Resistance strain gauge load cell principle
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A resistance strain gauge load cell operates based on the principle that when an external force is applied, the elastic body (also known as the sensitive beam or elastomer) undergoes elastic deformation. This deformation causes the strain gauges attached to its surface to also deform. As a result, the resistance of the strain gauges changes—either increasing or decreasing. This change in resistance is then converted into an electrical signal (such as voltage or current) by a measurement circuit, effectively transforming the external force into an electrical output.
It's clear that the strain gauge, the elastomer, and the detection circuit are all essential components of a resistance strain gauge load cell. The following sections will briefly discuss each of these elements in more detail.
First, the strain gauge
A strain gauge is essentially a resistor wire arranged on a substrate made from an organic material. It is a key component used for measuring mechanical strain. One important parameter associated with a strain gauge is its sensitivity coefficient, denoted as K. Let’s take a closer look at what this means.
Consider a metal wire with length L and circular cross-section radius r, where the area is S and the resistivity is Ï. When no external force is applied, the resistance R of the wire is given by:
R = ÏL/S (Ω) (Equation 2-1)
When an external force F is applied, the wire elongates by ΔL, and its cross-sectional area decreases by ΔS due to Poisson's effect. Additionally, the resistivity of the material may also change slightly, denoted as ΔÏ. To find how much the resistance changes, we take the total differential of Equation (2-1), resulting in:
ΔR = (ΔÏL)/S + (ÏΔL)/S - (ÏΔS)/S² (Equation 2-2)
Dividing both sides by R, we get:
ΔR/R = ΔÏ/Ï + ΔL/L - ΔS/S (Equation 2-3)
Since the cross-sectional area S = πr², we can express ΔS as 2πrΔr, leading to:
ΔS/S = 2Δr/r (Equation 2-4)
From material mechanics, we know that Δr/r = -μΔL/L, where μ is the Poisson's ratio. Substituting Equations (2-4) and (2-5) into (2-3), we obtain:
ΔR/R = ΔÏ/Ï + ΔL/L + 2μΔL/L
This simplifies to:
ΔR/R = K * ΔL/L (Equation 2-6)
Where:
K = 1 + 2μ + (ΔÏ/Ï)/(ΔL/L) (Equation 2-7)
The value of K depends on the material properties of the resistance wire and is independent of the shape or size of the strain gauge. Typically, K ranges between 2 and 5 for most materials. It is a dimensionless quantity.
In material mechanics, ΔL/L is referred to as strain, often denoted by ε. It is commonly expressed in microstrain (με), which is one millionth of a unit. Therefore, Equation (2-6) is often written as:
ΔR/R = K * ε (Equation 2-8)
Second, the elastomer
The elastomer is a specially shaped structural element that serves two main purposes. First, it supports the external force applied to the load cell and generates a reaction force to maintain static equilibrium. Second, it creates a high-quality strain field in the region where the strain gauges are mounted, allowing them to accurately convert mechanical strain into electrical signals.
Take, for example, the elastomer of a Toledo SB series load cell. It is a cuboid cantilever beam with a hole in the center. Under load, the bottom center experiences pure shear stress, while the upper and lower parts experience tensile and compressive stresses, respectively. If strain gauges are placed here, the upper half will stretch and increase in resistance, while the lower half will compress and decrease in resistance.
The strain at the bottom center of the beam is given by:
ε = [3Q(1+μ)/2Eb] * [(B(H²-h²)+bh²)/(B(H³-h³)+bh³)] (Equation 2-9)
Where Q is the shear force, E is Young’s modulus, μ is Poisson’s ratio, and B, b, H, h are the geometric dimensions of the beam.
Note that the above analysis considers local stress states, whereas the actual strain gauges experience an average state.
Third, the detection circuit
The detection circuit is responsible for converting the resistance changes in the strain gauges into a voltage output. Due to its advantages—such as temperature compensation, lateral force suppression, and ease of load cell calibration—the Wheatstone bridge is widely used in load cells.
Because the full-bridge configuration offers the highest sensitivity and better disturbance cancellation, most load cells use a full-bridge setup. During operation, the weight applied to the elastomer causes it to deform, which results in strain on the attached strain gauges. This strain is converted into an electrical signal. A simple curved beam load cell may have just one strain gauge, but typically, the elastomer and strain gauges are combined with other components like housings and sealing members to protect the gauges from environmental damage.
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A resistance strain gauge load cell operates based on the principle that when an external force is applied, the elastic body (also known as the sensitive beam or elastomer) undergoes elastic deformation. This deformation causes the strain gauges attached to its surface to also deform. As a result, the resistance of the strain gauges changes—either increasing or decreasing. This change in resistance is then converted into an electrical signal (such as voltage or current) by a measurement circuit, effectively transforming the external force into an electrical output.
It's clear that the strain gauge, the elastomer, and the detection circuit are all essential components of a resistance strain gauge load cell. The following sections will briefly discuss each of these elements in more detail.
First, the strain gauge
A strain gauge is essentially a resistor wire arranged on a substrate made from an organic material. It is a key component used for measuring mechanical strain. One important parameter associated with a strain gauge is its sensitivity coefficient, denoted as K. Let’s take a closer look at what this means.
Consider a metal wire with length L and circular cross-section radius r, where the area is S and the resistivity is Ï. When no external force is applied, the resistance R of the wire is given by:
R = ÏL/S (Ω) (Equation 2-1)
When an external force F is applied, the wire elongates by ΔL, and its cross-sectional area decreases by ΔS due to Poisson's effect. Additionally, the resistivity of the material may also change slightly, denoted as ΔÏ. To find how much the resistance changes, we take the total differential of Equation (2-1), resulting in:
ΔR = (ΔÏL)/S + (ÏΔL)/S - (ÏΔS)/S² (Equation 2-2)
Dividing both sides by R, we get:
ΔR/R = ΔÏ/Ï + ΔL/L - ΔS/S (Equation 2-3)
Since the cross-sectional area S = πr², we can express ΔS as 2πrΔr, leading to:
ΔS/S = 2Δr/r (Equation 2-4)
From material mechanics, we know that Δr/r = -μΔL/L, where μ is the Poisson's ratio. Substituting Equations (2-4) and (2-5) into (2-3), we obtain:
ΔR/R = ΔÏ/Ï + ΔL/L + 2μΔL/L
This simplifies to:
ΔR/R = K * ΔL/L (Equation 2-6)
Where:
K = 1 + 2μ + (ΔÏ/Ï)/(ΔL/L) (Equation 2-7)
The value of K depends on the material properties of the resistance wire and is independent of the shape or size of the strain gauge. Typically, K ranges between 2 and 5 for most materials. It is a dimensionless quantity.
In material mechanics, ΔL/L is referred to as strain, often denoted by ε. It is commonly expressed in microstrain (με), which is one millionth of a unit. Therefore, Equation (2-6) is often written as:
ΔR/R = K * ε (Equation 2-8)
Second, the elastomer
The elastomer is a specially shaped structural element that serves two main purposes. First, it supports the external force applied to the load cell and generates a reaction force to maintain static equilibrium. Second, it creates a high-quality strain field in the region where the strain gauges are mounted, allowing them to accurately convert mechanical strain into electrical signals.
Take, for example, the elastomer of a Toledo SB series load cell. It is a cuboid cantilever beam with a hole in the center. Under load, the bottom center experiences pure shear stress, while the upper and lower parts experience tensile and compressive stresses, respectively. If strain gauges are placed here, the upper half will stretch and increase in resistance, while the lower half will compress and decrease in resistance.
The strain at the bottom center of the beam is given by:
ε = [3Q(1+μ)/2Eb] * [(B(H²-h²)+bh²)/(B(H³-h³)+bh³)] (Equation 2-9)
Where Q is the shear force, E is Young’s modulus, μ is Poisson’s ratio, and B, b, H, h are the geometric dimensions of the beam.
Note that the above analysis considers local stress states, whereas the actual strain gauges experience an average state.
Third, the detection circuit
The detection circuit is responsible for converting the resistance changes in the strain gauges into a voltage output. Due to its advantages—such as temperature compensation, lateral force suppression, and ease of load cell calibration—the Wheatstone bridge is widely used in load cells.
Because the full-bridge configuration offers the highest sensitivity and better disturbance cancellation, most load cells use a full-bridge setup. During operation, the weight applied to the elastomer causes it to deform, which results in strain on the attached strain gauges. This strain is converted into an electrical signal. A simple curved beam load cell may have just one strain gauge, but typically, the elastomer and strain gauges are combined with other components like housings and sealing members to protect the gauges from environmental damage.
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