Strain gage
A device which measures mechanical deformation (strain). Normally it is attached to a structural element, and uses the change of electrical resistance of a wire or semiconductor under tension. Capacity, inductance, and reluctance are also used.
The strain gage converts a small mechanical motion to an electrical signal by virtue of the fact that when a metal (wire or foil) or semiconductor is stretched, its resistance is increased. The change in resistance is a measure of the mechanical motion. In addition to their use in strain measurement, these gages are used in sensors for measuring the load on a mechanical member, forces due to acceleration on a mass, or stress on a diaphragm or bellows.
Strain Gage
(also extensometer), a measuring transducer that converts the deformation (strain) of a solid induced by mechanical stress into a signal, usually an electrical signal; the signal is subsequently transmitted, converted, and recorded. Resistance strain gages, the most common type, use resistors whose electrical
resistivity changes as a result of deformations (expansion or compression). The resistors are constructed in the form of wire or foil grids (Figure 1, page 172) made of constantan, Nichrome, or various alloys of Ni, Mo, or Pt or in the form of thin sheets of a semiconductor material, such as silicon.
Resistors may be rigidly bonded (glued or welded) to the elastic element of the strain gage (Figure 2) or attached directly to the object being studied. The elastic element senses changes in a given parameter x (pressure, deformation of a machine part, or acceleration) and converts the changes into a deformation ∊(x) of the grid or sheet. This deformation changes the resistance of the resistor by the amount ∆R(∊) = ±kR0∊, where R0 is the initial resistance of the resistor and k is the coefficient of strain sensitivity (k ≤ 2–2.5 for a wire strain gage, and k ~ 200 for semiconductor strain gages). Resistance strain gages usually operate within the elastic limit, where ∊ ≤ 10-3.
The magnitude of ∆R depends not only on ε but also on the temperature of the elastic element: ∆R(θ) = α∆θ R0, where ∆θ is the temperature change of the elastic element and a is the temperature coefficient of relative change in the resistance of the resistor. For wire and foil resistors, ot ranges between 2 × 10-3/°K and 7 × 10-3/°K.
Temperature compensation or automatic introduction of temperature corrections is needed to decrease measurement errors. The most commonly used temperature compensation circuits use bridge circuits. Figure 3 shows an example of two identical strain-sensitive resistors incorporated in a bridge circuit and designed to sense the deformation of an elastic element. In this instance, ∆R1(∊) and ∆R2(∊) have opposite signs, whereas ∆R1(θ) and ∆R2(θ) have the same sign. When ∆R/R << 1, the current along the bridge diagonal, which constitutes the output signal of the strain gage, is given by the expression 
, where M is a proportionality coefficient and 
and 
, the resistances of the strain-sensitive resistors, are equal to R1 + ∆ + R1(∊), + ∆R1(θ) and R2 – ∆R2(∊) + ∆R2(θ), respectively. Compared with bridge circuits having a single resistor, those with two resistors double the sensitivity of the strain gage, and those with four resistors quadruple the sensitivity, thus ensuring complete temperature compensation.
REFERENCES
Turichin, A. M. Eleklricheskie izmereniia neelektricheskikh velichin, 4th ed. Moscow-Leningrad, 1966.Glagovskii, B. A., and I. D. Piven. Elektrotenzometry soprotivleniia, 2nd ed. Leningrad, 1972.
A. V. KOCHEROV
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