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Resistance strain gauge load cell principle

Resistance strain gauge load cell principle
 

The resistance strain gauge load cell is based on the principle that the elastic body (elastic element, sensitive beam) is elastically deformed under the action of an external force, so that the strain gauge (conversion element) attached to the surface is also deformed along with the resistance strain gauge. After the deformation, its resistance value will change (increase or decrease), and then the corresponding measurement circuit converts this resistance change into an electrical signal (voltage or current), thereby completing the process of converting the external force into an electrical signal. .

It can be seen that the resistance strain gauge, the elastomer and the detection circuit are indispensable parts of the resistance strain type load cell. The following is a brief discussion of these three aspects.

First, the resistance strain gauge

A strain gauge is a mechanical distribution of a resistor wire on a substrate made of an organic material, that is, a strain gauge. He is an important parameter is the sensitivity coefficient K. Let us introduce the meaning of it.

There is a metal resistance wire having a length L and a cross section of a circle having a radius r , the area of ​​which is denoted by S , and the resistivity thereof is denoted by ρ, and the Poisson coefficient of this material is μ. When the resistance wire is not subjected to an external force, its resistance value is R :

R = ρ L/S (Ω) ( 2 — 1 )

When both ends are subjected to the F force, they will elongate, that is, they will be deformed. Letting its elongation Δ L , its cross-sectional area is reduced, that is, its cross-sectional radius decreases by Δ r . In addition, it can be proved by experiments that the resistivity of the metal resistance wire changes after deformation, which is denoted as Δρ.

Find the full differential for equation ( 2--1 ), that is, how much the resistance value changes after the resistance wire is stretched. We have:

Δ R = Δρ L/S + Δ L ρ /S –Δ S ρ L/S2 ( 2 — 2 )

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

Δ R/R = Δρ / ρ + Δ L/L – Δ S/S ( 2 — 3 )

In addition, we know that the cross-sectional area of ​​the wire is S = π r2 , then Δ s = 2 π r* Δ r , so

Δ S/S = 2 Δ r/r ( 2 — 4 )

We know from material mechanics

Δ r/r = - μΔ L/L ( 2 — 5 )

Among them, when the negative sign indicates elongation, the radius direction is reduced. μ is the Poisson coefficient representing the transverse effect of the material. Substituting the formula ( 2 — 4 ) ( 2 — 5 ) into ( 2--3 ), there is

Δ R/R = Δρ / ρ + Δ L/L + 2 μΔ L/L

= ( 1 + 2 μ(Δρ / ρ) / (Δ L/L )) * Δ L/L

= K * Δ L/L ( 2--6 )

among them

K = 1 + 2 μ + (Δρ / ρ) / (Δ L/L ) ( 2--7 )

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

It should be noted that the magnitude of the sensitivity coefficient K is a constant determined by the properties of the metal resistance wire material. It is independent of the shape and size of the strain gauge. The K value of different materials is generally between - and then K. The value is a dimensionless quantity, ie it has no dimension.

In material mechanics, Δ L/L is called strain, which is called ε. It is often used to indicate that the elasticity is too large and inconvenient.

Often one millionth of its unit is recorded as με. Thus, the formula ( 2--6 ) is often written:

Δ R/R = K ε ( 2 — 8 )

Second, the elastomer

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 relative static balance. Second, it produces a high-quality strain field (zone) that is pasted in this area. The resistance strain gauge is ideal for performing the conversion task of the strained jujube electrical signal.

Take the elastomer of the Toledo SB series load cell as an example to introduce the stress distribution.

A cuboid cantilever beam with a boring is provided.

The center of the bottom of the pupil is subjected to pure shear stress, but tensile and compressive stresses will appear in the upper and lower parts. The principal stress direction is one for pulling and the other is compression. If the strain gauge is attached here, the upper half of the strain gauge will be stretched and the resistance will increase, and the lower half of the strain gauge will be compressed and the resistance will be reduced. The strain expressions at the center of the bottom of the pupil are listed below and are not deduced.

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

Where: Q-- shear force on the section; E-- Young's modulus: μ-Poisson's modulus; B , b , H , h —is the geometrical dimensions of the beam.

It should be noted that the stress states analyzed above are all "local" conditions, and the strain gauges actually experience the "average" state.

Third, the detection circuit

The function of the detection circuit is to convert the resistance change of the strain gauge into a voltage output. Because the Wheatstone bridge has many advantages, such as suppressing the influence of temperature changes, it can suppress lateral force interference, and it is convenient to solve the compensation problem of the load cell, so the Wheatstone bridge is obtained in the load cell. A wide range of applications.

Because the full-bridge equal-arm bridge has the highest sensitivity, the parameters of each arm are the same, and the effects of various disturbances are easily offset, so the load cell uses a full-bridge arm bridge.

The working process of the resistance strain gauge load cell during the measurement process, the weight is loaded onto the elastomer of the load cell and causes plastic deformation.

strain (forward and negative) The strain gauges mounted on the elastomer are converted into electrical signals. The simplest curved beam load cell has only one strain gauge. Generally, the elastomer and the strain gauge are combined in a variety of ways, such as a housing, a sealing member, etc. to protect the strain gauge.

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