22/6/13 [email protected]1 Chapter 7 Motion and Dimensional Measurement Instruments Liner Motion Angular Motion Displaceme nt Velocity Accelerati on Jerk( 冲冲冲 ) 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.
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Chapter 7 Motion and Dimensional Measurement Instruments
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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.
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)
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.
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:
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:
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.
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.
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
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.
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)
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
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.
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.
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.
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.
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?)
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-
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
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
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.
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.
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
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??
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.
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 .
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)
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)
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:
(* 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.
• 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.