Page 86 - Mechanical Engineers' Handbook (Volume 2)

3 The Resistance Strain Gage 75

gages to surface strain is much greater than metal gages. This allows them to be used in
transducers providing more signal output (typically 100–500 mV versus 30 mV) and on
stiffer flexures, resulting in smaller transducer size, higher frequency response, and increased
ruggedness. Although not strictly correct, by convention it has become equivalent to refer
to semiconductor-based transducers as either piezoresistive or solid-state transducers.

3.2 Gage Factor

The gage factor F for a strain gage is defined as
R
F (3)
R
where R is resistance and is strain equal to l/l ( l is the change in length of l ). Equation
0
(3) may be redefined as
d
F 1 2 (4)

where is Poisson’s ratio and is the resistivity of the grid material. Most metal gages have
a gage factor between 2 and 4.5. For strain gages made from a semiconductor material, the
change in resistivity with applied stress is the dominant factor and values as high as 170 are
possible. Table 1 lists properties and gage factors for various grid materials.

3.3 Mechanical Aspects of Gage Operation
To build effective bridge transducers, one must be aware of the interaction between the gage
and the surface of the transducer flexure to which it is mounted. Mechanical aspects of this
interaction include the influences of temperature, backing material, size, orientation, trans-

Table 1 Grid Material Composition, Trade Name, Properties, and Gage Factor
Composition Trade Name Properties Gage Factor
1. Copper–nickel (57%–43%) Constantan Strain sensitivity relatively 2.0
independent of level and
temperature; used to 200 C;
high resistivity applicable
to small grids; measures
strains to 20% in annealed
form
2. Nickel–chromium–iron– Isoelastic High gage factor; high fatigue 3.5
molybdenum (36%–8%–55.5%– life; used to 200 C; high
0.5%) temperature coefficient of
resistance; nonlinear at
strain levels above 5%
3. Nickel–chromium (80%–20%), Nichrome V Good fatigue life; stable; high 2.2
Nickel–chromium (75%–20%) Karma resistance applicable to
plus iron and aluminum small grids; used to 400 C

Note: Nickel alloy gages are susceptible to magnetic fields.