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 Basic Knowledge Strain & stress foundation 1. Strain Gauge There are many kinds of strain gauges. The metallic strain gage consists of a very fine wire or, more commonly, metallic foil arranged in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain in the parallel direction (Figure 1). The grid is bonded to a thin backing, called the carrier, which is attached directly to the test specimen. Therefore, the strain experienced by the test specimen is transferred directly to the strain gage, which responds with a linear change in electrical resistance. Strain gages are available commercially with nominal resistance values from 30 to 3000 Ω, with 120, 350, and 1000 Ω being the most common values. Figure 1: Strain gauge configuration 2. Wheatstone bridge In practice, the strain measurements rarely involve quantities larger than a few millistrain (ε x 10-3). Therefore, measuring strain requires accurate measurement of very small changes in resistance. For example, suppose a test specimen undergoes a substantial strain of 400με. A strain gauge with a gauge factor GF = 2 will exhibit a change in electrical resistance of only 2.(400 x 10-6) = 0.08%. For a 120 Ω gauge, this is a change of only 0.096Ω. All strain-gauge configurations are based on the concept of a Wheatstone bridge. A Wheatstone bridge is a network of four resistive legs. One or more of these legs can be active sensing elements. Figure 2 shows a Wheatstone bridge circuit diagram. The Wheatstone bridge is the electrical equivalent of two parallel voltage divider circuits. R1 and R2 compose one voltage divider circuit, and R4 and R3 compose the second voltage divider circuit. The output of a Wheatstone bridge is measured between the middle nodes of the two voltage dividers. Figure 2: Wheatstone bridge A physical phenomenon, such as a change in strain applied to a specimen or a temperature shift, changes the resistance of the sensing elements in the Wheatstone bridge. The Wheatstone bridge configuration is used to help measure the small variations in resistance that the sensing elements produce corresponding to a physical change in the specimen. The output voltage of the bridge, VO, will be equal to: From this equation, it is apparent that when R1/R2 = R4/R3, the voltage output VO will be zero. Under these conditions, the bridge is said to be balanced. Any change in resistance in any arm of the bridge will result in a nonzero output voltage. Therefore, if we replace R4 in Figure 2 with an active strain gage, any changes in the strain gage resistance will unbalance the bridge and produce a nonzero output voltage. As shown in Figure 3. Figure 3: Wheatstone bridge without balance 3. Strain gauge configuration Strain gauge configurations are arranged as Wheatstone bridges. The gauge is the collection of all of the active elements of the Wheatstone bridge. There are three types of strain gauge configurations: quarter-, half-, and full-bridge. The number of active element legs in the Wheatstone bridge determines the kind of bridge configuration. Table 1 shows the number of active elements in each configuration. Each of these configurations is subdivided into multiple configuration types. The orientation of the active elements and the kind of strain measured determines the configuration type. 4. Temperature compensation The strain gages which are installed on surface of a tested object without any outside force, when environmental temperature changes, the resistance value will be changed accordingly. In order to minimize temperature drift errors, the strain gauge must have a Self Temperature Compensation (STC) number that corresponds to the thermal expansion coefficient of the material under test. STC gauges have a temperature sensitivity that counteracts the thermal expansion coefficient of the test specimen. The STC number approximately equals the thermally induced change in strain with change in temperature and is expressed in unit of microstrain per degree Fahrenheit. This method base on the UUT material’s CTE to adjust the strain gauge’s metal resistance sheet. So use just one strain gauge, you can measure the UUT’s strain value and without temperature influence. Except the special situation, basically we use the self-temperature compensation strain gauge now. 5. Lead’s temperature compensation Use the self-temperature compensation strain gauge to solve the temperature effect problem. But the lead wire between strain gauge and measure instrument also influence by temperature. This problem has not solved. As shown in Figure 4, the double lead connection will connect the wire resistance into the strain gage completely. The short wire dose not cause the problem, but long wire will bring influence. Figure 4: Long lead wire In order to reduce the wire influence, you may use three-wire connection method. Show as Figure 5, use another wire connects with strain gauge to get long the bridge. Figure 5: Three-wire connection method The difference between this method and double wire is the lead resistance which subdivides by bridge adjacent edges. In the figure 5, the lead resistance r1 connects to the strain gauge Rg, and r2 connects to the strain gauge R2, r3 is the bridge output terminal. Therefore, any temperature-related changes in voltage drop across r1 or r2 caused by temperature variation of the leads counteract out.