7. Transduction Based on Changes in the Energy Dissipated
reversible transduction (previous chapters)
energy storage (capacitive, inductive transduction) energy transformation (linear magnetic transduction) mechanical input → electrical signal
or electrical input → mechanical signal : irreversible transduction (this chapter)
energy dissipation (
mechanical input → electrical signal : basic types
material properties
thermoresistivity = coupling between piezoresistivity = coupling between
thermoelectricity = coupling between thermal and electrical behaviors (§7.6) geometrical coupling
potentiometer : geometrical coupling between mechanical and electrical domains (§7.3) others : electrical switches(§7.1), resistance changes(§7.2)
magnetoresistivity (§7.7), shape memory alloys (§7.8)
7.1 Conductive Switches
dramatic shift between two states nearly infinite resistance → nearly zero resistance → behave like digital devices
modeled as a nonlinear, multiport resistance element at least one mechanical port +
two general classes
1. motion of some component either pushes the button of a switch or forces electrodes into (or out of) contact.
2. a set of electrodes is fixed and a conductive material moves to connect or disconnect the electrodes.
Examples
- pressure switch Fig. 7.1 Fig. 7.3 - liquid level switch Fig. 7.4 - acceleration/tilt switch Fig. 7.5
7.2 Continuously Variable Conductivity Transducers
provide resistance information on a continuum scale produce a change in resistance due to
1. a change in the medium between ex.1 liquid level sensor
correlating liquid level with the resistance ex.2 liquid or gas detector
distinguishing the resistivity substantially different from the normal medium or
2. a change in the distance between Examples
- carbon button microphone Fig. 7.6 - tunneling displacement transducer Fig. 7.8 - humidity sensor Fig. 7.9
Fig. 7.10
7.3 Potentiometric Devices
linear conversion from a mechanical signal to an electrical signal slide displacement →
simple model of a potentiometer (Fig. 7.11) supplied input voltage in (fixed)
monitored output voltage ou t : voltage drop across the measurement resistor or across
total electrical resistance + (fixed) >>
in
ou t
=
(5)
∵ ou t = ′ = ′ (2)
⇒ =
′ ≈ ′ (3)
in = ′ (1)
≈ ′ =
ou t
measurement
translational position
=
⇒ in
ou t
= (5)
angular position (Fig. 7.12)
= tot
⇒ in
ou t
= (6)
tot : total angular extent of the resistance potentiometer
advantage
disadvantages
low sensitivity wear due to
(can be overcome through innovative use of materials) Examples
- attitude transducer Fig. 7.13 - position sensor Fig. 7.14
7.4. Piezoresistivity
electrical resistance is a function of the mechanical property ( applications : strain gauge (piezoresistivity +
pressure sensor, load cell 7.4.1 material description
change in electrical resistance due to
1. geometric effect (change in the length and cross-sectional area) (§7.4.2) 2. piezoresistivity (change in the resistivity of a
change in resistivity
=
=
(8)
: resistivity, : strain, : stress
: elastoresistance coefficients, : coefficients (Table 7.1) piezoresistive effect
for an isotropic material or a cubic crystal =
if hydrostatic pressure = = = resistivity change
= + + = (10) volume change
=
= ≈ if << 1 (11)
= (12)
piezoresistive sensitivity
=
=
=
(13)
if uniaxial strain
= , = = ( : Poisson's ratio) (14) in the longitudinal direction (the direction of strain)
= - - = = (15)
= : longitudinal elastoresistance coefficient in the transverse directions (the direction normal to the strain)
= - - = = (16)
= : transverse elastoresistance coefficient values of , in Table 7.2
the needs of a specific application tend to dictate the material choice
7.4.2 strain gauge structures
change in electrical resistance due to
1. geometric effect (change in the length and 2. piezoresistivity (change in the resistivity of a gauge factor,
≡ (fractional increase in resistance)/(fractional increase in length) (17)
=
electrical resistance =
(18)
: length, A : cross-sectional area (Fig. 7.15)
=
-
+
=
-
+
(20)
= :
=
≈ (21)(22)
= : piezoresistivity contribution (15)
⇒
= + + = (23)
=
=
+ (24)
: dimensional change of the conductor
:
metals ( = 0.3) 0.1 ≤ ≤ 3.8 1.7 ≤ ≤ 5.4 Si, Ge (highly piezoresistive materials) 70 ≤ ≤ 135 cermets (ceramic-metal mixtures) 5 ≤ ≤ 50
piezoresistive strain gauges
made of semiconductors such as advantages
- high sensitivity (
- small dimensions of 0.5 mm length and 0.25 mm width - high fatigue life, >
- low hysteresis disadvantage
sensitive to temperature changes in single-crystals of semiconductor
→ develop polycrystalline semiconductor strain gauges
→ compensate by using a reference gauge
Examples
- longitudinal strain gauges
wire-type Fig. 7.16
metal foil Fig. 7.17
semiconductor Fig. 7.18
- rotational strain gauge Fig. 7.19 - three-directional strain gauges Fig. 7.20 - load cells
resistive Fig. 7.21
strain gauge Fig. 7.22
- bolt torque transducer Fig. 7.23
- load bolt Fig. 7.24
- pressure sensors Fig. 7.25 Fig. 7.26 Fig. 7.27
- accelerometer Fig. 7.28
7.4.3 electrical operation
Wheatstone bridge Fig. 7.29
produces a voltage difference linearly proportional to the resistance change of the gauge
can self-compensate for temperature changes
voltage driver Fig. 7.30
a reasonable approach to resistance detection when accuracy is less of an issue than cost
7.5 Thermoresistivity
the variation of electrical resistivity as a function of used for resistance
materials : platinum (expensive), Si, metal oxides, etc.
resistive thermal detectors, RTD
transducers made of metals and semiconductors temperature coefficient of resistivity (
for most metals above room temperature, the resistivity can be modeled as a linear function of temperature
=
(26)
for variety of materials in Table 7.3 ⇒ =
positive ⇒ resistivity increases with increasing materials with higher values of are best suited for thermistor
sensors made of the materials exhibiting a nonlinear relationship
=
(27)
: temperature characteristic (usually in the range of 3000 to 5000 K)
: temperature of the resistance
the resistance decreases as the temperature Fig. 7.31 materials (showing the largest resistance change with temperature) :
oxides of Ni, Mn, Co, Fe, Ti advantages :
faster, smaller, less expensive, and more sensitive disadvantages :
far less linear, narrower operating range of temperature Examples
- thermal detector Fig. 7.32, 7.34 - temperature sensor Fig. 7.33 - hot wire anemometer Fig. 7.35
- microflow sensors Fig. 7.36, 7.37, 7.38 - liquid level sensor Fig. 7.39
7.6 Thermoelectricity
direct interchange of thermal energy and thermoelectrical effects
irreversible effect : Joule heating in
reversible thermodynamically : Seebeck effect, Peltier effect, Thomson effect 7.6.1 Seebeck effect
principle of thermocouples, very common thermal sensors
thermal gradient between the two junctions of the conductors →
constitutive relation between a temperature difference and a voltage
= (28)
: absolute Seebeck coefficient of the material
→
→ magnetic disturbance observed by T. J. Seebeck in 1821 thermocouple
structure Fig. 7.40 principle
n et = i + ii + iii Fig. 7.41 = ( - ) + ( - ) + ( - TB)
, : Seebeck coefficients of materials 1 and 2, respectively
, : temperature at each junction A, B
: ambient temperature at the voltage measuring device = ( - ) + ( - )
= ( - ) ( - )
related to the temperature difference at the independent of the
voltage drop between the junctions of two materials
= ( - ) = (29)
Fig. 7.42 Seebeck effect in some materials slope ⇒ Seebeck coefficient
: differential Seebeck coefficient ⇒ of the sensor
= + (30)
linear function of temperature
Table 7.4 characteristics of thermocouple materials
Fig. 7.43 variation of the differential Seebeck coefficients with temperature advantages
relatively high sensitivity
potentially fast response times (1-100 ms)
Examples
- thermocouples
twisted wires Fig. 7.44
ribbons Fig. 7.45
trident Fig. 7.46
thin-foil Fig. 7.47 - thermopile Fig. 7.48 - heat flux sensor Fig. 7.49 - gas flow sensor Fig. 7.50
7.6.2 Peltier and Thomson effects
reversible thermoelectrical effects : Seebeck effect (§7.6.1), Peltier effect, Thomson effect Peltier effect
relate the heat generated or absorbed at the junction between two dissimilar conductors to the current going through the junctions
= (31)
: rate of heat absorption at the junction between materials 1 and 2
: current from material 1 to 2
: Peltier coefficient (a function only of the materials at the junction and junction temperature)
ex. water can be frozen at a bismuth-antimony junction ⇒ small scale refrigerator ex. ice can be melt by the reverse direction of the current
Thomson effect
a reversible transformation of electrical energy and heat due to a finite temperature gradient
present in a pure material
= (32)
: current flow
: temperature difference in the x-direction
: Thomson coefficient in a conductor
(a function of the material and the average temperature) Thomson's analysis result
= (33)
absolute Peltier coefficient in terms of the Seebeck coefficient
no example.
7.7 Magnetoresistivity
transducers based on changes in resistance due to variations in mechanical variables - pressure :
temperature : heat flow : presence of a magnetic field : magnetoresistivity
basis for most magnetic disk heads
links magnetic and electric energy domains
⇒ not strictly an electromechanical transduction mechanism often used to sense the position of a magnetic field
⇒ links mechanical and electrical variables ex.
galvanomagnetic effects
occurring when a current-carrying conductor is exposed to a magnetic field 1. longitudinal magnetoresistance effect
resistivity changes in the magnetic induction field to the direction of current flow
// , B //
2. transverse magnetoresistance effect
resistivity changes in the direction of current flow to the magnetic induction field
// , B ⊥ 3. Hall effect
resistivity changes in the direction to the magnetic induction field and current flow, to each other
⊥ , ⊥ B , B ⊥ magnetoresistive sensor
resistivity change (in the longitudinal magnetoresistance effect)
= ( (34)
: magnetoresistivity coefficient
: magnetic induction field strength
= (0) resistivity with = 0
△ = () - (0) cf. in the Hall effect
∝ (
Example
magnetic disk heads
magnetic transition embedding information
→ magnetic induction as a function of position
→ change in advantages
quite small high sensitivity low cost
to electromagnetic noise, dirt, and light disadvantage
cf. good linearity in Hall effect sensors
7.8 Shape Memory Alloys in Transduction
not truly electromechanical transduction
but links mechanical and electrical behavior ex. magnetoresistivity (
shape memory alloys
metals undergoing thermally induced phase transition Fig. 7.51 at low temperatures in a martensitic phase, very ductile
at high temperatures in an austenitic phase, strong and stiff thermomechanical transformation : temperature changes →
resistive electromechanical transducers Fig. 7.52
resistivity → ohmic heating → temperature rise → dimensional changes advantage
devices can be made small as these heat and cool quickly → materials Table 7.5
types of shape memory effect 1. one-way effect
occurs
transforms from martensitic to austenitic phase
returns the material to the original (remembered) shape of the austenitic phase 2. two-way effect
revert (partially) to a deformed state
upon transformation from austenitic to martensitic phase, i.e. upon ex. shape memory alloy
Examples
- robot hand Fig. 7.53 - crank engine Fig. 7.54 - micro-valve Fig. 7.55 - micro-tweezer
