2. TRANSDUCERS AND STRAIN GAUGES

  For 4th Semester Polytechnic ME Students

Written by Garima Kanwar | Blog: Rajasthan Polytechnic

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Course Code : ME 4001(Same in MA 4001)
Course Title : MEASUREMENTS & METROLOGY

2.1 Introduction and Transducers

Definition of Transducer: A transducer is a device that converts one form of energy into another. In the context of measurements, it typically converts a physical quantity (like pressure, temperature, force) into an electrical signal that can be measured and analyzed.

Types of Transducers:

1. Active Transducers: These transducers generate an electrical signal on their own without the need for an external power source.
   • Example: Thermocouples (convert temperature to voltage).
2. Passive Transducers: These require an external power source to operate and convert the physical quantity into an electrical signal.
   • Example: Strain gauges (convert mechanical deformation to electrical resistance).

Characteristics of Transducers:

• Sensitivity: The ratio of output signal change to the change in the measured quantity.
• Accuracy: The degree to which the transducer provides a true representation of the physical quantity.
• Range: The range of the physical quantity the transducer can measure effectively.
• Response Time: The time the transducer takes to respond to changes in the input quantity.

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2.2 Strain Gauge

Definition: A strain gauge is a sensor used to measure the strain (deformation) of an object. It works on the principle that the electrical resistance of a material changes when it is deformed.

Working Principle:

• A strain gauge consists of a thin metallic foil or wire arranged in a grid pattern. When the object to which the strain gauge is attached deforms, the gauge stretches or compresses.
• As the gauge deforms, its length and cross-sectional area change, leading to a change in its electrical resistance.
• This change in resistance is proportional to the strain on the object.

Formula: $\Delta R = R_0 \cdot GF \cdot \varepsilon$ Where:

• $\Delta R$ = Change in resistance
• $R_0$ = Original resistance
• $GF$ = Gauge factor (a constant specific to the strain gauge material)
• $\varepsilon$ = Strain (deformation)

Applications:

• Force measurement: Strain gauges are used in load cells to measure force.
• Stress analysis: Strain gauges are applied to study the mechanical properties of materials in engineering structures.

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2.3 Force Measurement

Force Measurement Using Strain Gauges:

• When a force is applied to an object, it deforms. A strain gauge can be attached to the object, and the resulting change in resistance can be correlated to the force applied.
• Load Cells: These are devices that use strain gauges to measure force. A load cell typically has four strain gauges arranged in a Wheatstone bridge configuration. The resistance change from the strain gauges gives a direct measurement of force.

Wheatstone Bridge:

• The Wheatstone Bridge is a circuit that is often used to precisely measure the small changes in resistance that occur in strain gauges. The configuration consists of four resistive elements (which can be strain gauges) arranged in a diamond shape. Any imbalance in the bridge due to strain causes a voltage difference that is proportional to the applied force.

Example: If a strain gauge with a gauge factor of 2.0 experiences a strain of 0.001, and its original resistance is 120 Ω, then the change in resistance will be: $\Delta R = 120 \cdot 2.0 \cdot 0.001 = 0.24 \, \Omega$

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2.4 Torque Measurement

Torque Measurement Using Strain Gauges: Torque is the rotational force applied to an object. Strain gauges can be used to measure the strain that occurs when a shaft or similar object experiences torque.

Working:

• Strain gauges are attached to a rotating shaft at specific locations. The torque causes the shaft to twist, inducing strain on the material. The strain gauges measure the strain and convert it to a change in electrical resistance, which can then be used to calculate the applied torque.
• Torsional Strain: When torque is applied to a shaft, it experiences a torsional strain, and strain gauges can measure this strain to determine the magnitude of the torque.

Example of Torque Measurement Using a Strain Gauge: In a rotating shaft, strain gauges are applied at known positions. The strain $\varepsilon$ is measured, and the torque $T$ can be calculated using the formula: $T = \frac{\varepsilon \cdot J \cdot G}{r}$ Where:

• $\varepsilon$ = Strain
• $J$ = Polar moment of inertia of the shaft
• $G$ = Shear modulus of the material
• $r$ = Distance from the axis of rotation to the strain gauge

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2.5 Pressure Measurement: McLeod Gauge

Pressure Measurement: Pressure is defined as force per unit area. Various types of pressure sensors and transducers can be used to measure pressure, including piezoelectric transducers, capacitive pressure transducers, and the McLeod gauge.

McLeod Gauge: The McLeod gauge is a device used to measure low pressures (typically in the range of 10⁻³ to 10⁻⁸ atmospheres). It operates on the principle of compressing a known volume of gas and measuring the resulting pressure.

Working Principle:

• The McLeod gauge works by trapping a small volume of gas in a sealed chamber and compressing it. According to Boyle's law, when the volume is decreased, the pressure increases. By measuring the pressure before and after compression, the original low pressure can be calculated.
• The McLeod gauge typically consists of a U-tube filled with mercury, where the gas to be measured is sealed at the bottom of one arm of the tube. By adjusting the mercury levels, the gas is compressed, and the pressure can be determined based on the height difference of the mercury column.

Advantages:

• High Accuracy: It is particularly accurate for measuring very low pressures.
• Simple to Use: It does not require complicated electronics.

Limitations:

• Not suitable for high pressures.
• Mercury handling issues make it less practical for certain environments.

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Summary of Key Topics and Key Formulae

• Transducers: Devices that convert energy from one form to another. They can be active or passive.
• Strain Gauge: Measures strain by converting deformation into resistance change.
  • Formula: $\Delta R = R_0 \cdot GF \cdot \varepsilon$
    
• Force Measurement: Force is measured using strain gauges attached to objects. A Wheatstone bridge is often used for precise force measurement.
• Torque Measurement: Strain gauges are attached to rotating shafts to measure torque by analyzing torsional strain.
• Pressure Measurement (McLeod Gauge): Measures very low pressures by compressing a known volume of gas.

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Important Questions for Exam Preparation:

1. What is a transducer? Explain the different types with examples.
2. Describe the working principle of a strain gauge and its applications.
3. Explain how a strain gauge can be used to measure force and torque.
4. What is the Wheatstone bridge, and why is it used in strain gauge measurements?
5. Discuss the working principle and applications of the McLeod gauge for pressure measurement.
6. How can torque be measured using strain gauges?
7. What are the advantages and limitations of the McLeod gauge?
8. Derive the formula for measuring force using a strain gauge.

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Diagrams:

1. Wheatstone Bridge Circuit: Diagram of a Wheatstone bridge with strain gauges.
2. Strain Gauge Configuration: A diagram showing how strain gauges are attached to a material.
3. McLeod Gauge Working Principle: Diagram illustrating the U-tube structure and how pressure is measured.

These notes should give you a strong understanding of transducers, strain gauges, force, torque, and pressure measurement systems. Be sure to review the practical examples and formulas thoroughly.

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