23/4/21 [email protected] 1
Chapter 7 Motion and Dimensional Measurement Instruments
Liner Motion Angular MotionDisplaceme
nt
Velocity
Acceleration
Jerk( 冲击量 )
Repetitive displacement-time relationships are called vibration, while a single event may be called a shock. These two fundamentally different events may be measured with the same diagnostics, although the measurement technique may be quite different.
23/4/21 [email protected] 2
Conversion factors for distance
1 inch (in) = 2.540000 centimeter (cm)1 foot (ft) = 12 inches (in)1 yard (yd) = 3 feet (ft)1 mile (mi) = 5280 feet (ft)
23/4/21 [email protected] 3
Conversion factors for velocity
1 mile per hour (mi/h) = 88 feet per minute (ft/m) = 1.46667 feet per second (ft/s) = 1.60934kilometer per hour (km/h) = 0.44704 meter per second (m/s) = 0.868976 knot (knot – international)
23/4/21 [email protected] 4
Chapter 7 Motion and Dimensional Measurement Instruments
A. Motion and Displacement( 运动量和位移量 )
Resistive Potentiometers
a. Ideal Characteristics
Resistive potentiometers are used for two basic functions:
i). Voltage Control (Wheatstone Bridge – variable resistor)
ii. Motion Measurement (linear or angular)
Range ~ 102 – 105 Ohms/inch
23/4/21 [email protected] 5
Resistive PotentiometersDeviations for Ideality
i. Finite Resolution
~ 500 – 1,000 “turns”/inch (20-40 /mm) for typical wire wrapped devices
23/4/21 [email protected] 6
Resistive Potentiometers Deviations from Ideality (cont.)
ii. Loading
Any “reading” device constitutes a “load” on the system which is being read. More specifically, the device draws current, which causes a drop in voltage of the “source” (eo in this case).
In effect, an additional resistance, Rm, is inserted in parallel with the device.
For a voltage divider, the result is:
Note: As RP/Rm 0, eo/eex xi/xt
(“High” input impedence Low i draw)
Note: “Max %” Error ~ 15 RP/Rm
(Text: p. 233)
23/4/21 [email protected] 7
R2
23/4/21 [email protected] 8
23/4/21 [email protected] 9
23/4/21 [email protected] 10
23/4/21 [email protected] 11
Resistive Potentiometers Deviations from Ideality (cont.)
iii. Power Constraints
Since RP is limited (since Rm is typically 106 Ohms), sensitivity is maximized by increasing eex (in order to maximize eo).
However, there are power constraints due to “Joule Heating” (i2R = iV)
PMAX ~ 5 Watts (typically)
which gives
Example
P = 2 WattsRP = 104 Ohmseex, max ~ 150 V (total)
23/4/21 [email protected] 12
Some Pictures of Potentionmetric Displacement Sensors
Linear Motion Rotational Motion
23/4/21 [email protected] 13
B. Resistance Strain Gauge( 电阻应变规 )
Consider a conductor having a uniform cross-sectional area, Ac, and a length, L,
made of a material having a resistivity, . For this electrical conductor,the resistance,R,is given by:
8
23/4/21 [email protected] 14
If the conductor is subjected to a normal stress along the axis of the wire,the cross-sectional area and the length will change,resulting in a change in the total electrical resistance,R. The total change in R is due to several effects,as illustrated in the total differential:Which may be expressed in terms of Poisson’s ratio νp as:
23/4/21 [email protected] 15
The dependence of resistivity on mechanical strain is called piezoresistance. And may be expressed in terms of a piezoresistance coefficient, ( 纵向压阻效应系数 )defined by:
With this definition,the change in resistance may be expressed:
23/4/21 [email protected] 16
Gauge Factor
The change in resistance of a strain gauge is normally expressed in terms of an empirically determined parameter called the gauge factor,GF. It can be expressed as:
The gauge factor is dependent on the Poisson ratio for the gauge material and its piezoresistivity.
23/4/21 [email protected] 17
Semiconductor Strain Gauges
Silicon crystals are the basic material for semiconductor strain gauges; the crystals are sliced into very thin sections to form strain gauges.
* In general,materials exhibit a change in resistivity with strain,characterized by the piezoresistance coefficient,
23/4/21 [email protected] 18
R1 R2
R3 R4
E1
E0
A simple strain gauge Wheatstone bridge circuit is shown in right FIGURE.
Consider the case all the resistors are equal,and the bridge balanced,if the gauge experiences a change in resistance ,then
23/4/21 [email protected] 19
EXAMPLE
A strain gauge,having a gauge factor of 2,is mounted on a rectangular steel bar( ),as shown in Figure. The bar is 3cm wide and 1cm high,and is subjected to a tensile force of 30kN. Determine the resistance change of the strain gauge. If the resistance of the gauge was 120 in the absence of the axial load.
23/4/21 [email protected] 21
KNOWN: GF=2 ; FN=30kN ;
FIND: The resistance change of the strain gauge for a tensile force of 30kN.
SOLUTION:The stress in the bar under this loading condition is:
And the resulting strain is
23/4/21 [email protected] 22
For strain along the axial of the strain gauge,the change in resistance is:
23/4/21 [email protected] 23
Linear Variable Differential Transformer(LVDT)
Basic Principlesa. AC current flows through “primary” coil, due to excitation voltage eex.b. Current is “induced” through a pair of secondary coils (eo1, eo2).c. The frequency of the induced AC current is the same as the excitation
frequency.d. The amplitude of the induced current in each secondary coil depends upon
the location of the movable “core”.
23/4/21 [email protected] 24
Ferromagnetic Core
Core
x
vo
(Measurement)
vref
Primary Coil
Insulating Form
Secondary Coil Segment
Secondary Coil Segment
An LVDT transducer shown in FIG comprises a coil former on to which three coils are wound.
The primary coil is excited with an AC current, the secondary coils are wound such that when a ferrite core is in the central linear position, an equal voltage is induced in to each coil.
The secondary are connected in opposite so that in the central position the outputs of the secondary cancels each other out.
23/4/21 [email protected] 25
LVDT Basic Principle (cont).If core is located in “null” position then secondary voltages are equal, as illustrated below.
23/4/21 [email protected] 26
LVDT Basic Principles (cont.)If the two secondary coils are connected in anti-series (+ + and - -) then the resulting output is the difference between the outputs of the individual seconary coils. The amplitude depends upon the position of the rod.
(There is also a Phase shift between eex and eo as we will show later)
23/4/21 [email protected] 27
LVDT As Displacement Sensor
The input, xi, is the MOTION of the rod to which the core is connected.
The output, eo, is the voltage difference between the induced voltages in the two secondary loops.
Note: The output is inherently AM modulated
(The “carrier” is AC excitation of the primary loop).
Note: Phase Shift occurs as xi crosses “null” point
23/4/21 [email protected] 28
LVDT – Simulated Output (lvdtsim01.dsb)
Generator00
FFT00Formula00
Y/t Chart00
Generator01
Y/t Chart01
ms25 50 75 100 125 150 175
1.000.750.500.250.00
-0.25-0.50-0.75-1.00
5.0
2.5
0.0
-2.5
-5.0
Hz250 500 750 1000 1250 1500 1750 2000 2250
0.90.80.70.60.50.40.30.20.10.0
2.252.001.751.501.251.000.750.500.250.00
xi
eo
23/4/21 [email protected] 29
More Accurate LDVD Simulation (lvdtsim02)
xi
eo,1
eo,2
eo
ms25 50 75 100 125 150 175
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
-0.75
23/4/21 [email protected] 30
A Closer Look at the LVDT Output
ms5 10 15 20 25 30 35 40 45 50 55 60 65 70
Y/t Chart 0
1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
(Note Phase Shift at Null Point)
23/4/21 [email protected] 31
How Do We Recover the LVDT Signal?
l(vdtsim03.dsb)
ms25 50 75 100 125 150 175
1.00
0.00
-1.00
1.00
-0.75
4
0
-4
1.5
0.0
-1.5
Motion
LVDT output
Demod LVDT
Recovered Motion
23/4/21 [email protected] 32
LVDT Signal Recover – Frequency Domain
Motion
LVDT output
Demod LVDT
Recovered Motion
Hz250 500 750 1000 1250
Y/t Chart 0 Y/t Chart 1
Y/t Chart 2 Y/t Chart 3
0.8
0.4
0.0
0.35
0.00
1.25
0.00
1.25
0.00
23/4/21 [email protected] 33
The DasyLab ProgramGenerator00
Generator01
1Formula00 Y/t Chart00
Formula00
Y/t Chart01
Generator02Formula01
Filter00
FFT00 Y/t Chart02
23/4/21 [email protected] 34
LVDTs – Some Math(Where does the Phase shift come from?)
23/4/21 [email protected] 35
Bandwidth of LVDT (Demodulation)
The “transfer function” derived previously describes the sensitivity of the output signal to the Excitation frequency of the Primary Loop
(NOT the frequency response to input motion!!)
The frequency response to input motion is dictated by the requirement to Demodulate the signal.
Let’s look at this in more detail.
23/4/21 [email protected] 36
Modulation/Demodulation
SignalS
Input Signal s (t)
Carrier c (t)
Demodulated Output
2 C + S
S
2C - S
S
Carrier c (t)
Amplitude Modulation Process
Amplitude Demodulation Process
Output
Primary Loop Excitation
C
LVDT Transducer AM OutputC + S
C - S
23/4/21 [email protected] 37
Frequency Domain Picture(Fill in in Class)
We need to filter demodulated output such that we transmit at s and attenuate at 2c z
23/4/21 [email protected] 38
Some Examples (Worked in Class)
Example 1: Single Stage RC filter
c = 10 KHz (a typical value)
What is Maximum frequency of motion that can be detected with LVDT?
(Lets verifty our conclusion with DaisyLab)
23/4/21 [email protected] 39
Piezoelectric Materials - Intro Piezoelectricity describes the phenomenon of generating an electric
charge in a material when subjecting it to a mechanical stress (direct effect) and conversely generating a mechanical strain in response to an applied electric field.
Discovered in 1880 by Pierre and Jacques Curie Types
Natural and Synthetic Crystals ( 单晶压电晶体 ): Quartz, Rochelle Salt (Natural)( 石英、罗歇尔盐(四水酒石酸钾
钠) ) Lithium Sulfate, Ammonium Dihydrogen Phosphate (Synthetic) ( 硫酸锂、磷酸二氢铵 )
Piezoceramic elements( 多晶压电陶瓷 ) Lead Zirconate Titanate (PZT)( 锆钛酸铅 ) Barium Titanate ( 极化的铁电陶瓷(钛酸钡) ) , Cadmium Sulfide
Piezoelectric Polymer ( 高分子压电薄膜 ) Polyvinylidene Fluoride (PVDF)
23/4/21 [email protected] 40
Piezoelectric Materials Piezoelectric materials belong to a class of materials called
Ferroelectrics. Piezoelectric Crystals exhibit the piezoelectric effect naturally, without any processing.
Piezoelectric Ceramics must be polarized by applying a strong electric field to the material while it is simultaneously heated. They are (isotropic) before poling and after poling exhibit tetragonal symmetry (anisotropic structure) below the Curie temperature. Above this temperature they lose the piezoelectric properties.
On a microscopic level the materials are made of ions which is the reason for electric dipole behavior. Groups of dipoles with parallel orientation are called Weiss domains. The Weiss domains are randomly oriented in the raw ceramic material, before the poling treatment has been finished. For this purpose an electric field (> 2000 V/mm) is applied to the (heated) piezo ceramics.
When an electric voltage is applied to a poled piezoelectric material, the Weiss domains increase their alignment proportional to the voltage. The result is a change of the dimensions (expansion, contraction) of the PZT material.
23/4/21 [email protected] 41
Piezoelectric Materials (PZT)
Unpolarized Crystal
Polarized Crystal
After poling the zirconate-titanate atoms are off center. The molecule becomes elongated and polarized
(1) Unpolarized- Random Weiss Domains
(2) During Polarization(3) After polarization; Remnant
Polarization exist
23/4/21 [email protected] 42
石英晶体是常用的压电材料之一。其中纵轴 Z—Z 称为光轴, X—X 轴称为电轴,而垂直于 X—X轴和 Z—Z 轴的 Y—Y 轴称为机轴。沿电轴 X—X 方向作用的力所产生的压电效应称为纵向压电效应,而将沿机轴 Y—Y 方向作用的力所产生的压电效应称为横向压电效应。当沿光轴 Z—Z 方向作用有力时则并不产生压电效应。
石英晶体
( a )左旋石英晶体的外形 ( b )坐标系 ( c )切片
23/4/21 [email protected] 43
Piezoelectric Materials - Intro
Applications: Mechanical to Electrical
Force, Pressure, and acceleration sensors Smart Sensors for Side Impact Diagnostics High Voltage - Low Current Generators: Spark Igniters for Gas
grills, small engines, etc. Yaw Rate( 偏航角速度 )Sensors Platform Stabilization Sensors
Electrical to Mechanical: Ultrasonic motors, Small Vibration Shakers Microactuators (High Precision Macro actuators) Sonar( 水声测位仪 ) array arrays for collision avoidance Pumps for Inkjet Printers
23/4/21 [email protected] 44
Actuator Types
Actuators are sometimes called motors Sensors are called generators
Bimorph (bending) Bimorph (extension)
Longitudinal Wafer
Transverse Wafer
Stack Actuator
23/4/21 [email protected] 45
Actuator Types Longitudinal and Transverse Wafers: When an electrical field having
the same polarity and orientation as the original polarization field is placed across the thickness of a single sheet of piezoceramic, the piece expands in the thickness or "longitudinal" direction (i.e., along the axis of polarization) and contracts in the transverse direction (perpendicular to the axis of polarization). Reversing the field reverses the effect.
Unimorphs: A unimorph is a single -layer piezoelectric element bonded to shim stock. They can be made to elongate, bend, or twist depending on the polarization. Electrode pattern and wiring configuration of the layers. The shim laminated between the two piezo layers adds mechanical strength and stiffness and amplifies motion in bending.
Bimorphs: Two -layer elements can be made to elongate, bend, or twist depending on the polarization and wiring configuration of the layers. A center shim laminated between the two piezo layers adds mechanical strength and stiffness, but reduces motion.
Stack Actuators: Stack actuators can be formed when a large number of piezo layers (wafers) are combined into one monolithic structure. The tiny motions of each layer contribute to the overall displacement.
23/4/21 [email protected] 46
Piezoelectric Coordinate System
The behavior of the materials are defined by the g and d constants. For the piezoelectric constants gij and dij, the first value (i) in the
subscript represents the axis of initial polarization. This is usually the axis that the electrodes are parallel to. The second value (j) relates to the mechanical axis or the axis or applied stress or strain.
g33 or d33 (which we will now define as g)
g31 or d31
23/4/21 [email protected] 47
Piezoelectric Coefficient g(Piezoelectric Pressure Transducers)
t = thicknessw = widthL = length
eo = Potential Difference Developed (V)F = Force (normal to LW plane)
23/4/21 [email protected] 48
g coefficient (cont.)
Example: (worked in class)
Quartz pressure transducer
t = 1 mmF/Area = 106 Pascals (N/m2)
eo =
23/4/21 [email protected] 49
Piezoelectric d Coefficient
Piezoelectrics are fundamentally charge-based devices
(Application of stress results in charge separation)
23/4/21 [email protected] 50
A Digression on Parallel Plate Capacitors
In General,
lCl = an appropriate length scaleC = capacitance = permittivity of medium (Farads/m)
o
dielectric constant (dimensionless)
For a parallel plate capacitor:
εwL
t
CQ
e
C
Qe
100
(text calls the “dielectric constant”)
23/4/21 [email protected] 51
Back to Piezos
For quartz, ~ 4 x 10-11 (farads/m) (very small!!)
(This means that small charge separation results in large voltage!)
We will show in class that:d = g
So for quartz:
(Note: farads x volts = Coulombs)
(2 picocoulombs / Newton
23/4/21 [email protected] 52
Displacement to Voltage (displacement transducer / actuator)
The Charge generated by a deformed crystal is given by:
Kq = Constant, C/m xi = deflection, cm
(4.63)
(Note: text notations changes from Q to q)
e0 = q/C so that eoC = q = Kqxi
Where Kq/C is defined as K, the static sensitivity (Volts/cm)
K ~ 10 – 100 V per 10-6 meters (or ~ 10 nm / Volt!!)
23/4/21 [email protected] 53
A Few Summary Notes
Piezoelectric transducers are inherently charge devices. Input displacement results in charge separation between
faces.
iqxKq
• Charge is related to output voltage by means of:
(K =Kq/C is the “static” sensitivity)
• Charge eventually “leaks” off due to internal resistance
23/4/21 [email protected] 54
A Few More Additional Summary Notes
Because the piezo is based on charge, capacitance is of fundamental importance.
Ccr ~ 10-9 farads
(This is rather high, but not so high that we can ignore capacitance of other system components)
• The internal resistance is very high (Rleak ~ 1011 ohms). For this reason resistance of other system elements (cables, amplifiers, meters, etc.) is of fundamental importance.
Let’s look at this a bit more??
23/4/21 [email protected] 55
Displacement to Voltage Measurement
The voltage generated by a deformed crystal is
Fig 4.40
But we MUST consider the capacitance of the ENTIRE MEASUREMENT SYSTEM!
(We will also need to consider the effective impedance of the entire system, as we will see shortly)
23/4/21 [email protected] 56
Example – Sensitivity (K)
A piezoelectric transducer has a Kq value of 10-5 C/inch
and an internal capacitance of 10-9 F.
What is the “static” sensitivity, K, of the transducer alone?
If the transducer is part of a measurement system in which
i. Ccable = 300 pFii.Camplifier = 50 pF
What is K for the system?
23/4/21 [email protected] 57
Piezoelectrics – Frequency Response
The Charge generated by a deformed crystal is
Kq = Constant, C/m
xi = deflection, cm
Fig 4.40
From figure 4.40 e
4.63
4.66
4.67
4.68
23/4/21 [email protected] 58
Displacement to Voltage Measurement – Dynamic Response
Taking the derivative of (68) and subbing in (66) gives (after a bit of manipulation, which we will do in class)
cm/V ,C
KysensitivitK q s ,RC
4.70
4.69
(or in “s” notation)
23/4/21 [email protected] 59
Time Domain – Step / Pulse Inputs
Step Input
At t = 0, eo = AK (Input “steps” to a finite value, xi, resulting in voltage output)
Pulse Input
At t = 0, eo = AK (Input “steps” to a finite value)
At t = T eo (Input steps to –xi)
23/4/21 [email protected] 61
Piezo Dynamic Response – Frequency Regime
Lets Return to eqn. (4.70) 1
s
sKs
x
e
i
21
K
)(x
e
i
o 190 tan
23/4/21 [email protected] 62
Sensitivity – Bandwidth Trade off
We mentioned previously that increasing the bandwidth (frequency range) of an instrument often requires that the sensitivity be decreased. Consider the magnitude of the frequency response.
where
To Increase Bandwidth we need to increase which generally means we need to increase C. (Why not increase R?)
But
So Increasing C decreases K!!
23/4/21 [email protected] 63
An Example – Static/Dynamic Sensitivity
Problem
A piezoelectric transducer has a capacitance of 1,000 pF and Kq of 10-5 C/in. The connecting cable has a capacitance of 300 pF while the oscilloscope used for readout has in input impedance of 1 M paralleled with 50 pF.
a. What is the sensitivity (V/in) of the transducer alone?b. What is the high-frequency sensitivity of the total system.c. What is the lowest frequency that can be measured with 5%
amplitude error.d. What value of C must be connected in parallel to extend the
range of 5% error down to 10 Hz.e. If the value of C in part d is used, what will the system high-
frequency sensitivity be?
23/4/21 [email protected] 64
Ccr= 1,000 pF , Kq =10-5 C/in ,Ccable= 300 pF , Rample=1 M Cample= 50 pFC=Ccr+Ccable+Cample=1000+300+50=1350pF ,R=Rample=1M
23/4/21 [email protected] 65
Seismic Transducers
A seismic transducer consists of two basic components:i. Spring – Mass – Damper Elementii. Displacement Transducer
(MS Fig 4.77)
(Note: xo = xi – xM)
23/4/21 [email protected] 66
Seismic Transducers – Acceleration Sensor
Let’s explore the dynamic response of the spring-mass-damper element alone.
Noting the sign conventions in Fig. 4.77, we have, from Newton’s second law for the motion of mass M, xM:
oioosM xxMxBxKxMF (Where xM = xi – xo)
(A classic 2nd Order System)
We define (again)
With the result
23/4/21 [email protected] 67
Seismic Transducer – Acceleration (cont).
Let’s associate the following:
ii xq
oo xq
21
n
K
Input is object accelerationOutput is relative displacement of M and objectStatic Sensitivity (sec2)
Classic 2nd Order System
23/4/21 [email protected] 68
Seismic Accelerometer – Freq. Responce
23/4/21 [email protected] 69
Seismic Accelerometer – Freq Response (cont)
Question:Over what range of frequencies can we
actually use a seismic accelerometer?
Answer: To be most useful we desire a “flat”
frequency response and a “linear” phase shift. In other words, we need
i. SIG << n
ii. ~ 0.4 – 0.6
But recall that
23/4/21 [email protected] 70
Seismic Accelerator – “Readout”
The previous discussion ignored the response of the displacement sensor used to measure xo!!
We need to consider this!RECALL
System 1
qi,1 System 2
qi,2 qo,1
qo,2
23/4/21 [email protected] 72
Acceleration-measuring transducers (accelerometer)
10-2
10-1
100
10110
-3
10-2
10-1
100
101
n /
0
20
un
Directly proportional region between ü0 and 0
Best value of for accelerometer = 0.65
Accelerometer gives accurate result when forcing frequency is 60% less than natural frequency.
Accelerometer must have relatively very large natural frequency
23/4/21 [email protected] 73
Weakness of high natural frequency
10-2
10-1
100
10110
-3
10-2
10-1
100
101
n /
0
20
un
For a given value of u0, the relative displ. is directly proportional to 1/n2 .
So, high natural freq. makes electric signal very small.
Large amplification is needed.
System will be very sensitive.
We must compromise between high sensitivity and the highest attainable natural frequency.
23/4/21 [email protected] 74
Accelerometer requirement for shock Accelerometer must have relatively low natural period:
The response of accelerometer follows up the pulse most faithfully when the natural period of the accelerometer is smallest relative to the period of the pulse.
Accelerometer must have sufficient damping: Damping in the transducer reduces the response of the
transducer.
Accelerometer must have low zero shift as possible: Zero shift is the displacement of zero reference line due to
intense shock involving zero frequency.
23/4/21 [email protected] 75
Important Characteristics of Accelerometer Sensitivity
Ratio of its electrical output to its mechanical input Parameters used in checking sensitivity:
Average, rms, peak
Resolution Smallest change in mechanical input for which a change in the
electrical output is discernible Resolution can be limited by noise levels in the instrument.
23/4/21 [email protected] 76
Transverse sensitivity Coordinate transformation can be applied in sensitivity.
where e is output voltage
Amplitude linearity and limits A transducer is linear only over a certain range of
amplitude values. The lower end of this range is determined by the electrical
noise. The upper end of linearity imposed by the electrical
characteristics of the transducing element.
cosmaxee
23/4/21 [email protected] 77
Frequency range
Lower frequency limit
frequency
ampl
itude
peak-to-peak displ.ac
celer
ation
Upper frequency limit
Maximum acceleration
Minimum acceleration
Maximum displacement
Operating range
23/4/21 [email protected] 78
Environmental effect
Temperature The sensitivity, natural frequency and
damping can be affected.
Humidity A transducer which operated at a high
electrical impedance is affected by humidity.
23/4/21 [email protected] 79
Acoustic noise High-intensity sound wave often
accompany high-amplitude vibration.
Strain sensitivity Accelerometer may generate a
spurious output when its case is strained or distorted.
Typically, this occurs when the transducer mounting is not flat against the surface.
23/4/21 [email protected] 80
Physical properties
Size and weight of transducer are very important considerations.
A large instrument may require a mounting structure. it changes local vibration, so it can be treated as added mass.
The smaller is the transducer, the higher is its sensitivity.
23/4/21 [email protected] 81
Piezoelectric Accelerometer
Principle of operation
mass
Electrical output
Piezoelectric element
Mechanical input (Vibration)
23/4/21 [email protected] 82
Typical response curve
frequency
Ou
tpu
t vo
ltag
e
Low frequency
limit
High frequency
limit
Usable frequency
range
23/4/21 [email protected] 83
Determination of acceleration
we can determine acceleration in low frequency region before resonance frequency.
10-2 10-1 100 10110-3
10-2
10-1
100
101
n /
0
20
un
frequency
Ou
tpu
t vo
ltag
e
23/4/21 [email protected] 84
Types of piezoelectric accelerometers
Compression type
mass
Piezoelectric element
baseoutput
23/4/21 [email protected] 86
Beam type
+
-
Tension part
Compression part
Two piezoelectric plates which are rigidly bonded together
23/4/21 [email protected] 87
Piezoresistive Accelerometers
Principle of operation
mass
beam
Piezoresistive element
• semiconductor material
• change its resistance in proportion to applied stress or strain
• connected electrically in a Wheatstone-bridge circuit
23/4/21 [email protected] 88
Seismic Accelerometer
ii. Piezo Readout
“Usable” range
depends upon
damping
23/4/21 [email protected] 89
reflecting surface
displacement to check
check intensity
fibercheck intensity
Fiber-optic displacement sensor
23/4/21 [email protected] 90
Electrodynamic(velocity coil) pickups
uses Lenz’s law. Blve
NS S
edirection of motion
23/4/21 [email protected] 91
Eddy Current TransducersPrinciple of Eddy current:
An eddy current is caused by a moving magnetic field intersecting a conductor or vice-versa.
The relative motion causes a circulating flow of electrons, or current, within the conductor.
These circulating eddies of current create electromagnets with magnetic fields that oppose the change in the external magnetic field.
The stronger the magnetic field, or greater the electrical conductivity of the conductor, the greater the currents developed and the greater the opposing force.
This principle is used in eddy current proximity sensor
FIG illustrates concept of Eddy current FIG
23/4/21 [email protected] 92
Eddy current proximity sensor The Eddy Current Transducer
uses the effect of eddy (circular) currents to sense the proximity of non-magnetic but conductive materials.
A typical eddy current transducer contains two coils: an active coil (main coil) and a balance coil as shown in FIG
The active coil senses the presence of a nearby conductive object, and balance coil is used to balance the output bridge circuit and for temperature compensation.
FIG
23/4/21 [email protected] 93
Schematic diagram of eddy current proximity sensor
•Active coil and compensating coil forms arms of inductance bridge.
•When a measurand brought to near to active coil, due to eddy current which produces eddy current magnetic field that opposes active coil field causes change in inductance and thus creates imbalance in inductance bridge.
•This change is noted in calibrated unit.
23/4/21 [email protected] 94
Accelerometer Calibration
1) Static
a) Plus or minus 1 g turnover method
b) Centrifuge method
2) Steady-state periodic
a) Rotation in a gravitational field
b) Using a sinusoidal shaker or exciter
3) Pulsed
a) One-g step, using free fall
b) Multiple Spring-mass device
c) High-g methods.
23/4/21 [email protected] 95
1. Static Calibration
Plus of minus 1g
You can calibrate an accelerometer through ±1g by simply putting it upright, and then rotating it exactly 180º.
Centrifugal Method
In a rotating situation, the normal acceleration is
Axis of rotation is vertical
an r2 r 2f 2
23/4/21 [email protected] 96
Steady-State Periodic CalibrationRotation in a gravitational field
Same as centrifugal, but axis of rotation is horizontal
Sinusoidal Vibrational Exciter
23/4/21 [email protected] 97
Pulsed CalibrationFree-Fall Method
If suspend the accelerometer and suddenly drop it, it experiences a step change in acceleration of 1g.
High-g Methods
23/4/21 [email protected] 98
Seismic Displacement
How about a seismic displacement transducer?
(We’ll let you do this one as homework).
23/4/21 [email protected] 99
Capacitance Transducers
Consider a basic parallel plate capacitor, with
C = Capacitance (pF)A = Plate Area (in2)x = Plate Separation (in)If either x or A are changed, then C will change!!
23/4/21 [email protected] 100
Basic Capacitance Transducer Geometries
Linear Motion Rotational Motion
Typical Capacitance Values
23/4/21 [email protected] 101
Capacitance Transducers – Signal Conversion
Capacitance is not easy to measure directly. We need to convert “signal” to current or voltage.a. AC Voltage ApproachWe apply a constant amplitude AC voltage, Vex, at = ex
This will result in a variable amplitude AC current at ex
Let’s Work This Out!
23/4/21 [email protected] 102
Capacitance Transducers – C to I ConversionV(t) = q(t)/C(t)q(t) = C(t)V(t)
IF we apply an AC Voltage with 1/ex which is short as compared to time scales for the change in displacement to be measured, then C can be considered approximately constant, so that:
dt
dVC
dt
dqI ex Or (taking LaPlace
transform)
Note: This approach is most useful for transducers in which xi modifiers A (the plate Area) Why??
23/4/21 [email protected] 103
Capacitance Transducers – Signal Conversion
b. AC Current Approach
We apply a constant amplitude AC current, Iex, at = ex
This will result in a variable amplitude AC Voltage at ex, eo
Let’s Work This Out!
Note: This approach is most useful for transducers in which xi modifiers the gap (x).
Why??
23/4/21 [email protected] 104
Signal Conversion – AM Modulation
Of course in either of the last two cases, the actual signal is AM modulated (Carrier Frequency = ex
MS Fig 4-37c
23/4/21 [email protected] 105
Signal Recovery – Current Measurement
A good approach to convert current to voltage is to use an Operational Amplifier as shown below
iai ~ 0
if + ix = 0
23/4/21 [email protected] 107
One Final Note
This configuration is best for transducers in which gap is varied. (because Cx 1/x so that eo varies linearly with xi)
Alternatively, we can exchange the positions of Cf and Cx, giving Best for transducers in
which Area is varied. (because Cx A so that eo again varies linearly with xi)
23/4/21 [email protected] 108
Elastic element methods
Sensors that are used for measurement of force, torque or pressure often contain an elastic element that converts the mechanical quantity into a deflection or strain which can then be transformed using another sensor into an electrical signal. Electrical resistance strain gauges are widely used in this capacity.
23/4/21 [email protected] 109
Diagram of strain gauge
23/4/21 [email protected] 110
Various forms of elastic members are used. The simplest is just a spring to make a device called spring balance. The extension of the spring represents the force applied.
Load cells, i.e. elastic members which transform force into displacement or strains, can take many forms .
23/4/21 [email protected] 111
The structure of typical elastic element and its designing calculation as follows:
Columnar load cell
23/4/21 [email protected] 113
The relative extension of strain gauge in elastic element :
l F
l AE E
Δl-------Total extension of strain gauge
l--------the original length of strain gauge
F------applied force
A------working area of elastic element
E------Yang model of elastic element
σ------stress of elastic element
23/4/21 [email protected] 114
Sensitivity : / /
/
R R R Rk
l l
31
1 3
2 4
2 4
RR Fk k
R R AE
R R Fk k
R R AE
----poison constant of elastic element
Total strain of elastic element:
0 1 2 3 4
2(1 )F
AE
23/4/21 [email protected] 115
Output of electrical bridge: 0
00
(1 )
2(1 )
2 4
i
i
U kU F
AEU k k
FU AE
Voltage sensitivity(mv/v):
0 1 2 3 4
2(1 )2(1 )F
AE
•In general, select k=2
23/4/21 [email protected] 116
An Introduction to Optical Detectors and CCD Cameras
I. The Photoelectric Effect
In 1887, Heinrich Hertz discovered that illuminating a metal surface with ultra-violet (UV) light ( < ~ 350 nm) caused electrons to be emitted from surface.
This is termed the photoelectric effect and was puzzling for two reasons.
i. The kinetic energy of ejected electrons was independent of light intensity.
ii. The effect ONLY occurred if the wavelength of light was LESS than a threshold value, which was different for different metals. (It also did NOT depend upon light intensity)
23/4/21 [email protected] 117
Einstein’s Explanation(for which he won the Nobel Prize)
hcvmEnergyKineticElectron e
2
2
1
(where is termed the “work function” of the metal)
Einstein, of course, was aware of the work of Planck in the area of Blackbody Radiation
Planck proposed (in late 19th century) that the energy of a light “photon” was equal to:
where h is now known as “Planck’s Constant”
(Note: Planck supposedly did not actually believe his theory, but it was the only way he could “fit” the data)
Einstein applied this idea to Hertz’s observation by stating that:
23/4/21 [email protected] 118
Illustration of Photoelectric Effect
(and Einstein’s Explanation)
hcKE
23/4/21 [email protected] 119
Photoelectric Effect – A Simple Example
When a lithium surface is irradiated with light the kinetic energy of the ejected electrons is found to be:
i) 2.935 x 10-19 Joules if = 300 nm
ii) 1.280 x 10-19 Joules if = 400 nm
Calculate
a. Planck’s Constant
b. The Threshold Frequency (and wavelength) for electron ejection
c. The work function
23/4/21 [email protected] 120
II Photodiode Detectors
Photodiodes (such as the one used in Lab 6) are semiconductors (usually silicon) in which absorption of a photon with h exceeding the work function results in the creation of an “electron – hole” pair.
If a potential difference (voltage bias) is applied across the interface of “p” and “n” type material, then the electrons will drift across the junction, creating a current.
This current is detected by the voltage drop across a “load” resistor.
The PE effect is basis for most optical detectors(Some thermal - passive solar hot water heater)
23/4/21 [email protected] 121
Photodiodes – Some Circuit Details
Photodiode Equivalent Circuit - “Conductive” Mode
23/4/21 [email protected] 122
Photodiode Sensitivity(Quantum Efficiency)
Silicon
Indium Gallium Arsenide(“InGas”)
23/4/21 [email protected] 123
Sensitivity – Bandwidth Trade-off
Photodiodes are fundamentally current devices, so that the static sensitivity is often given in units of:
Example: Typical laser pointer has output power of ~ 3 mWatts ( ~ 700 nm)Output current detected on photodiode is ~ 1 mamp (0.33 mamp/mWatt)
The detector output Voltage depends upon the load resistor.
i. 103 ohms 1 Voltii. 106 ohms ?? Volt (Detector “saturates” at ~ 5 Volts)
What about Bandwidth??
23/4/21 [email protected] 124
An Example: Laser Doppler Velocimetry
sindp
2
If two laser beams are crossed, an interference fringe pattern (of low and high intensity) are formed. (This occurs because laser beams are coherent).
The fringe spacing, dp, is given by:
If individual particles, seeded into the flow, traverse through the fringe pattern, they scatter light with an intensity which is amplitude modulated by the fringe pattern. The modulation frequency is:
sin
dp
vd
2 v = velocity
23/4/21 [email protected] 125
III. CCD Cameras*
(* Material taken from “Charge Coupled Devices and Their Applications,” J. Beynon and D. Lamb, McGraw-Hill, 1980)
CCD stands for “Charge Coupled Device”
It consists of a two-dimensional array of “pixels” which can be though of as micro scale (~ 5-10 microns) capacitors which store electrons in a “potential well”.
Each individual pixel has an optically sensitive surface, which is similar to a small silicon photodiode. Electrons are “ejected” at a rate proportional to the incident flux of photons.
However, “ejected” photo-electrons are temporarily trapped beneath the surface in a spatially localized area, and then read out using a set of shift registers.
23/4/21 [email protected] 126
Sensitivity vs Bandwidth (Again)
In class we have always described “bandwidth” in terms of temporal behavior
Freq = 1/time (sec-1)
However
In imaging applications we often consider “spatial frequency”
Spatial Frequency = 1/spatial resolution (m-1).
High spatial resolution means that we can resolve high spatial frequencies or “sharp” edges.
CCD cameras increase number of “Mpixels”) by decreasing their physical size!!
Higher spatial frequency comes at the cost of lower sensitivity because smaller pixels cannot store as much light!
23/4/21 [email protected] 127
CCD – How is Charge Stored?
CCD “Potential Wells” Formed by Application of “Gate” Voltage to Array of Pixels Each With Discrete Electrode.
• + Voltage repels “holes” near surface forming “depletion” layer• Ejected photoelectrons fill top portion, termed “Inversion Layer”
23/4/21 [email protected] 128
CCD – How is Charge “Coupled” Out?
• With all “gates” up, charge fills potential wells as surface irradiated.• After suitable “exposure” time, charge sequentially shifted through a series of
clocking pulses.• Depending upon chip architecture, charge is shifted over, up, and out (output
port)• A/D conversion performed on charge sequence.
23/4/21 [email protected] 129
More Realistic Picture of Charge Coupling
23/4/21 [email protected] 130
Interline Transfer Architecture
23/4/21 [email protected] 131
Frame Readout by “Frame” Transfer