Experiment No. 01
Objective:
To study the stain gauge and whetstone bridge.
Apparatus:
1. Stain gauge
2. Multi meter
Fig. 1.1: Strain gauge apparatus
Principle of Strain Gages:
The strain gage is tightly bonded to a measuring object so that the sensing element (metallic resistive foil) may elongate or contract according to the strain borne by the measuring object. When bearing mechanical elongation or contraction, most metals undergo a change in electric resistance. The strain gage applies this principle to strain measurement through the resistance change. Generally, the sensing element of the strain gage is made of a copper-nickel alloy foil. The alloy foil has a rate of resist-ance change proportional to strain with a certain constant.
Strain measurement with strain gages:
Since the handling method is comparatively easy, a strain gage has widely been used, enabling strain measurement to imply measurement with a strain gage in most cases. When a fine metallic wire is pulled, it has its electric resistance changed. It is experimentally demonstrated that most metals have their electrical resistance changed in proportion to elongation or contraction in the elastic region. By bonding such a fine metallic wire to the surface of an object, strain on the object can be determined through measurement of the resistance change. The resistance wire should be 1/50 to 1/200mm in diameter and provide high specific resistance. Generally, a copper-nickel alloy (Advance) wire is used.
Usually, an instrument equipped with a bridge circuit and amplifier is used to measure the resistance change. Since a strain gage can follow elongation/contraction occurring at several hundred kHz, its combination with a proper measuring instrument enables measurement of impactive phenomena. Measurement of fluctuating stress on parts of running vehicles
or flying aircraft was made possible using a strain gage and a proper mating instrument.
Theory:
Strain is the amount of deformation of a body due to an applied force. More specifically, strain (ΔL) is defined as the fractional change in length.
Types of strain measuring methods:
There are various types of strain measuring methods, which may roughly be classified into mechanical, optical, and electrical methods. Since strain on a substance may geometrically be regarded as a distance change between two points on the substance, all methods are but a way of measuring such a distance change. If the elastic modulus of the object material is known, strain measurement enables calculation of stress. Thus, strain measurement is often
performed to determine the stress initiated in the substance by an external
force, rather than to know the strain quantity. Let’s express the principle as follows:
where,
R: Original resistance of strain gage, Ω (ohm)
: Elongation- or contraction-initiated resistance change, Ω (ohm)
K: Proportional constant (called gage factor)
: Strain
The gage factor, K, differs depending on the metallic materials. The copper-nickel alloy (Advance) provides a gage factor around 2. Thus, a strain gage using this alloy for the sensing element enables conversion of mechanical strain to a corresponding electrical resistance change. However, since strain is an invisible infinitesimal phenomenon, the resistance change caused by strain is extremely small.
What’s the Wheatstone Bridge?
The Wheatstone bridge is an electric circuit suitable for detection of minute resistance changes. It is therefore used to measure resistance changes of a strain gage. The bridge is configured by combining four resistors as shown in Fig. 1.1.
Suppose: 
Fig. 1.2: Wheatstone bridge circuit
R1 = R2 = R3 = R4, or
R1 x R3 = R2 x R4
Then, whatever voltage is applied to the input, the output, e, is zero. Such a bridge status is called “balanced.” When the bridge loses the balance, it outputs a voltage corresponding to the resistance change.
As shown in Fig. 1.2, a strain gage is connected in place of R1 in the circuit. When the gage bears strain and initiates a Fig. 1.2 resistance change, R, the bridge outputs a corresponding voltage, e.
That is,
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Fig. 1.3: 2-gage system |
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The structure described above is called a 1-gage system since only one gage is connected to the bridge. Besides the 1-gage system, there are 2- gage and 4-gage systems.
Ø
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with the 2-gage system, gages are connected to the bridge in either of two ways, shown in.
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Ø Output voltage of 4-gage system
The 4-gage system has four gages connected one each to all four sides of the bridge. While this system is rarely used for strain measurement, it is frequently applied to strain-gage transducers.
When the gages at the four sides have their resistance changed to R1 + R1, R2 + R2, R3 + R3 and R4 + R4, respectively, the bridge output voltage, e, is:
Fig. 1.4: 4-gage system
If the gages at the four sides are equal in specifications including the gage factor, K, and receive strains, , , and , respectively, the equation above will be:
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Ø Output voltage of 1-gage system
In the cited equation for the 4-gage system, the 1- gage system undergoes resistance change, R1, at one side only. Thus, the output voltage is:
Fig. 1.5: 1-gage system
Ø Output voltage of 2-gage system
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Fig. 1.6 a: 2-gage system
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That is to say, the strain borne by the second gage is subtracted from, or added to, the strain borne by the first gage, depending on the sides to which the two gages are inserted, adjacent or opposite.
Fig. 1.6 b: 2-gage system
with adjacent strain position
Viva’s Questions:
1. What is the working principle of a strain gauge?
Ans: A Strain gauge (sometimes referred to as a Strain gage) is a sensor whose resistance varies with applied force; It converts force, pressure, tension, weight, etc., into a change in electrical resistance which can then be measured. When external forces are applied to a stationary object, stress and strain are the result.
2. How do you measure strain with strain gauge?
Ans: We can measure strain using several methods, but the most common is with a strain gage. A strain gage's electrical resistance varies in proportion to the amount of strain in the device. The most widely used strain gage is the bonded metallic strain gage.
3. What is strain gauge factor?
Ans: Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance R, to the mechanical strain ε.
4. What are the factors affecting accuracy of strain gauges?
Ans: The factors that affect a strain gauge are the temperature, electromagnetic interference, humidity, and the environment.
5. What is a strain gauge made of?
Ans: Most strain gauges are made from a constantan alloy. Various constantan alloys and Karma alloys have been designed so that the temperature effects on the resistance of the strain gauge itself largely cancel out the resistance change of the gauge due to the thermal expansion of the object under test.
6. What is Poisson's ratio used for?
Ans: Poisson's ratio is a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression. Conversely, if the material is stretched rather than compressed, it usually tends to contract in the directions transverse to the direction of stretching.
7. How does a Wheatstone bridge strain gauge work?
Ans: In order to measure strain with a bonded resistance strain gauge, it must be connected to an electric circuit that is capable of measuring the minute changes in resistance corresponding to strain.
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