stain gage measurements ys

Strain Gage Measurement System - Fundamentals From Vishay’s Web Site: http://www.vishay.com/brands/measurements_group/guide/ta/sgms/wbp.htm

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On the face of it, the bonded electrical resistance strain gage is a simple device, in fact deceptively so. The gage functions on the principle that when it undergoes strain, its electrical resistance changes. And if the relationship between the relative change in resistance (∆R/R) and the strain (∆L/L), (which is defined as the Gage Factor), is known, then the strain can be determined. All that is necessary therefore is to measure ∆R/R. But this is more easily said than done because the values of ∆R are very small (and ∆R/R, even smaller). The Gage Factor (GF) is approximately 2.0 for gages made of the metal alloys most commonly used in their manufacture. A typical gage resistance is 120 ohms. In order to use such a gage for detecting a strain of 1 µε (which corresponds to that produced by a 30 psi stress in steel for a simple uniaxial loading), a change of resistance ∆R of 0.00024 ohm must be measured.

Modern Strain Gage Indicator

Model P-3500 Portable Strain Indicator

While a precision digital multimeter, reading to eight significant figures, might be used to measure absolute resistance values with the necessary resolution to determine the ∆R values, this is not usually a practical way to make strain measurements.

Introduction

Modern strain gage instruments usually employ the Wheatstone bridge as the primary sensing circuit. A stable, high-gain DC amplifier is then used to amplify the small bridge output signal to a level suitable for driving some form of display or output device. In addition to these two basic components, a typical strain indicator includes the bridge power supply and built-in bridge completion resistors, along with balance and gain controls, provision for shunt calibration, and various convenience features. The following discussion briefly describes the principal considerations involved in combining these elements into an instrument for precision strain measurement.

Wheatstone Bridge Circuit

A very important feature of the Wheatstone bridge is that changes of ∆R/R in adjacent arms of the circuit are numerically subtractive when of the same sign, and tend to cancel each other. Likewise, when the relative resistance changes in adjacent arms are of opposite sign, the changes


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are numerically additive. Conversely, changes in opposite arms are numerically additive when they are of the same sign and tend to cancel when they are of opposite sign. These effects are important for achieving temperature compensation. They are also used in strain gage transducers (where generally all four arms of the bridge are active strain gages) to produce an increased output.

Wheatstone Bridge Circuit In the majority of present-day instrumentation the strain gage itself forms one or more arms of the Wheatstone bridge circuit (shown right), producing an output voltage that is proportional to resistance change. The output is, in fact, proportional to ∆R/R so that, for a given strain (∆L/L) and Gage Factor (GF), the output is independent of the initial value of the absolute resistance (R) in each arm of the bridge.

Bridge Voltage The strain gage and the Wheatstone bridge are in themselves passive elements; i.e., no output from the circuit is possible without a voltage input. The output of an unbalanced bridge (Vout) can be expressed in terms of both the ∆R/R and the voltage input (Vin), and is commonly taken as proportional to both of them, although the relationship is slightly nonlinear for certain configurations (Ref.1).

In a simplified form (which ignores nonlinearity) the output for a single active strain gage (one arm of the bridge is a strain gage subjected to strain, and the other three arms are inactive strain gages or resistors) can be expressed as:

RRVV in

out∆

×=4

or, substituting the Gage Factor equation:

LLGFRR ∆×=∆

then:

ε××=∆××= GFVLLGFVV ininout 44

where ε is strain.

With GF=2.0

ε = 1 x 10 -6 (1 microstrain) Vin = 1.0:

VoltsVout66 105.01012

40.1 −− ×=×××=

This yields an output of only 0.5 microvolt per volt input per microstrain. The output can, of course, be increased by increasing the bridge voltage, Vin (e.g., 5 microvolts/microstrain output at 10 volts input for the previous example). While it is usually desirable to obtain as high a


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bridge output as possible, there are limitations set by the self-heating effects due to the current in the gage (a function of gage resistance and bridge voltage), gage size, and heat-sink properties of the material to which it is bonded ( Ref.2 ). For most practical purposes, bridge voltages are normally in the range of 1 to 15 volts. Whatever the value, it must be accurately known and controlled because the bridge output is directly proportional to it. If the instrument offers only a fixed bridge voltage, then a low value is desirable in order to minimize gage heating effects in those cases where higher voltages would cause a problem. Much greater measurement flexibility is possible, particularly for dynamic measurements, when the instrument incorporates a variable bridge voltage supply.

Provision for separately switching off the bridge voltage while the remainder of the measuring circuit remains operational is an important and useful feature, particularly when measuring dynamic strains. Any output observed when the bridge voltage is switched off must be due to electrical noise, as the output cannot possibly be the result of resistance changes in the measuring circuit when a bridge voltage is not present. The ability to turn off the bridge power is therefore a useful diagnostic tool for establishing whether electrical noise is a problem.

Bridge Completion Because such very small resistance changes and voltage outputs are involved, each arm of the bridge circuit must consist of a strain gage or resistor with high stability, close resistance tolerance, and very low effective temperature coefficient of resistance. Modern foil strain gages have these qualities. But if only one arm of the bridge is an active strain gage, as is normal for experimental stress analysis, then the other arms required to complete the bridge must either be other inactive strain gages, or some other form of high precision resistors. Such resistors must have resistance tolerance of ±0.01%, temperature coefficient of resistivity of 1 ppm/° C, and stability of <25ppm/year drift. Certainly most carbon, deposited-film or wirewound resistors cannot be used, as their characteristics are clearly outside these specifications. A typical deposited-film resistor, for example, will have a tolerance of ±1%; but, more particularly, it will also have a temperature coefficient of ±100ppm/° C. This means that if such a resistor were used in one arm of the bridge circuit, and a temperature change of only 1° C took place, an output representing ±50 microstrain (equivalent to a uniaxial stress of about ±1500 psi in steel) would result.

Considerations of the self-heating effects of the current through the bridge-completion resistors are equally applicable. If these resistors do not have the required power-dissipation characteristics, then instability in the circuit will arise.

After all of these factors are taken into account, careful additional attention must be paid to the leadwires that connect the resistors and (particularly) the strain gages into the bridge. The leadwires themselves are resistors that are in series with these functional resistive elements. Although they do not measure strain when properly installed, leadwires are sensitive to temperature. It is especially important in making static measurements that the three-leadwire method of connection be used with the quarter-bridge arrangement to automatically provide for compensation of leadwire temperature effects, minimize initial unbalance due to the leadwires, and reduce the desensitizing effect of the leadwire resistance on bridge output ( Ref.3 ).


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Figure 1: Quarter-bridge, tbree-leadwire system.

Therefore, a typical measuring circuit (shown above) will have the strain gage (R1) connected with the three-leadwire system as one arm of the bridge. The adjacent arm (R4) can be a "dummy" strain gage or resistor of the same resistance. Two more matched resistors, R2 and R3, which are not necessarily the same value as R1 and R4, make up the other half of the bridge circuit.

With a voltage input to the bridge (Vin) and an appropriate device to measure the output (Vout), the system is capable of producing a signal which may be related to the strain in the gage. But, the system will not function in a very efficient or effective manner until the other features found in modern strain gage instrumentation are incorporated into the measurement system.

Bridge Balance The bridge circuit is only in balance (has no output when the bridge voltage is applied) provided that R1/R4 = R2/R3 (as shown previously). Taking into account the various resistance tolerances on the strain gage(s), resistors and leadwires, an initial unbalance is invariably present. Adjustment of initial balance so that at zero strain there is zero output is achieved fairly easily by incorporating a resistive balance control in the circuit (shown below). Consisting of a fixed resistor (connected to the junction of R2 and R3), and a variable resistor (across the bridge voltage supply), this arrangement enables adjustments to be made to bring the bridge circuit into balance. The balance range available depends on the value of the fixed (balance limit) resistor.

Figure 2: Resistive Balance Control

While resistive-balance circuits are widely used in strain gage instrumentation, an alternative electronic method of balancing the output to zero involves measuring the output of the amplifier and injecting an equal and opposite voltage. This method permits rapid automatic balancing in multi-channel systems and eliminates the bridge loading errors that are possible in the resistive system when making measurements with precision strain gage transducers.


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Shunt Calibration Shunt calibration is a powerful method of determining the performance of the overall circuit (including the instrument itself) into which the strain gage is connected. By introducing a known change of resistance ∆R (which can be equated to a strain value) into the Wheatstone bridge, an electrical output can be produced for checking or determining the sensitivity of the system. The change of resistance is achieved by shunting one or more arms of the bridge with a parallel resistor to produce a reduction in the resistance of the arm that is shunted. The simple shunt calibration equation is:

Strain simulated ( )gsh

g

RRGFR

+

×=

610µε

where:

Rg = Resistance of shunted arm of the bridge. (Resistance, Rg, if shunted in an inactive arm must be the same as that of the gage.)

Rsh = Resistance of shunt calibration resistor

GF = Gage Factor

As an example, a calibration resistor of 59,880 ohms shunting a 120-ohm bridge arm will simulate 1000 µε at a Gage Factor of 2.0.

Which bridge arm is shunted presents different advantages and disadvantages. One of the most popular approaches is to shunt the dummy or bridge completion resistor (shown below) in a quarter-bridge three-leadwire measuring system. In this case the desensitizing effect of leadwire resistance in series with the active strain gage is compensated for in the calibration.

Figure 3: Shunt Calibration of Dummy Resistor.

It must be emphasized, however, that as useful and powerful as shunt calibration is, it does not calibrate either the instrument or the strain gage as such. Rather, shunt calibration determines the measurement system sensitivity.


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Amplification Prior to this point, the discussion of bridge output has been in terms of the signal available from the bridge circuit. For all practical measurement purposes, this signal must be amplified to a level (typically up to ±10 volts) that is compatible with the input-voltage requirements of the readout device. The output voltage equation then includes one more term: amplifier gain.

For a single active gage: GainGFVV inout ×××= ε

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In particular, it should be noted that for a given strain the same will result from different combinations of and Gain. The ability to trade off between these can be very important in helping to obtain the best possible measurements and to maintain the same resolution for different values of

Amplifier Gain The amplifier characteristics must be such that they faithfully amplify the small signals at the bridge output in a stable and noise-free manner. Gain values for static measurements are normally lower than those for dynamic measurements where stability is somewhat less important, but amplification of electrical noise can become significant. While special techniques may be required to reduce noise in the measuring circuit ( Ref.4 ), the ability to trade off reduced amplifier gain for higher bridge voltage can become advantageous.

The amplifier gain in static measuring instruments may be preset so that no separate gain adjustment control is provided, or it may be changed automatically as bridge voltage is altered or gage factor setting adjusted. Variable gain control, typically from 100 or less up to several thousand, however, is normally found on instruments intended for dynamic measurements.

Amplifier Balance Amplifier balance, or zero control, is required to establish the electrical zero, i.e. zero output for zero input. (This should not be confused with bridge balance referred to previously.) Various methods can be used to achieve zero input to the amplifier. These include turning the bridge voltage off (so that there can be no output from the bridge) and/or automatically terminating the input to the amplifier when the amplifier zero function is selected.

Frequency Response An important feature to be considered when dynamic measurements are involved is the frequency response or bandwidth of the analog output from the amplifier. This is defined as the upper frequency beyond which the amplifier output will decrease with increasing frequency for a constant input (shown below), and is a function of amplifier design.


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Figure 4: Typical Frequency Response Cbaracteristics Normalized to -3dB Attenuation Frequency.

Bandwidth specifications are normally referred to the -0.5dB (5% loss of output) or the -3dB (30% loss of output) point. While the frequency at the -3dB point is normally between 2 and 2.5 times higher than at the -0.5dB point, it must be recognized that any measurements at frequencies above the latter will involve increasing errors due to loss of signal output. These errors cannot easily be assessed or allowed for without dynamic calibration with a frequency generator.

Filtering When measurements do not require the full bandwidth, the more elaborate dynamic instruments having a high frequency response may have built-in lowpass selectable filters for suppressing high frequency components of the input signal. Typical cutoff frequencies are 10, 100, 1000 and 10,000 Hz. Another facility which may be included in more sophisticated dynamic instruments is selectable AC coupling. This eliminates the static component of the signal such that only the dynamic component is available at the output. In this manner the dynamic component can be observed or recorded without any shift of the mean or zero value.

Output and Display

As previously stated, the amplifier output is normally in the form of an analog voltage (up to ±10 volts) which can be fed into any appropriate indicating or recording device. This may represent a wide range of strain values as a function of bridge voltage (Vin) and amplifier gain (shown below).


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Figure 5: Relationship of Amplifier Output to Bridge Voltage for Various Amplifier Gains.

For static measurements, the analog output will typically be input to an analog-to-digital converter (ADC) and the digital signal will be passed to a digital display or computer. For dynamic measurements, the analog voltages are normally fed into an oscilloscope, X-Y recorder, magnetic tape recorder, or recording oscillograph. In the case of magnetic tape recorders, the output will usually need to be attenuated in order that the tape input voltage limit (usually ±1.414 volts) is not exceeded. This can be easily achieved, when attenuation is not built into the instrument, by placing a simple voltage divider in the output circuit. For input to low-impedance devices, specifically galvanometers in light-beam recording oscillographs, provision for current-limiting of the output is important in order to prevent damage to the galvanometers.

Multi-channel Measurements Strain gage measurements may involve anything from a few channels to several hundred. For static measurements, sequential switching of measurement channels through a single strain indicator and/or controller is typical.

Where only a few channels are involved, manual or semiautomatic switching can be used at relatively low speeds. For many channels and computer-controlled systems, relatively high-speed switching or multiplexing is required.

In either case, the nature of the switching is very important because it can involve changes in resistance of switch contacts. These contact resistances may be of the same order as, or even larger than, the resistance changes in the strain gage.

Low-speed switching, whether automatic or manual, is usually made from within the bridge circuit itself and necessitates the use of high-quality, low-resistance switch contacts. High-speed solid-state multiplexing, however, involves significant switching resistance, which prohibits its use within the bridge. In this case, input circuits and associated scanners are designed such that each strain gage channel is a complete bridge and switching takes place in the signal output leads where the resistance changes have negligible effect.

Summary The aim of this section has been to describe in a basic and practical way some of the main features involved in strain gage instrumentation. It is these features, together with careful


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electronic design and a complete understanding of the characteristics of the electrical resistance strain gage itself, that make for accurate, reliable measurements. Modern strain gage instrumentation is designed, developed and manufactured to those standards and specifications that incorporate all the features necessary to obtain good, valid, measurements. There can be no compromise because of the very small initial signal levels involved.

References

1. " Errors Due to Wheatstone Bridge Nonlinearity ," Vishay Measurements Group Tech Note TN-507

2. " Optimizing Strain Gage Excitation Levels ," Vishay Measurements Group Tech Note TN-502

3. "The 3-Wire Quarter-Bridge Circuit ," Vishay Measurements Group Tech Note TT-612 4. "Noise Control in Strain Gage Measurements ," Vishay Measurements Group Tech Note TN-

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