STRAIN MEASURING DEVICES
Submitt ed by: Ankit Garg
08107009
Ashish Negi
08107011 Baibhav
Jha
08107012 Chandan
Gakhar 08107013
AIM: To study the different strain measuring devices and affect of temperature on them.
STRAIN GAUGE: While there are several methods of measuring strain, the most common is with a strain gauge. A strain gauge's electrical resistance varies in proportion to the amount of strain placed on it. The most widely used gauge is the bonded metallic strain gauge. The metallic strain gauge consists of a very fine wire or, more commonly, metallic foil arranged in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain in the parallel direction (shown as the "active grid length" in the Bonded Metallic Strain Gauge figure). The cross sectional area of the grid is minimized to reduce the effect of shear strain and Poisson strain.
It is very important that you properly mount the strain gauge onto the test specimen. This ensures the strain accurately transfers from the test specimen through the adhesive and strain gauge backing to the foil.
Electrical Properties of the Resistance Gage The fundamental formula for the resistance of a wire with uniform cross section, A, and resistivity, , can be expressed as:
……………………..(1)
where L is the wire length.
This relation is generally accurate for common metals and many nonmetals at room temperature when subjected to direct or low frequency currents*. We consider the gage to be formed from a length of uniform wire and subjected to an elongation as shown: The change in resistance can be expressed from Eq. 1 as
where signifies a change in the quantity. This is a complicated expression in its present form, however, it should be clear that for metallic wires subjected to engineering strain levels that L << L and A << A. If << as well, then we can simplify the expression by approximating with the infinitesimal differential change, d():
The differential expression on the right side is tedious to compute directly but can be easily determined using “log derivatives” as follows. First take the natural log (ln) of the equation yielding:
and now take the differential of this recalling that d(ln(x))=dx/x to get the simpler result:
In general we may write
where D is a cross section dimension and C is some constant (e.g., D=R and C= for a circle). Using the “log derivative” method, it follows that:
At this point we note that the longitudinal strain can be written in differential form as:
and the transverse or lateral strain as:
Also for linearly elastic and isotropic behavior of the wire:
Then using these results:
Finally, the resistance change per unit resistance ( R/R) can then be written:
………………..(2) This expresses the basic proportionality between resistance and strain in the gage element material. In practice, the strain measurements rarely involve quantities larger than a few millistrain ( x 10-3). Therefore, measuring strain requires accurate measurement of very small changes in resistance. For example, suppose a test specimen undergoes a substantial strain of 500 . A strain gauge with a gauge factor GF = 2 will exhibit a change in electrical resistance of only 2·(500 x 10-6) = 0.1%. For a 120
gauge, this is a change of only 0.12
.
Different types of circuit:
Quarter-Bridge Circut The Half-Bridge Circuit figure illustrates a bending beam application with one bridge mounted in tension (R G + R) and the other mounted in compression (RG - R). This half-bridge configuration, whose circuit diagram is also
illustrated in the Half-Bridge Circuit figure, yields an output voltage that is linear and approximately double that of the quarter-bridge circuit.
Half-Bridge Circuit Finally, you can further increase the sensitivity of the circuit by making all four of the arms of the bridge active strain gauges and mounting two gauges in tension and two gauges in compression. The full-bridge circuit is shown in the Full-Bridge Circuit figure below.
Full-Bridge Circuit The equations given here for the Wheatstone bridge circuits assume an initially balanced bridge that generates zero output when you do not apply strain. In practice however, resistance tolerances and strain induced by gauge application will generate some initial offset voltage. This initial offset voltage is typically handled in two ways. First, you can use a special offsetnulling, or balancing, circuit to adjust the resistance in the bridge to rebalance the bridge to zero output. Alternatively, you can measure the initial unstrained output of the circuit and compensate in software. With this in mind, there are several types of commonly measured strain (in order of relative popularity):
Bending Strain -- resulting from a linear force (FV) exerted in the vertical direction.
Axial Strain -- resulting from a linear force (Fa) exerted in the horizontal direction.
Shear Strain -- resulting from a linear force (F S) with components in both the vertical and horizontal direction.
Torsional Strain -- resulting from a circular force (F T) with components in both the vertical and horizontal direction.
Potentiometers They are widely used as displacement transducers because of their simple construction and ability to give large output signal. They can be used as a voltage divider to obtain a manually adjustable output voltage at the slider (wiper) from a fixed input voltage applied across the two ends of the pot. The formula for voltage across R is determined by the formula: Vo = V[R2/(R1+R2)]= V(R2/R1) One of the advantages of Potential Divider compared to a variable resistor in series with the source is that, while variable resistors have a maximum resistance where some current ill always flow, dividers are able to vary the output voltage from maximum (Vs) to ground as the wiper moves from one end of the pot to the other. There is, however, always a small amount of contact resistance. In addition, the load resistance is often not known and therefore simply placing a variable resistor in series with the load could have a negligible effect or an excessive effect, depending on the load.
Types of Potentiometers Potentiometers; most commonly known as Pot, consists of resistance element provided with a sliding contact. This sliding contact is known as wiper. Based on motion of sliding contact, potentiometers are classified as: 1. Translation type potentiometer 2. Rotational type and 3. Helix type or Helipot 1. Translation type potentiometer:
In translation type pot, motion of sliding contact is linear. The diagrammatic representation of translational potentiometer is as follows:
νο=Vι R'/R
V0 = Input Voltage x (resistance at output terminals/resistance at input terminals) 2. Rotational type potentiometer:
In rotational type potentiometers, motion of wiper is rotator in nature. These type of potentiometers are used to measure the angular displacement and are circular in shape. The displacement may be full scale angular displacement or as slam as upto 10 degrees.
3. Helipot: When there are two types of motion such as translational as
well as rotational, helix typw pot structure is used. Hence, this is also called heliport. The helical resistive element can be used for measurement of either transational or rotational motion.
Gauge factor Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance to the mechanical strain ε, which is the relative change in length.
In practice, the resistance is also dependent on temperature. The total effect is
ε = strain = ΔL / L ΔL = absolute change in length
L = original length
ν = Poisson's ratio
ρ = Resistivity
ΔR = change in strain gauge resistance resistance of strain gauge
R = unstrained
α = temperature coefficient change
θ = temperature
General examples of Gauge Factor values: Gau
Material
ge Factor
Metal foil strain gauge
2-5
Thin-film metal
Single crystal silicon Polysilicon Thick-film resistors
2 -125
to + 200 ±30 10
BONDING AND UNBONDING STRAIN GAUGE: The Gauge factor lies usually between 2 and 4. These sensors can be found as bounded (having the metal in the sensor covered) or unbounded (the metal is exposed to the environment).
Unbound Strain Gauge The unbounded strain gauge differs from the bounded strain gauges in that the strain sensitive resistive wire is mounted on a mechanical frame whose parts can move in relation to each other which causes the change in wire tension as load changes. The wire is applied with initial tension so that device can measure both tension and compression. In such strain gauges, the wire grid is wound over a moving mechanism supported over number of posts or pillars whose movements is governed by spring element attached to a diaphragm whose movement is affected by the applied pressure or pressure to be measured. The wire is used in the form of four windings of strain gauge which forms a part of bridge circuit. Motion of the spring centre on account of applied pressure to diaphragm causes the movement of posts upon which these wire are mounted. The strain is increased on two of the windings and is decreased in the other two windings. These windings in the form of Wheatstone bridge provide a millivolt output which is a linear function of process pressure to be measured.
TEMPERATURE COMPENSATION: Compensating for Temperature Drift of the Sensor Strain gage manufacturers attempt to minimize sensitivity to temperature by processing the gage material to compensate for the thermal expansion of the specimen material for which the gage is intended. While compensated gages reduce the thermal sensitivity, they do not totally remove it. A residual error on the order of 10 me/°C is still possible when you use a temperature compensating gage. Therefore, additional temperature compensation is sometimes necessary. Further correction is possible by measuring temperature and using a correction curve to correct the data. Manufacturers print the polynomial coefficients of this curve to fourth order on each package of gages (see Figure 2 below). With the coefficients you can conduct temperature correction in software. An error as small as 1 me/°C is possible using this technique.
Figure 2. Thermal Output Rating
Minimize Temperature Effects with Half-Bridge and Full-Bridge Sensors By using two or four strain gages in a Wheatstone bridge, you can minimize the effect of temperature. These are called half-bridge and full-bridge configurations, respectively. See Figures 4 and 5. With all strain gages in a bridge at the same temperature and mounted on the same material, any changes in temperature affect all gages in the same way. Because the temperature changes are identical in the gages, the ratio of their resistance does not change, and the output voltage of the gage does not change. The simplest way you can correct for temperature drift is by using half-bridge or full-bridge configurations.
Figure 4. Half-Bridge Configuration
Figure 5. Full-Bridge Configuration
