S train-analysis Procedure for Ful I- bridge Circuits

PAUL DARDEN Bell Helicopter rextron, ~ t . Worth, TX

Introduction

Most strain-gage transducers utilize a fully active bridge circuit and provide a single output which is a function of the strain seen by the four individual gages. During the development of strain-gage transducers, it is frequently necessary to analyze interactions, non- linearity, and other types of problems that are dis- covered after the strain-gage installation is complete. This often makes it necessary to determine the four individual gage strains in addition to the combined bridge output. Unfortunately, taking strain readings from the individual gages has required that bridge connections be broken and additional wiring added.

The procedure described herein simplifies the analysis of the full-bridge transducer circuit by allowing the determination of the four individual gage strains without any change to the transducer or wiring. The procedure is easily adapted to any conventional strain indicator or transducer readout and no changes to the instrument are required.

Approach

Normal readout of a full-bridge transducer is accom- plished by connecting the readout equipment to opposite terminals of the bridge circuit, in which case both input and output resistance are approxi- mately equal to the nominal resistance of the four gages used in the bridge. Also, the output voltage is equally affected (except for sign) by a resistance change in any one of the four legs. Determination of which of the four individual gages caused an observed output change is not normally possible.

Connection to any two adjacent bridge terminals yields a very different result. Here we observe that the circuit resistance is reduced to approximately three- fourths of the nominal gage resistance. A more im- portant characteristic of this circuit is that the gages no longer have an equal effect on circuit resistance and it is potentially possible to determine the source and magnitude of resistance changes within the bridge.

The adjacent terminal connection just described allows us to consider the full bridge as a single- variable resistance sensor with some characteristics similar to that of a single strain gage. The sensor’s observed ARIR will exhibit a desired response from one of the strain gages but will also exhibit a much smaller undesired response from the other three gages. In- tuitively, ARIR should provide sufficient information to solve for the four unknown gage strains.

The ARIR readings may be taken by connecting the bridge under test as one leg of another bridge circuit as shown in Fig. 1. Alternately, a conventional strain indicator or transducer readout may be used as shown in Fig. 2. The full bridge is connected to the readout as if i t were a quarter-bridge sensor with an external dummy resistor. A convenient dummy resistor of the

required 3/4 R equivalent value is provided by a second full bridge of dummy resistors of nominal value R. A conventional switching network or the one shown will facilitate use of the procedure.

Mathematical Solution

output voltage is Analysis of the circuit of Fig. 1 will show that the

VG e, = 48 {9 t , + t, + t3 + t 4 }

where V = excitation voltage and G = gage factor.

the remaining three gages, output will be With bridge connections switched sequentially to

VG 48 VG

VG 48

e2 = __ {E, + Qt, + t3 + t4 )

e3 = - 4 8 ( t , + t z + 9 t 3 + ~ 4 )

e4 = - - - { t l + t 2 + t 3 + 9 t 4 }

\ \

\

+-

Figure I - Bridge connections for determination of individual gage strains

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+E G-

120 o

0

3 5 3 0

- E G

- :; (&

S tr a lr. Ind 1 ca tor 1

Figure 2-Connections using strain indicator

Solution of these four simultaneous equations yields

6 l 4 E . = -{ei - - C e,} ' VG 12 , = 1

f o r i = 1 to4. If the readout instrument reads directly in units of

strain, a generalization of the above equation is more convenient. By comparing to the normal equation for a quarter-bridge circuit, where

4e VG

€ = -

the individual gage strains using the described pro- cedure are

3 2

1

(gage strain); = (-) (Indicated Strain),

- (x) (Sum of Indicated Strains 1-4)

f o r i = 1 to4.

Numerical Example

To illustrate the method, a set of readings were taken on a test bridge consisting of four 350-ohm resistors. Across resistor No. 4, a precision 100-K ohm shunt resistor was applied to simulate a strain in this leg of the bridge of -1748 microstrain (a gage factor of 2.0 was assumed). Readout equipment was a Strain- sert HW1-D strain indicator. Results were as follows.

Wlo shunt 0 -133 +92 + 244 100-Kshunt -146 -279 -54 -1066 IndicatedWLt -146 -146 -146 -1310

Using the above data in the previously derived formula,

(Sum of Indicated Strains 1-4) = - 146 - 146 - 146 - 1310 = - 1748 pt

3 1 (gage strain), = (-) ( - 146) - - ( - 1748) = 0 2 8

3 1 (gagestrain), = (-)(-146) - -(-1748) = 0 2 8

2 8

2 8

(gagestrain), = (-)(-146) 3 - -(-1748) 1 = 0

(gage strain), = (-)(-1310)--(-1748)~ 3 1 -1747pt

The above results, like numerous other experimental verifications of the procedure, are consistent with expected values and readout accuracy. The overall error when using this procedure should be no more than 11/z to 2 times that of the basic readout equipment.

PAULDARDEN

Paul Darden is group engi- neer of the Instrumentation Laboratory at Bell Helicopter Textron in Fort Worth, TX. Mr. Darden is responsible for the design of strain-gage transduc- ers and other types of instru- mentation installations used for laboratory and flight testing of helicopter components and systems. Mr. Darden received his BSEE degree from the Uni- versity of Texas at Arlington and is presently engaged in graduate studies at the same University.

EXPERIMENTAL TECHNIQUES 7