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Rose-Hulman ECE 470 - Stress and Strain Measurement

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lecture 16 outline 16-1 Stress and Strain Measurement Introduction Stress and strain can be measured in many ways, typically based in some fashion upon the fact that a structure is deformed, or strained, when it experiences stress. Piezoelectric transducers use the fact that, in piezoelectric materials, electric charge is separated when the materials is strained (and vice versa). Other transducers are often based on the resultant changes that the strain produces in capacitance, inductance or resistance. We are going to focus on perhaps the most widely used transducer, the metallic strain gage. Its fundamental principles of operation, use and application, necessary signal conditioning, and its limitations will be explored. Metallic electric resistance strain gages Metallic ER strain gages use the fact that a metal is deformed, or is strained, when it experiences stress. The strain results in a change in its resistance. The shape is usually not a simple bar.lecture 16 outline 16-2 The most common form for metallic strain gages is for the wire grid to be formed from constantan (a Cu-Ni alloy) and the backing to be polyimide (a high-temperature polymer). This metal foil is bonded to the element to be strained so that it will experience the same strain as that of the element. While this one type is most common, metallic-foil strain gages are manufactured from a variety of different metals and alloys, with a range of resistance values, a range of sensitivity of resistance to strain, and varying resistance-to-temperature characteristics. Common nominal resistance values (the resistance of the unstrained strain gage) are 120 Ω, 350 Ω, and 1000 Ω. Applications Strain gages can be related directly to stress through the elastic modulus (Young's modulus, E). Other typical measurements are force, torque, and pressure. 1. If the relationship between applied force and strain can be determined for a given structure, then strain gages can be used to measure the force. 2. If the relationship between applied torque and strain can be determined for a given structure, then strain gages can be used to measure the torque. 3. If the relationship between applied pressure and strain (examples include a container or a membrane) can be determined for a give structure, then strain gages can be used to measure the pressure.lecture 16 outline 16-3 Theoretical background For a resistor of uniform cross section A, of length L, and of resistivity ρ: If we take the differentials of the relation for resistance, we obtain. (1) Assuming a circular cross section (same end result is obtained, the boxed equation below, if other cross sections are used). The axial strain is related to the transverse strain via ν, Poisson's ratio, a material property. This permits us to write Substituting these relationships into (1). Strain gages are characterized by the strain gage factor, S. LR = AρdR d dL dA = + - RLAρρ2DdAdDA = , = 2 4A Dπta = - ενεadD dL = - = - DLννεaadR d = + + 2 RρενερaadR R dS = = 1 + 2 + ρρνεεlecture 16 outline 16-4 Overview of their characteristics For metallic strain gages, the gage factor is typically around 2-6, usually closer to 2. Semiconductor strain gages can have gage factors higher than 100. For metallic gages, strains as high as 0.04 (4% elongation) are measured routinely. For semiconductor gages, the strain is limited to about 0.003 (0.3% elongation). For a constant temperature, S is fairly constant with strain. Depending on the material, S can be sensitive to temperature changes. Specific examples Measuring force: Strain gages can be used to measure force. Given a structure's geometry and composition, the relationship between applied force and resulting stress is calculated. Knowing material properties, the resulting stress is related to the strain, ε. For a given gage factor, S, the resulting change in resistance is easily calculated. Measuring torque: Strain gages can be used to measure torque. Given a structure's geometry and composition, the relationship between applied torque and resulting stress can be calculated. Knowing material properties, the resulting stress is related to the strain, ε. For a given gage factor, S, the resulting change in resistance is easily calculated. R S R εΔ≈lecture 16 outline 16-5 Using strain gages in a measurement system In a system designed to measure (for example, stress), the strain gage provides a change in resistance. This is the signal available from the strain gage. This change in resistance is typically transformed to a change in voltage, often by using a Wheatstone bridge. Then, since the change in voltage is usually too small to be useful, an amplifying circuit is used to raise the voltage changes to a useful level. Signal conditioning for metallic strain gages Wheatstone Bridge The Wheatstone Bridge is used to convert a change of resistance into a change of voltage. With Vb measured across an open circuit, • the current through R1 is the same as that through R4 • the current through R2 is the same as that through R3 By voltage division, we have The bridge is "balanced" (that is, Vb = 0), for 34bs2314RRV = - VR + R R + R⎛⎞⎜⎟⎝⎠34b12RRV = 0 for = RRlecture 16 outline 16-6 Now, let's replace one of the resistances on the bridge with a strain gage resistor and make the other three resistances the resistance of the strain gage's nominal resistance. Note that, when the strain gage experiences no strain, all four resistances in the bridge will have the same value. Analysis to find Vb By voltage division, This configuration is called the one-active-arm bridge since only one of the arms responds to the measurand. Often benefits are available by placing more than one strain gage resistance into the bridge. Consider a cantilever beam. Place R1 and R3 in tension and R2 and R4 in compression. Benefits are 1) elimination of torsion loading effects 2) more sensitivity 3) temperature compensation bsRV V for one-active-arm bridge4RΔ≅22bs s2R + R R 2R + 2R R - 2R - R R V = - V = VR + R + R R + R4R + 2R R⎛⎞ΔΔΔ⎛⎞⎜⎟⎜⎟ΔΔ⎝⎠⎝⎠bssRRV = V V for R R (almost always the case)4R + R 4RΔΔ≅ΔΔlecture 16 outline 16-7 This


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