Strain Gauges

The original form of strain gauge was based on the ability of a metallic resistance wire to work as a transducer. If a length of wire is stretched, the resulting change in length is responsible for a proportionate reduction in diameter. Because the electrical resistance of a wire conductor is proportional to its cross-sectional area (and thus the square of the diameter), its effective resistance value will vary with strain. Provided the wire is not stretched beyond its yield point or elastic limit, it will recover its original length when the strain is released. Its actual electrical resistance under any strain up to its (mechanical) yield point is then a measure of the strain to which it’s being subjected.

The simple, wire strain gauge thus transfers strain into another measurable quantity—electrical resistance. The usual method is to connect the strain gauge into one arm of a Wheatstone bridge. Differences in actual wire resistance are determined by the amount of imbalance produced in the bridge circuit. Ideally, to eliminate the effect of differences in temperature, the resistance wire should have a zero temperature coefficient (that is, its resistivity should not change with temperature), although this can be compensated in other ways. What the simple, wire strain gauge does suffer from, though, is hysteresis effect, or a different response under decreasing strain compared with increasing strain.

Wire strain gauges are either unbonded or bonded. Unbonded strain gauge elements are made of one or more filaments of resistance wire stretched between supporting insulators. The supports are either attached directly to an elastic member used as a sensing element or are fastened independently, with a rigid insulator coupling the elastic member to the taut filaments. The displacement (strain) of the sensing element causes a change in the filament length, with a resulting change in resistance. Although transducers using unbonded gauges are still available, they are more fragile and less frequently used than bonded gauges.

The usual form of bonded strain gauge consists of a foil of a resistance alloy, such as constantan, bonded to an epoxy backing film (see ill. 4-1). The foil is either die cut or etched to produce a grid pattern sensitive to strain along one axis. Elongation or shortening of the gauge along the sensitive axis produces an increase or decrease in the resistance of the gauge. The backing film is then adhesive-bonded to an elastic member to sense the strain of the member due to applied stress. Foil gauges can measure tensile, compressive, or torsional stresses and so are used in transducers for practically every mechanical parameter. Foil gauges have also been constructed by thin-film techniques utilizing a ceramic film substrate on which the resistance alloy is vacuum deposited.

ill. 4-1. A bonded strain gauge. Resistance alloy is attached to an epoxy backing.

PIEZORESISTIVE STRAIN GAUGES

Piezoresistive strain gauges, also known as semiconductor strain gauges, are basically solid-state silicon resistors fabricated from a single piece of p- or n-doped silicon and incorporating an “active” length together with contacts at each end ( ill. 4-2).

Unlike a wire element, the resistance change in a piezoresistive strain gauge results largely from its change of resistivity with strain rather than its length and cross section. Compared with wire gauges, it’s also virtually free of mechanical hysteresis, and its resistance change is very much more sensitive to strain.

ill. 4-2. A silicon semiconductor strain gauge.

FATIGUE LIFE

The fatigue life of metallic foil gauges depends on the operating strain level, but with strains of 1000 pin, per inch (1000 micro strain) the life is typically 2 million cycles. For piezoresistive gauges the life is comparable if large strain levels are avoided. Otherwise, the life can be determined from the fatigue life (S/N) curve for silicon.

The piezoresistive strain gauge exhibits more than 100 times the unit resistance change of a foil gauge for any given strain. This means that if semiconductor gauges are connected as arms of a Wheatstone bridge, a very large output voltage can be produced, eliminating the need for subsequent amplification. However, such large resistance changes produce large unbalances in a Wheatstone bridge with constant-voltage excitation, resulting in very nonlinear outputs. This problem can be solved by exciting the bridge from a constant-current supply. A constant-current supply contains more complex circuitry than a constant-voltage regulator and may not always be as readily available.

Actually, the resistance change of a semiconductor strain gauge as a function of strain is not completely linear over its total strain range. This results in nonlinearity in some transducers, even with constant-current excitation. Foil gauge transducers require amplification because of low bridge output, but the linearity of the out put signal is not a problem.

TEMPERATURE EFFECTS

All resistance strain gauges are temperature sensitive to some extent. This sensitivity results from the change in the resistivity of the gauge material with temperature as well as from the differential expansion between the gauge material and the elastic member to which it’s bonded. This latter effect generates a false strain input to the gauge. Self-compensated foil gauges are being made with alloys whose thermal expansion is similar to that of the sensing element and whose coefficient of resistivity is very small.

ill. 4-3. A bridge circuit for minimizing the effects of temperature on a strain gauge.

No similar choice of materials is available for semiconductor gauges. The strain sensitivity of piezoresistive gauges is also significantly temperature sensitive, aggravating the other temperature effects.

Some of the temperature effects on strain gauges can be cancelled in the Wheatstone bridge circuit of ill. 4-3. If R1 and R2 or R3 and R4 both experience the same increase in resistance, their ratio will still be essentially the same, canceling much of the effect of the increased resistance. The effectiveness of bridge-circuit compensation is usually greater for self-compensated metallic strain gauges than for semiconductor strain gauges.

DIAPHRAGM BONDED STRAIN GAUGES

Strain gauges bonded to a flexible diaphragm are a common type of pressure transducer for measuring fluid pressure. With a diaphragm clamped around its edge, deflection under pressure will result in both tension and compression stresses being developed simultaneously (ill. 4-4). Thus, two gauges placed at the center of the diaphragm will measure tensile stress, and two more gauges towards the edge of the diaphragm will measure compression stress (ill. 4-5). They are connected in the bridge circuit shown in ill. 4-6. Tensile gauges are in opposite arms of the bridge, and compression gauges are in the other two opposite arms.

ill. 4-4. Deflection of a diaphragm under pressure.

ill. 4-5. Typical arrangement of strain gauges on a flexible diaphragm.

ill. 4-6. Interconnection of strain gauges, in the configuration of ill. 4-5, to form a bridge circuit.

Theoretically, any type of strain gauge can be used to sense bending of a diaphragm under pressure. However, semiconductor gauges have sensitivities some 50 to 100 times greater than wire or foil gauges and are normally preferred. Semiconductor gauges work equally well for low as well as high pressures (up to 50,000 lb/in. and can be made in extremely small sizes. A further reduction in size is possible by diffusing semiconductor gauges into a silicon chip and employing the chip itself as a diaphragm for a pressure transducer. Using this technique, manufacturers have produced pressure transducers as small as 0.050 inch overall diameter.

GAUGE FACTOR

The sensitivity of a strain gauge is defined as its gauge factor, which is the ratio of unit change in resistance to unit change in length:

gauge factor (GF) = ((ΔR/R)/(ΔL/L))

where Δ represents the change.

All electrical conductive materials exhibit a change in resistance with length, but in the majority of cases the gauge factor is too small to be useful. With the metal wires normally used for strain gauges, gauge factors from 2.0 to 5.0 are common. Much higher values are realizable, but high gauge factors are often accompanied by loss of stability (greater sensitivity to temperature or higher temperature coefficients).

Still higher values of the gauge factor can be realized with silicon semiconductor strain gauges, where figures from 50 to 200 are commonplace (but again with higher temperature coefficients). Another feature of semiconductor strain gauges is that by controlled processing they can be given either positive (increasing resistance) or negative (decreasing resistance) resistance characteristics with increasing length.

THE WHEATSTONE BRIDGE

The Wheatstone bridge is a basic but extremely useful circuit for detecting and /or measuring changes in the values of a resistor. It’s thus particularly useful as a simple signal conditioner for transducers that measure a parameter in terms of change of resistance produced in the transducer; such as a strain gauge transducer.

The standard form of a Wheatstone bridge is shown in ill. 4-7. Resistors R1 and R2 have fixed values. Rx is the unknown resistance to be measured. RA is a variable resistor used to adjust the bridge for zero output.

ill. 4-7. Wheatstone bridge for detecting small changes in the value of a resistance Rx.

The relationship is then

R_X = R_A - R2/R1

If R1 and R2 are equal, then R_x = R_A. In other words, with the bridge balanced by adjusting R_A to give zero output, the value of R is then equal to the adjusted value of R_A.

Now suppose R_x is a resistance-type transducer and R_A is adjusted to the same resistance so as to balance the bridge and give zero output. Any force applied to the transducer to change its resistance will unbalance the bridge, resulting in a signal output that can be read on a meter. This reading will be a direct measure of the transducer response.

This works both ways, so that with a zero-center meter, transducer reaction providing an increase in resistance will cause proportionate needle deflection one way; a decrease in resistance, a proportionate needle deflection the other way ( ill. 4-8). The sensitivity of such a bridge is then determined by the sensitivity of the meter to small changes about the center point. If necessary the output signal can be amplified.

ill. 4-8. A galvanometer deflects one way to indicate a decrease in the resistance R_x ( ill. 4-7), and the opposite way to indicate an increase.

ill. 4-9. Another arrangement of the bridge circuit for measuring strain on a flexible diaphragm.

Looking at the bridge circuit again but reallocating resistors R1, R2, R3, and R4 (as in ill. 4-9), we obtain the basic relationship for zero output:

R3 = R4 x R2/R1

or

R1 x R3 = R2 x R4

If R1 and R3 are strain gauges working in opposite con figuration (that is, force reaction produces an increase in resistance in one and a decrease in the other), the resulting signal output from bridge unbalance is now equal to the product of the two differences. For initial balancing of the bridge, either R2 or R4 would then need to be adjustable.

For even stronger signal output, strain gauges could be used in each of the four arms. In this case an external variable resistor would be needed to set up initial bridge balance.

A simpler form of bridge capable of accommodating one strain gauge is shown in ill. 4-10. Here R1 is a standard resistor setting the range, and R2 is variable to set up the bridge for zero output. Variation in the strain-gauge resistance Rx then generates a proportionate signal output. A particular feature of this circuit is that it can also be used with an ac input to measure the effect of changes in capacitance by replacing R1 and R2 with capacitors and R with a capacitive transducer.

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