Mechanical Engineering: Static and Dynamic Characteristics

General Performance Characteristics of Measuring Instruments

• Static characteristics: describe the behavior of measuring instruments under steady-state conditions
  • Accuracy: closeness of the measured value to the true value
  • Precision: consistency of repeated measurements under unchanged conditions
  • Resolution: smallest change in the measured quantity that the instrument can detect
  • Sensitivity: ratio of the change in the output signal to the change in the input quantity
  • Linearity: degree to which the output signal is directly proportional to the input quantity
  • Range: minimum and maximum limits within which the instrument can accurately measure the input quantity
  • Hysteresis: difference in output when the input quantity is increased and then decreased
• Types of errors: errors that can arise in measurements
  • Gross errors: human errors or mistakes during measurement or recording
  • Systematic errors: consistent, predictable errors that can often be corrected
    • Instrumental errors: due to imperfections or miscalibration of the instrument
    • Environmental errors: caused by external conditions like temperature, humidity, and pressure
    • Observational errors: errors due to the observer, such as parallax errors
  • Random errors: unpredictable variations in the measurement process that cannot be easily corrected
• Combination of component errors: errors in individual components can propagate and affect the overall accuracy of a measurement system

Dynamic Characteristics of Instruments

• Dynamic characteristics: describe how an instrument responds to changes in the measured variable over time
• General mathematical models: used to describe the behavior of zero-order, first-order, and second-order instruments
• Response to different inputs: instruments can respond to various inputs, including step, ramp, impulse, and frequency
• Zero-order instruments: characterized by an instantaneous response to changes in the input
• First-order instruments: characterized by a response that changes over time
• Second-order instruments: characterized by a response that changes over time and is influenced by damping and natural frequency

Strain Measurement

• Strain gauges: used to measure strain on various structures
• Types of strain gauges:
  • Metallic foil strain gauges: most common type, consisting of a grid of thin metallic foil bonded to an insulating backing material
  • Semiconductor strain gauges: made from silicon or germanium, higher sensitivity but more temperature-sensitive
  • Bonded and unbonded strain gauges: differ in how they are attached to the test specimen
  • Optical fiber strain gauges: use changes in light transmission to measure strain
  • Piezoresistive strain gauges: used in pressure sensors, utilize the change in electrical resistance of a piezoresistive material
• Strain gauge circuits:
  • Quarter-bridge circuit: simplest and least expensive, uses a single active strain gauge and three fixed resistors
  • Half-bridge circuit: uses two strain gauges, can measure bending strains and provide some temperature compensation
  • Full-bridge circuit: uses four strain gauges, provides maximum sensitivity and temperature compensation
• Calibration: process of ensuring accurate strain measurements
  • Applying known loads: apply known mechanical loads or strains to the test specimen and record the corresponding electrical output
  • Generating calibration curve: plot the known loads against the electrical output to create a calibration curve
  • Deriving calibration factor: calculate the calibration factor, which relates the electrical output to the actual strain
• Temperature compensation: methods to compensate for temperature changes that can affect strain gauge readings
  • Using temperature-compensated strain gauges: gauges designed with materials having matching thermal expansion coefficients
  • Dummy gauge method: uses a non-stressed dummy gauge in the same thermal environment as the active gauge
  • Quarter-bridge temperature compensation: uses an additional strain gauge in the bridge that is not subject to strain but experiences the same temperature changes
• Use of strain gauges on rotating shafts: special considerations for using strain gauges on rotating shafts
  • Wireless data transmission: use telemetry systems to transmit strain data wirelessly from the rotating shaft to a stationary data acquisition system
  • Slip rings: use slip rings to maintain electrical connections between the rotating strain gauge and the stationary measurement equipment
  • Careful installation: ensure strain gauges are securely bonded and the wiring is protected against centrifugal forces
• Selection and installation of strain gauges: critical for obtaining accurate and reliable strain measurements
  • Selection criteria: strain range, gauge factor, environmental conditions, and material compatibility
  • Installation process: surface preparation, bonding, wiring, and protection

Pressure Measurement

• Basic methods of pressure measurement:
  • Strain gauge pressure cell: uses the deformation of a diaphragm or other elastic element under pressure to measure strain
  • High pressure measurement: uses the Bridgeman type gauge, which measures high pressures by using the change in electrical resistance of a wire or material under pressure
  • Low pressure measurement: uses various methods, including McLeod, Knudsen, ionization, and thermal conductivity gauges
• Strain gauge pressure cell: components and operation
  • Diaphragm: a flexible membrane that deforms under pressure
  • Strain gauges: bonded to the diaphragm to measure deformation
  • Wheatstone bridge circuit: converts the strain gauge resistance changes into a measurable voltage output
• High pressure measurement - Bridgeman type gauge: principle, components, and operation
  • Principle: measures high pressures by using the change in electrical resistance of a wire or material under pressure
  • Components: pressure vessel, wire or material, and electrical circuit
  • Operation: measures the change in resistance of the wire or material under pressure
• Low pressure measurement methods:
  • McLeod gauge: measures low pressures by compressing a known volume of gas and measuring the resulting increase in pressure
  • Knudsen gauge: measures pressure based on the thermal transpiration effect, where gas molecules flow through a porous plug due to a temperature gradient
  • Ionization gauge: measures very low pressures by ionizing the gas and measuring the resulting ion current
  • Thermal conductivity gauges: measures pressure based on the thermal conductivity of the gas, which varies with pressure