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Tech Tip 60602 www.iotech.com TECHTIP 60602 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 Wheatstone Bridge 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 bridge circuit is and measure its minute dimensional changes when put in com- widely used to convert the gage’s microstrain into a voltage 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 resistors 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 Kelvin bridge 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 voltages. 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.
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