Gauge Factor
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Gauge Factor
Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance R, to the mechanical strain ε. The gauge factor is defined as: ::GF = \frac = \frac = 1 + 2\nu + \frac where * ε = strain = \Delta L / L_0 **\Delta L = absolute change in length ** L_0 = original length * ν = Poisson's ratio * ρ = resistivity * ΔR = change in strain gauge resistance due axial strain and lateral strain * R = unstrained resistance of strain gauge Piezoresistive effect It is a common misconception that the change in resistance of a strain gauge is based solely, or most heavily, on the geometric terms. This is true for some materials (\Delta\rho=0), and the gauge factor is simply: ::GF = 1 + 2\nu However, most commercial strain gauges utilise resistors made from materials that demonstrate a strong piezoresistive effect. The resistivity of these materials changes with strain, accounting for the \frac term of the defining equation above. In constantan ...
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Strain Gauge
A strain gauge (also spelled strain gage) is a device used to measure strain on an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. The gauge is attached to the object by a suitable adhesive, such as cyanoacrylate. As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge, is related to the strain by the quantity known as the gauge factor. History Edward E. Simmons and Professor Arthur C. Ruge independently invented the strain gauge. Simmons was involved in a research project by Dätwyler and Clark at Caltech between 1936 and 1938. They researched the stress-strain behavior of metals under shock loads. Simmon came up with an original way to measure the force introduced into the sample by equipping a dynamometer with fine resistance w ...
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Electrical Resistance
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm (), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ). The resistance of an object depends in large part on the material it is made of. Objects made of electrical insulators like rubber tend to have very high resistance and low conductance, while objects made of electrical conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by resistivity or conductivity. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are extensive rather than in ...
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Strain (physics)
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of ''relative'' displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the temperature field of the body. The relati ...
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Deformation (mechanics)
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of ''relative'' displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the temperature field of the body. The relat ...
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Poisson's Ratio
In materials science and solid mechanics, Poisson's ratio \nu ( nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, \nu is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. For soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression. Many typical solids have Poisson's ratios in the range of 0.2–0.3. The ratio is named after the French mathematician and physicist Siméon Poisson. Origin Poisson's ratio is a measure of the Poisson effect, the phenomenon in which ...
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Resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter  (rho). The SI unit of electrical resistivity is the ohm- meter (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter  (sigma), but  (kappa) (especially in electrical engineering) and  (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are intens ...
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Piezoresistive Effect
The piezoresistive effect is a change in the electrical resistivity of a semiconductor or metal when mechanical strain is applied. In contrast to the piezoelectric effect, the piezoresistive effect causes a change only in electrical resistance, not in electric potential. History The change of electrical resistance in metal devices due to an applied mechanical load was first discovered in 1856 by Lord Kelvin. With single crystal silicon becoming the material of choice for the design of analog and digital circuits, the large piezoresistive effect in silicon and germanium was first discovered in 1954 (Smith 1954). Mechanism In conducting and semi-conducting materials, changes in inter-atomic spacing resulting from strain affect the bandgaps, making it easier (or harder depending on the material and strain) for electrons to be raised into the conduction band. This results in a change in resistivity of the material. Within a certain range of strain this relationship is linear, s ...
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Constantan
Constantan is a proprietary name A brand is a name, term, design, symbol or any other feature that distinguishes one seller's good or service from those of other sellers. Brands are used in business, marketing, and advertising for recognition and, importantly, to create a ... for a copper–nickel alloy also known as Eureka, Advance, and Ferry. It usually consists of 55% copper and 45% nickel. Its main feature is the low thermal variation of its resistivity, which is constant over a wide range of temperatures. Other Alloy, alloys with similarly low temperature coefficients are known, such as manganin (Cu [86%] / Mn [12%] / Ni [2%] ). History In 1887, Edward Weston (chemist), Edward Weston discovered that metals can have a negative temperature coefficient of resistance, inventing what he called his "Alloy No. 2." It was produced in Germany where it was renamed "Konstantan". Constantan alloy Of all modern strain gauge alloys, constantan is the oldest, and st ...
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Temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called ''centigrade''), the Fahrenheit scale (°F), and the Kelvin scale (K), the latter being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in the third law of thermodynamics. It would be impossible to extract energy as heat from a body at that temperature. Tem ...
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Temperature Coefficient
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property ''R'' that changes when the temperature changes by ''dT'', the temperature coefficient α is defined by the following equation: :\frac = \alpha\,dT Here α has the dimension of an inverse temperature and can be expressed e.g. in 1/K or K−1. If the temperature coefficient itself does not vary too much with temperature and \alpha\Delta T \ll 1, a linear approximation will be useful in estimating the value ''R'' of a property at a temperature ''T'', given its value ''R''0 at a reference temperature ''T''0: :R(T) = R(T_0)(1 + \alpha\Delta T), where Δ''T'' is the difference between ''T'' and ''T''0. For strongly temperature-dependent α, this approximation is only useful for small temperature differences Δ''T''. Temperature coefficients are specified for various applications, including electric and magnetic properties of materials a ...
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