1. MECH 373 Instrumentation and Measurements
Lecture 20
Measuring Pressure and Temperature (Chapter 9)
• Measuring Pressure
• Measuring Temperature

2. Measuring Acceleration and Vibration
Accelerometers using Piezoelectric Sensing Elements
• An accelerometer using a piezoelectric material as the sensing element is shown below:
• It consists of a housing, a mass called the seismic mass, and a piezoelectric sensing element, which typically uses the longitudinal piezoelectric effect.
• An initial force between the mass and sensor is obtained with a preloading spring sleeve.

3. Measuring Acceleration and Vibration
• As the housing for the accelerometer is subject to an acceleration, the force exerted by the mass on the quartz crystal is altered.
• This generates a charge on the crystal, which can be sensed with a charge amplifier.
• Piezoelectric accelerometers are available in many ranges up to ±1000g, where g is the acceleration due to gravity.
• Quartz crystal accelerometers can have very high values of natural frequency up to 125 kHz.
• This allows them to measure frequencies as high as 25 kHz.

4. Measuring Acceleration and Vibration
Vibrometer
• An instrument that is used to measure the ground motion in earthquakes and sometimes to measure vibration in machines is called the vibrometer.

5. Measuring Acceleration and Vibration
• Although the basic components are the same as the piezoelectric or strain-gage accelerometers, the mode of operation is different.
• In the vibrometer, the spring is quite soft and as the housing moves, the mass remains approximately stationary. The relative motion, y, is large and sensed with a potentiometer.
• These devices are used to measure vibrations with frequencies that are high relative to the natural frequency of the spring-mass system, which is often less than 1 Hz.
• The vibrometer effectively measures the displacement of the base rather than the acceleration.
• Thus, these devices are most sensitive to vibrations with moderate frequencies and fairly large displacement amplitudes.
• High frequency vibrations usually have small values of displacement amplitude and are better measured with accelerometers.

6. Measuring Force Load Cell
• “Load cell” is a term used to describe a transducer that generates a voltage signal as a result of an applied force, usually along a particular direction.
• Virtually any simple metal structure deforms when subjected to a force, and as long as the resulting stresses are below the material yield stress, the deflection (δ) and resulting strain (ε) are linear functions of the applied force:
where C’s are constants determined from analysis or calibration.
• The most common force-measuring devices are strain-gage load cells. They are often constructed of a metal and have a shape such that the range of forces to be measured results in a measurable output voltage over the desired operating range.
• Figure 8.34(a) shows a cantilever beam instrumented with four strain gages, two on the top and two on the bottom, to measure normal or bending stresses. These four gages form the Wheatstone bridge and offer effective temperature compensation. The output of the bridge is four times the output of an individual gage.

7. An unbalanced Wheatstone Bridge
Rx is the STRAIN GAUGE, generally VAB ≠ 0
(STRAIN GAUGE
Unknown R
connected here)
VAB
Rx changes due to strain VAB changes

8. Measuring Force
• Figure 8.34(b) shows a hollow-cylinder load cell. It also uses four strain gages and is also temperature compensated. As the cylinder is compressed, it becomes slightly shorter, while the diameter becomes slightly larger. As a result, two gages measure the axial compression. The other two, mounted transversely, measure the tensile diametral strain. Since the transverse strain is only Poisson's ratio times the axial strain, the output is less than four times the output of a single axial strain gage. For a Poisson's ratio of 0.3, the output will be about 2.6 times the output of a single axial strain gage.

9. Measuring Force
• Due to their simple design, any range can be readily manufactured. Commercial load cells are available with ranges from ounces up to several hundred thousand pounds.
• Unlike accelerometers, it is not useful to specify the frequency response of commercial load cells because the mass and flexibility of the instrumented system control the dynamic response.
• Furthermore, an installed load cell will add flexibility to the system and also affect the dynamic response.
• If the flexibility of strain-gage load cells is too high, load cells using piezoelectric sensors, which are much stiffer, are commercially available.

10. Measurement Systems

11. Measuring Pressure
• Pressure is measured in three different forms: absolute pressure, gage pressure, and differential pressure.
• Absolute pressure is that used in thermodynamics to determine the state of a substance.
• Gage pressure is the pressure relative to the local ambient air pressure.
• Differential pressure is simply the difference in pressure at two points in a system.
• The relationship between different pressure forms is
Pressure Transducers
• A very common and inexpensive device used to measure fluid pressure is the diaphragm strain-gage pressure transducer, shown in next slide.

12. Measuring Pressure
• The test pressure is applied to one side of the diaphragm, a reference to the other side. A deflection of the diaphragm is sensed with strain gages.
• The reference pressure can be atmospheric, so the transducer measures gage pressure.
• The reference side could be sealed and evacuated so that the transducer measures absolute pressure.
• Both sides could be connected to different test pressures so that the measurement is of differential pressure.

13. Measuring Pressure
• In the past, the diaphragm was made of metal and foil strain gages were used. Recently, it has become common to make the diaphragm of a semiconductor material (usually silicon) with semiconductor strain gages formed into the diaphragm. This is a less expensive construction technique, and since semiconductor gages have high gage factors, the sensitivity is improved.
• Normally, the Wheatstone-bridge signal conditioner is built into the transducer (all branches of the bridge are active gages), and the strain gages are connected to give temperature compensation.
• Most strain-gage pressure transducers produce a DC output in the millivolt range, but some include internal amplifiers and have outputs in the range 0 to 5 or 0 to 10 V. The higher voltage output units are less susceptible to environmental electrical noise.
• Pressures can also be sensed with LVDT (linear variable differential transformer) devices like the one shown below:

14. Measuring Pressure
• This diagram shows an arrangement with a flexible chamber called a capsule and an LVDT to sense the displacement. This design is more expensive than those using strain-gage sensors but may be more durable in an application requiring a long lifetime.
• The output is a DC voltage with a range on the order of 0-5 or 0-10 V. In the process industries, the voltage output usually be converted to a 4 to 20 mA current for signal transmission.

15. Measuring Pressure
• Capacitive sensors are sometimes used in pressure transducers.
• When one or more fixed metal plates are placed directly above or below a metallic diaphragm, a capacitor is created that forms an effective secondary element. Displacement of the diagram changes the average gap separation, which varies the capacitance developed between the two plates.
• Capacitive pressure transducers, like those shown below, are particularly useful for very low pressures (as low as 0.1 Pa) since captive sensors can detect extremely small deflections.

16. Measuring Pressure
• Transducers used for high-frequency pressure measurements usually use a piezoelectric sensing element. A piezoelectric transducer is shown below:
• These transducers generally use transverse-effect piezoelectric sensing elements. The piezoelectric material is very stiff, and the transducers have a high natural frequency in many applications. If the diaphragm (or other displacing element) is very flexible, the natural frequency will be low and the transducer output will be misleading for high-frequency pressure measurements.

17. Measuring Pressure
• The diaphragm is of the flush-mounted type. When the transducer is installed, it comes into direct contact with the fluid in the pipe or chamber. There are two reasons for this:
- If a cavity were included as in the other transducers, it might significantly alter the measurand due to loading.
- The natural frequency would be reduced and the ability to respond to transients would be impaired.
• Piezoelectric pressure transducers can have natural frequencies up to 150 kHz and are usable up to about 30 kHz.

18. Measuring Pressure (Summary)
􀂋 Strain gage types
􀂋 Capacitive
very low pressures
􀂋 Piezoelectric
high-frequency pressure
􀂋 LVDT