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ME301StrainGaugeLaboratoryManual

# ME301StrainGaugeLaboratoryManual - 2 Strain Gauge Behavior...

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2. Strain Gauge Behavior 2.1. Purposes Use beam bending to examine the behavior of strain gauge and supporting circuitry. A Wheatstone bridge and amplifier are used to convert displacement into a voltage signal. 2.2. Background Chapter 11 of the textbook, in particular pages 430-431. Also see pages 203-206 (deflection method is important) and 212-214 (differential OP-AMP is important). The force transducer experiment, in section 10 of this manual has some background too. A strain gauge is transducer that converts small surface deflections into an electrical resistance change. The resistance change is usually very small but can be converted to a measurable voltage change by a Wheatstone Bridge circuit and an amplifier. The resistance change of a strain gauge is expressed in the definition of Gauge Factor, GF . With the strain gauge modeled as a long thin electrical wire, its resistance is due to its geometry (Length, L , and cross-sectional area A ) and its ‘resistivity’, k . With constant k , the resistance of the strain gauge increases when either the cross- sectional area decreases or the length of the wire increases. Accounting for Poisson’s Ratio , both geometry changes happen when the wire of the strain gauge is stretched. Therefore the resistance of the strain gauge increases when the wire is stretched. The wire is assumed to be very thin and offers little force to its surface mount. In this way,

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strain can be measured without affecting the stress state of the surface being measured. A long thin wire can not be mounted to most surface of engineering devices. Instead the long thin wire is folded many times into a rectangular package the size of postage stamp or much smaller (see textbook figure 11.5 on page 430). This way when the two active edges of the rectangle are deflected relative to each other, every wire strand is subjected to the same deflection. Essentially the strain is magnified because the wire strands are in electrical series but mechanically parallel. In general the k is not constant and a small change in resistance is a derivative of the (R,k,L,A) formula (use the derivative of the natural log) The main effect for resistance change is the strain in the primary direction This is a unitless number that compares the deflection to the original length. The
textbook (p. 429) relates all other effects to this strain. The resistivity, k , might change due to temperature changes in the ambient air or the surface mount. This effect is due to the material of the strain gauge wire and how temperature changes are transmitted from the environment to the strain gauge wire. As we will see later in the Force Transducer experiment, there is a way to compensate for the temperature effect by using more than one gauge in the Wheatstone bridge circuit (see pages 441-442 of the textbook for one example). The textbook models the resistivity change due to strain but we will determine the overall effect by measuring the strain gauge performance.

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ME301StrainGaugeLaboratoryManual - 2 Strain Gauge Behavior...

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