What is the principle of resistance strain gauge load cell?

What is the principle of resistance strain gauge load cell?

Principle of resistance strain type load cell:

The resistance strain type load cell is based on the 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, the resistance strain gauge After deformation, its resistance will change (increase or decrease), and then the resistance change will be converted into an electrical signal (voltage or current) by the corresponding measuring circuit, thus completing the process of transforming the external force into an electrical signal .

It can be seen that resistance strain gauges, elastomers and detection circuits are indispensable parts of resistance strain load cells. The following briefly discusses these three aspects.

1.Resistance strain gauge of load cell

The resistance strain gauge is to mechanically distribute a resistance wire on a substrate made of organic material, which becomes a strain gauge. One of his important parameters is the sensitivity coefficient K. Let's introduce its meaning.

There is a metal resistance wire with a length of L and a circular cross section with a radius of r. Its area is recorded as S, and its resistivity is recorded 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) (2—1)

When its two ends are subjected to F force, it will stretch, that is to say, it will deform. Assuming that it stretches by ΔL, its cross-sectional area is reduced, that is, its cross-sectional circle radius decreases by Δr. In addition, it can be proved by experiments that the resistivity of this metal resistance wire will also change after deformation, which is recorded as Δρ.

Calculate the total differential of formula (2--1), that is, find out how much the resistance value of the resistance wire has changed after it is stretched. We have:

ΔR=ΔρL/S+ΔLρ/S–ΔSρL/S2 (2-2)

Use formula (2--1) to remove formula (2--2) to get

ΔR/R=Δρ/ρ+ΔL/L–ΔS/S (2—3)

In addition, we know that the cross-sectional area of the wire S=πr2, then Δs=2πr*Δr, so

 ΔS/S=2Δr/r (2—4)

We know from the mechanics of materials

Δr/r=-μΔL/L (2-5)

Among them, the minus sign means that when it stretches, the radial direction is reduced. μ is the Poisson coefficient representing the lateral effect of the material. Substituting formula (2—4) (2—5) into (2--3), we have

ΔR/R=Δρ/ρ+ΔL/L+2μΔL/L

=(1+2μ(Δρ/ρ)/(ΔL/L))*ΔL/L

=K*ΔL/L (2--6)

among them

K=1+2μ+(Δρ/ρ)/(ΔL/L) (2-7)

Formula (2--6)) illustrates the relationship between the resistance change rate (relative change in resistance) of the resistance strain gauge and the elongation rate (relative change in length) of the resistance wire.

It should be noted that the sensitivity coefficient K value is a constant determined by the nature of the metal resistance wire material, and it has nothing to do with the shape and size of the strain gauge. The K value of different materials is generally between 1.7-3.6; Secondly, the K value is a dimensionless quantity, that is, it has no dimensions.

In material mechanics, ΔL/L is called strain and recorded as ε. It is often too large to express elasticity, which is very inconvenient.

It is often used as a unit of one millionth and recorded as με. In this way, the formula (2-6) is often written as: ΔR/R=Kε(2-8)

2.Elastomer the load cell block

The elastomer is a structural member with a special shape. It has two functions. The first is that it bears the external force of the load cell, and the external force produces a reaction force to achieve a relatively static balance; second, it must generate a high-quality strain field (zone) to stick in this area The resistance strain gauge is ideal to complete the conversion task of the strain date electrical signal.

Take the elastic body of the cantilever beam load cell as an example to introduce the stress distribution.

It is provided with a rectangular cantilever beam with a hole.

The center of the bottom of the hole is subjected to pure shear stress, but tensile and compressive stresses will appear in the upper and lower parts. The main stress direction is tension and compression. If the strain gauge is attached here, the upper part of the strain gauge will be stretched and the resistance will increase, while the lower part of the strain gauge will be compressed and the resistance will decrease. The strain expression at the center point of the bottom of the hole is listed below, and will not be deduced.

 ε=(3Q(1+μ)/2Eb)*(B(H2-h2)+bh2)/(B(H3-h3)+bh3)(2--9)

Among them: Q-shear force on the section; E-Young's modulus: μ-Poisson coefficient; B, b, H, h-the geometric dimensions of the beam.

It should be noted that the stress states analyzed above are all "local" situations, while the strain gauges 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 ability to suppress the influence of temperature changes, the side force interference, and the more convenient solution to the compensation problem of the load cell, the Wheatstone bridge is used in the load cell. It has a wide range of applications.

Because the sensitivity of the full-bridge equal-arm bridge is very high, the parameters of each arm are the same, and the influence of various interferences is easy to cancel each other, so the load cell adopts the full-bridge equal-arm bridge.