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Basic Strain Measurements using IOtech DAQ Hardware

INTRODUCTION DISCUSSION Strain gages are sensing devices used in a variety of physical test and STRAIN MEASUREMENT CONFIGURATIONS measurement applications. They change resistance at their output terminals when stretched or compressed. Because of this character- To make an accurate strain measurement, extremely small resis- istic, the gages are typically bonded to the surface of a solid material tance changes must be measured. The Wheatstone is and measure its minute dimensional changes when put in com- widely used to convert the gage’s microstrain into a change pression or tension. Strain gages and strain gage principles are often that can be fed to the input of the analog-to-digital converter used in devices for measuring acceleration, pressure, tension, and (ADC). (See Figure 1.). When all four in the bridge are force. Strain is a dimensionless unit, defined as a change in length absolutely equal, the bridge is perfectly balanced and V = 0. But per unit length. For example, if a 1-m long bar stretches to 1.000002 out when any one or more of the resistors change value by only a m, the strain is defined as 2 microstrains. Strain gages have a fractional amount, the bridge produces a significant, measurable characteristic gage factor, defined as the fractional change in voltage. When used with an instrument, a strain gage replaces one resistance divided by the strain. For example, 2 microstrain applied or more of the resistors in the bridge, and as the strain gage to a gage with gage factor of 2 produces a fractional resistance undergoes dimensional changes (because it is bonded to a test change of (2x2)10-6 = 4x10-6, or 4 . Common gage resistance μΩ specimen), it unbalances the bridge and produces an output values typically range from 120 to 350 , but some devices are as Ω voltage proportional to the strain. low as 30Ω or as high as 3 kΩ.

Figure 1: Full-Bridge Circuit

R1 R3

+ R1 R Motion – + 4 Vexc VOUT R2 R3 –

R2 R4

The full-bridge circuit provides the largest output with minimum errors. All four arms of the bridge are active; two are in tension while the two on the opposite side are in compression.

www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] Full-Bridge Circuits measurement as long as the input amplifier has high input imped- Although half-bridge and quarter-bridge circuits are often used, ance. For example, an amplifier with a 100-MΩ input impedance the full-bridge circuit is the optimal configuration for strain produces negligible current flow through the measurement leads, gages. It provides the highest sensitivity and the fewest error minimizing voltage drops due to lead resistance. components, and because the full bridge produces the highest output, noise is a less significant factor in the measurement. For Half-Bridge Circuits these reasons, the full bridge is recommended when possible. When physical conditions do not allow mounting a full-bridge gage, a half bridge might fit. Typically, two strain gages are A full bridge contains four strain gages mounted on a test mounted on a test member, and two discrete resistors complete member as shown in Figure 1. Two gages are mounted on the top the bridge. The output voltage is: surface to measure tension and the other two are mounted on the opposite surface to measure compression when the beam is Equation 2: Half-Bridge Output Voltage forced downward. As the member deflects, the two gages in V = V (X/2) tension increase in resistance while the other two decreases, o ex unbalancing the bridge and producing an output proportional Where: Vo = bridge output voltage, V to the displacement. Upward motion reverses the roles of the Vex = excitation voltage applied to the bridge, V strain gages. The bridge output voltage is given by: X = relative change in resistance, ΔR/R Equation 1: Full-Bridge Output Voltage For a large ΔR, half-bridge and quarter-bridge circuits can intro- V = (V )(X) o ex duce an additional nonlinearity error. (See Figure 2.) Also, the readings are not accurate when the temperature coefficients Where: Vo = bridge output voltage, V among the bridge completion resistors and strain gages are V = excitation voltage applied to the bridge, V ex different and the resistances do not change proportionally with X = relative change in resistance, ΔR/R temperature. Furthermore, bridge completion resistors are not usually located near the strain gages, so temperature differences The bridge nulls out potential error factors such as temperature contribute additional errors. In systems with long lead wires, the changes because all four strain gages have the same temperature bridge completion resistors should be attached close to the coefficient and are located in close proximity on the specimen. The gages. However, this may not always be practical due to test resistance of the lead wire does not affect the accuracy of the fixture limitations or other physical conditions. Figure 2: Half-Bridge Circuit Bridge Strain completion resistors gages

R R3 1 + R1 Motion – + Vexc VOUT R2 –

R4 R2

In a half-bridge circuit, only two arms are active. Two strain gages are on the specimen while the two fixed resistors that complete the bridge are not.

2 www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] Quarter-Bridge Circuits Figure 4: Kelvin Strain-Gage Bridge Circuit A quarter-bridge circuit uses one strain gage and three bridge RL completion resistors. The output voltage is: i≅0 RL Equation 3: Quarter-Bridge Output Voltage ie R Vo = Vex (X/4) 1 R4 Where: V = bridge output voltage, V o RL i≅0 V = excitation voltage applied to the bridge, V ex + + X = relative change in resistance, ΔR/R + Vsense R2 R3 Vexc Vout – – – This arrangement has the smallest output, so noise is a potential R problem. Furthermore, all the error sources and limitations in the half- L bridge circuit apply to the quarter-bridge circuit. (See Figure 3). RL ie

RL PROCEDURE Excitation Source The circuit uses one pair of wires to provide the Accurate measurements depend on a stable, regulated, and low- excitation voltage directly at the bridge, and another to sense the noise excitation source voltage. A regulated source is necessary excitation voltage. A third pair of wires measures the bridge output because the output voltage of a strain gage is also proportional voltage. This arrangement removes the voltage-drop error in the to the excitation voltage. Therefore, fluctuations in the excita- excitation wires from the measured strain signal. tion voltage produce inaccurate output . most standard circuits, the heat that each gage dissipates is less An ideal data acquisition system provides an excitation source than 100 mW, so it’s not usually a problem. This is especially for each channel, independently adjustable from 1.5 to 10.5 V true when the strain gage is bonded to a material that conducts with a current limit of 100 mA. An excitation voltage, V, used heat quickly, such as metal. However, because most wood, with a strain gage of resistance R, requires a current of I = V/R. plastic, or glass materials do not conduct heat away as rapidly, The resistance of a Wheatstone bridge measured between any use the lowest excitation voltage possible without introducing two symmetrical terminals equals the value of one of the noise problems. Also, heat can become a problem when the resistance arms. For example, four 350-Ohm arms make a 350- strain gages are uncommonly small, or numerous gages occupy Ohm bridge. The load current equals the excitation voltage a limited space. divided by the bridge resistance; in this case, 10 V/350 Ω = 0.029 A = 29 mA. Consider a Kelvin connection for applying the excitation volt- age. Because the excitation leads carry a small current, they drop

Heating a correspondingly small voltage; V = I/Rl, which reduces the Resistive heating in strain gages also should be considered voltage reaching the bridge terminals. As illustrated in Figure 4, because the gages respond to temperature as well as stress. In Kelvin connections eliminate this drop with a pair of leads

Figure 3: Quarter-Bridge Circuit Bridge Strain completion resistors gages

R3 R1 + R1 Motion – + Vexc VOUT

–

R4

R2

A quarter-bridge circuit uses only one active arm and is the least sensitive of the three types. It is also the most prone to noise and errors.

3 www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] added at the excitation terminals to measure and regulate the Conductors carrying such low level signals are susceptible to bridge voltage. For example, when ie = 50 mA, Rl = 5Ω, and the noise interference and should be shielded. Low-pass filters, combined voltage drop in the two leads is 500 mV, no voltage differential voltage measurements, and signal averaging are also drops in the sense wires. effective techniques for suppressing noise interference. Further- more, instrumentation amplifiers usually condition the ex- An IOtech strain-gage module uses a Kelvin connection to measure tremely low strain-gage signals before feeding them to ADCs. and regulate the voltage at the bridge. It supplies the voltage to the For example, a 10-V full-scale input provides 156 μV of resolu- strain gage with one pair of leads and measures it with another pair tion for a 16-bit ADC. The instrumentation amplifier gain as shown in Figure 5. The six wires are used in pairs for Sense, Excite, should be adjusted to provide the full-scale output of the strain and Measure. The Sense lead is a feedback loop to ensure that the gage or load cell over the entire range of the ADC. Excite voltage is constantly held within specifications. Force and pressure transducers typically generate an offset Strain-Gage Signal Conditioning output signal when no external force is applied. Instrumenta- Most strain-gage based transducers and load cells are assigned tion amplifiers usually contain a control to adjust this offset to units of measure for weight, force, tension, pressure, torque, and zero and let the load cell cover the full range of the ADC. Most deflection with a full-scale value measured in mV/V of excita- amplifiers also provide adjustable excitation and gain. tion. 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, Common mode rejection ratio whether the load cell was designed to handle 10, 100, or 1,000 A high common mode rejection ratio (CMRR) is essential for lbs. The difference is in the resolution of the system. That is, the strain-gage amplifiers. A strain-gage signal in a Wheatstone small 10-lb load cell produces 0.5 lbs/mV, and the large 1,000- bridge is superimposed on a common-mode voltage equal to lb load cell produces 50 lbs/mV. half the excitation voltage. CMRR is a measure of how well the

Figure 5: IOtech Strain-Gage Module

+Sense 6 +Exc 5 Excitation –Exc Regulator Exc. Adj.

Optional –Sense Bridge Completion Bypass Resistors Input Gain Adj. Scale Gain Adj. Bypass

4 + To AALPF A/D 3 –

R1 R2 Offset Adj. Shunt Cal.

Note: Use R1 or R2, not both simultaneously. 2 1

Typical of 8 channels

An IOtech strain-gage module provides adjustable excitation, gain, and offset for each channel. This lets it make use of the instrument’s entire dynamic range.

4 www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] Figure 6: Wheatstone-Bridge Circuit Figure 7: Shunt Bridge Circuit Strain gage +10 V

+10 V Ron +V 347 Ω 350 Ω 350 Ω 350 Ω Gain = 200

20 mV IA (+) 5.02 V V = 200 (0.02) out 350 = 4.00 V Ω Rs = 350 43.75 kΩ Ω 350 Ω 350 Ω 5.00 V –V Voltage ≅ 20 mV when shunted

Close RTN to shunt (–) Normally the strain gage signal in a Wheatstone bridge is superimposed on a common-mode voltage equal to half of the excitation voltage. A bridge may be calibrated with a shunt , which is switched Consequently, a high CMRR is necessary to reject the common-mode with a software command into either one of the two lower legs. voltage and amplify the strain gage signal. Strain gage signal-conditioning modules usually provide a regu- amplifier rejects common-mode voltages. For example, con- lated excitation source with optional Kelvin excitation. Onboard sider a 10-V excitation supply (Vmax = 5 V) for a strain gage with bridge-completion resistors may be connected for quarter and

2 mV/V (Vs = 20 mV) at full scale and an amplifier with a CMRR half-bridge strain gages. Instrumentation amplifiers provide of 90 dB. (See Figure 6.) The amplifier can introduce 0.158 mV input and scaling gain adjustments, and an offset adjustment of error, corresponding to about 0.80% full scale, which may not nulls large quiescent loads. This lets input signals use the full be acceptable: range of the data acquisition system, and the measurements cover the full resolution of the ADC. Equation 4: Common-Mode Rejection Ratio dB = 20log (V /V ) Some strain-gage signal conditioners provide fixed gain, offset, 10 s e and excitation settings, but fixed settings do not take advantage -1 Vmax/Ve = log10 (dB/20) of the maximum dynamic range of the ADC. It decreases the -1 actual available resolution of the measurement. For example, = log10 (90/20) many generic strain gage-signal conditioner modules can be set = 31,622 to a fixed 3-mV/V rating. At 10V, the excitation, offset, and gain trimming are all fixed and no adjustments can be made. V = V /log -1 (dB/20) e max 10 An excitation adjustment lets users set the excitation voltage to = 5.00/31,622 the maximum allowed by the manufacturer, which maximizes = 0.158 mV the bridge’s output. Also, the offset adjustment lets users zero the output offset produced by either a small bridge imbalance or a quiescent deformation of the mechanical member that it is

%error = (Ve/Vs)100 mounted upon. And the gain adjustment lets users set a gain = (0.158mV/20mV)100 that provides a full-scale output under maximum load, which optimizes the dynamic range of the ADC. = 0.79% Calibration The signal-conditioning module also typically provides a shunt Where: Ve = error voltage, V calibration feature. See Figure 7. It lets users switch their own V = signal voltage, 20 mV s shunt resistors into either one of the two lower legs of the bridge

Vmax = maximum voltage, 5V under software control. For example, a shunt resistor can be CMRR = 90 dB calculated to simulate a full load. Applying a shunt resistor is a convenient way to simulate an unbalance without having to By comparison, a CMRR of 115 dB introduces only 9 mV of error, apply a physical load. For any balanced bridge, a specific resistor which corresponds to only 0.04% of full scale. can be connected in parallel with one of the four bridge elements to obtain a predictable unbalance and output voltage.

5 www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] For example, a 350-Ω, 2-mV/V strain gage delivers full output variations can also affect the performance of the strain gages when one leg drops by 0.8% to 347.2Ω. A 43.75-kΩ resistor themselves. Transducers must contain temperature compensa- shunted across one or the other lower bridge elements swings tion circuits to maintain accurate pressure measurements in the output to full positive or full negative. environments with widely varying temperatures.

An appropriate equation for the shunt calibration resistor value is: All strained-diaphragm pressure gages require a regulated exci- tation source. Some gages contain internal regulators, so users Equation 5: Shunt Calibration Resistor for Transducers can connect an unregulated voltage from a power supply. Some strained-diaphragm pressure gages also employ internal signal conditioning, which amplifies the mV signal output of the Rs = Rba[Vex/4(Vo)] Wheatstone bridge to a full-scale voltage from 5 to 10 V. Gages Rs = 350[10/4(0.020)] of this type have low-impedance outputs. In contrast, other Rs = 43.75 k pressure gages have no internal signal conditioning so their output impedance equals the Wheatstone bridge resistance Where: Rs = shunt resistor, Ohms (several kΩ for semiconductor types), and their full-scale output Rba = bridge arm resistor, Ohms is in mV. Vex = excitation voltage, V

Vo = bridge output voltage, V IOtech Instruments Many products include calibration software with a Windows- The following product tables list the IOtech equipment most based program that provides several calibration methods, online suitable for measuring strain. The StrainBook/616™ contains instruction, and a diagnostic screen for testing the calibrated built-in signal conditioners for handling strain gages, load system. cells, and other strain-based sensors and actuators, while other instruments or boards are more general purpose and require Transducers and Load Cells WBK43A™ or DBK16™ type plug-in modules to provide the Strain gages are commercially available in prefabricated modules proper signal conditioning. such as load cells that measure force, tension, compression, and torque. Load cells typically use a full-bridge configuration and The tables are intended to allow users to select the most contain four leads for bridge excitation and measurement. The appropriate data acquisition system for the job at the most manufacturers provide calibration and accuracy information. reasonable cost. For example, the DaqBoards™ are the most economical, although they require DBK signal conditioners, Strain Diaphragm Pressure Gages and they cannot be used to measure low-level voltage signals. A strained-diaphragm pressure gage consists of two or four strain They are limited to strain measurements. On the other hand, the gages mounted on a thin diaphragm. The gages are wired in a LogBook™ can measure almost any variable, provided it has the Wheatstone bridge circuit, including bridge completion resistors appropriate signal-conditioning module. Although this con- when needed, so the pressure gage is electrically equivalent to a figuration is more expensive, it may be most appropriate for load cell. The output voltage is specified in mV/V of excitation for users who have a requirement to measure a mix of many more a full-scale pressure differential across the diaphragm. variables and more channels.

When one side of the diaphragm (called the reference pressure Consult the instruction manual for each product when con- side) is open to the ambient atmosphere, the gage compares the necting the various strain-type sensors. The manuals contain inlet pressure to the ambient pressure, which is about 14.7 psi the details necessary to ensure a robust measurement system. at sea level. When the gage measures ambient pressure, the They are available on IOtech’s Web site for viewing whether you reference chamber must be sealed with either a vacuum refer- have the product in hand or are considering purchasing one. ence (near zero psi) or the sea-level reference. Visit our Web site at www.iotech.com.

Temperature variations can affect the accuracy of strained- Contact Information diaphragm pressure gages. A pressure gage with a sealed non- IOtech zero reference pressure exhibits temperature variations consis- 25971 Cannon Road tent with the ideal gas law. For example, a 5˚C change in Cleveland, Ohio 44146 ambient temperature near normal room temp (25˚C) produces Phone: 1-440-439-4091 an error of 1.7% in the pressure measurement. Temperature Fax: 1-440-439-4093 Email: [email protected]

6 www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] TABLE 1 IOtech Hardware for Strain Measurements

Product* Number of Signal Configurability Excitation Maximum Included PC Possible Conditioner Aggregate View Connect Channels Option Speed Application

StrainBook/616 8 to 256 Built-in Software 0.5 to 10V 1 MHz WaveView Ethernet

WaveBook 8 to 256 WBK16 Software 0.5 to 10V 1 MHz WaveView Ethernet

DaqBook 2 to 256 DBK16 DBK43A Manual 1.5 to 10.5V 200 kHz DaqView Ethernet

DaqLab 2 to 256 DBK16 DBK43A Manual 1.5 to 10.5V 200 kHz DaqView Ethernet

LogBook 2 to 256 DBK16 Manual 1.5 to 10.5V 100 kHz LogView Stand-alone DBK43A Parallel RS-232 (PC-Card Optional)

DaqBoard/2000 Series 2 to 256 DBK16 Manual 1.5 to 10.5V 200 kHz DaqView PCI DBK43A

*All units support the following features: A. Shunt calibration B. File formats: 1. DADiSP 2. DIAdem 3. DASYLab 4. MATLAB 5. Snap-Master 6. ASCII/Excel 7. .wav Files C. Bridge Configuration: Full, 1/2, 1/4 D. Bridge Wiring Type: 2, 3, 4, 6 E. Bridge resistance in Ohms: 60 to 1000 F. Coupling: AC and DC G. Additional transducer support: numerous H. Maximum resolution: 16 bits

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7 www.iotech.com • IOtech • 25971 Cannon Rd • Cleveland, OH 44146 • (440) 439-4091 • Fax (440) 439-4093 • [email protected] Table 2 IOtech Hardware for Strain Measurements

Signal Number of Excitation Sensitivity Configuration Used with: Conditioner Possible Description Channels

DBK16 2 5V 0.8 to 10 mV/V PC Board LogBook 10V 0.4 to 5 mV/V DaqBook DaqLab DaqScan DaqBoard/2000-Series

DBK43A 8 5V 0.8 to 10 mV/V Module LogBook 10V 0.4 to 5 mV/V DaqBook DaqLab DaqScan DaqBoard/2000-Series

WBK16 8 Programmable: N/A Module WaveBook 0.5, 1, 2, 5, 10V

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