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A tutorial: making basic strain measurements.

Strain gages are sensing devices used in a variety of physical test and measurement applications. They change resistance at their output terminals when stretched or compressed. Because of this characteristic, the gages typically are bonded to the surface of a solid material and are used to measure its minute dimensional changes when put in compression or tension.

Strain gages and strain gage principles often are used in devices for measuring acceleration, pressure, tension, and force. Strain is a dimensionless unit, defined as a change in length per unit length. For example, if a 1-m long bar stretches to 1.000002 m, the strain is 2 microstrains.


Strain gages have a characteristic gage factor, defined as the fractional change in resistance divided by the strain. For example, 2 microstrain applied to a gage with a gage factor of 2 produces a fractional resistance change of (2 x 2)10.sup.-6] = 4 x [10.sup.-6] or 4 [micro][ohm]/[ohm]. Common gage resistance values typically range from 120 [ohm] to 350 [ohm], but some devices are as low as 30 [ohm] or as high as 3 k[ohm].


Data acquisition manufacturers have begun to use 24-bit ADCs in their improve resolution and accuracy in the strain-based measurement products. In the past, strain gage data acquisition hardware typically provided 16-bit resolution. These devices used every part of their 16-bit resolution to ensure accurate measurements.

With 24 bits the old practice of adjusting gain and offset voltages in hardware to pull out every last bit of a 16-bit ADC's resolution is no longer necessary. The old method had one very undesirable consequence; if you set the gain too close to the maximum, the ADC could go into limit, and valuable information would be lost. If the gain were set too low, low-level signal information would be lost. The 24-bit ADC has 256 times the resolution of the 16-bit ADC, so software offset and gain adjustments can be used to provide great resolution and large overhead.

Strain Measurement Configurations

Wheatstone Bridge

To make an accurate strain measurement, extremely small resistance changes must be measured. The Wheatstone bridge circuit is widely used to convert the gage's microstrain into a voltage change that can be fed to the input of the ADC.

When all four resistors in the bridge are equal, the bridge is perfectly balanced and [V.sub.out] = 0. But when any one or more of the resistors change value by only a fractional amount, the bridge produces a significant, measurable voltage. When a strain gage replaces one or more of the resistors in the bridge, and as the strain gage undergoes dimensional changes because it is bonded to a test specimen, it unbalances the bridge and produces an output voltage proportional to the strain.

Full-Bridge Circuits

Although half-bridge and quarter-bridge circuits often are used, the full-bridge circuit is the optimal configuration for strain gages. It provides the highest sensitivity and the fewest error components. And because the full bridge produces the highest output, noise is a less significant factor in the measurement. For these reasons, the full bridge is recommended when possible.

An example of a full bridge is the full bending bridge configuration containing four strain gages mounted on a test member as shown in Figure 1. Two gages are mounted on the top surface to measure tension, and the other two are mounted on the opposite surface to measure compression when the beam is forced downward.


As the member deflects, the two gages in tension increase in resistance while the other two decrease, unbalancing the bridge and producing an output proportional to the displacement. Upward motion reverses the roles of the strain gages. The full-bridge output voltage is given by

[V.sub.o] = ([V.sub.ex])(X) (1)

where: [V.sub.o] = bridge output voltage

[V.sub.ex] = excitation voltage applied to the bridge

X = relative change in resistance, [DELTA]R/R

The bridge nulls out potential error factors such as temperature changes because all four strain gages have the same temperature coefficient and are located in close proximity on the specimen. The resistance of the lead wire does not affect the accuracy of the measurement as long as the input amplifier has high input impedance and the bridge excitation is remotely sensed. For example, an amplifier with a 100-M[ohm] input impedance produces negligible current flow through the measurement leads, minimizing voltage drops due to lead resistance.


Half-Bridge Circuits

When physical conditions do not allow mounting a full-bridge gage, a half-bridge might fit. Typically, two strain gages are mounted on a test member, and two highly stable discrete resistors or a highly stable resistor network complete the bridge. The half-bridge output voltage is

[V.sub.o] = [V.sub.ex] (X/2) (2)

where: [V.sub.o] = bridge output voltage

[V.sub.ex] = excitation voltage applied to the bridge

X = relative change in resistance, [DELTA]R/R

For a large [DELTA]R, half-bridge and quarter-bridge circuits can introduce an additional nonlinearity error. Also, the readings are not accurate when the temperature coefficients among the bridge completion resistors and strain gages are different and the resistances do not change proportionally with temperature.

Furthermore, bridge completion resistors usually are not located near the strain gages, so temperature differences contribute additional errors. In systems with long lead wires, the bridge completion resistors should be attached close to the gages. However, this may not always be practical due to test-fixture limitations or other physical conditions.

Quarter-Bridge Circuits

A quarter-bridge circuit uses one strain gage and three bridge completion resistors. The quarter-bridge output voltage is

[V.sub.o] = [V.sub.ex] (X/4) [approximate] (3)

where: [V.sub.o] = bridge output voltage

[V.sub.ex] = excitation voltage applied to the bridge

X = relative change in resistance, [DELTA]R/R

This arrangement has the smallest output, so noise is a potential problem. All the error sources and limitations in the half-bridge circuit also apply to the quarter-bridge circuit.


Excitation Source

The Wheatstone bridge is a ratio-metric transducer; its output voltage to excitation voltage ratio is proportional to the resistive bridge unbalance. Many strain-based data acquisition instruments make use of a true ratiometric measurement system. Its measured output is proportional to the bridge output voltage to excitation voltage ratio. As such, this instrument is not sensitive to excitation voltage changes. The only excitation requirement is low short-term noise, and the voltage is between 2 V and 10 VDC.

An ideal data acquisition system provides an excitation source for each channel, independently adjustable from 1.5 V to 10.5 V with a current limit of 100 mA. An excitation voltage (V) used with a strain gage of resistance (R) requires a current of I = V/R.

The resistance of a Wheatstone bridge measured between any two symmetrical terminals equals the value of one of the resistance arms. For example, four 350-[ohm] arms make a 350-[ohm] bridge. The load current equals the excitation voltage divided by the bridge resistance; in this case, 10 V/350 [ohm] = 0.029 A = 29 mA.


Resistive heating in strain gages also should be considered because the gages respond to temperature as well as stress. The excitation voltage must be coordinated with the gage and the material to which it is bonded.

Like most engineering endeavors, strain measurement involves making compromises. In this case, it is errors due to self-heating vs. signal to noise ratio. Higher excitation results in a signal less affected by external electrical noise sources but produces higher errors due to self-heating.

Self-heating errors are more prevalent when the strain gage is bonded to a material that doesn't heat quickly, such as wood, plastic, or glass. Also, heat can become a problem when the strain gages are uncommonly small, or numerous gages occupy a limited space.

For full- and half-bridge configurations, consider a Kelvin connection for applying the excitation voltage. Because the excitation leads carry a small current, they drop a correspondingly small voltage which reduces the voltage reaching the bridge terminals.

As illustrated in Figure 2, Kelvin connections eliminate this drop with a pair of leads added at the excitation terminals to measure and regulate the bridge voltage. For example, when [i.sub.e] = 50 mA, [R.sub.1] = 5 [ohm], and the combined voltage drop in the two leads is 500 mV, no voltage drops in the sense wires.


Some data acquisition modules use a Kelvin connection to measure and regulate the voltage at the bridge. It supplies the voltage to the strain gage with one pair of leads and measures it with another pair as shown in Figure 3. The six wires are used in pairs for sense, excite, and measure. The sense lead is a feedback loop to ensure that the excite voltage is constantly held within specifications.


In the quarter-bridge configuration, it is not possible to remotely sense around the lead wire resistances so a three-wire connection is recommended. This configuration relies on the resistances of the lead wires being equal.

Strain Gage Signal Conditioning

Most strain gage-based transducers and load cells are assigned units of measure for weight, force, tension, pressure, torque, and deflection with a full-scale value measured in mV/V of excitation. For example, a load cell with a 10-V excitation supply and a 2-mV/V gain factor generates an output of 20 mV at full load whether the load cell was designed to handle 10, 100, or 1,000 lb. The difference is in the resolution of the system. That is, the small 10-lb load cell has a sensitivity of 0.5 lb/mV and the large 1,000-lb load cell 50 lb/mV.

Conductors carrying such low-level signals are susceptible to noise interference and should be shielded. Low-pass filters, differential voltage measurements, and signal averaging also are effective techniques for suppressing noise interference. Furthermore, instrumentation amplifiers usually condition the extremely low strain gage signals before feeding them to ADCs.

Common-Mode Rejection Ratio

A high common-mode rejection ratio (CMRR) is essential for strain gage amplifiers. A strain gage signal in a Wheatstone bridge is superimposed on a common-mode voltage equal to half the excitation voltage.

CMRR is a measure of how well the amplifier rejects common-mode voltages. For example, consider a 10-V excitation supply ([V.sub.max] = 5 V) for a strain gage with 2 mV/V ([V.sub.s] = 20 mV) at full scale and an amplifier with a CMRR of 90 dB (Figure 4). The amplifier can introduce 0.158 mV of error, corresponding to about 0.80% full scale, which may not be acceptable.


dB = 20[log.sub.10] ([V.sub.s]/[V.sub.e]) (4)

[V.sub.max]/[V.sub.e] = [log.sub.10.sup.-1] (dB/20)

= [log.sub.10.sup.-1] (90/20)

= 31,622

[V.sub.e] = [V.sub.mas]/[log.sub.10.sup.-1] (dB/20)

= 5.00/31.622

= 0.158 mV

%error = [V.sub.e]/[V.sub.s])100

= (0.158 mV/20mV)100

= 0.79%

Where: [V.sub.e] = error voltage

[V.sub.s] = signal voltage,20mV

[V.sub.max] = maximum voltage, 5 V

CMRR = 90 dB

By comparison, a CMRR of 115 dB introduces only 9 mV or error, which corresponds to only 0.04% of full scale.

Strain gage signal conditioning modules usually include a regulated excitation source with optional Kelvin excitation. Bridge completion resistors may be connected for quarter- and half-bridge strain gages. Instrumentation amplifiers provide input and scaling gain.


The signal-conditioning module also typically offers a shunt calibration feature (Figure 5). It lets users switch in an extremely stable, internal shunt cal resistor. For example, a shunt resistor can be calculated to simulate a full load. Applying a shunt resistor is a convenient way to simulate an imbalance without having to apply a physical load.


Transducers and Load Cells

Strain gages are commercially available in prefabricated modules such as load cells that measure force, tension, compression, and torque. Load cells typically use a full-bridge configuration and contain four leads for bridge excitation and measurement. The manufacturers provide calibration and accuracy information.

Strain Diaphragm Pressure Gages

A strained diaphragm pressure gage consists of two or four strain gages mounted on a thin diaphragm. The gages are wired in a Wheatstone bridge circuit, including bridge completion resistors when needed, so the pressure gage is electrically equivalent to a load cell. The output voltage is specified in mV/V of excitation for a full-scale pressure differential across the diaphragm.

When one side of the diaphragm, called the reference pressure side, is open to the ambient atmosphere, the gage compares the inlet pressure to the ambient pressure, which is about 14.7 psi at sea level. When the gage measures ambient pressure, the reference chamber must be sealed with either a vacuum reference near zero psi or the sea-level reference.

Temperature variations can affect the accuracy of strained diaphragm pressure gages. A pressure gage with a sealed non-zero reference pressure exhibits temperature variations consistent with the ideal gas law. For example, a 5[degrees]C change in ambient temperature near normal room temperature produces an error of 1.7% in the pressure measurement.

Temperature variations also can affect the performance of the strain gages themselves. Transducers must contain temperature compensation circuits to maintain accurate pressure measurements in environments with widely varying temperatures.

All strained diaphragm pressure gages require a regulated excitation source. Some gages contain internal regulators so users can connect an unregulated voltage from a power supply.

Some strained diaphragm pressure gages also use internal signal conditioning, which amplifies the mV signal output of the Wheatstone bridge to a full-scale voltage from 5 to 10 V. Gages of this type have low-impedance outputs. In contrast, other pressure gages do not have internal signal conditioning so their output impedance equals the Wheatstone bridge resistance (several k[ohm] for semiconductor types), and their full-scale output is in mV.


Making strain gage-based measurements can be a challenging process due to the nature and low value of the signal. Data acquisition systems that provide built-in signal amplification, on-board excitation, high resolution, shunt calibration, auto-zero, and bridge completion can reduce the risk for errors and improve the accuracy of measurements.

by Steve Radecky, IOtech

About the Author

Steve Radecky is a product marketing specialist at IOtech. He has been with the company since 1997, previously working as an OEM sales engineer. IOtech, 25971 Cannon Rd., Cleveland, OH 44146, 440-439-4091, e-mail:
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Title Annotation:STRAIN GAGES
Author:Radecky, Steve
Publication:EE-Evaluation Engineering
Geographic Code:1USA
Date:Aug 1, 2009
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