitive transducer, it is important to know the basics of a parallel plate capacitor. Being the simplest form of a capacitor, it has two parallel conducting plates that are separated to each other by a dielectric or insulator with a permittivity of Ε (for air). Other than paper, vacuum, and semi-conductor depletion region, the most commonly used dielectric is air.

Due to a potential difference across the conductors, an electric field develops across the insulator. This causes the positive charges to accumulate on one plate and the negative charges to accumulate on the other. The capacitor value is usually denoted by its capacitance, which is measured in Farads. It can be defined as the ratio of the electric charge on each conductor to the voltage difference between them.

The capacitance is denoted by C. In a parallel plate capacitor, C = [A*Er*9.85*1012 F/M]/d

A – Area of each plate (m)

d – Distance between both the plates (m)

Er – Relative Dielectric Constant

The value 9.85*1012 F/M is a constant denoted by Eo and is called the dielectric constant of free space.
From the equation it is clear that the value of capacitance C and the distance between the parallel plates,d are inversely proportional to each other. An increase of distance between the parallel plates will decrease the capacitance value correspondingly. The same theory is used in a capacitive transducer. This transducer is used to convert the value of displacement or change in pressure in terms of frequency.

You may also like: Capacitance Transducer

As shown in the figure below, a capacitive transducer has a static plate and a deflected flexible diaphragm with a dielectric in between. When a force is exerted to the outer side of the diaphragm the distance between the diaphragm and the static plate changes. This produces a capacitance which is measured using an alternating current bridge or a tank circuit.

Capacitive Transducer

A tank circuit is more preferred because it produces a change in frequency according to the change in capacitance. This value of frequency will be corresponding to the displacement or force given to the input.

• It produces an accurate frequency response to both static and dynamic measurements.

• An increase or decrease in temperature to a high level will change the accuracy of the device.
• As the lead is lengthy it can cause errors or distortion in signals.

Like other inductive transducers, this transducer is also used for converting a linear motion into an electrical signal. The basic construction of an LVDT is explained and shown in the figure below.

Construction

LVDT Construction

The device consists of a primary winding (P) and two secondary windings named S1 and S2. Both of them are wound on one cylindrical former, side by side, and they have equal number of turns. Their arrangement is such that they maintain symmetry with either side of the primary winding (P). A movable soft iron core is placed parallel to the axis of the cylindrical former. An arm is connected to the other end of the soft iron core and it moves according to the displacement produced.

#### Working

As shown in the figure above, an ac voltage with a frequency between (50-400) Hz is supplied to the primary winding. Thus, two voltages VS1 and VS2 are obtained at the two secondary windings S1 and S2 respectively. The output voltage will be the difference between the two voltages (VS1-VS2) as they are combined in series. Let us consider three different positions of the soft iron core inside the former.

• Null Position – This is also called the central position as the soft iron core will remain in the exact center of the former. Thus the linking magnetic flux produced in the two secondary windings will be equal. The voltage induced because of them will also be equal. Thus the resulting voltage VS1-VS2 = 0.
• Right of Null Position – In this position, the linking flux at the winding S2 has a value more than the linking flux at the winding S1. Thus, the resulting voltage VS1-VS2 will be in phase with VS2.
• Left of Null Position – In this position, the linking flux at the winding S2 has a value less than the linking flux at the winding S1. Thus, the resulting voltage VS1-VS2 will be in phase with VS1.

From the working it is clear that the difference in voltage, VS1-VS2 will depend on the right or left shift of the core from the null position. Also, the resulting voltage is in phase with the primary winding voltage for the change of the arm in one direction, and is 180 degrees out of phase for the change of the arm position in the other direction.

The magnitude and displacement can be easily calculated or plotted by calculating the magnitude and phase of the resulting voltage.

Difference output Voltage Vs Displacement Curve

The graph above shows the plot between the resulting voltage or voltage difference and displacement. The graph clearly shows that a linear function is obtained between the output voltage and core movement from the null position within a limited range of 4 millimeter.

The displacement can be calculated from the magnitude of the output voltage. The output voltage is also displayed on a CRO or stored in a recorder.

1. Maintains a linear relationship between the voltage difference output and displacement from each position of the core for a displacement of about 4 millimeter.

2. Produces a high resolution of more than 10 millimeter.

3.Produces a high sensitivity of more than 40 volts/millimeter.

4. Small in size and weighs less. It is rugged in design and can also be assigned easily.

5. Produces low hysteresis and thus has easy repeatability.

1. The whole circuit is to be shielded as the accuracy can be affetced by external magnetic field.

2. The displacement may produce vibrations which may affect the performance of the device.

3. Produces output with less power.

4. The efficiency of the device is easily affected by temperature. An increase in temperature causes a phase shift. This can be decreased to a certain extent by placing a capacitor across either one of the secondary windings.

5. A demodulator will be needed to obtain a d.c output.

This type of transducer is used for finding the linear displacement in terms of voltage or other digital parameters. Another transducer for finding the linear displacement is the Linear Motion Variable Inductance Transducer.

There are mainly two types of proximity inductance transducers. They are

#### Mutual Inductance Type Proximity Transducer

This transducer consists of a primary and secondary coil. The constructional diagram of the transducer is shown below.

Proximity Inductive Transducers

Working

An ac source is given to the primary. This ac source excites the primary and a flux is produced. This flux is linked to the secondary coil and thus a voltage ‘V’ is induced. If the mutual inductance between the primary and secondary windings is represented by ‘M’ (Hertz) and the frequency of ac excitation is represented by ‘w’, then the voltage ‘V’ developed in secondary coil can be written as V = MwIp.
Ip – The current due to excitation in primary (Amperes).

As shown in the figure, a ferromagnetic displacement plate is placed very near to the windings. The current in the primary coil produces a magnetic flux that links with the secondary coil through the displacement plate. Thus, the movement of the ferromagnetic plate to the right causes a greater value of flux linkage between the two terminals. This in turn causes an increase in the resulting output voltage across the secondary terminal with a value of (T1-T2). This output is given to the input of the CRO or a recorder and the amount of displacement can be known in terms of voltage. A

1. The device is small when compared to other transducers.

2. Wear and tear is minimized as there is no physical contact between the target and coil configuration.

3. The output value will be accurate for small displacements as there is a linear relation between the output voltage and linear displacement.

4. There will not be any external effects by contamination.

5. The device works accurately even at higher temperatures up to 400 degree Celsius.

1. The accuracy decreases when it comes to the measure of large displacement. This is because the linear relation between voltage and displacement is less at higher ranges.

2. The external magnetic field may cause harm to the ferromagnetic material.

#### Variable Reluctance Type Proximity Transducers

This device can be set up in two ways. Both the diagrams are shown below.

Variable Reluctance Type Proximity Transducers

Working

The device consists of a coil that is wound on a core made up of ferromagnetic material. The displacement is given to the core through a target that makes an upward and downward movement according to the displacement produced. It does not touch the core of the coil and a smaller air gap is made between them.
When the target moves closer to the coil due to the displacement, the air gap becomes less causing the reluctance of the magnetic field to reduce and thus the coil inductance to increase. The value of inductance keeps on varying according to the variation in target movement. A CRO or a recorder takes these values and displays it to the user.

In the right side figure shown above, an E-type core is used for finding the displacement. The target is also pivoted at the central limb of the core. Thus, a single coil is divided into two turns and the end of each coil works as the arms of an inductance bridge.

As the displacement value changes, an output signal is produced. This is given to a CRO after amplification.

The biggest advantage of this device is that it shows a linear relationship between the output and the displacement.