Strain Gauges and Their Applications
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Questions and Answers

What is the gauge sensitivity or gauge factor commonly denoted as?

  • ε
  • g (correct)
  • ρ
  • R

The formula for calculating the resistance of a wire includes the cross-sectional area and the resistivity.

True (A)

What does the symbol σ represent in the context of force measurements?

Stress

The _____ strain gauge has a higher gauge factor than its resistive counterpart.

<p>semiconductor</p> Signup and view all the answers

Which material is most commonly used for wire-bonded strain gauges?

<p>Constantan (D)</p> Signup and view all the answers

Match the following terms related to strain gauges:

<p>g = Gauge sensitivity σ = Stress R0 = No strain resistance E = Modulus of elasticity</p> Signup and view all the answers

A strain gauge can only measure strain in one direction.

<p>False (B)</p> Signup and view all the answers

What relationship does the equation R(ε) = R0 (1 + g ε) describe?

<p>The relationship between resistance and strain.</p> Signup and view all the answers

What is the most common material used for strain gauges due to its properties and ease of production?

<p>Silicon (B)</p> Signup and view all the answers

Strain gauges do not require temperature compensation.

<p>False (B)</p> Signup and view all the answers

What is the general behavior equation for a semiconductor strain gauge?

<p>R = g1 ε + g2 ε^2</p> Signup and view all the answers

Strain gauges are subject to errors caused by ________ and the strain itself.

<p>temperature</p> Signup and view all the answers

Match the errors in strain gauges to their solutions:

<p>Temperature variation = Use materials with low temperature coefficients Permanent deformation = Periodic re-calibration</p> Signup and view all the answers

Which solution can help minimize errors caused by temperature in strain gauges?

<p>Using temperature compensators (A)</p> Signup and view all the answers

What is the purpose of periodically re-calibrating strain gauges?

<p>To account for permanent deformation over time.</p> Signup and view all the answers

The gauge factor can be estimated by comparing the resistance of the sensor with and without ________.

<p>strain</p> Signup and view all the answers

The nominal resistance of the strain gauge at 20°C is 350 Ω.

<p>True (A)</p> Signup and view all the answers

What is the maximum resistance expected for a maximum strain of 2%?

<p>412.3 Ω</p> Signup and view all the answers

The change in resistance due to a maximum strain of 2% is ______ Ω.

<p>62.3</p> Signup and view all the answers

Match the following parameters with their respective values:

<p>Nominal Resistance = 350 Ω Gauge Factor = 8.9 Temperature Coefficient = 0.00385 Ω°C Maximum Strain = 2%</p> Signup and view all the answers

What is the temperature range the sensor is exposed to?

<p>-50 to 200°C (C)</p> Signup and view all the answers

A temperature coefficient of resistance α = 0.00385 Ω°C means resistance increases with temperature.

<p>True (A)</p> Signup and view all the answers

Calculate the change in resistance due to a temperature change from 20°C to -50°C.

<p>This requires specific calculations based on resistance and the temperature coefficient, which are not explicitly provided.</p> Signup and view all the answers

What does Vo represent in the given equation?

<p>Output voltage of the bridge (D)</p> Signup and view all the answers

The change in output voltage is zero if the resistance changes are equal for R1, R2, R3, and Rx.

<p>True (A)</p> Signup and view all the answers

What happens to the output if a force is applied to the strain gauge S1?

<p>The output changes since the resistance of S1 changes.</p> Signup and view all the answers

The bridge sensitivity can be calculated by taking the first ______.

<p>derivatives</p> Signup and view all the answers

Match the variables with their corresponding definitions:

<p>Vo = Output voltage of the bridge Vin = Input voltage to the bridge R1 = Resistance in the first leg of the bridge R3 = Resistance in the third leg of the bridge</p> Signup and view all the answers

What is the role of the resistor S3 in the experiment?

<p>It is exposed only to temperature. (D)</p> Signup and view all the answers

R2 and Rx are alleged to be different resistances in the system.

<p>False (B)</p> Signup and view all the answers

What is the significance of having two identical resistors R2 and Rx?

<p>They ensure a balanced measurement when no force is applied.</p> Signup and view all the answers

What happens to Vo when there is no change in resistance?

<p>Vo becomes Vin (A)</p> Signup and view all the answers

The temperature coefficient of resistance for the strain gauge described is α = 0.00385 Ω◦ C.

<p>True (A)</p> Signup and view all the answers

What is the gauge factor of the strain gauge in the example?

<p>8.9</p> Signup and view all the answers

The nominal resistance of the sensor at 20◦ C is ______.

<p>350 Ω</p> Signup and view all the answers

Which of the following resistances corresponds to a 2% strain condition?

<p>413.2 Ω (C)</p> Signup and view all the answers

Match the temperature conditions with their corresponding resistances at no strain:

<p>-50◦ C = 255.675 Ω 20◦ C = 350 Ω 200◦ C = 592.55 Ω</p> Signup and view all the answers

What is the maximum strain that the bridge circuit is designed to accommodate?

<p>2%</p> Signup and view all the answers

The input voltage of the bridge circuit is set at ______.

<p>10 V</p> Signup and view all the answers

What is the value of R0 at 2% strain and T = 20°C?

<p>413.2 Ω (B)</p> Signup and view all the answers

At -50°C with no strain, the value of R0 is 350 Ω.

<p>True (A)</p> Signup and view all the answers

What is the formula for Vo in terms of Z1, Z2, Z3, and Z4?

<p>Vo = Vin * (Z1 * Z4 - Z3 * Z2) / (Z1 + Z2) * (Z3 + Z4)</p> Signup and view all the answers

The value of Vo at 2% strain and T = 20°C is ______.

<p>0.041 V</p> Signup and view all the answers

Which of the following values corresponds to R200 at 2% strain?

<p>698.02 Ω (B)</p> Signup and view all the answers

Z2, Z3, and Z4 all have the same value of 350 Ω.

<p>True (A)</p> Signup and view all the answers

At 2% strain and T = -50°C, the value of R−50 is ______.

<p>255.675 Ω</p> Signup and view all the answers

Match the following resistance values with their respective strains:

<p>R0 (2% strain) = 413.2 Ω R−50 (no strain) = 255.675 Ω R200 (no strain) = 592.55 Ω R−50 (2% strain) = 301.185 Ω</p> Signup and view all the answers

Flashcards

Resistance of a wire

Resistance of a wire, calculated as resistivity times length divided by cross-sectional area.

Gauge sensitivity (gauge factor)

The change in resistance of a strain gauge is proportional to the applied strain, with a proportionality factor called the gauge sensitivity or gauge factor.

Resistance-Strain relationship

The relationship between resistance and strain of a wire can be expressed as: R(ε) = Ro (1 + g ε), where R(ε) is the resistance under strain, Ro is the resistance without strain, g is the gauge factor, and ε is the strain.

Force applied on a wire

The force F applied on a wire is calculated as the product of Young's Modulus E, strain ε, and the cross-sectional area A of the wire.

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Wire-bonded strain gauge

A type of strain gauge consisting of a thin layer of resistive material deposited on a substrate, etched into a long winding pattern.

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Constantan

A common material used in wire-bonded strain gauges, known for its low temperature coefficient of resistance.

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Semiconductor strain gauge

A strain gauge that uses a semiconductor material instead of metal, resulting in a higher gauge factor.

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Stress Gauge

A type of strain gauge used to measure stress, where the change in resistance is proportional to the applied stress.

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Semiconductor Strain Gauge Response

The resistance change is proportional to the strain, but it is not linear. The higher sensitivity is an advantage.

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Strain Gauge Temperature Effects

A strain gauge's resistance can change due to temperature fluctuations. This error is unavoidable because the material's resistance changes with temperature.

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Strain Gauge Temperature Compensation

Selecting materials with low temperature coefficients of resistance reduces temperature related changes. Use temperature compensators to minimize the impact of temperature variations.

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Strain Gauge Deformation Error

The strain gauge can deform permanently due to the applied force causing long-term drift in the measurements.

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Strain Gauge Calibration

To ensure accurate measurements over time, periodically calibrate the strain gauge by applying known forces and comparing the readings to the initial calibration.

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Gauge Factor

The ratio of the change in resistance to the applied strain. It is a measure of the gauge's sensitivity to strain.

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Constantan Property

Constantan is a material that has a low temperature coefficient of resistance, meaning its resistance changes very little with temperature changes.

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Resistance Equation

The equation used to calculate the resistance of a wire-bonded strain gauge at a given temperature.

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Temperature Coefficient of Resistance (α)

The change in resistance of a strain gauge due to temperature variation.

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Gauge Factor (GF)

A measure of how much the resistance of a strain gauge changes in response to strain. A higher gauge factor means greater sensitivity.

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Bridge Circuit Temperature Compensation

A circuit that uses a combination of resistors to compensate for changes in resistance due to temperature.

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Strain

The change in length of a material divided by its original length.

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Platinum Strain Gauge

A type of strain gauge made with platinum, known for its high resistance and precise measurements.

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Nominal Resistance (R0)

The nominal resistance of a strain gauge at a specific temperature (usually 20°C).

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Bridge Circuit Output Voltage

The output voltage of a bridge circuit is proportional to the strain and the gauge factor, providing a way to measure applied force.

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Temperature Coefficient of Resistance

The change in resistance of a strain gauge due to a change in temperature. This is a potential source of error in strain measurements.

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Nominal Resistance

The resistance of a strain gauge at its nominal (standard) temperature.

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Strain-Induced Resistance Change

The change in resistance of a strain gauge due to the applied strain. This is the actual signal you're trying to measure.

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Resistance at a Given Temperature

The resistance of a strain gauge at a given temperature, considering both the nominal resistance and the temperature-induced resistance change.

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Maximum Resistance

The maximum resistance a strain gauge can reach under a specific strain and temperature condition.

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Temperature-Induced Resistance Change

The change in resistance due to temperature fluctuations. This is a potential error term in strain measurements.

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Maximum Error Due to Temperature

The maximum error in strain measurement due to temperature variations. This is the potential error you need to consider.

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Bridge Sensitivity

The change in output voltage (Vo) due to a change in resistance (R) in a Wheatstone bridge circuit.

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Temperature Compensation

A method used to minimize the effect of temperature changes on strain gauge measurements.

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Wheatstone Bridge for Strain Measurement

A Wheatstone bridge circuit is used to measure strain, and the sensitivity of the bridge is the change in output voltage per change in resistance.

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Temperature Compensation Using Two Gauges

Two strain gauges (S1 and S3) are used in a Wheatstone bridge. S1 is exposed to force and temperature, while S3 is only exposed to temperature. This helps to eliminate temperature-induced changes in output.

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Zero Output Voltage Change with Temperature

In a temperature-compensated strain gauge setup, the output voltage change is zero when the temperature changes but the resistance change is the same for both gauges. This is because the changes in output voltage due to temperature cancel out.

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Force and Resistance Change

When a force is applied to a strain gauge, the resistance of the gauge changes. This change in resistance then results in a change in the output voltage of the bridge.

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Output Voltage Change Due to Force

The resistance change of the strain gauge (S1) due to force causes an output voltage change in the Wheatstone bridge. This output voltage change is proportional to the force applied.

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Importance of Temperature Compensation

In strain measurement, temperature compensation is crucial to obtain accurate readings. The design of the strain gauge system with two gauges and a balanced bridge minimizes temperature effects on the output.

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Resistance change proportional to strain

The change in resistance of a strain gauge is directly proportional to the applied strain. This relationship tells us how the gauge's electrical resistance changes when it's stretched or compressed.

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Constantan Properties

A common material for wire-bonded strain gauges due to its low temperature coefficient of resistance. This means it's less susceptible to changes in resistance caused by temperature fluctuations.

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Study Notes

Course Information

  • Course Title: Sensors, Measurements and Data Acquisition System
  • Course Code: MSE 355
  • Instructor: Dr. Mohamed Atef Ismail Kamel
  • Program: Mechatronics Systems Engineering (MSE)
  • University: MSA University
  • Semester: Fall 2023
  • Year Level: 3

Force, Tactile, and Pressure Sensors

  • Force Measurement Methods:

    • Strain gauge
    • Acceleration (F = ma)
    • Spring displacement (F = kx)
    • Pressure (F = PA)
    • Piezoelectric transducer

  • Strain Gauges:

    • Main tool for sensing force
    • Strain is related to stress, force, torque, displacement, acceleration, and position
    • Can measure temperature, level, and related quantities
    • Resistance of a wire: R = (ρL)/A
    • For small deformation: (ΔR/R) = gε
    • g is the gauge sensitivity (gauge factor)
    • Strain relationship to Resistance: R(ε) = Ro (1 + gε)
    • Different types: Wire-bonded, Semiconductor

  • Wire-Bonded Strain Gauge

    • Thin conducting material (Constantan) on an insulator (plastic/ceramic)
    • Etched into a long, meandering wire
    • Constantan (60% copper, 40% nickel) used for low temperature coefficient
    • Multiple strain gauges used for multiple axis strain
    • Standardized configurations for strain gauges

  • Semiconductor Strain Gauge

    • Same operation principle as resistive gauges
    • Higher gauge factor than metals
    • Large change in conductivity due to strain compared to metals
    • Sensitive to temperature variations (requires temp compensation)
    • Silicon is common due to properties and ease of production
    • Typical behavior: dR/R = g1ε + g2ε2 (nonlinear)
    • Higher sensitivity is an advantage

  • Strain Gauges: Sources of Error

    • Temperature changes (affect resistance: Ro (1 + α[T – To]))
      • Solution: Use strain gauges with low temperature coefficients and use temp compensators
    • Strain itself: Permanent gauge deformation over time
      • Solution: Periodic re-calibration

Example Calculations and Applications

  • The Example section details calculations for resistance measurements under various conditions and strain levels, with provided materials data (conductivity and temp coefficients)
  • Example calculations involve the given geometries and materials parameters
  • These calculations and examples aim to illustrate calculating resistances for given scenarios, demonstrating sensor applications and error sources.
  • Example calculation of gauge factor, showing the strain effect on resistance change and how to calculate the error.
  • An example of how a bridge circuit is used to compensate for the temperature effect within the strain measurement

Tactile Sensors

  • Low-force sensors
  • Sense force presence with magnitude reaction
  • Keypads, robotic arm grippers use tactile sensors
  • Piezoelectric films; used for force distribution detection
  • Examples: Conductive-foam (membrane keypads)
  • Force sensitive resistive (FSR) tactile sensor (pressure-dependent material resistance)

Pressure Sensors

  • Consists of two parts: pressure conversion and transduction
  • Gauge pressure: Difference between measured pressure and ambient pressure
  • Differential pressure: Difference between pressures at two locations
  • Absolute pressure: Differential pressure referenced to zero
  • Types include mechanical (Bourdon tube), bellows, and piezoelectric

Bourdon Tube

  • Short bent tube, one end closed
  • Pressurization causes tube straightening
  • Proportional to pressure
  • Position sensor or LVDT convert to electrical signal

Bellows

  • Used to convert pressure into linear motion
  • Expansion proportional to the pressure increase
  • Detected by position sensors (like potentiometers)

Piezoelectric Pressure Sensor

  • Uses piezoresistive property of silicon to measure pressure
  • Advantage: no moving parts

Q&A and Discussion

  • Open forum for questions

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MSE 355 Sensors, Measurements and Data Acquisition System PDF

Description

Test your knowledge on strain gauges and their properties. This quiz covers the fundamentals, including gauge sensitivity, materials, and formulae related to strain measurements. Understand the critical concepts that underpin the efficient use of strain gauges in various applications.

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