Strain Gauge

Chapter 1: What is a Strain Gauge?

A strain gauge is a sensor designed to measure changes in resistance resulting from applied force, and it converts these resistance changes into measurable data. It consists of a thin metal conductor foil attached to a flexible backing material, known as the carrier. Electrical leads are soldered to the foil, allowing current to flow through the strain gauge. As the surface under test stretches or contracts, the strain gauge deforms accordingly, leading to variations in electrical resistance that correspond to changes in the surface dimensions.

The process begins by mounting strain gauges on the object to be tested. When force is applied, the strain gauge measures the resulting deformation, which can include elongation, stretching, contraction, or other changes due to compressive or tensile forces. These deformations lead to measurable variations in resistance.

Strain gauges are capable of measuring various types of stress, including tensile, compressive, bending, torsional, and shear stresses. They can detect even the smallest changes in an object's geometry. Given that the resistance change they measure is very minimal, strain gauges use very thin metallic strips that are highly sensitive to these small variations in resistance.

The main application for strain gauges is in the manufacture of force and pressure transducers such as load cells, a type of transducer that measures the mechanical load on an object by converting it to readable electronic signals. Strain gauge load cells are the most common type of load cell and are widely used for reading weight.

In weighing applications, strain gauge load cells are affixed to a structural member that deforms under the application of weight. Modern load cells often incorporate multiple strain gauges to enhance measurement accuracy. Beyond weight measurement, strain gauge load cells are also used in automation, process control, biomechanics, equipment monitoring, building integrity assessments, bulk material weighing, testing, and quality control. This technology was further developed by William Thomson in 1856.

Chapter 2: What is the history of strain gauges?

The development of strain gauges was influenced by the Wheatstone bridge circuit, invented and popularized by Charles Wheatstone in 1843. Wheatstone's work introduced the concept of measuring changes in resistance due to mechanical stress. This concept was further refined by William Thomson in 1856.

Decades later, in the early 20th century, two American engineers independently explored this effect. Edward Simmons, an electrical engineer from California, created a woven strain gauge using thin resistance wires and silk threads. His prototype was attached to a steel cylinder and tested to measure force impulses from a pendulum ram striking the cylinder.

At the same time, Arthur Ruge, a mechanical engineer at MIT, developed a strain gauge to measure stress in his model of an earthquake-resistant water tank. He used very thin wires attached to a piece of paper as the strain gauge, which was then affixed to a bending beam that acted as its support.

Ruge and his team advanced their strain gauge invention to the production stage, leading to its widespread adoption. Today, the design of the strain gauge carrier is much simpler, and newer circuit production methods have largely replaced the traditional wound-wire techniques. Modern technologies such as chemical etching and circuit printing have significantly enhanced the manufacturing process.

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Chapter 3: What is the operating principle?

Different physical phenomena can cause changes in the electrical resistance of a conductor. For example, temperature, strain, and photo illumination are known factors that affect electrical resistance. Force transducers, such as load cells, use strain gauges to take advantage of the relationship between mechanical strain and the electrical resistance of a conductor.

All components undergo loading when subjected to motion or forces. To determine if a component can handle the applied loads effectively, it is crucial to understand mechanical stress and strain. Strain gauges are essential tools that provide accurate and precise measurements, allowing for the monitoring of the stress a component experiences. They are valuable for predicting potential failures or damage, helping to ensure the reliability of the application.

The electrical resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. When a strain gauge is stretched, its wire length increases while its cross-sectional area decreases, leading to an increase in electrical resistance. Conversely, compressing the strain gauge without causing the wires to buckle results in a decrease in electrical resistance.

As discussed earlier, the strain gauge utilizes the Wheatstone bridge circuit. This circuit consists of four resistors and a power source. One of the resistors is variable, which is the strain gauge, while the other three are fixed. The bridge circuit is powered by a direct current (DC) supply, known as the excitation source.

The output of the Wheatstone bridge is the voltage measured across the gap, labeled as Vg in the figure below. The bridge is considered balanced when this gap voltage is zero, which is typically the device's initial state. An imbalance occurs when the resistance of the variable resistor changes, leading to a potential difference across the gap.

Chapter 4: What are the different strain gauge bridge configurations?

Strain gauges are classified based on their bridge configuration. A basic load cell or force transducer typically employs a single strain gauge and uses a quarter-bridge configuration. For enhanced performance, most designs incorporate either two or four strain gauges. Systems with two strain gauges are known as half-bridge configurations, while those with four strain gauges are referred to as full-bridge circuits.

Quarter Bridge

The Wheatstone bridge configuration described earlier is known as a quarter-bridge circuit. In this setup, a single active strain gauge serves as the variable resistor. Because only one strain gauge is employed, it measures only one type of strain and is therefore the least sensitive among the different configurations.

Quarter-bridge circuits can be further categorized into two configurations.

• Simple Quarter Bridge: This is the simplest among the strain gauge types in this category. It is composed of one active gauge and three completion resistors. The completion resistor paired with the strain gauge is called a dummy resistor. This type is the least sensitive and is prone to errors caused by temperature variations.

  

  
  
• Quarter Bridge with Dummy Gauge: In this circuit, two strain gauges are employed. One strain gauge is active, while the other is used as a dummy. The active gauge is aligned according to the direction of the strain to be measured. In contrast, the dummy gauge is oriented in the transverse direction. When a mechanical load is applied, the active gauge experiences greater strain and, therefore, greater change in electrical resistance than the dummy gauge.

  Regarding the temperature variations, the change is felt with the same magnitude by both the active and dummy gauges. Since the active and dummy gauges are in the same leg, the ratio of their resistances does not change. Thus, the effect of temperature is nulled or minimized.

  

  
  

Double Quarter Bridge or Diagonal Bridge

This configuration features two active strain gauges. One strain gauge is placed on one leg of the circuit, while the other is positioned on the second leg. These gauges are mounted on opposite sides of the elastic element or structure, oriented parallel to the direction of the applied load.

The diagonal bridge design offers two main advantages. Firstly, it provides increased sensitivity. Since both strain gauges in this configuration experience the same deformation, the output signal is roughly twice as large as that of a simple quarter-bridge circuit.

Secondly, it effectively rejects bending strain. Diagonal bridge strain gauges are designed to measure only tensile and compressive strains. If the gauges detect strains in opposite directions, their effects cancel each other out, ensuring accurate measurements as long as the strains are aligned in the same direction.

However, this configuration also has a notable drawback: it is highly sensitive to temperature variations. This sensitivity can double the error introduced by temperature changes. To mitigate this issue, dummy gauges are used in conjunction with each active gauge to compensate for temperature-induced errors.

Half Bridge

Half-bridge circuits use two active strain gauges, making them more sensitive than quarter-bridge circuits due to the presence of two strain-measuring elements. There are two possible configurations for the strain gauges in a half-bridge circuit.

• Half Bridge with Poisson Gauge: In this design, one strain gauge is oriented in the longitudinal or axial direction while the other is in transverse. It can measure tensile, compressive, and bending strains with higher sensitivity.

  

  
  

  This half bridge configuration operates on the Poisson effect. The Poisson effect is the tendency of a material to change its cross-section in the direction perpendicular to the load. Most materials experience opposite strains in perpendicular directions. Since both strain gauges are used to measure the change in dimension of both axes, the effect on the varying resistances is increased. This, in turn, improves the magnitude of the output voltage. The additional output depends on the Poisson ratio of the material.

  Moreover, by having both strain gauges at the same leg of the bridge circuit, they cancel out the effect of temperature. This is similar to the advantage seen in the quarter bridge with a dummy gauge circuit.

• Bending Half Bridge: The second type of the half bridge configuration features two parallel strain gauges mounted on opposite sides of the transducer‘s elastic element. The strain gauges are not coplanar with each other, unlike the previous type.

This configuration is specifically designed for measuring bending strain. When an elastic element is bent, the sides perpendicular to the applied force experience either tension or compression. The two strain gauges in this setup measure the resulting deflection of the elastic element.

A notable feature of this design is its ability to eliminate the effects of axial strain. The transducer processes the voltage readings so that one strain gauge experiences tension while the other experiences compression. This arrangement ensures that any resistance change in one gauge due to tension is counterbalanced by the change in the other gauge, effectively negating axial strain. Additionally, this configuration also helps to cancel out temperature-induced errors.

Full Bridge

A full-bridge circuit utilizes four active strain gauges in place of all resistors, offering high versatility due to the multiple configurations possible. Since all resistances are variable, temperature effects are effectively canceled out across the entire circuit, regardless of the specific configuration used. Below are the different subtypes of full-bridge circuits.

• Axial and Bending Full Bridge: In this configuration, all four strain gauges are mounted on one side of the structure. As much as possible, the gauges are coplanar with each other. The gauge pairs on one leg of the bridge are oriented such that one is perpendicular to the other.

  

  
  

  An axial and bending full bridge circuit is regarded as two Poisson half bridge circuits working in tandem. The result is an output signal with twice the magnitude of its half bridge counterpart.

• Axial Full Bridge: In this design, two strain gauges are mounted on one side of the structure while the other two are mounted on the opposite side. The coplanar gauges are aligned perpendicularly with their pair.

  Similar to the previous type, this configuration works like two Poisson half bridge circuits. This results in an extremely sensitive sensor.

  

  
  

  Axial full bridge circuits eliminate bending strain readings similar to that to diagonal bridge circuits. The strain gauges on opposite sides of the structure are assumed to have the same strain direction. When these strain gauges are inversely directed strains, the effect on the resistance ratio is nulled.

• Bending Full Bridge: This circuit is created by placing the strain gauge pairs on the opposite sides of the structure and parallel with each other. The arrangement may seem similar to that of the axial type. However, both Poisson gauges are placed on one leg of the circuit.

  

  
  

  This version of the bending full bridge circuit combines the characteristics of the Poisson half bridge and bending half bridge circuits. Not only is the axial strain eliminated, but the signal sensitivity is increased. The output signal produced is twice that of a Poisson half bridge.

• Bending Full Bridge without Poisson Gauge: This bending full bridge circuit has all four strain gauges aligned in one direction. Thus, this type does not have a Poisson gauge. Strain gauge pairs are placed on opposing sides of the structure.

  

  
  

This configuration operates similarly to two bending half-bridge circuits. The strain gauge pairs on one leg of the circuit experience tension and compression, effectively eliminating the effects of axial strain when deflection is detected in a single direction.

With four strain-measuring conductors, this setup offers quadruple the sensitivity of a simple quarter-bridge circuit.

Chapter 5: What are the different types of strain gauges?

Understanding the various bridge configurations helps in comprehending the different types of strain gauges. Strain gauges are generally named based on their arrangement of measuring elements. Depending on the specific application, a single strain gauge type can be used in multiple bridge configurations.

Linear Strain Gauges

Linear strain gauges measure strain along a single direction. They are characterized by their simple construction and low cost, making them ideal for general applications such as load testing, fatigue testing, and structural integrity monitoring. Linear strain gauges can be used in quarter-bridge, diagonal bridge, or axial full-bridge circuits.

Rosette Strain Gauges

Rosette strain gauges are made from multiple measuring elements bonded to a common carrier. As the name suggests, the arrangement of strain gauges resembles a rosette or circular pattern. They are oriented to have different measuring axes to measure strains generated by biaxial stress conditions.

There are various types of rosette strain gauges, with the basic examples briefly described below.

• Tee Rosette Strain Gauges: Sometimes referred to as 90° rosettes, these strain gauges are composed of two measuring elements oriented perpendicularly with each other. They are used in applications where the principal strain directions are known. One measuring element is aligned with the direction of a strain.

  

  
  

  90° Rosette strain gauges can be configured into half bridge circuits. Full bridge circuits can also be created by using multiple rosettes.

• Rectangular Rosette Strain Gauges: These rosette strain gauges have three measuring elements crossed at 0°/45°/90°. They are used when the principal strain directions are unknown.

  

  
  

• Delta Rosette Strain Gauges: Like rectangular strain gauges, they are also used when the principal strain directions are unknown. The measuring elements are aligned at 0°/60°/120°.

  

  
  

Rectangular and delta rosettes differ in configuration from other strain gauges. The data from their measuring elements are often fed into computer programs for simulation and data analysis. These rosettes are particularly well-suited for stress analysis and dynamic load monitoring.

Shear Strain Gauge

Shear strain gauges are designed to measure shear strain resulting from torque or torsional loading. They can feature either one or two measuring grids attached to a single carrier. In a single-grid configuration, the strain gauge element is oriented at a 45° angle relative to the shaft axis. A two-grid shear strain gauge, also known as a V Rosette, has measuring elements set at 45° and 135°. These gauges are commonly used in applications such as engine shafts and drivetrains, where they can be used to calculate shaft power based on strain measurements.

Double Parallel Strain Gauges:

This type consists of two linear strain gauges arranged in parallel. They can be utilized with various bridge circuit configurations. A common example is the bending full-bridge circuit, where two parallel strain gauges are positioned on opposite sides of the structure.

Diaphragm Strain Gauges:

Diaphragm strain gauges measure radial and tangential strains in structures such as columns, beams, or shafts. They are commonly arranged in a full-bridge circuit. The four measuring elements are typically configured in either circular or linear patterns. Tangential elements are placed near the periphery of the carrier, while radial elements are bonded closer to the center.

Chapter 6: What are the other design considerations?

In addition to the bridge circuit and strain gauge arrangement, several other important factors must be considered when selecting a strain gauge. A significant portion of the engineering design focuses on these additional criteria.

Measuring Element Material

The strain gauges described throughout this article are made from metals. Metal strain gauges can be further divided into wire-wounded and metal foil types. The wire-wounded type is the earliest form of the device. Today, metal-foil strain gauges are the most common type. They are manufactured through photochemical etching or circuit printing. Some raw materials used for producing metal strain gauges are copper-nickel (Constantan), nickel-chromium, and platinum alloys.

In addition to metal-based strain gauges, there is a second type known as semiconductor strain gauges, which use semiconductor materials like silicon and germanium. Unlike metal strain gauges that operate based on changes in geometry, semiconductor strain gauges function through changes in electrical properties.

Semiconductor strain gauges rely primarily on the piezoresistive effect, which causes significant changes in electrical resistance and, consequently, a higher voltage output. This makes them particularly effective for measuring very small strains. However, they have some drawbacks, including sensitivity to high temperatures, brittleness that can make handling challenging, and non-linear resistance changes.

Strain Gauge Mounting

Strain gauge mounting is typically classified into two types: bonded and unbonded.

• Bonded strain gauges are directly attached to the surface of the elastic element or structure to be analyzed. These are the more common type and are achieved through adhesive bonding. Other types of bonding, such as welding, can also be used.
  • Weldable strain gauges are used for high-temperature applications. Strain gauges with this kind of mounting have a steel carrier or are encapsulated in a metal enclosure. They are installed to the surface of the structure through spot welding.

Unbonded strain gauges are less common and are primarily used in transducer applications. They consist of a thin wire, with one end attached to a rigid frame and the other end connected to a movable carrier. The wire is preloaded and secured using a spring-loaded mechanism.

Rosette Construction

Strain gauges with multiple measuring elements offer two main construction options: planar and stacked. In planar strain gauges, the measuring grids are positioned side by side on a single plane. This arrangement provides more accurate results because both grids are equidistant from the axis of the structure.

Stacked strain gauges feature measuring grids arranged one above the other, with a slight offset that makes them non-coplanar. This stacked design is ideal for applications with limited or restricted mounting space.

Compensation Methods

In practical applications, both strain and temperature affect the resistance of the conductor. Since the goal is to measure strain, temperature changes can act as an interfering factor.

In addition to temperature, creep can affect the reading of the strain gauge. Creep is caused by prolonged exposure to load. It alters the mechanical properties of the conductor, carrier, and bonding adhesive, which leads to a change in output. Transducer designs aim to minimize the effects of temperature and creep to maintain accurate measurements of mechanical load.

Several compensation methods are outlined below.

• Dummy Gauge: This has been discussed in the previous chapters. A dummy gauge is a non-active conductor aligned perpendicular to the strain direction. It only changes resistance because of temperature. It pairs with an active gauge that senses both strain and temperature change. The dummy gauge nulls the change in temperature sensed by the active gauge. This is because the ratio of their resistance is unchanged.
• Self-Temperature-Compensated Strain Gauges: These strain gauges use special alloys as measuring elements that are produced to have an adjusted resistive temperature coefficient over the temperature range of the application. This minimizes the effect of temperature on the signal output over the specified temperature range
• Signal Conditioning: This covers all techniques used to eliminate signal errors. They account for varying temperature, creep, humidity, and changing lead wire resistance. The design of signal conditioning methods varies from each manufacturer. Common examples are bridge completion using high precision resistors, offset nulling, signal amplification, and shunt calibration.

Conclusion

• A strain gauge is a sensing device used for measuring strain experienced by an object. It is a measuring element or conductor that varies its electrical resistance when a change in dimension occurs.
• A load cell is a type of transducer that measures the mechanical load on an object by converting it to readable electronic signals.
• The strain gauge is an application of the Wheatstone bridge circuit. A Wheatstone bridge circuit is composed of four resistors and an electrical energy source. Among the four resistors, one or more can be a strain gauge, while the rest are fixed or reference resistors.
• The configurations of a strain gauge bridge circuit are classified as a quarter, half, or full bridge.
• The other classification of strain gauges is according to the arrangement of the measuring elements. Examples are linear, rosette, shear, double parallel, and diaphragm.

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