lec 4 counts & displacement

7/30/2019 Lec 4 Counts & Displacement

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Determination of Count, Eventsper Unit Time, and Time Interval

Chapter 10

Beckwith

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Counts, Events per Unit Time, and Time Interval

EPUT (Events Per Unit Time)

the counting of events that take place intermittently orsporadically (occurring only sparsely or occasionally); notdependant on steady rate. E.g. counting of variousparticles radiated from a radioactive source.

Frequency

Events per unit of time (EPUT) for phenomenon understeady-state oscillations, such as mechanical vibrations

or ac voltage or current.

Period

Time interval becomes a period if it is the duration of acycle of a periodic event.


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Counting and timing measurement

Classification

1) Basic counting;1) either to determine a total or

2) to indicate the attainment of a predetermined count.

2) Number of events or items per unit of time(EPUT) independent of rate of occurrence.

3) Frequency, or number of cycles of uniformlyrecurring events per unit of time.

4) Time interval between two predeterminedconditions or events.

5) Phase relation, or percentage of periodbetween predetermined recurring conditions orevents.

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Use of Counters

Electronic Counters Require that the counted input be converted to simple

voltage pulses, a count being recorded for each phase. A simple switch can be used actuated by the function to

be counted. Photocell, variable resistance, inductance, or capacitance

devices, Geiger counter, and like may be employed. Simple amplifiers may be used to raise the voltage level if

required. Signal inputs may include almost any mechanical

quantity, such as displacement, velocity, acceleration,

strain, pressure, and load, so long as distinct cycles orpulses of the input are provided. A variation is the count-control instrumentProvision is

made for setting a predetermined count, and when thecount is reached, the instrument supplies and electricaloutput that may be used as a control signal.


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EPUT Meters

Combine the simple electronic counter and an internaltime base with a means for limiting the counting processto preset time interval.

This permits direct measurement of frequency and it isquite useful for accurate determination of rotationalspeeds.

Intermittent or sporadic events per unit of time may alsobe counted along with regular rate.

Time-Interval Meter

In this case, input pulses start and stop the countingprocess, and the pulses from an internal oscillator makeup the counted information.

In this manner the time interval taking place betweenstarting and stopping may be determined, provided thefrequency of the internal oscillator is known.


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Photocells are arranged so that the interruption of the beams oflight provide pulsesfirst to start the counting process andsecond to stop it.

The counter records the number of cycles from the oscillatorwhich has an accurately known stable output.

In the example, the count would represent the number of hundred-thousandths of a second required for the projectile to traverse thedistance between the light beams.

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The Stroboscope

During the intervals when openings in the disk and the stationary mask coincided,the observer would catch rapid glimpses of an object behind the disk.

If the disk speed was synchronized with the motion of the object, the object wouldbe made to appear to be motionless.

Modern stroboscopes operate on a somewhat different principle. Instead of

whirling disk, a controllable intense flashing light source is used. Repeated short duration (1040 s) light flashes of adjustable frequency are

supplied by the light source. The frequency, controlled by an internal oscillator, is varied to correspond to the

cyclic motion being studied. The readout is the flashing rate required for synchronization. These devices are often called Strobe Lights.


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Cautions required during measurements withstroboscope

Geometry of the item to be kept in mind Multiple ratios of the flashing rate to the objects true

cycling rate

An obvious approachstop the motion, note the rateand then double the rate and check again. Or

Use following convenient procedure1) Determine a flashing rate f1 that freezes the motion

2) Slowly reduce the rate until the motion is frozen once more. Notethis rate, f2.

Then

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ff

fffobjecttheofratecyclingActual o

Stroboscopic lighting can also be used to study nonrepeating action.

By using a stil l camera with shutter locked in the open position, it can beused to track the position of a moving object, e.g. a moving bullet.

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Electronic Oscillators Electronic oscillators are sources of periodic voltage variation

of either fixed or variable frequency.

Electronic oscillators are used in a wide variety ofapplications:

as energy sources for circuitry measurement

as audio sources for electronic musical instruments,

as sweep generators for oscilloscopes and TV receivers,

as carriers for radio and TV signal propagation,

as clocks for synchronizing computer actions and so forth.

Sources of frequency

Mechanical sources such as pendulum or tuning fork

Electromechanical such as piezoelectric crystals

Pneumatic

Hydraulic

Thermal


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Displacement andDimensional Measurement

Beckwith ; Chapter 11

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Displacement and Dimensional Measurement


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Internal diameter

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Gage Blocks for direct comparison

Blocks must be wrung together in such a way as toeliminate all but the thinnest oil film between them.

This oil film, incidentally, is an integral part of the blockitself; it cannot be completely eliminated, since it waspresent even at manufacture.


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Surface Plates

Provides an accurate reference plane for

gage blocksmust be made with anaccuracy comparable to that of the blocksthemselves.

Materials Carefully ground and lapped cast iron plates

Machined lapped and polished granite plates Granites are almost free from residual stresses than

any other material

Less tendency to warp when the plates are prepared

Residual stresses are not induced even by dropping oftool or work piece etc. as are in metals. Granite simplypowders somewhat at the point of impact.

Granite does not corrode.

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Temperature Problems

Temperature differences or changes are major problems inaccurate dimensional gaging.

Coefficient of expansion () of gage-block steels is about11.2 ppm/oC.

Hence, even a shift of 1oC in temperature would causedimensional changes of the same order or magnitude as thegage tolerances.

The standard gaging temperature has been established as20oC.

Several solutions: Use air-conditioned gaging roomnot a complete solution. Use of

insulating gloves and tweezers is recommended in order to avoid

thermal changes during handling which require 20 minutes tocorrect. Use of a constant temperature bath such as of kerosene oil. The

gages may be removed from the bath for comparisonIn extremecases measurement may be made in submerged condition.

If the gage block and the work piece are of like materials, there willbe no temp. error as long as the two parts are at the sametemperature.


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Corrections may be made by application of the following:L = Lb[1-()(T)(10

-6)

where = (p-b)L = the true length of the dimension being gauged (at reference temperature)

Lb = the nominal length of the gage blocks determined by summation of

dimensions etched thereon.

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Pneumatic Comparators


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Application of Monochromatic Light and Optical Flats

Optical Flats and

monochromatic light sourcemay be used to:

compare gage blockdimensions with unknowndimensionsi.e. dimensionalcomparator.

determine the contour of analmost flat surface.

Principles of Interferometryare applied

Light waves from a singlesource may be caused to add

or subtract, increasing ordecreasing the light intensity,depending on the phaserelation.

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Two requirements must be met:1)An air gap (a wedge of varying thickness must exist between the twosurfaces, and

2)The work surface must be reflective.

Light is reflected from both the working face of the flat andthe work surface of the part being inspected.

At the particular points where multiples of half wavelengthsoccur, we can see dark interference bands or fringes.

A fringe represents a locus of separation between work andthe flat of definite integral number of half wavelengths of thelight used.

Adjacent fringes may be interpreted, therefore, asrepresenting contours of elevation differing by one-halfwavelength. This distance is called the fringe interval.


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Point or line of contact between Flat and the work surface

There will be at least one primary support point for the flat. On a convex surface, as the flat is rocked, the point of contact is

determined as the spot or line in the pattern that does not shift. Actually in some situations the point will move slightly, but in general it

does not stray far from its starting point. Each adjacent fringe represents a change in elevation, or fringe interval,

of one-half wavelength of the light that is used. For a helium lamp, wouldbe 0.295 m.

On a concave surface, if the flat ispressed at an edge, the center pointmay shift slightly the edge point orline will remain stationary, and doesnot move as the pressure is varied.

d = (fringe interval) x N = (/2)N d = the difference in elevation

between contact and the point inquestion.

N = the fringe order at the point inquestion

= the wavelength of the lightsource used.

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Use of optical flats and monochromatic light fordimensional comparison


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Interference Interference is a phenomenon that occurs whenever two

waves (e.g. sound waves, light waves, ocean waves,

seismic waves from earthquakes) come together at the sametime and place. Interference can be visualized as the adding together of two

waves with each other. Depending on wave size (amplitude)and the degree to which they are in or out of phase witheach other, they will either add together or cancel. Thecanceling out is still really an "addition''; in this case, it's likeadding plus one to minus one.

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Interferometry

Interferometry is the use of interference phenomena formeasurement purposes, either for very small angles or tiny distance increments (the displacement of two objects relative to

one another).

Interferometer An interferometer is a device to make such measurements.

Though there are many different types and designs ofinterferometers, virtually all of them operate on the samebasic principle.

From a beam of light coming from a single source (a star, alaser, a lamp, etc.), two or more flat mirrors are used to splitoff different light beams. These beams are then combined soas to interfere with each other.

One well-known basic design for an interferometer is theMichelson interferometer, invented by the Americanphysicist, Albert Michelson (1853-1931)


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Basically, in the Michelson interferometer, one is looking "down''along the axis of two combined beams towards the light source. Abeamsplitter mirror is used to bring the beams together from the twoflat mirrors. It has a deliberately thin reflective coating to permitabout one-half of the light to pass through. If the light is of a singlewavelength, fringes will form all along the optical axis of thecombined beams, oriented perpendicular to this axis and will appearto stand still, even though the beams are traveling at the speed oflight -- a standing wave phenomenon. To the eye, the fringes appearas alternating small rings of light and dark surrounding the centralimages of the light source.

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What makes the interferometer such a precise

measuring instrument is that these fringes are only onelight-wavelength apart. In visible light, about 590nanometers --that corresponds to 1/43,000th of an inch!Any movement along the optical axis by either flat mirrorwill cause the fringes to shift an equal amount inlockstep. The measurement of this movement is madeby literally counting the number of fringes - eachdimming and brightening of light - one wavelength at atime!

Such a precise system is also incredibly sensitive -- somuch so that any vibration, movement, thermalexpansion, etc. is picked up as well. In fact, Michelson'searly experiments were affected by street trafficvibrations up to 1,000 feet away! Using shorterwavelengths of light allow greater precision, but aremuch more difficult to work with (the fringes are closertogether).


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At the detector, the two reflecting beams will interfereconstructively (bright) or destructively (dark), depending on thenumber of wavelengths by which their paths differ.

One reflector can be traversed along the length of an unknowndimension.

If the distance is then the beam path increases by 2.

The number of successive dark fringes that occur at the detectoris equal to the number of wavelengths, N, in the path change:

2 = N

By counting the passing fringes,Nis obtained and the distance is measured.

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Measuring Microscopes

Microscopes formechanicalmeasurementrelatively lowpower.

1) Fixed scale

2) Filar

3) Traveling

4) Traveling-stage

5) Draw-tube


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Fixed-scale microscopes

Usually 100 divisions with

each div 0.1mm

Filar microscope

Uses moving reticles

A single or double hairline ismoved by a fine pitch screw

threadIn general a bifilar

type is more easily used than

the single hairline type.

Problem in keeping track ofnumber of turns of the

micrometer screw.A filar-type microscope

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Traveling Microscope andTraveling-stageMicroscope Traveling microscope

Microscope is movedrelative to the work bymeans of a fine-pitch leadscrew, and the movement ismeasured.

Microscope is merely toprovide a magnified index.

Traveling-stage microscope Work is moved relative to

the microscope.

Draw-type microscope Uses a scale on the side of

optical tube Determines displacement ina direction along the opticalaxis, e.g. the height of a stepcan be determined byfocusing first and secondelevations.


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Precision alignment of parts of relatively large

dimension is often of great importance. Tolerances of a few thousandths of an inch or less

Special equipment for optical methods includes: Alignment telescope

Collimators

Autocollimators

Accessories

Alignment telescope Consists of a medium- to high-power telescope with a

cross-hair reticle at the focal point of eye-piece.

May be used in the same manner as the surveyor's transitfor establishing datum lines and levels.

Often used in conjunction with a collimator.

Optical tooling and long path interferometry

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A collimator is a device that narrows abeam of particles or waves. To "narrow"can mean either to cause the directions ofmotion to become more aligned in aspecific direction (i.e. collimated orparallel) or to cause the spatial cross-section of the beam to become smaller.

A device capable of collimating radiation,

as a long narrow tube in which stronglyabsorbing or reflecting walls permit onlyradiation traveling parallel to the tube axisto traverse the entire length.


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Optical collimators

In optics, a collimator may consist of a curved

mirror or lens with some type of light sourceand/or an image at its focus. This can be used toreplicate a target at infinity without parallax.Optical collimators can be used to calibrate otheroptical devices, to check if all elements arealigned on the optical axis, to set elements atproper focus, or to align two or more devicessuch as binoculars and gun barrels/gunsights.

Optical collimators are also used in gunsightsand other pointing devices to give the viewer an

image of a reticle at infinity. Collimators may be used with laser diodes and

CO2 lasers.

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Collimator A source or bundle of parallel light rays

Essential parts are: A light source and A lens system for projecting the bundle of rays Reticles whose images are projected by the collimator. Important features are:

When reticle R2 is in place, the observed image at the telescope is afunction of angular alignment only, independent of lateral or transversepositioning.

When reticle R3 is observed, its image is dependent only on lateralposition and is independent of angular alignment.

Possible to first establish correct angular relation between the collimatorand the telescope and then to determine the magnitude of any lateralmisalignment.

Magnitudes are independent of distance of separation and are read from

scales inscribed on the reticles.


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An Autocollimator uses light to measure angles. It operates byprojecting light made parallel (collimated) through an objective onto

an object with a reflective surface. If the surface is perpendicular to the projected light, the beam is

reflected back to its point of origin. If, however, the surface is tiltedrelative to the optical axis of the collimator, the reflected light isdisplaced (visualized against a graticule - usually a crossline). Anydeviation between the projected and reflected beam is measuredagainst a scale and measured in arcseconds*).

Autocollimators may use either visual detection (by eye) or digitaldetection using a photodetector.

Autocollimators can be used to detect and visualize microscopicedges enabling measurement of angular deviations in fromparallelism, flatness and perpendicularity.(*An arcsecond is one sixtieth of an arcminute, which is equal onesixtieth (1/60) of a degree or pye/10800 radians).

APPLICATIONS: Autocollimators are used in industrial and manufacturingenvironments for precision alignment of mechanical components,the detection of angular movement and angular monitoring over timeand to ensure there is no angular error in a system and to ensurecompliance with angle specifications and standards.


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Autocollimator A combination of a telescope and a collimator

a) It projects a bundle of parallel light rays andb) Uses the same lens system for a viewing a reflected image.

An important accessory is some form of mirror for reflecting the light beama

cube corner (trihedral) prism can be used. Intermediate targets may be set up to provide a reference point from which

dimensional measurements can be made. The reflected beam emerges parallel to the direction of the incident beam,

regardless of alignment. Laser interferometeran important advancement Also used for distance measurement by echo-pulse technique.

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Some of basic methods are:1. Visual comparison with a standard surfacebased on

appearance.

2. The tracer method, which uses a stylus that is draggedacross the surface. This method is the most common forobtaining quantitative results.

3. The plastic-replica method, wherein a soft, transparent,plastic film is pressed into the surface, then stripped off.Light is then passed through the replica and measured.Refraction caused by the roughened surface reducesthe transparency, and the intensity of transmitted light is

used as the measure.4. Reflection of light from the surface measured by a

photocell.

5. Magnified inspection, using a binocular microscope oran electron microscope.

Surface Roughness


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6. Adsorption of gas or liquid, wherein the magnitude ofadsorption is used as the surface roughness criterion.Radioactive materials have been used for providing a

method of quantitative measurement.

7. Parallel plane clearance. Leakage of low viscosity liquidor gas between the subject surface and a reference flatis used as the measure of roughness.

8. The electrolytic method, which assumes that theelectrical capacitance is a function of the actual surfacearea, the rough surface providing a greater capacitancethan a smooth surface.

9. The scanning tunneling microscope. This device detectsquantum-mechanical (tunneling) effects on a tiny stylus

passing over a surface to determine the surfacestructure on an atomic scale.

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The Tracer Method

lec 4 counts & displacement

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