In order to convert force into electrical signals, we bond a sensor called a “strain gauge” to the load cell. Let’s examine a strain gauge in more detail.
1. Strain Gauge
1.1. History
The electrical resistance of a metallic object changes due to pressure or tension. This phenomenon has been known for a long time. In 1878, Tomlinson quantitatively measured increases in resistance for each unit of resistance (called the “gauge factor).
1.2. Strain Gauge
The electrical resistance of many metals change when the metals are mechanically elongated or contracted.
The strain gauge utilizes this principle and detects a strain by changes in resistance.
A load cell is made by bonding strain gauges to a spring material. To efficiently detect the strain, strain gauges are bonded to the position on the spring material where the strain will be the largest.
There is a linear relationship between the strain of the strain gauge and the change in its resistance. The following formula is valid:
The gauge factor K varies depending on the type of the metallic foil used. When a copper-nickel alloy such as constantan is used (a common material used for strain gauges) the value is approximately 2.
2. Spring Material
The spring material generates a strain when external force is applied. When force is exerted to a spring material, it causes a strain, and the resistance value of the strain gauge bonded to the spring material will change. The spring material converts force into an electrical output by utilizing the same principle. In order to enhance the performance of a load cell, the characteristics of the spring material are very important.
The following characteristics are required for a spring material:
1. Creep should be small. Creep is defined as the phenomenon that occurs when the deformation of an object caused by external force becomes larger with time.
2. The material should have a high proportional limit, which guarantees a wide range of linearity.
3. The secular change of the material should be small and there should be no variation of shape due to the remaining stress.
4. The resistance to impact should be high.
5. It should have good workability.
Generally, nickel-chrome-molybdenum steel, stainless steel, and aluminum steel are considered to be materials that meet the above requirements.
2.1. How the Strain Occurs
An object changes its shape when acted upon by an external force. If an object is deformed by an external force, a molecular force works between each molecule that constitutes the object, generating an internal force that tries to prevent the deformation by the external force. When the external force that the object receives is balanced with the internal force generated inside the object, the deformation of the object will cease. At this moment, the internal force per unit area that is generated on the cross section of the object is called the “stress.”
He has received a punch on the head
The fist represents an external force and the head is an object. Stress will be generated in the head in response to the external force created when the fist punches the head.
When the external force of the fist is P(N) and the planar dimension of the head is A(m2), the stress σ (sigma) is calculated as follows:
2.2. Strain
When an object changes its form after being acted upon by an external force, the changed portion from the original dimensions expressed per unit length is called the “strain.” In the dictionary, strain is defined as the proportion of change, such as elongation, contraction, contortion, etc. that occurs when an external force is applied to an object.
He is being pulled by the cheek.
If the original length of the cheek is L, and the increased length when pulled is ΔL, the strain ε (epsilon) will be expressed as follows:
Strain is defined as the ratio between the original length and the increased length.
Strain cannot be expressed as a unit.
2.3. Poisson Ratio
An object becomes thinner and longer when stretched. The strain in the same direction as the external force is called the “longitudinal strain” (ε1), the strain at the right angle is called the “transverse strain” (ε2), and the ratio between these two values, the “poisson ratio” ν (Nu). Many materials have a poisson ratio of approximately 0.3.
The elongation, which is longitudinal to the external force, is negative (+), and the contraction, which is transverse to the external force is positive (-).
2.4. Relationship between Stress and Strain
As the external force being applied to an object gets larger，first the strain increases linearly with the stress generated in the object. However, when the stress exceeds a certain limit, the linear relationship will no longer be true. This limit is known as the “proportional limit,” the “elastic limit,” or the “yield point.” As the stress-strain relationship is linear while the stress is below the proportional limit, we can immediately determine the amount of stress based on the strain.
“Hooke’s law” can be used to explain the linear relationship between stress and strain below the proportional limit. The range where Hooke’s law is valid is called the “elastic stage,” whereas the range where it is not valid is called the “plastic stage.” At the plastic stage, the object will not return to its original shape even after removing the external force and the strain will remain. The remaining strain is called the “permanent
strain,” or the “residual strain.”
3. Adhesive
The adhesive used to bond strain gauges to a spring material has to accurately transmit the strain of the spring material to the gauge. The following characteristics are required for the adhesive:
1. The adhesive bond should have enough strength to withstand temperature and humidity changes
2. The bonding should have sufficient insulation against temperature and humidity.
3. The degree of shrinkage should be small when curing.
The following are various adhesive agents used to conduct strain measurements:
1. Solvent-vaporization adhesives
Solvent-vaporization adhesives such as K-4 harden at room temperature, and paper gauges, porous base gauges, etc. can easily be attached.
2. Contact-curing adhesives
Alpha-cyanoacrylate adhesives such as CY-10 and Eastman 910. Gauges can be bonded in a few minutes.
3. Epoxy adhesives
Each epoxy adhesive differs in adhesive pressure and curing time.
4. Phenol adhesives
Phenol “Bakelite” adhesive is one type of thermoset that requires relatively high adhesive pressure and a long curing time. Phenol adhesives remain stable for a long period in a loaded state.
4. The Shapes of Spring Materials and How Strains Occur
Spring materials have various shapes and each shape has different characteristics. The five most commonly used spring materials are the column, Roberval, shear, ring, and diaphragm types. Let’s examine the distinctive characteristics of these five types of spring materials and the ways in which strains occur when a force is applied.
4.1. Column Type
Figure shows a conventional column load cell.
When the column is compressed by a force (F), strain gauge 1 contracts while strain gauge 2 stretches. Now, when the strain of strain gauge 1 is ε1 and that of strain gauge 2 is ε2, the relationship between the two gauges is expressed as ε2 = με1 (μ: Poisson ratio).
Since
and
therefore the strain that occurs in the strain gauge 1 is:
The column structure is simple and this makes it possible to downsize the load cell even when the capacity is large. On the other hand, this structure is not suitable for a small capacity. Generally, the measurement range for the structure is between 2t and 300t. It can be used for both tension and compression measurements.
4.2. Roberval Type (Double-beam Type, Parallel-beam Type)
Figure shows a conventional Roberval-type load cell.
When a force (F) is applied to the Roberval-type load cell, strain gauge 1 contracts while the strain gauge 2 stretches.
Since
and
M is the moment in the bonding area of the strain gauge
Z is the unifacial factor in the bonding area of the strain
As a result:
The formula above is valid and therefore the strain that occurs in the strain gauge 1 will be:
This structure is suitable for high-precision load cells. The most remarkable feature of this structure is that it can make a scale with no four-corner errors without using the scale mechanism. Roberval-type load cells are used for such scales as value-weighing scales and platform scales. The measurement range is generally between 1kg and 1ton, and not suitable for large capacities.
4.3. Shear Type
Figure shows a typical shear-type load cell.
Strain gauges are bonded at a 45˚ angle on the neutral axis of the load cell.
The above formula is valid and judging only from the results, the strain that occurs can be expressed as follows:
A particular characteristic of shear-type load cells is that they can be made smaller than Roberval-type load cells with the same capacity. In addition, shear-type load cells are strongly resistant to transverse loading and it is easy to make them highly precise. The measurement range is generally between 100kg and 20t.
4.4. Ring Type (Annular Type)
The shape of the spring material is shown.
The ring load cell is a high precision load cell and primarily has an intermediate capacity, ranging from 500kg to 20ton.
4.5. Diaphragm Type
The diaphragm-type load cell has a round shape. A cross section of the diaphragm-type is shown below. The primary advantage of using a diaphragm-type load cell is that its height can be lowered and it is resistant to transverse loading. However, the precision is approximately 1/100 at best.
5. Basic Circuit of Load Cells
When a force is applied to a load cell the electrical resistance of the strain gauges attached to the spring material will vary. This change in the resistance value is measured in volts. As the resistance change of the gauges is very small, a Wheatstone Bridge is generally used
5.1. Wheatstone Bridge
The Wheatstone Bridge is an electrical circuit that is ideal for detecting minor changes in resistance. It is also used to measure changes in the resistance of a strain gauge. The Wheatstone Bridge is the combination of four resistors as shown in Figure 2.12. Gauges R1, R2, R3, R4 are bonded to the positions shown in Figure 2.12 above and they serve as bridges. The output voltage before loading can be obtained as follows:
When the gauges connected to the four sides of the bridge are strained, each side R1, R2, R3, R4 is changed slightly, and the strains +ΔR1, −ΔR2, +ΔR3, −ΔR4 are generated. The output voltage at this moment can be expressed using the following equation:
Here, R1 = R2 = R3 = R4 holds true, and in the case of the Roberval structure,
|∆R1| = |∆R2| = |∆R3| = |∆R4| is also true. Therefore,
and the output voltage ( ∆e ) is proportional to the strain ( ε ).
6. Various Correction Circuits
A conceptual diagram of load cell circuit was shown in Figure 2.12. However, a diagram of an actual load cell would be more similar to the load cell circuit shown below.
Various resistors are attached in order to adjust the output sensitivity, the temperature, etc. in order for the load cell to satisfy its specifications. Let’s examine the purpose and type of each resistor.
R1 ~ R4 are strain gauges and R5 and R11 are resistors that compensate for temperature changes that influence the output voltage. The factors that have the most significant effect on the output voltage relating to temperature are temperature changes in the elastic coefficient of the spring material (approx. -0.003%/˚C for irons, approx. -0.07%/˚C for aluminum alloys) and temperature changes of the gauge factor of the spring gauge.
In order to compensate for errors caused by temperature in the output voltage of the load cell, an element whose resistance value varies with changes in temperature is connected to R5. The amount of current—which corresponds to changes in output caused by the special temperature characteristics of the gauge factor of the strain gauges and the Young modulus of the spring material—is adjusted.
Materials that have a large, positive temperature resistance coefficient, such as pure nickel or copper, are normally used for resistance temperature detectors. R11 is a fixed resistor and used to adjust the linearity of R5, etc.
R10 and R12 are resistors for correcting the non-linearity of the output voltage. Column load cells are often used for weighing systems with a large capacity. However, since the cross-sectional area of the spring material changes when a force is applied, a linearity error will occur. Thus, in addition to strain gauges, other elements that can detect the stress of the spring material are also attached. As such, the linearity of the output voltage of the load cell can be corrected by automatically adjusting the current that runs through the bridge circuit. For R10, semiconductor gauges are often used. R12 is a fixed resistor and used to adjust the linearization of R10, etc.
R8 is a resistor that is used to adjust the zero balance. When R1 = R2 = R3 = R4, the output voltage should theoretically be zero, but in actuality there is a variation of approximately ±0.5Ω between R1 = R2 = R3 = R4. Therefore the zero-point output is uneven. Thus, the zero balance will be kept at a fixed value by placing some form of fixed resistance in the bridge.
R9 is a resistor used to adjust a zero-point change due to temperature. The zero-point change of load cells can be attributed to the heat expansion or compression of the spring material. To prevent this error, self-temperature compensation gauges are used. These gauges reduce errors even though the ambient temperature changes. A resistor with a large temperature coefficient is used for this correcting resistor.
R6 are fixed resistors for adjusting the output sensitivity, and R7 for adjusting the input resistance.
