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Simultaneous Measurement of Tempearture and Strain Using Four Connecting Wires
National Aeronautics and
Space Administration

NASA Technical Memorandum 104271

Simultaneous Measurement of
Temperature and Strain Using
Four Connecting Wires

Allen R. Parker, Jr.

November 1993
National Aeronautics and
Space Administration
Dryden Flight Research Facility
Edwards, California 93523-0273
1993
NASA Technical Memorandum 104271

Simultaneous Measurement of
Temperature and Strain Using
Four Connecting Wires

Allen R. Parker, Jr.
NASA Dryden Flight Research Facility
Edwards, California
ABSTRACT

This paper describes a new signal-conditioning technique for measuring strain and temperature which uses
fewer connecting wires than conventional techniques. Simultaneous measurement of temperature and strain has
been achieved by using thermocouple wire to connect strain gages to signal conditioning. This signal conditioning
uses a new method for demultiplexing sampled analog signals and the Anderson current loop circuit. Theory is
presented along with data to conrm that strain gage resistance change is sensed without appreciable error because
of thermoelectric effects. Furthermore, temperature is sensed without appreciable error because of voltage drops
caused by strain gage excitation current owing through the gage resistance.

INTRODUCTION

Strain measurement during hot structural testing requires simultaneously measuring strain and temperature to
correct for apparent strain output at the strain gage [1]. The traditional approach is to attach two independent sensors
and signal-conditioning equipment for a strain gage and a thermocouple at the desired location. This paper shows
that both sensors can be combined to form one sensor called the thermostrain gage. This combining process mixes
the signals of both sensors.
In theory, appropriate signal processing separates and measures the voltages representing temperature and
strain [2]. Such a system can use thermocouple wire to connect a strain gage to the data readout equipment. A new
demultiplexer design accomplishes this goal through a combination of transducer wiring, alternating excitation, and
signal processing to separate thermoelectric (thermocouple) and resistance change (strain gage) signals in such a
manner that each signal contributes negligible contamination to the other. This design for signal separation is
comprised of three main parts: the transducer wiring scheme, the Anderson current loop technique [2], and the
analog demultiplexer design.
The key to system performance rests in the analog demultiplexer design. The demultiplexer separates the two
signals which represent temperature and strain and which exist concurrently on the same pair of sense wires. The
driving force behind the development of the new demultiplexer design was the need to acquire the temperature data
at a strain gage location without using additional connecting wires. The demultiplexer design separates temperature
and strain signals which originate at the strain gage location on a test specimen while using the same set of
connecting wires. This paper describes a fully developed and laboratory-demonstrated signal demultiplexer design
which implements Andersons theory [2] with performance normally encountered in systems employing separate,
independent strain and temperature sensors.

NOMENCLATURE

A

1,

A

2,

A

3,

A

4
difference ampliers
Cu
copper

e

AB

Seebeck voltage, V

emf

electromagnetic force, V

I

ac

alternating current level, mA

I

dc

direct current level, mA
INV
inverter amplier
J
thermocouple junction
2
L
distance between two transducers
metal A, metal B
metal types for thermocouples
metal C
metal type for strain gage
PLD
programmable logic device

R

gage

total gage resistance,

R

I

initial gage resistance,

R

ref

reference resistance,

Rw

resistances of connecting wire,

TC
thermocouple

V

gage

strain gage voltage, V

V

out

demultiplexer-sensed voltage, V

V

outA

demultiplexer A half-cycle voltage, V

V

outB


demultiplexer B half-cycle voltage, V

V

ref

reference resistor voltage, V

V

T

thermocouple voltage, V

R

change in gage resistance,

µ

e
microstrain

ohm

THERMOCOUPLE THEORY

The thermocouple (TC), a commonly used device for measuring temperatures [3], is used in many high-
temperature applications because of its wide temperature range and ability to be optimized for use in various
atmospheres. Each of the several types of TCs has its own set of properties. The process of selecting a specic type
of TC for a particular application is beyond the scope of this paper.
A thermocouple is formed when two metal wires composed of different alloys are joined to form an electrical
circuit. Figure 1 shows a thermocouple circuit. The joining of the two dissimilar metal wires completes an electrical
circuit which sums the voltages produced when a temperature gradient exists along the different conductors. This
Figure 1. Thermocouple circuit.
+
AB
e
Metal A
Metal B
emf
emf
Temperature
reference
area
Temperature
gradient
region
Thermocouple
junction 930362
3
voltage, called Seebeck voltage, is denoted as

e

AB

. For example, two wires composed of different metals, metal A
and metal B, are joined at one end to create the thermocouple junction. The thermoelectric output of a TC is a
function of temperature gradients along the TC wires. In a practical application, the output develops from
temperature gradients between the thermocouple junction, where temperature is to be measured, and a temperature
reference area, where the TC wire terminates.

ANDERSON CONSTANT CURRENT LOOP TECHNIQUE

The Anderson constant current loop technique is a new form of signal conditioning to observe remote resistance
changes that signicantly improves on the conventional Wheatstone bridge circuit [4]. This technique renders
connecting wire resistance changes irrelevant while improving performance, linearity, and output efciency.
As the name implies, the constant current loop technique is a constant current series circuit. This circuit has a
constant current source which provides steady excitation for the strain gage transducers and other resistances in the
loop in spite of changes in circuit resistance. The current is constant in all parts of the series circuit, regardless of
connecting wire resistances. This consistency of the current holds true as long as the compliance range of the
constant current source has not been exceeded. As in the classic Kelvin resistance measurement circuit, connecting
wire resistances of the basic current loop can vary wildly and have no signicant inuence on the observed strain
gage voltage,

V

gage

, as long as no appreciable current is conducted to the voltmeter which indicates

V

gage

. Figure 2
shows the Anderson constant current loop.
Figure 2. Anderson constant current loop.
Rgage
Rref
Analog subtractor
Rw1
ldc
Rw2
Rw3
Rw4
Vout
930363
Vgage
+ +Vref

The following equations are derived from this loop:
(1)
where
(2)
In equation (1), the

I

dc

is the direct current level. In equation (2),

R

I

represents the initial resistance of the strain gage
under initial conditions of strain. The

R

I

can range from 60 to over 1000

, depending on the particular strain gage
being used. The

R

represents the change in resistance because of strain which can vary from several milliohms to
several ohms, proportional to the strain measured by the gage.
V
gage
I
dc
R
gage
=
R
gage
R
I R
+
=
4
The Anderson constant current loop technique depends on the ability to perform precise analog voltage
subtraction. The subtraction is performed on two voltage drops caused by the same constant loop current: a
reference voltage drop,

V

ref



, and the gage voltage drop,

V

gage

. Both are sensed by a high-impedance voltmeter to
achieve an essentially zero voltage drop along sense lines

Rw

2 and

Rw

3. The reference voltage is produced by a
precision series resistance

R

ref

which approaches the value of

R

I

. In practice,

R

I

and

R

ref

differ slightly. This
difference will result in a small output offset which is eliminated in data reduction. The analog subtraction calculates
the difference in the voltage drops across

R

ref

and

R

gage

.
A conventional data acquisition channel for voltage has difculty in reliably indicating a

µ

V-level voltage
change in the presence of much larger gage voltages of a few volts. By means of precise analog subtraction, the
larger initial voltage produced by the excitation current owing through

R

I

is precisely removed by subtracting from
it the equivalent voltage drop across

R

ref



, leaving the much smaller voltage produced by

R

to be measured directly.
When

R

ref

approaches the value of

R

I



,
(3)
(4)
Therefore,
(5)
While derived here in terms of electrical resistance and direct current excitation for simplicity, the Anderson
current loop is a general measurement technique which can provide additional information when an alternating
excitation current is used. In fact, alternating current excitation is necessary to comb