Strain Gage Thermal Output and Gage Factor Variation with Temperature

In theory, at least, the error due to thermal output can be completely eliminated by employing, in conjunction with the "active" strain gage, but connected in an adjacent arm of the Wheatstone bridge circuit, an identical compensating or "dummy" gage - mounted on an unstrained specimen made from the identical material as the test part, and subjected always to the same temperature as the active gage. Under these hypothetical conditions, the thermal outputs of the two gages should be identical. And, since identical resistance changes in adjacent arms of the Wheatstone bridge do not unbalance the circuit, the thermal outputs of the active and dummy strain gages should cancel exactly - leaving only the stress-induced strain in the active strain gage to be registered by the strain indicator. For this to be precisely true requires additionally that the leadwires to the active and dummy gages be of the same length and be routed together so that their temperature-induced resistance changes also match identically.

The principal problems encountered in this method of temperature compensation are those of establishing and maintaining the three sets of identical conditions postulated above. To begin with, it is sometimes very difficult to arrange for the placement of an unstrained specimen of the test material in the test environment; and even more difficult to make certain that the specimen remains unstrained under all test conditions. There is a further difficulty in ensuring that the temperature of the compensating gage on the unstrained specimen is always identical to the temperature of the active gage. This problem becomes particularly severe whenever there are temperature gradients or transients in the test environment. And, as indicated in the preceding paragraph, the same considerations apply to the leadwires. Finally, it must be recognized that no two strain gages - even from the same lot or package - are precisely identical. For most static strain measurement tasks in the general neighborhood of room temperature, the difference in thermal Output between two gages of the same type from the same lot is negligible; but the difference may become evident (and significant) when measuring strains at temperature extremes such as those involved in high-temperature or cryogenic work. In these instances, point-by-point correction for thermal output will usually be necessary. With non-self-temperature-compensated gages, the gage-to-gage differences in thermal output may be so great as to preclude dummy compensation for temperatures which are remote from room temperature. In general, when the three identity criteria already mentioned can be well satisfied, the method of compensating with a dummy gage is a very effective technique for controlling the thermal output error. There is, moreover, a special class of strain measurement applications which is particularly adaptable to compensation of thermal output with a second gage. This class consists of those applications in which the ratio of the strains at two different but closely adjacent (or at least thermally adjacent) points on the test object are known a priori. Included in this class are bars in pure torsion, beams in bending, columns, diaphragms, etc., all stressed within their respective proportional limits. In these applications, the compensating gage can often be located strategically on the test member itself so as to provide two active gages which undergo the same temperature variations while sensing strains that are preferably opposite in sign and of known ratio. The two gages in adjacent arms of the Wheatstone bridge circuit then function as an active half bridge.

For example, when strain measurements are to be made on a beam which is thin enough so that under test conditions the temperatures on the two opposite surfaces normal to the plane of bending are the same, the two strain gages can be installed directly opposite each other on these surfaces (Fig. 2a). The active half bridge thus formed will give effective temperature compensation over a reasonable range of temperatures and, since the strains sensed by the gages are equal in magnitude and opposite in sign, will double the output signal from the Wheatstone bridge. Similarly, for a bar in pure torsion (Fig. 2b), the two gages can be installed adjacent to each other and aligned along the principal axes of the bar (at 45 deg to the longitudinal axis). As in the case of the beam, excellent temperature compensation can be achieved, along with a doubled output signal.

When making strain measurements along the axis of a column or tension link, the compensating gage can be mounted on the test member adjacent to the axial gage and aligned transversely to the longitudinal axis to sense the Poisson strain (Fig. 2c). The result, again, is compensation of the thermal output, accompanied by an augmented output signal [by the factor in this case]. It should be borne in mind in this application, however, that the accuracy of the strain measurement is somewhat dependent upon the accuracy with which the Poisson's ratio of the test material is known. The percent error in strain measurement is approximately equal to times the percent error in Poisson's ratio. A further caution is necessary when strain gages are mounted transversely on small-diameter rods (or, for that matter, in small-radius fillets or holes). Hines has shown (see Appendix) that under these conditions the thermal output characteristics of a strain gage are different than when the gage is mounted on a flat surface of the same material.

In all strain-measurement applications which involve mounting the compensating gage on the test object itself, the relationship between the strains at the two locations must be known with certainty . In a beam, for example, there must be no indeterminate axial or torsional loading; and the bar in torsion must not be subject to indeterminate axial or bending loads. This requirement for a priori knowledge of the strain distribution actually places these and most similar applications in the class of transducers. And the same method of compensation is universally employed in commercial strain gage transducers. Such transducers, however, ordinarily employ full-bridge circuits and special arrangements of the strain gages to eliminate the effects of extraneous forces or moments.

Compensation for Thermal Output - Compensating (Dummy) Gage