Fundamental Considerations: Force and Torque

Fundamental Considerations

High-quality transducers utilizing strain gages as the primary sensing element incorporate sophisticated techniques to minimize thermal effects, nonlinearities, hysteresis, and other sources of error. These same techniques can be engaged when a portion of a structure or loading frame must be adapted to function as the spring element. For now, however, considerations will be limited to how the unique characteristics of the Wheatstone bridge itself can be utilized for measuring force and torque. And only the most significant unresolved errors or potential errors associated with the various configurations will be noted.

The output from the Wheatstone bridge can be expressed as:

(1)
where

is the bridge output voltage,

is the bridge excitation voltage, and

, and

are the resistances of the gages in the bridge.

Note that changes of resistance in adjacent gages (

and

, for example) have the same (or numerically additive) effect on bridge output when the changes are of opposite sign. When the changes in adjacent arms are of the same sign, they have opposite (or numerically subtractive) effects. Conversely, the effects of resistance changes in opposite arms (

and

, for example) are reversed: changes in resistance with like signs in opposite arms have the same effects on the output and changes with unlike signs in opposite arms have opposite effects. These phenomena are used later to eliminate the effects of bending strains on the measurement of axial strains, the effects of axial strains on measurements of bending strains, eradication of thermally induced apparent strain, and even elimination of nonlinearity in the output from unbalanced Wheatstone bridges.

The bridge is balanced and produces no output when:

or when:

A change in resistance of one or more of the gages will unbalance the bridge so that an output signal is produced. Equation (1) can be used to determine the output of any unbalanced bridge simply by adding the resistance change of each affected resistor to the initial value of that resistor.

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