Principle of resistance strain load cell

The resistance strain type load cell is based on such a principle: the elastic body (elastic element, sensitive beam) produces elastic deformation under the action of external force, so that the resistance strain gauge (transformation element) attached to the other surface also deforms along with it. After deformation, its resistance value will change (increase or decrease), and then this resistance change will be converted into an electrical signal (voltage or current) through the corresponding measurement circuit, thus completing the process of converting external force into electrical signal . It can be seen that the resistance strain gauge, elastic body and detection circuit are the indispensable main parts of the resistance strain load cell. The following briefly discusses these three aspects. 1. Resistance strain gauges Resistance strain gauges are mechanically distributed a resistance wire on a substrate made of an organic material, which becomes a strain gauge. One of his important parameters is the sensitivity coefficient K. Let us introduce its significance. There is a metal resistance wire, whose length is L, and its cross-section is a circle with radius r. Its area is denoted as S, and its resistivity is denoted as ρ. The Poisson coefficient of this material is μ. When this resistance wire is not subjected to external force, its resistance value is R: R = ρL / S (Ω) (21) When its two ends are subjected to F force, it will elongate, that is, deformed . Suppose its elongation ΔL, its cross-sectional area is reduced, that is, its cross-sectional circle radius is reduced by Δr. In addition, it can also be experimentally proved that the resistivity of this metal resistance wire will also change after deformation, which is recorded as Δρ. Find the total differential of formula (2-1), that is, how much the resistance value of the resistance wire has changed after elongation. We have: ΔR = ΔρL / S + ΔLρ / S – ΔSρL / S2 (22) Use equation (2——1) to remove equation (2——2) to get ΔR / R = Δρ / ρ + ΔL / L – ΔS / S (23) In addition, we know that the cross-sectional area of ​​the wire S = πr2, then Δs = 2πr * Δr, so ΔS / S = 2Δr / r (24) From the material mechanics, we know that Δr / r = -μΔL / L (25 ) Among them, the minus sign means that the radius direction is reduced when it is extended. μ is the Poisson coefficient of the lateral effect of the material. Substituting equations (24) and (25) into (2-3), ΔR / R = Δρ / ρ + ΔL / L + 2μΔL / L = (1 + 2μ (Δρ / ρ) / (ΔL / L)) * ΔL / L = K * ΔL / L (2-6) where K = 1 + 2μ + (Δρ / ρ) / (ΔL / L) (2-7) Equation (2-6)) explains the resistance The relationship between the rate of change of strain gauge resistance (relative change in resistance) and the elongation of resistance wire (relative change in length). It should be noted that the size of the K value of the sensitivity coefficient is a constant determined by the nature of the material of the metal resistance wire, which is independent of the shape and size of the strain gauge. The K value of different materials is generally between 1.73.6; Secondly, the K value is a dimensionless quantity, that is, it has no dimension. In the mechanics of materials, ΔL / L is called strain and is recorded as ε. Using it to express elasticity tends to be too large, and it is inconvenient to often take its parts per million as a unit and record as με. In this way, formula (2-6) is often written as: ΔR / R = Kε (28) 2. Elastomer Elastomer is a structural member with a special shape. It has two functions. First, it bears the external force on the load cell and generates a reaction force against the external force to achieve a relatively static balance; second, it must generate a high-quality strain field (area) to be pasted in this area. The resistance strain gauge is ideal for accomplishing the task of converting electrical signals of strain. Take the elastic body of Toledo's SB series load cell as an example to introduce the stress distribution. A rectangular parallelepiped cantilever beam is provided. The bottom center of the hollow hole is subjected to pure shear stress, but tensile and compressive stress will appear on the upper and lower parts. The principal stress direction is tension and compression. If the strain gauge is attached here, the upper half of the strain gauge will be stretched and the resistance will increase, while the lower half of the strain gauge will be compressed and the resistance will decrease. The strain expression of the center point of the bottom of the hole is listed below, and will not be derived. ε = (3Q (1 + μ) / 2Eb) * (B (H2-h2) + bh2) / (B (H3-h3) + bh3) (2-9) where: Q——shear on the cross section ; E-Young's modulus: μ Poisson's coefficient; B, b, H, h are the geometric dimensions of the beam. It should be noted that the stress states analyzed above are all local conditions, while the strain gages actually feel the average state. 3. Detection circuit The function of the detection circuit is to convert the resistance change of the resistance strain gauge into a voltage output. Because the Wheatstone bridge has many advantages, such as the effect of suppressing the temperature change, the lateral force interference, and the compensation problem of the load cell, etc., the Wheatstone bridge is obtained in the load cell Has been widely used. Because the full-bridge equal-arm bridge has the highest sensitivity, the parameters of each arm are the same, and the effects of various interferences are easy to cancel each other out, so the load cells use full-bridge equal-arm bridges.

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