Principle of resistance strain type load cell

The resistance strain type load cell weighing sensor 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 (conversion element) pasted on its surface also deforms. After the resistance strain gauge deforms, its resistance value will change (increase or decrease), and then the resistance change will be converted by the corresponding measuring circuit Change into electrical signal (voltage or current), thus completing the process of transforming external force into electrical signal.

It can be seen that resistance strain gauge, elastomer and detection circuit are indispensable parts of resistance strain type load cell weighing sensor.

Resistance strain gauge:

Resistance strain gauge is a kind of strain gauge that a resistance wire is mechanically distributed on a substrate made of organic material. One of his important parameters is the sensitivity coefficient K. Let's talk about its significance.

There is a metal resistance wire whose length is l and 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 the resistance wire is not subjected to external force, its resistance value is R: r=ρL/S(Ω(2-1))

When its two ends are subjected to f force, it will elongate, that is to say, it will deform. Let its elongation be Δ L, and its cross-sectional area be reduced, that is, its cross-sectional circle radius be reduced by Δ R. In addition, it can also be proved by experiments that the resistivity of the metal resistance wire will change after deformation, which is recorded as Δρ.

The total differential of equation (2 -- 1) is to find out how much the resistance value has changed after the resistance wire has stretched.

We have: Δr= Δρ L/S + ΔL ρ/s – Δsρ L/S2 (2-2)

The equation (2 -- 2) is removed from equation (2 -- 1)

ΔR/R = Δρ/ρ + ΔL/L – ΔS/S （2—3）

In addition, we know that the cross-sectional area of the conductor s = π R2, then Δ s = 2 π R * Δ R,

So Δ s / S = 2 Δ R / R (2-4)

From the mechanics of materials, we know that Δ R / r = - μ Δ L / L (2-5), where the negative sign indicates that the radius direction is reduced when the elongation is made. μ is the Poisson coefficient of the transverse effect of the material. Substituting formula (2-4) (2-5) into (2 -- 3), the,

There are Δ R/r = Δ ρ / ρ + Δ L/L + 2 μ Δ L/L=(1+2μ(Δρ/ρ)/(ΔL/L))*ΔL/L= k*Δ L/L (2 --6)

Where k = 1+2μ + (Δρ/ρ) / (Δ L/L) (2 --7) formula (2 --6)) shows the relationship between the resistance change rate (relative resistance change) and the resistance wire elongation (relative length change).

It should be noted that the value of sensitivity coefficient K is a constant determined by the properties of metal resistance wire material, which has nothing to do with the shape and size of strain gauge. The value of K for different materials is generally between 1.7 and 3.6. Secondly, the value of K 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. It is often too large and inconvenient to use it to express elasticity. One millionth of it is often taken as a unit and recorded as μ ε. Thus, formula (2--6) is often written as follows: ΔR/r=kε(2-8);