Automatic Control, Robot and Mechatronics Labs of Mechanical Engineering Department

THE STRAIN GAUGE

The strain gauge has been in use for many years and is the fundamental sensing element for many types of sensors, including pressure sensors, load cells, torque sensors, position sensors, etc.

The majority of strain gauges are foil types, available in a wide choice of shapes and sizes to suit a variety of applications. They consist of a pattern of resistive foil which is mounted on a backing material. They operate on the principle that as the foil is subjected to stress, the resistance of the foil changes in a defined way.

The strain gauge is connected into a Wheatstone Bridge circuit with a combination of four active gauges (full bridge), two gauges (half bridge), or, less commonly, a single gauge (quarter bridge). In the half and quarter circuits, the bridge is completed with precision resistors.

The complete Wheatstone Bridge is excited with a stabilised DC supply and with additional conditioning electronics, can be zeroed at the null point of measurement. As stress is applied to the bonded strain gauge, a resistive changes takes place and unbalances the Wheatstone Bridge. This results in a signal output, related to the stress value. As the signal value is small, (typically a few millivolts) the signal conditioning electronics provides amplification to increase the signal level to 5 to 10 volts, a suitable level for application to external data collection systems such as recorders or PC Data Acquistion and Analysis Systems.

Some of the many Gauge Patterns available Most manufacturers of strain gauges offer extensive ranges of differing patterns to suit a wide variety of applications in research and industrial projects. They also supply all the necessary accessories including preparation materials, bonding adhesives, connections tags, cable, etc. The bonding of strain gauges is a skill and training courses are offered by some suppliers. There are also companies which offer bonding and calibration services, either as an in-house or on-site service. More about the Strain Gauge... If a strip of conductive metal is stretched, it will become skinnier and longer, both changes resulting in an increase of electrical resistance end-to-end. Conversely, if a strip of conductive metal is placed under compressive force (without buckling), it will broaden and shorten. If these stresses are kept within the elastic limit of the metal strip (so that the strip does not permanently deform), the strip can be used as a measuring element for physical force, the amount of applied force inferred from measuring its resistance.

Such a device is called a strain gauge. Strain gauges are frequently used in mechanical engineering research and development to measure the stresses generated by machinery. Aircraft component testing is one area of application, tiny strain-gauge strips glued to structural members, linkages, and any other critical component of an airframe to measure stress. Most strain gauges are smaller than a postage stamp, and they look something like this:

A strain gauge's conductors are very thin: if made of round wire, about 1/1000 inch in diameter. Alternatively, strain gauge conductors may be thin strips of metallic film deposited on a nonconducting substrate material called the carrier. The latter form of strain gauge is represented in the previous illustration. The name "bonded gauge" is given to strain gauges that are glued to a larger structure under stress (called the test specimen) The task of bonding strain gauges to test specimens may appear to be very simple, but it is not. "Gauging" is a craft in its own right, absolutely essential for obtaining accurate, stable strain measurements. It is also possible to use an unmounted gauge wire stretched between two mechanical points to measure tension, but this technique has its limitations. Typical strain gauge resistances range from 30 Ohms to 3 kOhms (unstressed). This resistance may change only a fraction of a percent for the full force range of the gauge, given the limitations imposed by the elastic limits of the gauge material and of the test specimen. Forces great enough to induce greater resistance changes would permanently deform the test specimen and/or the gauge conductors themselves, thus ruining the gauge as a measurement device. Thus, in order to use the train gauge as a practical instrument, we must measure extremely small changes in resistance with high accuracy.

Such demanding precision calls for a bridge measurement circuit. Unlike the Wheatstone bridge shown in the last chapter using a null-balance detector and a human operator to maintain a state of balance, a strain gauge bridge circuit indicates measured strain by the degree of imbalance, and uses a precision voltmeter in the center of the bridge

to provide an accurate measurement of that imbalance:

Typically, the rheostat arm of the bridge (R2 in the diagram) is set at a value equal to the strain gauge resistance with no force applied. The two ratio arms of the bridge (R1 and R3) are set equal to each other. Thus, with no force applied to the strain gauge, the bridge will be symmetrically balanced and the voltmeter will indicate zero volts, representing zero force on the strain gauge. As the strain gauge is either compressed or tensed, its resistance will decrease or increase, respectively, thus unbalancing the bridge and producing an indication at the voltmeter. This arrangement, with a single element of the bridge changing resistance in response to the measured variable (mechanical force), is known as a quarter-bridge circuit.

As the distance between the strain gauge and the three other resistances in the bridge circuit may be substantial, wire resistance has a significant impact on the operation of the circuit. To illustrate the effects of wire resistance, I'll show the same schematic diagram, but add two resistor symbols in

series with the strain gauge to represent the wires:

The strain gauge's resistance (Rgauge) is not the only resistance being measured: the wire resistances Rwire1 and Rwire2, being in series with Rgauge, also contribute to the resistance of the lower half of therheostat arm of the bridge, and consequently contribute to the voltmeter's indication. This, of course, will be falsely interpreted by the meter as physical strain on the gauge.

While this effect cannot be completely eliminated in this configuration, it can be minimized with the addition of a third wire, connecting the right side of the voltmeter directly to the upper wire of the strain gauge:

Because the third wire carries practically no current (due to the voltmeter's extremely high internal resistance), its resistance will not drop any substantial amount of voltage. Notice how the resistance of the top wire (Rwire1) has been "bypassed" now that the voltmeter connects directly to the top terminal of the strain gauge, leaving only the lower wire's resistance (Rwire2) to contribute any stray resistance in series with the gauge. Not a perfect solution, of course, but twice as good as the last circuit! There is a way, however, to reduce wire resistance error far beyond the method just described, and also help mitigate another kind of measurement error due to temperature. An unfortunate characteristic of strain gauges is that of resistance change with changes in temperature. This is a property common to all conductors, some more than others. Thus, our quarter-bridge circuit as shown (either with two or with three wires connecting the gauge to the bridge) works as a thermometer just as well as it does a strain indicator. If all we want to do is measure strain, this is not good. We can transcend this problem, however, by using a "dummy" strain gauge in place of R2, so that both elements of the rheostat arm will change resistance in the same proportion when temperature changes, thus

canceling the effects of temperature change:

Resistors R1 and R3 are of equal resistance value, and the strain gauges are identical to one another. With no applied force, the bridge should be in a perfectly balanced condition and the voltmeter should register 0 volts. Both gauges are bonded to the same test specimen, but only one is placed in a position and orientation so as to be exposed to physical strain (the active gauge). The other gauge is isolated from all mechanical stress, and acts merely as a temperature compensation device (the "dummy" gauge). If the temperature changes, both gauge resistances will change by the same percentage, and the bridge's state of balance will remain unaffected. Only a differential resistance (difference of resistance between the two strain gauges) produced by physical force on the test specimen can alter the balance of the bridge. Wire resistance doesn't impact the accuracy of the circuit as much as before, because the wires connecting both strain gauges to the bridge are approximately equal length. Therefore, the upper and lower sections of the bridge's rheostat arm contain approximately the same amount of stray resistance, and their effects tend to cancel:

Even though there are now two strain gauges in the bridge circuit, only one is responsive to mechanical strain, and thus we would still refer to this arrangement as a quarter-bridge. However, if we were to take the upper strain gauge and position it so that it is exposed to the opposite force as the lower gauge (i.e. when the upper gauge is compressed, the lower gauge will be stretched, and visa-versa), we will have both gauges responding to strain, and the bridge will be more responsive to applied force. This utilization is known as a half-bridge. Since both strain gauges will either increase or decrease resistance by the same proportion in response to changes in temperature, the effects of temperature change remain canceled and the circuit will suffer minimal temperature-induced measurement error:

An example of how a pair of strain gauges may be bonded to a test specimen so as to yield this effect is illustrated here:

With no force applied to the test specimen, both strain gauges have equal resistance and the bridge circuit is balanced. However, when a downward force is applied to the free end of the specimen, it will bend downward, stretching gauge #1 and compressing gauge #2 at the same time:

In applications where such complementary pairs of strain gauges can be bonded to the test

specimen, it may be advantageous to make all four elements of the bridge "active" for even greater sensitivity. This is called a full-bridge circuit:

Both half-bridge and full-bridge configurations grant greater sensitivity over the quarter-bridge circuit, but often it is not possible to bond complementary pairs of strain gauges to the test specimen. Thus, the quarter-bridge circuit is frequently used in strain measurement systems.

When possible, the full-bridge configuration is the best to use. This is true not only because it is more sensitive than the others, but because it is linear while the others are not. Quarter-bridge and half-bridge circuits provide an output (imbalance) signal that is only approximately proportional to applied strain gauge force. Linearity, or proportionality, of these bridge circuits is best when the amount of resistance change due to applied force is very small compared to the nominal resistance of the gauge(s). With a full-bridge, however, the output voltage is directly proportional to applied force, with no approximation (provided that the change in resistance caused by the applied force is equal for all four strain gauges!). Unlike the Wheatstone and Kelvin bridges, which provide measurement at a condition of perfect balance and therefore function irrespective of source voltage, the amount of source (or "excitation") voltage matters in an unbalanced bridge like this. Therefore, strain gauge bridges are rated in millivolts of imbalance produced per volt of excitation, per unit measure of force. A typical example for a strain gauge of the type used for measuring force in industrial environments is 15 mV/V at 1000 pounds. That is, at exactly 1000 pounds applied force (either compressive or tensile), the

bridge will be unbalanced by 15 millivolts for every volt of excitation voltage. Again, such a figure is precise if the bridge circuit is full-active (four active strain gauges, one in each arm of the bridge), but only approximate for half-bridge and quarter -bridge arrangements.

Strain gauges may be purchased as complete units, with both strain gauge elements and bridge resistors in one housing, sealed and encapsulated for protection from the elements, and equipped with mechanical fastening points for attachment to a machine or structure. Such a package is typically called a load cell.

This article is from 'All about circuits'...click here to visit.

Strain Rosette for Strain Measurement

A wire strain gage can effectively measure strain in only one direction. To determine the three independent components of plane strain, three linearly independent strain measures are needed, i.e., three strain gages positioned in a rosette-like layout.

Consider a strain rosette attached on the surface with an

angle from the x-axis. The rosette itself contains three strain

gages with the internal angles and , as illustrated on the right.

Suppose that the strain measured from these three strain

gages are a, b, and c, respectively.

The following coordinate transformation equation is used to convert the longitudinal strain from each strain gage into strain expressed in the x-y coordinates,

Applying this equation to each of the three strain gages results in the following system of equations,

These equations are then used to solve for the three unknowns, x, y, and xy.

Note: 1. The above formulas use the strain measure xy as opposed to the engineering shear strain xy,

. To use xy, the above equations should be adjusted accordingly.

2. The free surface on which the strain rosette is attached is actually in a state of plane stress, while the formulas used above are for plane strain. However, the normal direction of the free surface is indeed a principal axis for strain. Therefore, the strain transform in the free surface plane can be applied.

Special Cases of Strain Rosette Layouts

Case 1: 45º strain rosette aligned with the x-y axes, i.e., = 0º, = = 45º.

Case 2: 60º strain rosette, the middle of which is aligned with the y-axis, i.e., = 30º, = = 60º.

Top of Page

This article is from . Click on the logo to visit.

Thermistor Preamp

CIRCUIT

THERM_PREAMP.CIR Download the SPICE file

Suppose you're asked to design a circuit using a thermistor that measures room temperature, 0 °C (32 °F) to 40 °C (102 °F). The circuit's output should be scaled to 0.1 V / °C such that a Digital Voltmeter (DVM) can directly display the temperature. Choosing an appropriate bias resistor, you can transform the thermistor's highly non-linear R vs. T curve into a linear voltage. But, how do you choose the gain and offset of your preamp? How accurate is the reading between calibration points? How hot or cold of a temperature can you measure before the sensor's non-linearity sends the error beyond +/- 1 °C? Armed with a SPICE circuit, an Excel Spreadsheet and a couple rules-of-thumb you can design a decent circuit complete with life's compromises and trade-offs.

SENSOR BRIDGE

SENSOR Part of your design challenge is using a thermistor that's already stocked by the company. The specs look like Ro = 10 kΩ at To = 25 °C, Beta = 3450. The highly non-linear Rth vs. T curve is predicted by

where the temperatures in the equation are in K.

BIAS RESISTOR An easy way to straighten out the Rth vs. T curve is by adding a series bias resistor. What value? A good rule of thumb - choose a bias resistor to have the same value that the thermistor exhibits in the middle of your measurement range. For starters we'll choose RBIAS = 10 kΩ, the thermistor's nominal value at 25 °C.

You may have noticed the thermistor placed in the top leg of the bridge. Given the thermistor's negative temperature coefficient, this creates a positive voltage change as T increases.

BIAS VOLTAGE SUBTRACTION Components VBIAS = 5V, RBIAS = 10 kΩ and Rth = 10 kΩ at 25 °C create a bias voltage of 2.5 V at the sensor. How can you subtract it before passing the sensor's output to the next stage?

That's where the other leg of the sensor bridge comes in. Resistors RA = RB = 10 kΩ together with VBIAS = 5 V produce a handy Vref = 2.5 V that gets subtracted from the thermistor's voltage by the instrumentation amp. The bridge's output voltage is described as

VS = Vsens - Vref

INSTRUMENTATION AMP

GAIN Here's the classic 3 opamp instrumentation amp. It amplifies the input voltage difference (VS = Vin+ - Vin-) according to

where R1=R3 and R4 = R5 = R6 = R7. All of the gain is housed in the first stage, XOP1 and XOP2.

OFFSET To plumb in an offset, just drive R7 with a voltage, VOFF. The same offset appears at the output! The complete equation describing the output looks like this

which can be simply rewritten as the familiar equation of a line.

y = m x + b

The trick now lies in choosing m and b to produce Vo = 0.1 V / °C.

CHOOSING GAIN AND OFFSET

The equation y = m x + b transforms the sensor's output x into the desired output y. For example, if we let x0 be a point in the sensors output, then y0 is the desired output of the amplifier.

y0 = m ∙ x0 + b

Picking another sensor voltage x1, the output becomes

y1 = m ∙ x1 + b

From these two equations and two unknowns, we can easily find m and b!

b = y0 - m ∙ x0

THE REAL DEAL

Let's pull it all together with a real example. Using an Excel spreadsheet Thermistor_Preamp.xls, you can see the big picture of the sensor chain. Over a large temperature range, the spreadsheet calculates the sensor resistance Rth, the sensor voltage Vsens, and the differential output of the bridge Vsens - Vref. Check out the curve of the highly non-linear Rth vs. T graph. At first glance, it appears almost useless! But a simple resistor RBIAS converts it to a reasonably linear voltage as shown in the Vsens - Vref graph.

First, choose a couple of calibration points like the end-points of our range, T = 0 and 40 °C. Here are the numbers for the two temperatures.

Temp Rth Vsens VS = Vsens - Vref (x)

Desired Vout 0.1 V/°C (y)

0 °C 28.84 kΩ 1.29 V -1.21 V 0.0 V

40 °C 5.74 kΩ 3.18 V + 0.68 V 4.0 V

Next, calculate the slope and offset for your preamp.

m = (y1 - y0) / (x1 - x0) = (4.0 - 0.0) / (0.68 - -1.21) = 2.1184

b = y0 - m∙x0 = 0.0 - 2.1184∙-1.21 = 2.569

So what kind of Vo vs. T output does the preamp produce? The spreadsheet calculates the preamp output y = m∙x+ b. For comparison, the spreadsheet graphs this actual preamp output, along with the desired output, a linear line between 0 (0 °C) and 4 V (40 °C). How close are they? At what temperatures do they go their separate ways?

To make the preamp a reality, you need to calculate the gain resistor R2 of the instrumentation amplifier. For R1 = R3 = 10 kΩ, R2 becomes

R2 = 2∙R1 / (m - 1) = 2∙10k / (2.1184 - 1) = 17.883 kΩ

Given the tolerances of the sensor and other resistors, you might want to make R1 some combination of a resistor and a potentiometer for a precise gain adjustment.

Finally, set VOFF = b = 2.569 V. In real life, VOFF can be derived from a resistor divider hung from VBIAS followed by a unity-gain opamp buffer. Exchange one of the resistors for a potentiometer and you've got yourself an offset adjustment.

SPICE TIME

Voltage source VTEMP generates a ramp from 0 to 40V representing temperature from 0 to 40 °C. Thermistor XTH1 is defined by subcircuit NTC_10k, a Negative Temperature Coefficient (NTC) device with a resistance value of 10 kΩ at 25 °C.

CIRCUIT INSIGHT Run a simulation of THERM_PREAMP.CIR. Take a look at the bridge output by plotting V(1) - V(2). Next, view the preamp's output by plotting V(10). As you can see, the preamp does a nice job of transforming the bridge's output into a very readable 0 to 4 V achieving the 0.1 V / C design goal.

Although the preamp's output looks fairly linear, how straight is it? Let's check the error between the calibration points by plotting 10*V(10) - V(20) where 10*V(10) converts the preamp's output directly to °C. V(20) is the output of VTEMP. Not too bad! The error is near 0 at the calibration points as expected! But in between, the sensor shows its non-linear nature. The maximum error should be around 0.8 C.

HANDS-ON DESIGN Is there a better value for RBIAS that reduces the maximum error? Try a different RBIAS value. Use the spreadsheet to help calculate your new gain and offset.

Rerun the simulation over a larger temperature range like -10 C to 50 °C. (In the VTEMP statement, change the voltage points to 0 and 50.) How quickly does the error grow at temperatures outside the calibration points of 0 and 40 °C.

HANDS-ON DESIGN Try your hand at designing a sensor preamp over a different temperature range. Suppose your range must be optimized for reading body temperature 95 to 10°5 F. Choose RBIAS to be some value in the middle of the range, then calculate your slope and offset. Use the spreadsheet if you wish. How accurate is your new sensor circuit?

PRECISION PARTS, ADJUSTMENTS AND TRADEOFFS

Of course, the wonderful results we achieved above assumed perfect components - the thermistor Resistance / Beta, opamps, resistors, bias voltage were all spot on! Reality, being not so kind, says all of these parts come with tolerances. Depending on the accuracy required and budget available, you have several options. Pay a

premium for precision parts that you can drop into the circuit to meet your spec. Or, include offset / gain adjustments and invest your money in calibration time on the manufacturing floor.

REFRESHER NOTES

This circuit pulls together many topics - thermistor model, linearized thermistor, sensor bridge, instrumentation amp, subcircuits, and opamp models. You can browse other circuits and topics at the Circuit Collection.

SPICE FILE

Download the file or copy this netlist into a text file with the *.cir extension.

THERM_PREAMP.CIR - THERMISTOR WITH PREAMP GAIN AND OFFSET

*

* TEMPERATURE

VTEMP 20 0 PWL(0MS 0DEG 100MS 40DEG)

RD1 10 0 1MEG

*

* SENSOR BRIDGE

VBIAS 12 0 DC 5V

XTH1 12 1 20 0 NTC_10K

RBIAS 1 0 10K

RA 12 2 10K

RB 2 0 10K

*

* 3 OPAMP INSTRUMENTATION AMPLIFIER

* GAIN STAGE

XOP1 2 4 6 OPAMP1

R1 4 6 10K

R2 4 5 17.883K

R3 5 7 10K

XOP2 1 5 7 OPAMP1

* DIFF AMP

R4 6 8 10K

R5 8 10 10K

R6 7 9 10K

R7 9 11 10K

XOP3 9 8 10 OPAMP1

VOFF 11 0 DC 2.569V

*

* MEASUREMENT ERROR

E_ERR 21 0 VALUE = { V(10)*10-V(20)}

R_ERR 21 0 1MEG

*

* THERMISTOR SUBCIRCUIT ****************************************

* thermistor terminals : 1,2

* temperature (deg C) input+,-: 4,5

*

.SUBCKT NTC_10K 1 2 4 5

ETHERM 1 3 VALUE={i(VSENSE)*10K*EXP(3450/(V(4,5)+273.15)-3450/(25+273.15))}

VSENSE 3 2 DC 0

.ENDS

*

* OPAMP MACRO MODEL, SINGLE-POLE *******************************

* connections: non-inverting input

* | inverting input

* | | output

* | | |

.SUBCKT OPAMP1 1 2 6

* INPUT IMPEDANCE

RIN 1 2 10MEG

* GAIN BANDWIDTH PRODUCT = 10MHZ

* DC GAIN (100K) AND POLE 1 (100HZ)

EGAIN 3 0 1 2 100K

RP1 3 4 1K

CP1 4 0 1.5915UF

* OUTPUT BUFFER AND RESISTANCE

EBUFFER 5 0 4 0 1

ROUT 5 6 10

.ENDS

*

*

* ANALYSIS

.TRAN 1MS 100MS

*

* VIEW RESULTS

.PRINT TRAN V(1) V(10)

.PROBE

.END

this article is from eCircuit Center . Click on the 'eCircuitCenter' logo to visit eCircuit Center.

Copyright by Automatic Control Lab of Mechanical Engineering Department of DEU. For problems or questions regarding this Web site contact aytac.goren@deu.edu.tr Last updated: 14-Ara-2007 15:08.