i. measurement of temperature - u of s … – measurements of temp, strain, pressure, motion page 1...

EE323 – Measurements of temp, strain, pressure, motion of 40

I. MEASUREMENT OF TEMPERATURE

• Most frequent measurement and control

• Direct contact: thermometer,

• Indirect contact: pyrometer (detect generated heat or sensing optical properties)

1. Definition of temperature

• Temperature relates to average translational kinetic energy of molecule due to heat (no motion at absolute temp., 0K).

• Different from heat measurement (joules, calories).

2. Temperature scales

• Fahrenheit, Celsius, Kelvin 273CK

)32F(95

C

32C59

F

+=

−=

+=


3. The thermocouple (wider measuring range)

• Current flow when one junction is at different temperature from the other.

• Current is proportional to the temperature difference.


2 more junctions


• Voltmeter leads should be in an isothermal block placed in a known reference temperature.

)TT(V 21 −−−−≈≈≈≈

V= thermoelctric (Seebeck) voltage, V

α = Seebeck coefficient, V/OC


Ex: A general-purpose temperature probe is needed to cover the range from -100oC to +500oC. Select a thermal-couple and design a circuit to provide an output voltage proportional to temperature such that the voltage is -1.00V when the probe is -100oC and +5.00V at 500oC.


4. The Resistance Temperature Detector .

• Resistivity of metal is a positive function of temperature.

• Constructed with fine wire of platinum, nickel, germanium.

• Mounted in enclosed case for protection from environment, strain, …

• )t1(RR nt ++++====

• Rn= nominal resistance at 0OC,Ω

• α= resistance coefficient, Ω/Ω/0OC


• Use Bridge measurement, lead resistance important

RTD

Lead resistances


5. Thermistors

• Resistance changes with temperature.

• Negative coefficient, non-linear

3)R(lnC)R(lnBA

T1 ++++++++====

• T= temperature, K

• A,B,C = curve-fitting constants

• Fast response, high sensitivity

• Small, encapsulated beads

• Use bridge measurement to detect small temperature changes (0.01OC).


Ex: A thermistor is to be used as a liquid sensor. When the level of the liquid reaches the height of the sensor, the pump being used to fill the tank is to be shut off by means of a 12V relay. Design a circuit to interface the thermistor to the pump relay. The liquid is at room temperature. The thermistor has an operating range of -25oc t0 110oC. R0=100Ohms at 25oC.


6. Semiconductor temperature sensors

• Diode junction voltage as a function of temperature

• -2.2mV/OC, low current, measure voltage.

• Low cost, limited range.

)1e(Ii TD

Vv

sD −−−−====

7. IC sensors

• Low cost, IC form

• Current or voltage output proportional to temperature.

• LM135, 2-terminal Zener diode breakdown voltage (+10mV/K)


8. Radiation pyrometer

• Non-contact, measure remotely

• Detect infrared radiation from the source

• Converted absorbed radiation into voltage or current

• Used in high temperature, inaccessible location, harsh environment


Ex: A remote control unit has a transmitting infrared LED with a peak radiant intensity of 150mW per steradian. The photodiode receiver has an active area of 10 square millimeters and it is 3m away from the remote control. The photodiode has a sensitivity of 0.6A/W and a dark current of 30nA in the photovoltaic mode. What is the incident radiant power (irradiance) on the photodiode? What is the expected photocurrent? Design a circuit which applies a 10V reverse bias to the photodiode and which creates a TTL-compatible low output voltage in the absence of input light and a TTL-compatible high output for the incident power expected at 3m.


II. MEASUREMENT OF STRAIN

• A small force is applied to the length of a block, length changed (not permanently deformed).

• Elasticity

• As long as the material remains elastic, the change in length is proportional to the applied force (Hooke's law):

F ∝∝∝∝∆∆∆∆l


• Divide the change in length by the original length of the block,

llF ∝∝∝∝

• Strain (µε): ll

====


• Effect of the force on the strain is reduced by the area of the block:

ll

AF ∝∝∝∝

• Young's modulus, E, N/m2, is a property only of the material.

• Young's modulus is a measure of the stiffness of a material, (resist a change in length when loaded).

• Modified Hooke's law:

llE

AF ====

• Stress (force per unit area on a given plane within a body).

AF

====

σ = stress, N/m2


• Stress-strain relationship:

σσσσ = Eεεεε


1. The strain gage

• Resistance of wire (or a metallic bar):

AlR ====

• The bar undergoes a compression force, Length decreases Area increases. Volume un-changes.

• This causes the resistance of the bar to decrease:

AA)ll(RR

++++−−−−====−−−−


• The change in resistance:

llRGFR ⋅⋅⋅⋅====

GF = constant called the gage factor, (dimensionless)


• Metallic strain gages are made from very thin conductive foils with a conductor folded back and forth to allow a long path for the conductive elements while maintaining a short gage length.

• The back-and-forth pattern is designed to make the gage sensitive to strain only in the direction parallel to the wire and insensitive in the direction perpendicular to the wire.

• Gages exhibit some transverse sensitivity, but the effect is generally small.

• Foils are made from special alloys such as constantan, a combination of 60% copper and 40% nickel.

• Standard foil resistances are 120Ω and 350Ω; some gages are available with resistances of up to 5000Ω.

• Bonded strain gages: made with a carrier adhesive on an electrically insulating. The gage is attached to the specimen with a special adhesive

• Unbonded strain gages consist of pre-tensioned wires assembled in some type of fixture.


2. Measurement with strain gage

• Change in resistance within the elastic region is an extremely small quantity (i.e., requires

sensitive instrumentation).

• Wheatstone bridge circuit is used to measure tiny change.

• Strain gage measurements are complicated by temperature (heating and specimen expansion and contraction).


• One arm Wheatstone bridge (quarter-bridge configuration)

• Dummy gage does not experience the strain; included for temperature compensation.

• Balance adjust the bridge (zeroed) with no strain.

• The gage is then subject to strain, output voltage is observed

)V21(GFV4

r

r++++

====


• V r (dimensionless) represents the difference in the ratios of the output to input voltage between the strained and unstrained condition:

unstrainedin

outstrained

in

outr )

VV()

VV(V −−−−====

• The equations take into account the non-linearity of the bridge.

• This error is very minor at the low levels.

• Initially balanced (Vout, unstrained = 0V):

)V(GFV4

in

out====


• Half-bridge configuration (two active gages) o Best applied to measuring bending beams o Causes temperature effects, change the resistance of both gages in the same way (i.e.,

to be canceled).

)V(GFV2

in

out====


• Full-bridge configuration (active gages in all four arms). o Two strain gages in opposite diagonals are in tension and the other two are in

compression. o Temperature compensation can be included.

)V(GFV

in

out====


III. MEASUREMENT OF PRESSURE

• Pressure = force per unit area

)Pam/N(AFP 2 ========

• In a static fluid, pressure increases in proportion to the depth, density of the liquid,

and additional pressure acting on the surface (for example atmospheric pressure). •

ghP ====

P= pressure at the bottom of a liquid, Pa ρ=mass density, kg/m3

h= height of the liquid, m

• With gases, pressure is exerted equally in all directions.


1. Pressure transducers

• Principle of balancing an unknown pressure against a known load.

• Common technique is to use a diaphragm to balance the unknown pressure against the mechanical restraining force keeping the diaphragm in place.

• Diaphragm: a flexible disk that is fastened on its periphery and changes shape under pressure.

• A spring may be used to push against the diaphragm and provides a load.

• The amount of movement of the diaphragm is proportional to the pressure (i.e., the displacement of the diaphragm)


• Requires converting mechanical motion of the pressure-sensing element into an electrical signal.

• Conversion techniques: potentiometric, reluctive, capacitive, and strain gage methods.


• Potentiometric method converts the displacement of the sensor into a resistance (simple, less expensive, mechanical wear and is electrically noisy.

• Reluctive method changes the inductance of one or two coils by moving some part of the magnetic circuit. The coils are electrically connected in a bridge circuit.

• In capacitive transducers, the motion changes the capacitance of an internal capacitor (electrically connected into a bridge circuit). High-frequency response (due to low mass), quick response to changes in pressure.

• A strain gage can be used as a sensing element by bonding it to the diaphragm.

Pressure on the diaphragm introduces strain, which is sensed by the gages and converted to an electrical resistance.

Gages are bonded on both sides of the diaphragm and connected in a full- or half-bridge arrangement.

Transducers may also contain temperature compensation and zero-balance resistors.


Sensing element is a stain gauge


IV. MEASUREMENT OF MOTION

• Motion can be rectilinear-along a straight line or it can be circular-about an axis.

• The measurement of motion includes displacement, velocity, and acceleration

1. Displacement transducers

• Contacting or noncontacting.

• Electrical output signal can be either a voltage or a current.

• Potentiometric displacement transducers are simple, can be designed to measure large displacements, (subject to wear and dirt and electrically noisy).

• Displacement can be converted into an electrical quantity using a variable inductor and monitoring the change in inductance.


• A related displacement transducer is the linear variable differential transformer (LVDT). The sensing shaft is connected to a moving magnetic core inside a specially wound

transformer. As the core moves off-center, the voltage in one secondary will be greater than the

other. The transducer has excellent sensitivity, linearity, and repeatability.


• Noncontacting displacement transducers include optical and capacitive transducers.

• Photocells can be arranged to detect light through holes in an encoding disk or to count fringes painted on the surface to be measured. Optical systems are fast, but noisy.

• Fiber-optic sensors make excellent proximity detectors for close ranges. The major disadvantage is limited dynamic range.

• Capacitive sensors can be made into very sensitive displacement and proximity transducers.

• The capacitance is varied by moving one of the plates of a capacitor with respect to the second plate.

• The capacitor can be used to control the frequency of a resonant circuit to convert the capacitive change into a usable electrical output.


2. Velocity transducers

• Velocity = rate of change of displacement

• Can be determined by using a displacement sensor and measuring the time between two points.

V=x/t=dx/dt • Direct measurement with certain transducers that have an output proportional to the velocity

to be measured (either linear or angular velocity).

• Linear velocity transducers: coil forming a simple motor by generating an emf proportional to the velocity.

• Angular velocity: tachometers provide a dc or ac voltage output. DC tachometers: speed and direction of rotation. AC tachometers: output frequency proportional to the rotational speed.


3. Acceleration transducers

• Measured by use of a spring-supported seismic mass mounted in a suitable enclosure.

A=dv/dt=d2x/dt2


• Damping is provided by a dashpot.

• Relative motion between the case and the mass is proportional to the acceleration.

• A secondary transducer such as a resistive displacement transducer is used to convert the relative motion to an electrical output.

• The mass does not move (ideally) when the case accelerates because of its inertia; in practice it does because of forces applied to it through the spring.

• The accelerometer has a natural frequency, the period of which should be shorter than the time required for the measured acceleration to change.

• Accelerometers used to measure vibration should also be used at frequencies less than the natural frequency.


• An accelerometer that uses the basic principle of the LVDT can be constructed to measure vibration. The mass is made from a magnet that is surrounded by coils. Voltage induced in the coils is a function of the acceleration.

• Another type of accelerometer: a piezoelectric crystal in contact with the seismic mass. The crystal generates an output voltage in response to forces induced by the

acceleration of the mass. Piezoelectric crystals are small in size and have a natural frequency that is very high

(measure high-frequency vibration). The drawback to piezoelectric crystals is that the output is very low and the impedance

of the crystal is high, (subject noise problem).

i. measurement of temperature - u of s … – measurements of temp, strain, pressure, motion page 1...

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