Summary of "Strain Gauges and load cells part: 1"
Summary of “Strain Gauges and Load Cells Part: 1”
This lecture introduces strain gauges and load cells, focusing on their principles, applications, and measurement techniques, especially using the Wheatstone bridge circuit. It blends sensor theory with practical circuit analysis to explain how strain gauges work and how to measure strain-induced resistance changes.
Main Ideas and Concepts
Introduction to Strain Gauges and Load Cells
- Strain gauges are essential sensors for measuring strain (deformation) in materials.
- Load cells are combinations of strain gauges used to measure force or load.
- The Wheatstone bridge circuit is a fundamental tool for analyzing strain gauge signals.
Basic Definitions: Stress and Strain
- Stress = Force / Area applied to a material.
- Strain = Change in length / Original length of the material.
- Tensile stress/strain: material is stretched.
- Compressive stress/strain: material is compressed.
- Stress and strain have a linear relationship within the elastic limit of the material.
- Young’s modulus (E) = Stress / Strain, a measure of material stiffness.
Why Measure Strain?
- Monitoring structural health (e.g., bridges, rails) to detect early deformation or damage.
- Prevent accidents by detecting small strains that can lead to structural failure.
- Strain gauges must be highly sensitive, small in mass, robust against environmental conditions, and inexpensive.
Strain Gauge Construction and Working Principle
- Composed of a metallic wire arranged in a grid pattern, with terminals for electrical connection.
- Wire resistance depends on length, cross-sectional area, and resistivity.
- When stretched, length (l) increases and cross-sectional area (A) decreases, causing resistance (R) to increase.
- When compressed, length decreases and area increases, causing resistance to decrease.
- Backing material electrically insulates the wire from the structure but efficiently transmits strain.
Mathematical Relations and Gauge Factor
- Resistance formula: [ R = \rho \frac{l}{A} ] where (\rho) is resistivity.
- Change in resistance due to strain: [ \frac{\Delta R}{R} = \text{Gauge Factor} \times \text{Strain} ]
- Gauge factor (k): [ k = \frac{\Delta R / R}{\Delta l / l} ] typically around 2 for metallic strain gauges.
- A higher gauge factor means better sensitivity (larger resistance change for small strain).
Example Calculation
Given a steel bar with known area, force, original resistance, and Young’s modulus, calculate: 1. Stress = Force / Area. 2. Strain = Stress / Young’s modulus. 3. Change in resistance: [ \Delta R = \text{Gauge Factor} \times \text{Strain} \times R ]
Example yields a very small resistance change (~0.12 Ω for 120 Ω original resistance).
Measuring Resistance Changes Using Wheatstone Bridge
- Directly measuring small resistance changes with an ohmmeter is impractical for continuous monitoring.
- Wheatstone bridge balances four resistors; strain gauge replaces one resistor.
- Bridge is balanced when: [ \frac{R_1}{R_2} = \frac{R_3}{R_4} ] and output voltage ( V_{out} = 0 ).
- Strain changes resistance, unbalancing the bridge and producing a measurable voltage.
- Voltage output is proportional to the resistance change, which correlates to strain.
- Voltage measurement is preferred over resistance because it allows continuous, remote monitoring using microcontrollers.
Derivation of Voltage Output Formula
Assuming all resistors equal ( R ), and one resistor changes by ( \Delta R ):
[ V_{out} = \frac{V_s \Delta R}{4R} ]
- ( V_s ) is the supply voltage.
- Small ( \Delta R ) leads to small ( V_{out} ) (millivolts), requiring sensitive measurement equipment.
Significance of Voltage Polarity
- Positive ( V_{out} ) indicates tensile strain (resistance increase).
- Negative ( V_{out} ) indicates compressive strain (resistance decrease).
- This polarity helps determine force direction.
Using Two Strain Gauges in Wheatstone Bridge
- One strain gauge on top (tension), one at bottom (compression).
- Their resistance changes are opposite (( R + \Delta R ) and ( R - \Delta R )).
- This configuration doubles sensitivity: [ V_{out} = \frac{V_s \Delta R}{2R} ]
- Improves voltage output for the same strain.
Limitations and Practical Considerations
- If strain gauges are oriented such that their resistance changes cancel out, the output voltage can be zero despite applied force, which is undesirable.
- Proper placement and orientation of strain gauges are critical for meaningful measurements.
Methodology / Instructions
To measure strain using strain gauges and Wheatstone bridge:
- Attach strain gauge(s) to the material where strain is to be measured.
- Ensure strain gauge is electrically insulated from the material but mechanically coupled to transmit strain.
- Connect strain gauge as one resistor in a Wheatstone bridge circuit.
- Balance the Wheatstone bridge so that ( V_{out} = 0 ) under no strain.
- When strain occurs, the resistance of the strain gauge changes, unbalancing the bridge.
- Measure the output voltage ( V_{out} ), which is proportional to the strain.
- Use the formula:
- For one gauge: [ V_{out} = \frac{V_s \Delta R}{4R} ]
- For two gauges (tension/compression): [ V_{out} = \frac{V_s \Delta R}{2R} ]
- Calculate strain from the voltage output using the gauge factor and known resistor values.
- Use microcontrollers and data acquisition systems to continuously monitor ( V_{out} ) remotely.
- Interpret polarity of ( V_{out} ) to determine direction of applied force.
Key points for practical use:
- Use materials with high gauge factor for better sensitivity.
- Ensure strain gauges are properly installed to avoid signal cancellation.
- Use voltage measurement rather than direct resistance measurement for accuracy and remote monitoring.
- Consider environmental robustness of strain gauges for outdoor applications.
Speakers / Sources Featured
- Primary Speaker: The lecturer/professor delivering the course on strain gauges and load cells (unnamed).
- Students/Participants: Brief interactions with students named Chloe and Dean during Q&A.
This summary encapsulates the foundational concepts, mathematical derivations, practical considerations, and measurement techniques for strain gauges and load cells as presented in the video lecture.
Category
Educational
