Alciatore D.G., Histand M.B. Introduction to Mechatronics and Measurement Systems

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Figure 9.49 Vibrometer amplitude response.

9.5 Vibration and Acceleration Measurement 421

Figure 9.49 illustrates the amplitude ratio to frequency relationship for different val-

ues of the damping ratio. The phase angle relationship is the same as for the accel-

erometer (see Figure 9.48 ). The input displacement amplitude X

is related to the

measured relative displacement amplitude X

ω()

---------------

(9.77)

If we design the vibrometer so that H

( ␻ ) is nearly 1 over a large frequency

range, then the input displacement amplitude is given directly by the relative dis-

placement amplitude:

(9.78)

As can be seen in Figure 9.49 , the largest frequency range resulting in a unity ampli-

tude ratio occurs when the damping ratio ␨ is 0.707 and the natural frequency ␻

as small as possible (so ␻ / ␻

is large). We can make the natural frequency small by

choosing a large seismic mass and a small spring constant. This explains the large

size of seismographs used to measure motion due to an earthquake.

9.5.1 Piezoelectric Accelerometer

The highest quality accelerometers are constructed using a piezoelectric crystal,

a material whose deformation results in charge polarization across the crystal.

In a reciprocal manner, application of an electric field to a piezoelectric material

results in deformation. As illustrated in Figure 9.50a , a piezoelectric accelerometer

consists of a crystal in contact with a mass, supported in a housing by a spring.

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Figure 9.50 Piezoelectric accelerometer construction.

(a) schematic illustration

preloaded

spring

mass

conductive

coating

accelerometer

housing

piezo-

crystal

damper

vibrating

object

(b) actual device

(Courtesy of Endevco, San Juan Capistrano, CA)

422 CHAPTER 9 Sensors

The purpose for the preload spring is to help keep the mass in contact with the

crystal and to keep the crystal in compression, which can help prolong its life. The

crystal itself also has stiffness that contributes to the overall stiffness of the sys-

tem. Figure 9.50b shows a commercially available piezoelectric accelerometer.

In addition to the natural damping properties inherent in the crystal, additional damp-

ing is sometimes incorporated (e.g., by filling the housing with oil). When the sup-

porting object experiences acceleration, relative displacement occurs between the

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Figure 9.51 Equivalent circuit for

piezoelectric crystal.

charge

source

Figure 9.52 Thevenin equivalent of

piezoelectric crystal.

V = q/C

9.5 Vibration and Acceleration Measurement 423

case and the mass due to the inertia of the mass. The resulting strain in the piezoelec-

tric crystal causes a displacement charge between the crystal conductive coatings as

a result of the piezoelectric effect. Note that an accelerometer using a piezoelectric

crystal requires no external power supply. Also, it is important to recognize that the

accelerometer measures acceleration only in the direction in which it is mounted

(i.e., along the axis of the spring, mass, and crystal).

A piezoelectric material produces a large output for its size. Naturally occurring

piezoelectric materials are Rochelle salt, tourmaline, and quartz. Some crystalline

materials can be artificially polarized to take on piezoelectric characteristics by heat-

ing and then slowly cooling them in a strong electric field. Such materials are barium

titanate, lead zirconate (PZT), lead titanate, and lead metaniobate. These ferroelec-

tric ceramics are more often used in accelerometers because the sensitivity can be

controlled during manufacturing.

A simple equivalent circuit for a piezoelectric crystal is shown in Fig-

ure 9.51 , implying that the crystal is effectively a capacitor and a charge source

that generates a charge q across the capacitor plates proportional to the deforma-

tion of the crystal. Representing the accelerometer by a Thevenin equivalent cir-

cuit (see Figure 9.52 ), the open circuit voltage V is equal to the charge, typically

in the picocoulomb range, divided by the capacitance, typically in the picofarad

range:

------

(9.79)

The sensitivity of the accelerometer is the ratio of the charge output to the

acceleration of the housing expressed in pC/ g, (rms pC)/ g, or (peak pC)/ g, where

g is the acceleration due to gravity. The output of the accelerometer is attached to a

charge amplifier, which converts the displacement charge on the crystal to a voltage

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Figure 9.53 Piezoelectric accelerometer frequency response.

(Courtesy of Endevco, San Juan Capistrano, CA)

424 CHAPTER 9 Sensors

that can be measured. Most accelerometers are calibrated in millivolts per g for a

specified charge amplifier.

In general, piezoelectric accelerometers cannot measure constant or slowly

changing accelerations, because the crystals can measure a change in force only by

sensing a change in strain. But they are excellent for dynamic measurements such as

vibration and impacts. The response at low frequencies is further limited by the low-

frequency cutoff of the charge amplifier, which may be on the order of a few hertz.

The response at high frequencies is a function of the mechanical characteristics of

the accelerometer. The dynamic range of an accelerometer ranges from a few hertz

to a fraction of the resonant frequency given by

2π

------

----=

(9.80)

usually in the kHz range. A typical frequency response curve for a piezoelectric

accelerometer is shown in Figure 9.53 .

Lab Exercise 14 explores how to use an accelerometer to monitor vibrations

from rotating equipment. The health of bearings in a system can be determined by

monitoring the spectrum of the vibration signal. This is called bearing signature

analysis. Video Demo 9.14 shows a demonstration of the experiment, and Internet

Links 9.5 and 9.6 point to some example results. Scratches and wear in roller bear-

ings create more high-frequency content in the vibration spectrum.

Lab Exercise

Lab 14Vibration

measurement with

an accelerometer

■ CLASS DISCUSSION ITEM 9.14

Piezoelectric Sound

How does a piezoelectric microphone work? How about a piezoelectric buzzer?

Internet Lin

9.5Sample

bearing signature

analysis result for

a good bearing

9.6Sample

bearing signature

analysis result for

a bad bearing

Video Demo

9.14Accelerom-

eter bearing

signature analysis

experiment

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9.7 Semiconductor Sensors and Microelectromechanical Devices 425

9.6 PRESSURE AND FLOW MEASUREMENT

Most techniques for measuring pressure involve sensing a displacement or deflec-

tion and relating it to pressure through calibration or theoretical relations. One type

of pressure sensor is a manometer, which measures a static pressure or pressure

difference by detecting fluid displacements in a gravitational field. Another type is

the elastic diaphragm, bellows, or tube where deflection of an elastic member is

measured and related to pressure. Another type is the piezoelectric pressure trans-

ducer that can measure dynamic pressures when the piezoelectric crystal deforms in

response to the applied pressure. References that cover these and other techniques

are included in the bibliography at the end of the chapter. Internet Link 9.7 is also an

excellent resource.

There are also many techniques for measuring gas and liquid flow rates. A pitot

tube measures the difference between total and static pressure of a moving fluid.

Venturi and orifice meters are based on measuring pressure drops across obstruc-

tions to flow. Turbine flow meters detect the rate of flow by measuring the rate of

rotation of an impeller in the flow. Coriolis flow meters measure mass flow rate

through a U-tube in rotational vibration. Hot-wire anemometers sense the resistance

changes in a hot current-carrying wire. The temperature and resistance of the wire

depend on the amount of heat transferred to the moving fluid. The heat transfer coef-

ficient is a function of the flow rate. Laser doppler velocimeters (LDVs) sense the

frequency shift of laser light scattered from particles suspended in a moving fluid.

Most fluid mechanics textbooks present the theoretical foundation of a variety of

flow measurement techniques. References that cover these and other techniques are

included in the bibliography at the end of the chapter. Internet Link 9.8 is also an

excellent resource.

9.7 SEMICONDUCTOR SENSORS AND

MICROELECTROMECHANICAL DEVICES

The advent of wide-scale semiconductor electronic design and manufacturing cha-

nged more than the way we process electronic signals. Many of the techniques devel-

oped for producing integrated circuits have been adapted for the design of a new class

of semiconductor sensors and actuators called microelectromechanical (MEM)

devices. In 1980, the first MEM sensor was developed using integrated circuit tech-

nology to etch silicon and produce a device that responded to acceleration. It consisted

of a tiny silicon cantilever with an integral semiconductor strain gage. Acceleration

deflected the cantilever (due to its inertia), and the strain gage sensed the magnitude

of acceleration. The strain gage and the bar were etched from a single piece of silicon

using the processing methods developed earlier to modify silicon for semiconduc-

tor electronics. MEM accelerometers are now used in automobiles to control airbag

systems. Other common successful applications of MEM sensors include pressure

sensors for automobile tire pressure monitoring systems (TPMS), and accelerometers

and gyros for detecting orientation and motion of video game and TV controllers and

portable electronic devices (e.g., smart phones and cameras).

Internet Lin

9.7Pressure

measurement

techniques and

devices

Internet Lin

9.8Flow

measurement

techniques and

devices

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Figure 9.54 Surface acoustic wave transponder device.

piezoelectric substrate

interdigital transducer reflector grating

antenna

transmitted pulse reflected signal pattern

426 CHAPTER 9 Sensors

ICs are made by a series of processes consisting of photoresist lithographic

layering, light exposure, controlled chemical etching, vapor deposition, and doping

(see Video Demos 5.3 and 5.4). The chemical etching process is important in that

tiny mechanical devices can be created by a technique known as micromachining.

Using carefully designed masks and timed immersion in chemical baths, micromin-

iature versions of accelerometers, static electric motors, and hydraulic or gas-driven

motors can be formed.

Semiconductor sensor designs are based on different electromagnetic proper-

ties of doped silicon and gallium arsenide and the variety of ways that semicon-

ductors function in different physical environments. The following list summarizes

some of the semiconductor properties that are the basis for different classes of semi-

conductor MEMs:

■ The piezoresistive characteristic of doped silicon, the coupling between resis-

tance change and deformation, is the basis for semiconductor strain gages and

pressure sensors.

■ The magnetic characteristics of doped silicon, principally the Hall effect, are

the basis of semiconductor magnetic transistors where the collector current can

be modulated by an external magnetic field.

■ Electromagnetic waves and nuclear radiation induce electrical effects in

semiconductors, forming the basis of light color sensors and other radiation

detectors.

■ The thermal properties of semiconductors are the basis for thermistors, thermal

conductivity sensors, humidity sensors, and temperature sensor ICs.

Surface acoustic wave (SAW) devices are an important class of MEM sen-

sors. A SAW device consists of a flat piezoelectric substrate with metallic patterns

lithographically deposited on the surface. These patterns form interdigital transduc-

ers (IDTs) and reflection coupler gratings as shown in Figure 9.54 . An input sig-

nal applied to an interdigital transducer excites a deformation in the piezoelectric

Video Demo

5.3Chip

manufacturing

process

5.4How a CPU is

made

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Questions and Exercises 427

substrate generating an acoustic wave that propagates on the surface. Conversely, a

SAW wave can induce a voltage in an IDT resulting in an output signal.

Figure 9.54 illustrates a common application of a SAW device: a wireless iden-

tification system. A transmitter sends out a pulse that is received by the passive SAW

device via an antenna. The resulting SAW wave is reflected as a pattern of pulses

unique to the spacings within the reflector grating. The pulses are retransimitted

through the same antenna back to a receiver allowing identification of the SAW

device. This device is commonly used in automatic highway toll booths to identify

vehicles as they pass under a transceiver.

Other applications of SAW devices include delay lines, frequency filters, and

a variety of sensors. Their function depends on the substrate SAW propagation and

resonance and the patterns and spacings of IDTs and reflector gratings.

With the development of so many different semiconductor sensors, engineers

have now begun to integrate sensors and signal processing circuits together in a

hybrid circuit that contains transducers, A/D converters, programmable memory, and

a microprocessor. The complete package provides a micromeasurement system

(MMS) that is small, accurate, and less expensive than a discrete measuring sys-

tem. Distributed micromeasurement systems will be used more and more in future

mechatronic system design.

QUESTIONS AND EXERCISES

Section 9.2 Position and Speed Measurement

9.1. Draw schematics for each switch in Figure 9.4 .

9.2. Show how an SPDT switch can be wired, with a 5 V supply and resistor(s), to pro-

vide a digital signal that is low when the switch is open and high when it is closed.

9.3. Show how an NO pushbutton switch can be wired, with a 5 V supply and resistor(s),

to provide a negative logic (active low) reset signal to a microprocessor. The signal

should be low only while the button is held down.

9.4. Draw a schematic for a DPDT switch and show how it can be wired to switch two

separate circuits on and off.

9.5. Document a complete and thorough answer to Class Discussion Item 9.1.

9.6. Document a complete and thorough answer to Class Discussion Item 9.2.

9.7. Document a complete and thorough answer to Class Discussion Item 9.3.

9.8. You are using a poorly constructed 4-bit natural binary-coded absolute encoder and

observe that, as the encoder rotates through the single step from code 3 to code 4, the

encoder outputs several different and erroneous values. If misalignment between the

photosensors and the code disk is the problem, what possible codes could result dur-

ing the code 3-to-4 transition?

9.9. Document a complete and thorough answer to Class Discussion Item 9.4.

9.10. What is the angular resolution of a two-channel incremental encoder with a 2X

quadrature decoder circuit if the code disk track has 1000 radial lines?

9.11. Write a PicBasic program to perform the functionality in Figure 9.18 .

9.12. Document a complete and thorough answer to Class Discussion Item 9.5.

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428 CHAPTER 9 Sensors

Section 9.3 Stress and Strain Measurement

9.13. Derive Equation 9.9 for a circular conductor instead of a rectangular conductor.

9.14. A new experimental strain gage is mounted on a 0.25 inch diameter steel bar in the

axial direction. The gage has a measured resistance of 120 Ω, and when the bar is

loaded with 500 lb in tension, the gage resistance increases by 0.01 Ω. What is the

gage factor of the gage?

9.15. Document a complete and thorough answer to Class Discussion Item 9.8.

9.16. A steel bar with modulus of elasticity 200 GPa and diameter 10 mm is loaded in ten-

sion with an axial load of 50 kN. If a strain gage of gage factor 2.115 and resistance

120 Ω is mounted on the bar in the axial direction, what is the change in resistance

of the gage from the unloaded state to the strained state? If the strain gage is placed

in one branch of a Wheatstone bridge ( R

) with the other three legs having the same

base resistance ( R

⫽ R

⫽ 120 Ω), what is the output voltage of the bridge

( V

out

) in the strained state, as a function of the excitation voltage? What is the stress

in the bar?

9.17. Document a complete and thorough answer to Class Discussion Item 9.10.

9.18. Draw a schematic diagram illustrating the wiring of a Wheatstone bridge circuit that

takes advantage of both three-wire lead connections and dummy gage temperature

compensation.

9.19. A strain gage bridge used in a load cell dissipates energy. Why? Compare the power

dissipated in a bridge circuit with equal resistance arms for gages of 350 Ω and

120 Ω when the excitation voltage is 10 V. What strategies can one employ if heating

becomes a problem? Do these strategies have any deficiencies?

9.20. Even when we use three-wire connections to a strain gage to reduce the effects of

leadwire resistance changes with temperature, we can have a phenomenon called

leadwire desensitization. If the magnitude of the leadwire resistance exceeds 0.1% of

the nominal gage resistance, significant error can result. Assuming a 22AWG lead-

wire (0.050 Ω/m) and a standard 120 Ω gage, how long can the leads be before there

is leadwire desensitization?

Section 9.4 Temperature Measurement

9.21. Find the approximate sensitivity (in mV/ ⬚ C) of a J-type thermocouple by evaluating

or plotting its polynomial function.

9.22. Find the approximate sensitivity (in mV/ ⬚ C) of a T-type thermocouple by evaluating

or plotting its polynomial function.

9.23. If a J-type thermocouple is used in a standard two-junction thermocouple configura-

tion (see Figure 9.42 ) with a 0 ⬚ C reference temperature, what voltage would result

for an input temperature of 200 ⬚ C?

9.24. If a J-type thermocouple is used in a standard two-junction thermocouple configura-

tion (see Figure 9.42 ) with a 100 ⬚ C reference temperature, what measurement tem-

perature would correspond to a measured voltage of 30 mV?

9.25. Solve Question 9.24 if the reference temperature were 11 ⬚ C instead of 100 ⬚ C with

everything else the same.

9.26. Using a J-type thermocouple with a fixed 0 ⬚ C reference, how much would the volt-

age reading change if the measurement temperature changes from 10 ⬚ C to 120 ⬚ C?

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Bibliography 429

Section 9.5 Vibration and Acceleration

Measurement

9.27. Derive Equation 9.67.

9.28. An accelerometer is designed with a seismic mass of 50 g, a spring constant of

5000 N/m, and a damping constant of 30 Ns/m. If the accelerometer is mounted

to an object experiencing displacement, x

( t ) ⫽ 5 sin(100 t ) mm, find each of the

following:

a. the actual acceleration amplitude of the object.

b. the amplitude of the steady state relative displacement between the seismic mass

and the housing of the accelerometer.

c. the acceleration amplitude, as measured by the accelerometer.

d. an expression for the steady state relative displacement of the seismic mass

relative to the housing as a function of time [x

(t)].

9.29. A spring-mass-damper vibrometer is designed with a seismic mass of 1 kg, a coil

spring of spring constant 2 N/m, and a dashpot with damping constant 2 Ns/m.

Determine an expression for the steady state displacement of the seismic mass x

out

( t )

given an object input displacement of x

( t ) ⫽ 10 sin(1.25 t ) mm.

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430 CHAPTER 9 Sensors

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