Transducers and Sensors - Philadelphia University 3... · Transducers and Sensors...

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Advanced Measurement Systems and Sensors

Dr. Ibrahim Al-Naimi

Chapter one

Transducers and Sensors

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Transducers and Sensors Transducers/Sensors Classifications

• Based on power type classification:

- Active

- Passive

• Based on the type of output signal:

- Analogue

- Digital

Transducers and Sensors Transducers/Sensors Classifications • Based on the electrical phenomenon or parameter

that may be changed due to the whole process. - Resistive - Capacitive - Inductive - Photoelectric • According to the physical variable to be measured,

the transducers can be classified to: - Mechanical Transducers - Thermal Transducers - Optical Transducers

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Transducers and Sensors Transducers/Sensors

• Pyroelectric Infrared (PIR) sensor

• Vortex flow meter

• Hall effect sensor

• Strain gauge

• Oxygen sensor

• Resistance Temperature Detector (RTD)

• Piezoelectric sensor


Transducers/Sensors

• Principled of operation

• Classifications and types.

• Construction.

• The relationship between input and output signals (static and dynamic transfer functions)

• Characteristics (linearity, resolution, sensitivity, load effect, dynamic response, power dissipation).

• Advantages and disadvantages.

• Applications.

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Detectors of Thermal Radiation

1. Quantum/Photons Detectors (Photovoltaic)

2. Thermal Detectors (Pyroelectric)

PIR Sensors

• Infrared radiation is the electromagnetic waves in the wavelength region longer than the visible light wavelengths, lying from 0.75 μm to 1000 μm.

• The wavelength region of 0.75 μm to 3 μm is often called the near infrared, the wavelength region of 3 μm to 6 μm the middle infrared, and the wavelength region of 6 μm to 15 μm the far infrared.

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PIR Sensors

PIR Sensors

Infrared radiation has the following characteristics:

(1) Invisible to human eyes: This is useful for security applications.

(2) Small energy

(3) Long wavelength: This means infrared radiation is less scattered and offers better transmission through various medium.

(4) Emitted from all kinds of objects

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PIR Sensors

• Referring to the principles of radiation heat transfer, all bodies emit energy in the form of electromagnetic radiations. The majority of these radiations are within the infrared spectrum.

• The intensity of energy flux, measured in unit area, emitted from a body depends upon the body’s temperature and the nature of its surface.

• In general, a radiation heat exchange normally happens between hot and cold objects.

PIR Sensors

As shown in the following figure, the net heat radiation (Qnet) from the hotter object (1) to the colder object (2) depends on the following factors:

• Objects’ temperatures T1 and T2,

• the areas of the two objects A1 and A2,

• the shapes, orientations, and the distance between the two objects,

• the radiative properties of the surfaces, and

• the transmission medium

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PIR Sensors

PIR Sensors

According to Steffen Boltzmann law, the net radiation heat exchange between the two objects can be calculated by the following equation:

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PIR Sensors

Where:

• σ: Stefan Boltzmann constant (5.669×10-8 W/m2K4).

• A1: The surface area of body 1.

• F1-2: The shape or view factor (depends on the object shape and area).

• ε: The equivalent emissivity of the two objects.

• T1 and T2: The absolute temperatures of the two objects.

PIR Sensors • The human body is one of these objects that emit

infrared radiation and has the same features as these objects have.

• In fact, a heat exchange is usually happen between the human’s body and the environment or other objects due the dissimilarity in their temperatures.

• In general, the typical human body emits infrared radiation in the range of 5 ~ 14 µm wavelength. Moreover, the temperature of a typical human body is about 37 0C, and the average IR power intensity radiated from the typical human body is about 100 W/m2.

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PIR Sensors

• The Pyroelectric Infrared sensor is made of a crystalline material that responds to the change of incident thermal radiation and develops a related electrical signal when a heat source (human body) crosses over the sensor Field of View (FOV).

• This type of sensor responds to the variation of infrared radiation rather than the infrared radiation itself.

PIR Sensors

• A pyroelectric ceramic plate (sensing element) generates electric charge in response to a thermal energy flowing through its body. The plate has two deposited electrodes: one on its upper side, while the other on the bottom side.

• In a very simplified way, a pyroelectric response may be described as a secondary effect of a thermal expansion.

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PIR Sensors

• Since all pyroelectrics are also piezoelectrics, IR heat absorbed by the front electrode causes the upper side temperature Ts to increase over the base temperature Ta.

• As a result, the upper side size expands, causing a mechanical stress in the piezoelectric crystals.

• In turn, the stress leads to development of a piezoelectric charge.

• This IR-induced charge is manifested as voltage across the electrodes.

PIR Sensors

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PIR Sensors

• Unfortunately, piezoelectric properties of the element have also a negative effect. If the sensor is subjected to a minute mechanical stress due to any external force, like sounds or structural vibrations, it generates a spurious charge which often is indistinguishable from that caused by the infrared heat.

• To separate thermally induced charges from the mechanically induced charges, a pyroelectric sensor is usually fabricated in a symmetrical form.

PIR Sensors

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PIR Sensors

• Two identical sensing elements are positioned inside the sensor’s housing. The elements are connected to the interface circuit in such a manner as to produce the out-of-phase signals when subjected to the same in-phase inputs. The idea is based on the fact that the piezoelectric or spurious thermal interferences are applied to both sensing elements simultaneously (in phase) and thus will be cancelled at the input of the electronic circuit.

• On the other hand, since the IR flux that is focused by the lens is absorbed by only one element at a time, cancellation is avoided. This arrangement is called a differential PIR detector

PIR Sensors • A symmetrical sensing element should be mounted

in a way to assure that both parts of the element generate the equal (but out-of-phase) signals if subjected to the same external factor.

• At any moment, the optical component (e.g. a Fresnel lens) must focus thermal image of an object on a surface of one part of the sensor only, otherwise signals will be cancelled.

• The element generates a charge only across the electrode pair that is subjected to a heat flux.

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PIR Sensors

PIR Sensors The PIR response to the variation of thermal radiation

takes place in three stages: 1- Thermal to thermal conversion: Pyroelectric material,

which is the main sensor constituent, absorbs certain amount of infrared radiation emitted from human body and causes a change in the PIR unit temperature.

2- Thermal to electrical conversion: In response to this temperature variation, the PIR crystalline material generates a spontaneous electric charge on its surface, i.e. the material acts as a capacitor which can be electrically charged by influx of heat.

3- Electrical to electrical conversion: the spontaneous electrical charge is converted to electrical signal with a preamplifier.

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The PIR Equivalent Circuit and the Mathematical Model

PIR Sensors

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PIR Sensors

PIR Sensors

The Previous figure shows how typically, the FET source connects through a pulldown resistor of about 100 K to ground and feeds into a two stage amplifier having signal conditioning circuits. Each of the two cascaded stages has a gain of 100 for a total gain of about 10,000. The amplifier is typically bandwidth limited to below 10Hz to reject high frequency noise and is followed by a window comparator that responds to both the positive and negative transitions of the sensor output signal.

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PIR Sensors

• The sensor in the previous circuit has two sensing elements connected in a voltage differential configuration. This arrangement cancels signals caused by vibration, temperature changes and sunlight.

• A body passing in front of the sensor will activate first one and then the other element as shown in the following figure whereas other sources will affect both elements simultaneously and then cancelled.

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PIR Sensors • The PIR sensor can sense the change in the amount

of infrared energy within small distances, approximately up to 10 inches. For detecting movements at longer distance (up to 10 m), infrared radiation has to be focused. This focusing is done by a Fresnel lens.

• A Fresnel lens divides the whole area into different zones. Any movement between zones leads to a change in the IR (infrared) energy received by the sensor.

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PIR Sensors

• There are different types of Fresnel lenses depending on the range (distance) and coverage angle.

• Fresnel lenses are controlling devices that collect (focus) the infrared radiation and shape the required FOV.

• The Fresnel lens is designed to have its grooves facing the IR sensing element so that a smooth surface is presented to the subject side of the lens which is usually the outside of an enclosure that houses the sensor.

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PIR Sensors

PIR Sensors

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PIR Sensors

PIR Sensors

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PIR Sensors • The following Figure shows the main components

of dual element PIR sensor and summarises its principle of operation.

• As shown in this figure, when a person crosses the sensor FOV, the two PIR elements detect the change in radiation flux in sequence and generate two opposite peaks according to the corresponding polarisation.

• The PIR sensor generates a low frequency signal output of an AC voltage shape.

• This type of sensor can detect the motion and indicate the direction of motion as well.

Pyroelectric Sensors

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PIR Sensors

• Applications:

1- Security system.

2- Automatic lighting system.

3- Automatic door openers.

Vortex Flow Meter • Flow measurement is essential in most industrial

applications and the need for very accurate flow measurement devices is ever-present.

• One of the most versatile, yet very accurate, flow meters used in modern plants is the Vortex flowmeter.

• The design of which takes advantage of the Vortex shedding effect, first described by the Hungarian-born engineer and physicist Theodore von Kármán around 1912.

• This type of flowmeter allows measurement of the volume flow rate by measuring the frequency of creation of vortices in the flow due to an obstacle.

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Vortex Flow Meter

The von Kármán vortex street

• Theodore von Kármán discovered that an obstacle placed in a stream would cause the fluid to shed from its downstream faces in a peculiar manner.

• At low velocities, the flow separates symmetrically at the front of the obstacle and rejoins behind it where it forms two eddies rotating in opposite directions.

Vortex Flow Meter

• As the velocity is increased above a threshold point (about Re>90 for a cylindrical obstacle), the fluid alternatively sheds from one side of the obstacle and then the other, producing a pattern of propagating vortices on the downstream side.

• This regular pattern of vortices alternating in a constant fashion is akin to footsteps left in the snow by a pedestrian, hence the vortex street appellation.

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Vortex Flow Meter

Vortex Flow Meter

• The vortices shed from the bluff body form a wake known as a Von Karman vortex street. This is shown in the following figure both in idealised form (a) and as a computer simulation of the flow behind the bluff body (b).

• This consists of two rows of vortices moving downstream, parallel to each other, at a fixed velocity.

• The distances (L) between each vortex and (h) between the rows are constant, and a vortex in one row occurs halfway between two vortices in another row.

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Vortex Flow Meter

Vortex Flow Meter

• If (d) is the width of the bluff body, then:

• The frequency of vortex shedding (f) is the number of vortices produced from each surface of the bluff per second. This is given by:

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Vortex Flow Meter

Vortex Flow Meter

• Where (v1)is the mean velocity at the bluff body, (d) is the width of the bluff and (S) is a dimensionless quantity called the Strouhal number.

• Since (S) is practically constant, (f) is proportional to (v1), thus providing the basis of a flowmeter.

• The Czech physicist Vincenc Strouhal experimented with vortex shedding and a dimensionless number came to be associated with his name: The Strouhal number. This number characterizes mechanisms in which oscillating flows are present.

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Vortex Flow Meter • Since the cross-sectional area (A) of the pipe is

fixed, it is possible to define a flowmeter factor (K) that relates the volumetric flow rate (Q) to the vortex shedding frequency (f). Given that:

• Finally, the relationship between the volumetric flow of the fluid and the frequency of shedding is:

• K is a constant depends on the bluff shape and usually determined experimentally.

Vortex Flow Meter

• For a vortex shedding flowmeter, an obstacle (bluff) is chosen that will produce a constant K factor over a wide range of pipe Reynolds numbers.

• Therefore, simply counting the vortices that are shed in a given amount of time and dividing by the K factor will give a measurement of the total volume of fluid that has passed through the meter.

• The vortex mechanism produces approximately sinusoidal variations in fluid velocity and pressure, at the shedding frequency f, in the vicinity of the bluff body.

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Vortex Flow Meter Bluff body characteristics and geometry

• Investigations show that the Strouhal number S is a constant for a wide range of Reynolds numbers.

• This means that, for a given flowmeter in a given pipe, i.e. fixed D and d, the meter factor K is practically independent of flow rate, density and viscosity.

Vortex Flow Meter Bluff body characteristics and geometry

• The vortex shedding from a number of bluff body shapes has been investigated in order to establish which shape gives the most regular shedding. The power spectral density of the vortex signals for bluff bodies, of the same width d, with cross-sectional shapes in the form of a circle, semicircle, equilateral triangle, trapezium and rectangle have been measured at the same flow conditions. More information is provided in “Principles of Measurement Systems” book page 337.

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Vortex Flow Meter

• The linearity of the proportion of v/f (where the velocity is proportional to the vortex frequency) depends on the shape and the dimensions of the bluff body.

• Rectangular bluff body: when instruments are equipped with these bodies, the linearity fluctuates greatly with the process parameters.

Vortex Flow Meter

• Round bluff body: the original bluff bodies were cylindrical. The shedding point of the vortex fluctuated upwards and downwards with the rate of flow. Because of this the frequency was not proportional to the velocity.

• Delta bluff body: many tests have revealed that the linearity of the delta shape is very good. The vortex shedding angle is outlined clearly. Pressure variations, viscosity or other process parameters do not affect the level of accuracy.

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Vortex Flow Meter

• Double bluff body: this body is obtained when the manufacturer connects the sensor to the bluff body. The secondary section moves and the Karman vortex street is transformed into a twisted movement. Another possibility is to place two bluff bodies after each other. In this case the permanent pressure loss is doubled, but a stronger vortex is generated (hydraulic amplification). This means that fewer complex sensors and amplifiers can be used.

Vortex Flow Meter

Vortex detection systems and practical flow meters

• As explained before, vortex shedding is characterised by approximately sinusoidal changes in fluid velocity and pressure in the vicinity and downstream of the bluff body.

• The following figure shows three commonly used bluff body shapes; these use three different methods of vortex detection:

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Vortex Flow Meter


Vortex Flow Meter


a) Piezoelectric: The figure (a) shows a T-shaped bluff body; part of the tail is not solid but fluid filled. Flexible diaphragms in contact with the process fluid detect small pressure variations due to vortex shedding. These pressure changes are transmitted to a piezoelectric differential pressure sensor which is completely sealed from the process fluid.

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Vortex Flow Meter


b) Thermal: Figure (b) shows an approximately triangular-shaped bluff body with two semiconductor thermal sensors on the upstream face. The sensors are incorporated into constant-temperature circuits which pass a heating current through each sensor; this enables small velocity fluctuations due to vortices to be detected.

Vortex Flow Meter


c) Ultrasonic: Figure (c) shows a narrow circular cylinder which creates a von Karman vortex street downstream. An ultrasonic transmission link sends a beam of ultrasound through the vortex street. The vortices cause the received sound wave to be modulated in both amplitude and phase.

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Vortex Flow Meter

Characteristics of Vortex flow meters

• Vortex flow meters are a very reliable and accurate type of flow meter which do not require much maintenance due to their simple design.

• The stability of the calibration is excellent as frequency measurement systems are typically free of measurement drift.

Vortex Flow Meter

Advantages of Vortex flow meters

• Suitable for liquid, gas, or steam

• High accuracy (the error is typically about ±0.25% of the flow rate) and linear response

• Low maintenance, no moving parts

• Relatively low installation cost

• Not subjected to changes in density, pressure, or temperature.

• Able to withstand vibrations and thermal shocks (< 150 K/s).

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Vortex Flow Meter

Limitations of Vortex flow meters

• Unidirectional measurement

• Large pressure drop

• Not suitable to measure the flow rate of liquids undergoing partial phase change or viscous liquids

• The fluids must be clean

• The device requires specific minimal lengths of straight pipe runs

• Not suitable when cavitation occurs

Vortex Flow Meter Installation Requirements • This device requires a fully developed flow profile to

correctly measure the flow rate of the fluid. For this reason, it is necessary for the liquids to flow upwards through the device to insure complete filling of the pipe.

• Vortex flow meters can be placed both horizontally and vertically. In a vertical position, the flow should preferably run from bottom to top.

• The measuring instrument should be correctly aligned with the pipe.

• The installation should be performed at a location with little vibration, if necessary the pipes should be supported in front of and behind the meter.

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Vortex Flow Meter

Installation Requirements

• The vortex flow meter only works well if the flow profile is completely developed and undisturbed. Thus, a minimum length of straight pipe runs must be respected. The lengths vary according to the nature of the upstream and downstream disturbances, the type of obstacle (bluff body) used to generate the vortices, and the required accuracy. Typically, a minimum of 30 PD (pipe diameters) in length upstream and 5 PD downstream of the flow tube with no flow disturbing elements located within these sections

Vortex Flow Meter

The following occurrences can heavily influence the output of the reading instrument:

• Shape shifting of the bluff body as a result of corrosion.

• Corrosion of the pipe in which the meter is placed.

• Contamination of the bluff body.

• Hydraulic vibrations of pipe and instrument.

• Incorrect alignment of the flange gaskets.

• Incompletely filled measuring instrument.

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Hall Effect Sensor

• Probably the most widely used magnetic detectors are the Hall-effect sensors.

• Many smart phones and tablets employ these sensors for detecting the Earth magnetic field for controlling the electronic compasses.

Hall Effect Sensor

• The Hall effect was discovered in the last century by E. Hall. He discovered that a voltage difference is created on the opposite sides of a small thin gold plate, through which a current passes, if a magnetic field operates vertically to this. Subsequently, it was discovered that this effect also occurs with many semiconductors. Certain physical characteristics are required for this. The thickness of the small plate must be less than the dimensions of length and width. Voltages of up to 1.5 V can be created.

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Hall Effect Sensor

Hall Effect Sensor

The formula for Hall voltage is:

• Hall sensor elements are used for the measurement of current and magnetic field or in combination with moving magnets for angle and position.

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Strain Gauge

Types of strain gauges:

1- Metallic strain gauges

2- Piezoresistive (semiconductor) strain gauges

Strain Gauge

1- Metallic strain gauges (the resistance of which changes in response to the change in the mechanical dimensions caused by the strain).

• Metallic strain gauges are of two types: bonded strain gauges consisting of a metallic foil glued to a metallic component; and unbonded strain gauges usually made of wires stretch between columns.

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Strain Gauge

The bonded resistance strain gage is by far the most widely used strain measurement tool for today’s experimental stress analyst. It consists of a grid of very fine wire (or, more recently, of thin metallic foil) bonded to a thin insulating backing called a carrier matrix. The electrical resistance of this grid material varies linearly with strain. In use, the carrier matrix is attached to the test specimen with an adhesive.

Strain Gauge

When the specimen is loaded, the strain on its surface is transmitted to the grid material by the adhesive and carrier system. The strain in the specimen is found by measuring the change in the electrical resistance of the grid material. The bonded resistance strain gauge is low in cost, can be made with a short gage length, is only moderately affected by temperature changes, has small physical size and low mass, and has relatively low sensitivity to strain. It is suitable for measuring both static and dynamic strains

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Structure of Strain Gauge

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Strain Gauge Typically, the nominal unstrained resistances of metallic strain gauges are usually 120 Ω, 350 Ω or 1000 Ω. The following is a typical set of parameters for a strain gauge:

• Unrestrained resistance: 120Ω±1Ω

• Gauge factor: 2.0-2.2

• Linearity: ±0.3%

• Maximum tensile strain: +2x10-2

• Maximum compressive strain:-1x10-2

• Maximum operating temperature: 150 °C

• Maximum gauge current: 15 mA to 100 mA

Strain Gauge

Ideally we would like the material to have a low coefficient of resistance. The alloy Advance is used as the basis of many strain gauges has the following characteristics:

• Composition: 54% Copper, 44% Nickel, 1% Manganese

• Temperature coefficient of resistance: 2x10-5 K-1

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Strain Gauge

2- Piezoresistive elements (the resistance of which changes in response to a change in resistivity caused by the strain).

• These are also sometimes referred to as semiconductor strain gauges to distinguish them from metallic strain gauges. The semiconductor strain gauge is based on the piezoresistive effect in certain semiconductor materials such as silicon and germanium. Semiconductor gauges have elastic behaviour and can be produced to have either positive or negative resistance changes when strained.

Strain Gauge

They can be made physically small while still maintaining a high nominal resistance. The strain limit for these gages is in the 1000 to 10000 με range, with most tested to 3000 με in tension. Semiconductor gauges exhibit a high sensitivity to strain, but the change in resistance with strain is nonlinear. Their resistance and output are temperature sensitive, and the high output, resulting from changes in resistance as large as 10-20%, can cause measurement problems when using the devices in a bridge circuit.

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Strain Gauge

However, mathematical corrections for temperature sensitivity, the nonlinearity of output, and the nonlinear characteristics of the bridge circuit (if used) can be made automatically when using computer controlled instrumentation to measure strain with semiconductor gauges. They can be used to measure both static and dynamic strains. When measuring dynamic strains, temperature effects are usually less important than for static strain measurements and the high output of the semiconductor gauge is an advantage.

Strain Gauge

Comparison between metallic strain gauges and piezoresisitve sensors

1- The main advantage of piezoresistive sensors over metallic strain gauges is their high gauge factor. The Poisson ratio for most metals ranges from 0.25 to 0.35 giving a gauge factor ranging from 1.9 to 2.1. However, in piezoresistive sensors the resistivity term is the dominant term with much higher values. For example p-doped Silicon has a value of +100 to +175, while n-doped Silicon has a value ranging from -100 to -140 (a positive value denotes an increase in resistance with strain, while a negative value denotes a decrease in resistance with strain).

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Strain Gauge

2- The main disadvantage of piezoresistive sensors is their nonlinearity and high temperature dependence. For example the gauge factor could change from 135 down to 120 when the temperature changes from 0 to 40 °C .

Strain Gauge

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Steps in fitting a strain gauge to a surface

1- Select strain gauge: Select the strain gauge model and gauge length which meet the requirements of the measuring object and purpose.


2- Prepare the surface: This will involve removing any rust, and making the surface very polished. Application of certain acids and conditioners is also required.

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3- Mark the correct orientation: The orientation of the strain gauge on the surface has to be marked. This ensures that the strain gauge is oriented exactly in the right direction of the strain to be measured.

4- Prepare the Gauge for Mounting: The gauge is then prepared for mounting, by the use of special sticky tape.


5- Position gauge on the shaft: The gauge is then positioned on the shaft. This has to be done accurately to ensure that the orientation is correct.

6 -Glue the gauge: The gauge is then glued onto the shaft by the use of super-glue. It is held in position for a period of time to ensure that the super-glue has dried.

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7- Connect the lead wires: The lead wires are then soldered onto the pads. Some solder is first applied onto the pad. The wires are then soldered.

8- Protect the strain gauge: The strain gauge can be protected by the application of a certain varnish. This provides electrical insulation. This can also be followed by physical protection (e.g., cover).

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Strain Gauge

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Thermal Effect on Strain Gauge

• Fluctuations in ambient and in operating temperatures produce the most severe effects generally dealt with in strain measuring circuitry.

• The problems arise primarily from two mechanisms:

1. Changes in the gage resistivity with temperature.

2. Temperature induced strain in the gage element.

3. Additionally, for certain bridge circuits in which the elements are widely separated (20-100 feet), the thermally induced resistance changes in the lead wires may also be significant.


Changes in the gauge resistivity with temperature

• Several alloys have obviously been chosen for their very low temperature coefficient of resistivity. The “constantan” alloy is probably the most common material for general static applications.“Isoelastic” alloy is frequently used for gages which are subjected to dynamic strains but when interest is in the measurement of peak-to-peak values only. In this case the higher gage factor is attractive while the thermally induced change in resistance appears as a steady state offset and is not recorded in peak-to-peak measurements.

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Changes in the gauge resistivity with temperature


Temperature induced strain in the gauge element

• One of the problems of strain measurement is thermal effect. Besides external force, changing temperatures elongate or contract the measuring object with a certain linear expansion coefficient. Accordingly, a strain gage bonded to the object bears thermally-induced apparent strain. Temperature compensation solves this problem.

1. Active-Dummy method

2. Self-Temperature-Compensation Method

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Thermal Effect on Strain Gauge Active-Dummy method

• The active-dummy method uses the 2-gage system where an active gage, A, is bonded to the measuring object and a dummy gage, D, is bonded to a dummy block which is free from the stress of the measuring object but under the same temperature condition as that affecting the measuring object. The dummy block should be made of the same material as the measuring object. As shown in the following figure, the two gages are connected to adjacent sides of the bridge. Since the measuring object and the dummy block are under the same temperature condition, thermally-induced elongation or contraction is the same on both of them. Thus, gages A and B bear the same thermally-induced strain, which is compensated to let the output, e, be zero because these gages are connected to adjacent sides.

Thermal Effect on Strain Gauge Active-Dummy method

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Self-Temperature-Compensation Method

• Theoretically, the active-dummy method described above is an ideal temperature compensation method. But the method involves problems in the form of an extra task to bond two gages and install the dummy block. To solve these problems, the self-temperature-compensation gage was developed as the method of compensating temperature with a single gage. With the self-temperature-compensation gage, the temperature coefficient of resistance of the sensing element is controlled based on the linear expansion coefficient of the measuring object. Thus, the gage enables strain measurement without receiving any thermal effect if it is matched with the measuring object.



• Suppose that the linear expansion coefficient of the measuring object is (βs) and that of the resistive element of the strain gage is (βg). When the strain gage is bonded to the measuring object as shown in the following figure, the strain gage bears thermally-induced apparent strain/°C, (εT), as follows:

• Where:

α: Temperature coefficient of resistance of resistive element

Ks: Gage factor of strain gage

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• The gage factor, Ks, is determined by the material of the resistive element, and the linear expansion coefficients, βs and βg, are determined by the materials of the measuring object and the resistive element, respectively.

• Thus, controlling the temperature coefficient of resistance, α, of the resistive element suffices to

make the thermally-induced apparent strain, εT, zero in the above equation.

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Self-Temperature Compensation Method

• The temperature coefficient of resistance, α, of the resistive element can be controlled through heat treatment in the foil production process.

• Since it is adjusted to the linear expansion coefficient of the intended measuring object, application of the gage to other than the intended materials not only voids temperature compensation but also causes large measurement errors.



• The self-temperature-compensation gage is designed so that εT in the above equation is approximated to zero by controlling the resistive temperature coefficient of the gage's resistive element according to the linear expansion coefficient of the measuring object.

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Temperature induced strain in the leadwires

Leadwires compensation

Strain Gauges

• Stress measurements

• Strain gauge bridge applications

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