Strain Gauge

Chapter 1: What is a Strain Gauge?

A strain gauge, or strain gage, is a sensing device used for measuring strain experienced by an object. It is made from a long, thin piece of conductor bonded to an elastic backing material called a carrier. The conductor varies its electrical resistance when a change in dimension occurs.

The strain gauge is mounted by coupling it to the object to be inspected. Both the object and the strain gauge are deformed when a load is applied. Strain gauges measure strain from different types of stresses, namely tensile, compressive, bending, torsional, and shear stress.

The main application of strain gauges is the manufacture of force and pressure transducers, particularly load cells. A load cell is a type of transducer that measures the mechanical load on an object by converting it to readable electronic signals. They are used in various industries such as automation, process control, biomechanics, equipment monitoring, building integrity analysis, bulk material weighing, testing, and quality control.

Chapter 2: History of Strain Gauges

The development of strain gauges was brought about by the technical applications of the Wheatstone bridge circuit. The Wheatstone bridge was invented and popularized in 1843 by Charles Wheatstone. Its publication mentions an effect that describes the change in resistance of an object due to mechanical stress. This invention was further worked on by William Thomson in 1856.

Eighty years later, two American engineers independently investigated the effect. Edward Simmons, an electrical engineer based in California, used thin resistance wires and silk threads to create a woven strain gauge. The prototype strain gauge was bonded onto a steel cylinder. It was then tested to measure force impulses from a pendulum ram impacting the cylinder.

Simultaneously, Arthur Ruge, a mechanical engineer working at MIT, developed a device initially intended to measure the stress caused by simulated earthquakes to his model of an earthquake-resistant water tank. He used very thin wires stuck to a piece of paper as the strain gauge. The gauge was then bonded into a bending beam, which served as its carrier.

Ruge and his team took the development of his invention to the production stage. This began the strain gauge’s widespread application. Today, the design of the carrier is much simpler. Also, various circuit production techniques have emerged that are far superior to wound-wire techniques. Examples of new circuit production technologies are chemical etching and circuit printing.

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Chapter 3: Operating Principle

Changes in the electrical resistance of a conductor can be caused by different physical phenomena. 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.

The electrical resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. When stretching a strain gauge, the length of its wire increases while the cross-section decreases. Thus, the electrical resistance of the wire is increased. Conversely, compressing the strain gauge without buckling its wires causes the electrical resistance to decrease.

As mentioned in the previous chapter, 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 is variable while the rest are fixed. This variable resistor is the strain gauge. Regarding the energy source, a direct current (DC) supply is fed across the bridge circuit. This is called the excitation source.

The Wheatstone bridge output is the gap voltage measured at Vg indicated in the figure below. The bridge is said to be balanced when the gap voltage is zero. This is typically the initial state of the device. Imbalance is caused when the resistance changes across the variable resistor. This results in an electric potential present across the gap.

Chapter 4: Bridge Configurations

One classification of strain gauges is their bridge configuration. A simple load cell or force transducer uses only one strain gauge. They use a circuit called quarter-bridge configuration. To achieve better performance, most designs use two or four strain gauges. Those that use two strain gauges are called half bridges, while those that use four are called full bridge circuits.

Quarter Bridge:

The previously described Wheatstone bridge is called a quarter bridge circuit. A single active strain gauge takes the place of the variable resistor. Since only one strain gauge is used, it can only measure one type of strain. For the same reason, they are also the least sensitive.

Quarter bridge circuits are further divided 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 type has two active strain gauges. One strain gauge is placed on one leg of the circuit, while the other gauge is on the second leg. In terms of position on the elastic element or structure, the gauges are mounted on opposite sides parallel to the loading direction.

There are two known advantages when using a diagonal bridge design. The first is the increased sensitivity. Since two strain gauges experience the same amount of deformation, a larger output can be obtained. The increase is approximately twice that of a simple quarter bridge circuit.

Another advantage is its ability to reject bending strain. Diagonal bridge strain gauges only measure tensile and compressive strains. When the gauges detect oppositely directed strains, the effect is negated. The strains experienced by the gauges must be in the same direction.

However, the downside of using this type is the large effect of temperature variation. This configuration doubles the error. To counter this, dummy gauges must be paired with each active gauge.

Half Bridge:

Half bridge circuits feature two strain gauges used as active gauges. They are more sensitive than the quarter bridge types since there are two strain measuring elements. The strain gauges in a half bridge circuit can be configured in two ways.

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 only applicable for measuring bending strain. When the elastic element is bent, the sides normal to the direction of the applied force experience either tension or compression. The two strain gauges measure the deflection of the elastic element.

A unique feature of this design is its ability to eliminate the measured axial strain. The transducer interprets the voltage reading such that one strain gauge is in tension while the other is in compression. When both strain gauges are in either tension or compression, the resistance change of one strain gauge is negated by the other. Similarly, this ability also negates the effect of temperature.

Full Bridge:

A full bridge circuit replaces all resistors with active gauges. They are the most versatile due to the many different configurations possible using four strain gauges. Since all resistances are varying, temperature effects are negated throughout the circuit, regardless of the configuration. Enumerated below are the 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 of 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 type functions like two bending half bridge circuits. The strain gauge pairs on one leg of the circuit experience tension and compression. It also eliminates the effect of axial strain when the pairs detect deflection in a single direction.

Since there are four strain measuring conductors, the sensitivity of this configuration is quadrupled in comparison to the simple quarter bridge type.

Chapter 5: Types of Strain Gauges

Knowing the different bridge configurations allows a better understanding of the different strain gauge types. Strain gauges are typically named according to the arrangement of the measuring elements. They can be utilized in more than one bridge type depending on the application.

Linear Strain Gauge:

Linear strain gauges measure strain in one direction. They have the simplest construction and the lowest cost. This makes them suitable for general use such as load testing, fatigue testing, and structural integrity monitoring. These types can have circuits that are quarter bridge, diagonal bridge, or axial full bridge.

Rosette Strain Gauge:

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 several types of rosette strain gauges. The basic examples are briefly explained 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 are configured differently than other strain gauges. The readings from the measuring elements are typically supplied to a computer program for simulation and data reduction. They are mostly suitable for stress analysis and dynamic load monitoring.

Shear Strain Gauge:

Shear strain gauges are used for measuring shear strain caused by torque or torsional loading. They can have one or two measuring grids bonded to a single carrier. A single strain gauge element is aligned at a 45° angle to the axis of the shaft. A two-grid shear strain gauge (V Rosettes) has measuring elements aligned at 45° and 135°. Applications of shear strain gauges are engine shafts and drivetrains. Shaft power can be calculated from the strain gauge measurement.

Double Parallel Strain Gauges:

This type is made from two linear strain gauges aligned in parallel with each other. They can be used with different bridge circuit configurations. A typical example is a bending full bridge circuit where two double parallel strain gauges are placed on opposite sides of the structure.

Diaphragm Strain Gauges:

Diaphragm strain gauges are used to measure radial and tangential strains in a column, beam, or shaft. They are typically configured into a full bridge circuit. The four measuring elements are arranged into either circular or linear patterns. The tangential measuring elements are positioned near the periphery of the carrier while the radial measuring elements are bonded near the center.

Chapter 6: Other Design Considerations

Aside from the bridge circuit and strain gauge arrangement, there are other important criteria to be considered when selecting a strain gauge. Most of the engineering design is put into these other factors.

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.

Aside from metals, a second type of measuring element is also available. These are called semiconductor strain gauges, and they use semiconductor materials such as silicon and germanium. Their measurement principle is different from the metal types, which operate through a change in geometry.

Semiconductor strain gauges primarily make use of the piezoresistive effect. The piezoresistive effect produces greater changes in electrical resistance, and in turn, greater voltage output. This makes semiconductor strain gauges desirable for measuring very small strains. However, the downside of using this type is its susceptibility to high-temperature effects, brittleness resulting in difficult handling, and non-linear resistance change.

Mounting

Strain gauge mounting is generally classified as 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 the less common type. They are exclusively used for transducer applications. They use a thin wire with one end connected to a rigid frame and the other pinned to a movable carrier. The wire is preloaded and held by a spring-loaded mechanism.

Rosette Construction: For strain gauges with multiple measuring elements, there are two construction options to consider. Rosette strain gauges are either planar or stacked. In planar strain gauges, the measuring grids are placed next to each other on a single plane. They yield more precise results since both grids are the same distance from the axis of the structure.

Stacked strain gauges have measuring grids placed one on top of the other. The grids have a slight offset from one another, making them non-coplanar. Because of their stacked construction, they are suitable for applications where mounting space is limited or restricted.

Compensation Methods

In actual applications, both strain and temperature have a direct relationship with the resistance of the conductor. Since only strain is the parameter intended to be measured, temperature becomes 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.

Some compensation methods are mentioned below.

Dummy Gauge

This has been discussed in the previous chapters. A dummy gauge is a non-active conductor that is 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 factors such as 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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