Strain Gauge

Introduction

A strain gauge is a resistive sensor whose resistance is a function of applied strain. Under the effect of external force, the length and cross-section area of a conductor changes. Due to this resistance change takes place. The resistivity of the conductor also changes and this property is known as the piezoresistive effect and is expressed through the gauge factor G_f of the conductor. The value of Guage factor is ≈ 2 for most conductors. For Platinum its value is 6. For silicon its value is upto 150.

Early strain gauges were fine metal filaments. Modern strain gauges are manufactured primarily as metallic foil using the constantan or Semiconductor elements (e.g., silicon with trace impurity boron). They are manufactured by first forming a thin film (foil) of metal or a single crystal of Semiconductor material and then cutting it into a suitable grid pattern. This process is much more economical and is more precise than making strain gauges with metal filaments.

The strain-gauge element is formed on a backing film of electrically insulated material of polymide plastic. This element is cemented or bonded using epoxy, onto the member whose strain is to be measured. strain from the object must be reliably coupled to the gauge wire, whereas the wire must be electrically isolated from the object. The coefficient of thermal expansion of the backing should be matched to that of the wire. Alternatively, a thin film of insulating ceramic substrate is melted onto the measurement surface, on which the strain gauge is mounted directly. The direction of sensitivity is the major direction of elongation of the strain-gauge element. To measure strains in more than one direction, multiple strain gauges (e.g., various rosette configurations) are available as single units. These units have more than one direction of sensitivity.

Gage resistance values range from 30 to 3000 ohms, with 350 ohms being the most
commonly used.

Theory

The change of electrical resistance of a material when mechanically deformed is the property used in resistance-type strain gauges. The resistance R of a conductor of length ℓ and area of cross-section A is given by

Under the influence of tensile force F, the length of the conductor increases by dL and diameter decreases by dD and the resistance changes by dR.

 

Differentiating both sides,

where

If the change in the value of resistivity of a material under strain is neglected, the Gauge factor can be written as

The Poisson’s ration for all metals is between 0 to 0.5. This gives a gauge factor of about 2.

Strain gauge Applications

Many variables—including displacement, acceleration, pressure, temperature, liquid level, stress, force, and torque—can be determined using strain measurements. Some variables (e.g., stress, force, and torque) can be determined by measuring the strain of the dynamic object itself at suitable locations. In other situations, an auxiliary front-end device may be required to convert the measurand into a proportional strain. For instance, pressure or displacement may be measured by converting them to a measurable strain using a diaphragm, bellows, or a bending element. Acceleration may be measured by first converting it into an inertia force of a suitable mass (seismic mass) element, then subjecting a cantilever (strain member) to that inertia force, and finally, measuring the strain at a high-sensitivity location of the cantilever element. Temperature may be measured by measuring the thermal expansion or deformation in a bimetallic element.

Strain Gauge measurement

The preferred circuit for use in strain-gauge measurements is the Wheatstone bridge. One or more of the four resistors R1, R2, R3, and R4 in the bridge may represent strain gauges. The output relationship for the Wheatstone bridge circuit is given by

When this output voltage is zero, the bridge is balanced. It follows from Equation above that for a balanced bridge,

Equation above is valid for any value of the load resistance R_L, because when the bridge is balanced, current i through the load become zero.

Bridge Sensitivity

Strain-gauge measurements are calibrated with respect to a balanced bridge. When a strain gauge in
the bridge deforms, the balance is upset. If one of the arms of the bridge has a variable resistor, it can be
adjusted to restore the balance. The amount of this adjustment measures the amount by which the resistance of the strain gauge has changed, thereby measuring the applied strain. This is known as the null-balance method of strain measurement. This method is inherently slow because of the time required to balance the bridge each time a reading is taken.

A more common method, which is particularly suitable for making dynamic readings from a strain-gauge bridge, is to measure the output voltage resulting from the imbalance caused by the deformation of an active strain gauge in the bridge. To determine the calibration constant of a strain-gauge bridge, the sensitivity of the bridge output to changes in the four resistors in the bridge should be known. For small changes in resistance, this may be determined as dVo/Vin.

Tee Rosette

Rectangular Rosette

Figure below shows a rectangular rosette which is used when orientation of principal axes is unknown. The gauge elements are mounted in 0°, 45° and 90° orientation. Typical setup is for each gauge element to become an active arm in separate Wheatstone bridge circuits (i.e. a Wheatstone bridge for each gauge element of the rosette).

Strain gauge installation

Proper strain gauge installation is necessary to obtain accurate
experimental stress results. Skilled technicians usually install strain gauges after attending a
strain gauge school or training course. The decision on locations of the desired stress
measurements is usually made by the test sponsor or mechanical design team of the test item.
The instrumentation engineer must then ensure the following items are addressed. Failure to
proceed in this fashion will result in poor gauge adhesion, faulty data, and engineer frustration.

a. The supplies should be on hand for the technicians to apply the gauges when the time comes.

b. The type of gauge, the material to which the gauge is to be mounted, and the environment in which the gauge will be exposed.

c. Are the principal axes known (many times they are not)?

d. How long do these gauges need to be used?

e. Will the gauges be submersed in a liquid?

f. Will the gauges be exposed to temperature extremes?

g. How long will the lead wires need to be?

h. Can the bridge completion resistors be co-located at the site of the strain gauge?

Once all of the supplies are on hand and the desired locations of the gauges known, the installation process can begin. The following steps should be followed.

a. Surface preparation. The surfaces to which the gauges are to be applied must be free of paint, oil, grease, etc. The surface preparation usually involves paint stripping, sanding, and degreasing.

b. Install gauge or rosette. The gauge (or rosette) is applied to the surface with an adhesive. Adhesives exist for a variety of environments and desired lifespan. Cure times vary from a few hours to several days. Cure temperatures can vary from room temperature to several hundred degrees Centigrade. During the curing process, evenly distributed pressure is usually required on the applied gauge(s). 

c. Install bridge. The bridge completion resistor assemblies and small wire terminals or solder tabs may be bonded near the gauge. Small gauge wire is typically used to connect the gauge to the bridge completion packs and to the wire solder tabs. The larger gauge lead wires are then soldered to these tabs and completion networks (not directly to the gauge itself).

d. Epoxies and sealants. Finally, depending on the test environment, several additional coatings of specialized epoxies and sealants may be needed to protect the gauge(s), bridge completion packs, and/or wire tabs.

e. Patience and skill. Skipping steps is not advisable.

GATE QUESTIONS

GATE-2007

GATE-2008

GATE-2009

GATE-2010

GATE-2012

GATE-2014

Semiconductor strain gages typically have much higher gage factors than those of metallic strain gages, primarily due to :

(A) higher temperature sensitivity

(B) higher Poisson’s ratio

(C) higher piezoresitive coefficient

(D) higher magnetostrictive coefficient

GATE-2015

A p-type semiconductor strain gauge has a nominal resistance of 1000 Ω and a gauge factor of +200 at 25 °C. The resistance of the strain gauge in ohms when subjected to a strain of +10−4 m/m at the same temperature is __________ Ω.

GATE-2018

A 1000 Ohm strain gage (Rg) has a gage factor of 2.5. It is connected in the bridge as shown in
figure. The strain gage is subjected with a positive strain of 400 um/m. The output Vo (in

mV) of the bridge is (up to two decimal places) _____.

LVDT- Linear Variable Differential transformer

LVDT- Linear Variable Differential transformer

Position and displacement may be sensed by methods of electromagnetic induction. The most commonly used inductive transducer to convert linear motion into electrical signals is the Linear Variable Differential Transformer or LVDT as they are commonly known.

An LVDT consists of one primary coil and two secondary coils. The primary coil carries ac excitation (Vref) that induces a steady ac voltage in the secondary coils. The induced amplitude depends on flux coupling between the coils.

There are two techniques for changing the coupling.

• One is the movement of a core made of ferromagnetic material within the flux path. This changes the reluctance of the path, which, in turn, alters the coupling between the coils. This is the basis for the operation of a LVDT (linear variable differential transformer), a RVDT (rotary variable differential transformer).
• The other method is to physically move one coil with respect to another.

Generally, the core is made of high permeability, nickel iron which is hydrogen annealed. It gives low harmonics, low null voltage.

The ac excitation in the primary coil produces an alternating magnetic field which induces an alternating current in the secondary coils. The secondary coils are connected in series opposition. Hence the polarity of voltage induces is opposite in the two secondary coils. When the core is positioned in the magnetic center of the transformer, the secondary output signals cancel and there is no output voltage. This is known as “null position”.

Moving the core away from the central position unbalances the induced magnetic flux ratio between the secondaries, developing an output. As the core moves, reluctance of the flux path changes. Hence, the degree of flux coupling depends on the axial position of the core. At a steady state, the amplitude of the induced voltage is proportional to the core displacement. Consequently, voltage may be used as a measure of a displacement. The LVDT provides the direction as well as magnitude of the displacement. The direction is determined by the phase angle between the primary (reference) voltage and the secondary voltage. Excitation voltage is generated by a stable oscillator.

The LVDT is considered a passive transducer because the displacement of the core, which is being measured, itself provides energy for changing the induced voltage in the secondary coil. Even though an external power supply is used to energize the primary coil, which in turn induces a steady voltage at the carrier frequency in the secondary coil, which is not relevant in the definition of a passive transducer.

Note: Because of opposed secondary windings, the LVDT provides the direction as well as the magnitude of displacement. When the output signal is demodulated, its sign gives the direction. If the output signal is not demodulated, the direction is determined by the phase angle between the primary (reference) voltage and the secondary (output) voltage, which includes the carrier signal.

For an LVDT to measure transient motions accurately, the frequency of the reference voltage (the carrier frequency) has to be at least 10 times larger than the largest significant (useful) frequency component in the measured motion, and typically can be as high as 20 kHz. For quasi-dynamic displacements and slow transients of the order of a few hertz, a standard ac supply (at 50/60 Hz line frequency) is adequate. The performance (particularly sensitivity and accuracy) is known to improve with the excitation frequency, however. Since the amplitude of the output signal is proportional to the amplitude of the primary signal, the reference voltage should be regulated to get accurate results. In particular, the power source should have a low output impedance.

Ideally the output at the null position should be equal to zero. However in practice there exists a small voltage at the null position. This may be due to presence of harmonics in the input supply  voltage, stray magnetic fields, temperature effect among other reasons.

Calibration and Compensation

An LVDT may be calibrated in millimeter per volt (mm/V), in its linear range. In addition, and a displacement offset (mm) may be provided. This typically represents the least squares fit of a set of calibration data. Since ambient temperature and other environmental conditions will affect the LVDT output, in addition to the primary and secondary coils, a reference coil may be available for compensation of the LVDT output.

Advantages of the LVDT include the following:

1.       It is essentially a non-contacting device with no frictional resistance. Lightweight core will result in very small resistive forces.

2.       Hysteresis (both magnetic hysteresis and mechanical backlash) is negligible.

3.       It has low output impedance, typically in the order of 100 Ω.

4.       It provides directional measurements (positive/negative).

5.       It is available in miniature sizes as well (e.g., length of 1 or 2 mm, displacement measurements of a fraction of a millimeter, and maximum travel or stroke of 1 mm).

6.       It has a simple and robust construction (inexpensive and durable)

7.       It has fine resolutions (theoretically, infinitesimal resolution; practically, much better than a coil potentiometer)

Disadvantages

1.      They are sensitive to stray magnetic field.

2.      Output signal need amplification due to its small magnitude.

3.      Measurement is affected by vibrations.

4.      Affected by temperature variation.

Piezo electric effect

Electrical charges are produced on the opposite surfaces of some crystals when subjected to force or torsion. The electrical charge produced is proportional to the effective force. By application of force, dimension of the crystal changes causing a displacement of charge. Piezoelectric effect is reversible, i.e. if a varying potential is applied to the crystal, it will change the dimension of the crystal along a certain axis.

It must be remembered that a piezoelectric crystal can convert a changing force into a changing electrical signal, whereas a steady-state force produces no electrical response.

Piezo-electric crystals are available in two forms- natural and man-made. Quartz and ceramic are examples of naturally available piezo-electric crystals whereas Rochelle salts, Lithium sulphate, Ammonium dihydrogen phosphate etc are examples of man-made crystals. Quartz is considered as one of the most stable piezo-electric crystal and is known for its ability
to perform accurate measurement for time and frequency. Its output is independent of temperature variation. They have low voltage sensitivity but high charge sensitivity.

Description of operation

The piezoelectric effect causes a realignment and accumulation of positively and negatively charged electrical particles, or ions, at the opposed surfaces of a crystal lattice, when that lattice undergoes stress. The number of ions that accumulate is directly proportional to the amplitude of the imposed stress or force.

PE transducers use a spring-mass system to generate a force proportional to the amplitude and frequency of the input quantity. The stress imposed upon the piezoelectric material is the direct result of a physical input such as acceleration, force, or pressure. To accomplish this, a mass is attached to the crystal, which, when accelerated, causes force to act upon the crystal. The mass, also known as a seismic mass, creates a force directly proportional to acceleration according to Newton’s law of motion, F=ma. Thin metallic electrodes collect the accumulated ions. Small lead wires interconnect the electrodes to an electrical connector or feed-through, to which cabling is attached. An advantage of PE materials is that they are self-generating and require no external power source.

A piezo-elecric crystal can be considered as charge generator and a capacitor. External force generates a charge and this charge appears as voltage across the electrodes.

The voltage V=Q/C . The voltage polarity depends on the direction of applied force.

The amount and polarity of charge produced is proportional to the magnitude and direction of force.

Charge Q = k_q x F Coulomb,                                                  (1)

where k_q is the charge sensitivity of the crystal; C/N and F is applied force; N

From Hooke’s Law, the Young’s modulus Y of the crystal is given as

Where A = area of crystal; t = thickness of crystal; Y = Young’s modulus; A = area of crystal;

From above equations,

The voltage output V_o is given as 

Where C is the capacitance between the electrodes;

From above equations, 

Where                          P = F/A= stress or pressure, N/m²

Electrical analysis of Piezo-electric crystals

Piezo-electric crystal can be considered a charge generator. The amount of charge is q= k_q x F.

The charge appears across capacitance C_p of the crystal. R_p is the leakage resistance of the crystal. The equivalent circuit with voltage source id shown above. The voltage

V=q/C_p = k_q x F/C_p

If a load is connected at the output, the load capacitance C_L and resistance R_L will make the loaded circuit as below.

We can consider Rp as very large (open).

The equivalent impedance of load is

The total impedance is

Displacement measurement using Piezo-crystal

At steady state when ω=0, M=0. Hence piezo-crystals are not suitable for static measurements.

Uses

They are used in numerous applications such as environmental stress screening, vibration control, active vibration reduction, flight testing, wind tunnel testing, structural testing, modal analysis, seismic vibration, package testing, shock, motion and attitude detection and stabilization, ride quality response and simulation, acoustic testing and noise, harshness and vibration testing. Fast response, ruggedness, high stiffness, extended range, and the ability to also measure quasi-static forces are standard features associated with PE sensors.

Gate Questions
GATE-2008

GATE-2012

 GATE-2013

 GATE-2014

 GATE-2018

Ultrasonic Flowmeters

Working Principle

The working principle of the ultrasonic flow meter is based on the transmission
of ultrasonic waves in a medium. One or more ultrasonic transmitting-receiving pairs are mounted in or on the pipe, diametrically opposite to each other. The first pair is placed slightly more downstream than the second pair, so they make a certain angle with the pipe longitudinally.

The main idea behind the principle is the detection of frequency or phase shift caused by flowing medium. The effective velocity of sound in a moving medium is equal to the velocity of sound relative to the medium plus the velocity of the medium with respect to the source of the sound. Thus, a sound wave propagating upstream will have a smaller effective velocity, and the sound propagating downstream will have a higher effective velocity. Because the difference between the two velocities is exactly twice the velocity of the medium, measuring the upstream–downstream velocity difference allows us to determine the velocity of the flow.

Types of Ultrasonic Flowmeters

There are various types of ultrasonic flowmeters in use for discharge measurement:

(1)   Transit time

This type of ultrasonic flowmeter makes use of the difference in the time for a sonic pulse to travel a fixed distance, first against the flow and then in the direction of flow. Transmit time flowmeters are sensitive to suspended solids or air bubbles in the fluid.

Figure above shows two ultrasonic generators positioned on opposite sides of a pipe of flow. Piezoelectric crystals are usually employed for that purpose. Each crystal can be used for either the generation of the ultrasonic waves or for receiving the ultrasonic waves. Two crystals are separated by distance D and positioned at angle ‘ф’ with respect to flow. The transit time of sound between two transducers A and B can be found through the average fluid velocity v:

where c is the velocity of sound in the fluid. The velocity v is the flow velocity averaged along the path of the ultrasound. By taking the difference between the downstream and upstream velocities, we find

(2)   Doppler frequency shift

This type is more popular and less expensive, but is not considered as accurate as the transit time flowmeter. It makes use of the Doppler frequency shift caused by sound reflected or scattered from suspensions in the flow path and is therefore more complementary than competitive to transit time flowmeters.

This technique is more popular in so-called “clamp-on” meters. The Doppler effect occurs with sound as well as electromagnetic waves. When a source or receiver moves in a wave medium, the frequency at the receiver will differ from the frequency at the transmitter. The frequency increases with a movement towards the source and it decreases with a movement away from the source. This is caused by the constant velocity of the wave in the medium. If all velocities in the same direction are counted positively, we can describe the Doppler effect as follows:

Where

f_o: observed frequency for movement

f_s: frequency of the source in rest

c: transmission velocity in the medium

v_o: velocity of the observer with respect to the medium

v_s: velocity of the source with respect to the medium

During the measurement the source (transmitting crystal) and the observer (receiving crystal) are fixed and the fluid is moving. The transmitted signal is only detected if dispersed by moving fluid particles. These particles can be solids or small gas pockets. The Doppler technique only works in liquids that contain enough solids or gas pockets.

The Doppler frequency shift is:

For the Doppler flow measurements, continuous ultrasonic waves can be used. Figure below shows a flowmeter with a transmitter–receiver assembly positioned inside the flowing stream. Here angles are zero. That differential is defined as

Installation requirement:

In general acoustic flow meters need no special requirements regarding installation on or in the process pipe:

-        A vibration-free location is recommended especially when applying the Doppler type flowmeter, as vibrations cause false signals which may fool the electronics.

-          Similar to most flow meters, the measuring pipe must be completely filled with the fluid.

-          A well-developed flow profile is absolutely required for a reliable and accurate measurement. That is why equalization pipes 10 D in front of and 5 D behind the meter are recommended to obtain the given level of accuracy (2%).

-          Pilot valves closely behind the flow meter negatively influence the measurement, especially when cavitation or supersonic velocities occur.

Characteristics:

–        No pressure loss in the pipe.

–        It is possible to measure without making contact with the fluid (“clamp-on”).

–        Only useful for liquids that are acoustically transparent.

–        A small, but not excessive amount of contamination of the liquid is necessary for the Doppler effect. The time-of-flight principle needs as little pollution as possible.

–        Difficult for small diameters, especially when using the time-of-flight principle.

–        For the time-of-flight difference meter the turndown can amount to 1:1,000 and an accuracy level from 1% to 2.5% is possible. For the Doppler type meter the turndown can amount to 1:3,000 with an accuracy level from 2% to 5%.

–        Individual calibration is needed for every medium.

–        Using the Doppler effect, the reading depends on the flow profile.

–        Accuracy levels up to 1% are possible (not when using clamp-on realizations).

–        At present it is also possible to ultrasonically measure the flow of gases, steam and even high-temperature steam.

Questions
GATE 2014
A transit time ultrasonic flowmeter uses a pair of ultrasonic transducers placed at 45° angle, as shown in the figure.

The inner diameter of the pipe is 0.5 m. The differential transit time is directly measured using a clock of frequency 5 MHz. The velocity of the fluid is small compared to the velocity of sound in the static fluid, which is 1500 m/s and the size of the crystals is negligible compared to the diameter of the pipe. The minimum change in fluid velocity (m/s) that can be measured using this system is_________.

GATE 2018
T he average velocity v of flow of clear water in a 100 cm (inner) diameter tube is measured
using the ultrasonic flow meter as shown in the figure. The angle ø is 45 degree. The measured
transit times are t1 = 0.9950 ms and t2 = 1.0000 ms. The velocity v (in m/s) in the pipe is (up

to one decimal place) ___.

Electromagnetic Flowmeter

The electromagnetic flow sensors are useful for measuring the movement of conductive liquids. They are true noninvasive measurements. The operating principle is based on Faraday’s Law of electromagnetic induction.

“If a conductor of length L (m) is moving with a velocity v (m/s), perpendicular to
a magnetic field of flux density B (Tesla), then the induced voltage e across the ends of conductor can be expressed as:

e = BLv

The magnetic field, the direction of the movement of the conductor, and the induced emf are all
perpendicular to each other.”

In the case of electromagnetic flowmeters, the conductor is the liquid flowing through the pipe, and the length of the conductor is the distance between the two electrodes, which is equal to the tube diameter. The velocity of the conductor is proportional to the mean flow velocity of the liquid.

The generated voltage does not depend on parameters such as pressure, temperature, viscosity, conductivity, etc. Only a minimal level of conductivity is required to give this signal a (very small) minimal power.

The accuracy of these meters can be as low as 0.25% and, in most applications, an accuracy of 1% is used.

The traditional magnetic flow meter consists of two units: the measuring probe and electronic converter-amplifier that transforms this mV signal into one or more standard analog or digital signals.

The electrodes are placed at positions where maximum potential differences occur. The electrodes are electrically isolated from the pipe walls by nonconductive liners to prevent short-circuiting of electrode signals. The liner also serves as protection to the flow tube to eliminate galvanic action and possible corrosion due to metal contacts.

The main body of a flowmeter and electrodes can be manufactured from stainless steel, tantalum, titanium, and various other alloys.

The measuring probe consists of two electrodes made of a non-magnetic material
and is positioned at the inside covered with an electric insulating layer. Commonly used insulating layer are Natural rubber or neoprene, PTFE (Teflon), PFA (Per Fluor Alkoxy), Ceramic.

Coil excitation

The magnet coils generate a magnetic field that depends on the form of the field
excitation signal. There are several types of flow meters coil excitation.

(a)    DC excitation: It is only applicable with liquid metals. DC excitation results in electrolysis and hence they are hardly ever used.

(b)   AC or Sinusoidal excitation: An alternating current of 50 Hz to 60 Hz in coils creates
the magnetic field to excite the liquid flowing within the pipe. The disadvantage of these applications is that the electronic noise causes the zero point to drift after a certain time. It is essential to manually readjust the zero point at regular time intervals.

(c)    Pulsed DC field: here the converter feeds the magnetic coils with a pulsed DC (low frequency square wave) current. Because the converter is provided with the necessary intelligence, it can independently control the zero point, so that the zero point is stable. This method has lower power consumption (5-25W).

(d)   Capacitive detection: Here the electrodes, which are in contact with the medium are replaced by capacitive plates and that function as the electrodes of a capacitor. For this model the minimum required conductivity is 100 times lower than for the model with the contact electrodes.

The installation of the flow sensor may occur in every position, as long as the measuring instrument is completely filled with the fluid. If the fluid contains solid particles or fats, the magnetic flow meter is best positioned vertically. When placing it horizontally, the heavier particles will precipitate and the lighter particles will come up.

Theoretically the direction of the flow is not important, as long as the correct electric connection is used.

At a low rate of flow (< 1 m/s) the desired accuracy cannot be obtained. The velocity can be increased by reducing the pipe.

The flow profile is not very important for the magnetic flow meter. In practice,

however, a straight pipe segment of 5 times the pipe’s diameter is recommended. The grounding is of vital importance. This is very important because the voltage on the electrodes amounts to only a few mV.

The pipes of electromagnetic flowmeters must be full of liquid at all times for accurate measurement. If the liquid does not make full contact with electrodes, the high impedance prevents the current flow; hence, measurements cannot be taken. Also, if the pipe is not full, even if contact is maintained between the liquid and electrodes, the empty portions of the pipe will lead to miscalculated flow rates.

Important features

·         Completely obstruction-free and hence no pressure loss.

·         Highly accurate, better than 1% FS for higher flow.

·         Wide span, good linearity.

·         Measuring principle not dependent on pressure, temperature or viscosity.

·         Expensive because of electronics.

·         Minimum conductivity required (5µS/cm).

·         Not dependent on the flow profile

·         No mechanically moving components, maintenance-free.

·         Ideal for contaminated liquids.