Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 7
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The Egyptiansappreciated that, provided that all four sides of a square are the samelength and the two diagonals are equal, then the interior angles will all bethe same – 90 . They were able to compare the two diagonals and look forsmall differences between the two measurements to determine how squarethe base of the pyramid was.Humans have walked on the moon because a few brave people wereprepared to sit on top of a collection of ten thousand manufactured parts allFundamental Principles of Engineering NanometrologyCopyright Ó 2010 by Elsevier Inc. All rights reserved.CONTENTSIntroduction tomeasurementUnits of measurementand the SILengthMassForceAngleTraceabilityAccuracy, precision,resolution, error anduncertaintyThe laserReferences56C H A P T ER 2 : Some basics of measurementFIGURE 2.1 An ancient Egyptian cubit (a standard of mass is also shown).built and assembled by the lowest bidder, and finally filled with hundreds oftons of explosive hydrogen and oxygen propellant.
A principal reason that it alloperated as intended was that the individual components were manufacturedto exacting tolerances that permitted final assembly and operation as intended.The phrase ‘mass production’ these days brings visions of hundreds ofcars rolling off a production line every day. From Henry Ford in the 1920sthrough to the modern car plants such as BMW and Honda, the key to thisapproach is to have tiers of suppliers and sub-contractors all sending the rightparts to the next higher tier and finally to the assembly line. The wholemanufacture and assembly process is enabled by the vital traceablemeasurements that take place along the route.Modern manufacturing often involves the miniaturization of productsand components.
This ‘nanotechnology revolution’ has meant that not onlyhave the parts shrunk to micrometres and nanometres, but tolerances havetoo. The dimensional and mass measurements that are required to ensurethat these tiny parts fit together, or ensure that larger precision parts are fit forpurpose, are the subject of this book.2.2 Units of measurement and the SIThe language of measurement that is universally used in science and engineering is the Système International d’Unités (SI) [2]. The SI embodies theLengthmodern metric system of measurement and was established in 1960 by the11th Conférence Générale des Poids et Mesures (CGPM). The CGPM is theinternational body that ensures wide dissemination of the SI and modifiesthe SI as necessary to reflect the latest advances in science and technology.There are a number of international organizations, treaties and laboratoriesthat form the scientific and legal infrastructure of measurement (see [3] fordetails).
Most technologically advanced nations have national measurementinstitutes (NMIs) that are responsible for ensuring that measurementscomply with the SI and ensure traceability (see section 2.7). Examples ofNMIs include the National Physical Laboratory (NPL, UK), PhysikalischTechnische Bundesanhalt (PTB, Germany), National Metrology InstituteJapan (NMIJ, Japan) and the National Institute of Standards and Technology(NIST, USA). The web sites of the larger NMIs all have a wealth of information on measurement and related topics.The SI is principally based on a system of base quantities, each associatedwith a unit and a realization. A unit is defined as a particular physical quantity,defined and adopted by convention, with which other particular quantitiesof the same kind are compared to express their value.
The realization of a unitis the physical embodiment of that unit, which is usually performed at anNMI. The seven base quantities (with their associated units in parentheses)are: time (second), length (metre), mass (kilogram), electric current (ampere),thermodynamic temperature (kelvin), amount of substance (mole) andluminous intensity (candela). Engineering metrology is mainly concernedwith length and mass, and these two base quantities will be given someattention here. Force and angle are also important quantities in engineeringmetrology and will be discussed in this chapter. The other base quantities, andtheir associated units and realizations, are presented in Appendix 1.In addition to the seven base quantities there are a number of derivedquantities that are essentially combinations of the base units. Some examples include acceleration (unit: metres per second), density (unit: kilogramper cubic metre) and magnetic field strength (unit: ampere per metre).
Thereare also a number of derived quantities that have units with special names.Some examples include frequency (unit: hertz or cycles per second), energy(unit: joule or kilogram per square metre per second) and electric charge (unit:coulomb or the product of ampere and second). Further examples of derivedunits are presented in Appendix 2.2.3 LengthThe definition and measurement of length has taken many formsthroughout human history (see [4,5] for more thorough historical overviews).78C H A P T ER 2 : Some basics of measurementThe metre was first defined in 1791, as ‘one ten millionth of the polarquadrant of the earth passing through Paris’.
The team of surveyors thatmeasured the part of the polar quadrant between Dunkirk and Barcelonatook six years to complete the task. This definition of the metre was realizedpractically with a bar (or end gauge) of platinum in 1899. This illustrates thetrade-offs between physical stability and reproducibility, and the practicalrealizability of standards.
Of course the earth’s quadrant is far more stablethan a human’s arm length, but to realize this in a standard is much moretedious. Some years after the prototype metre was realized, some errors werefound in the calculation of its length and it was found that the platinummetre was about 1 mm short. However, it was decided to keep the materialartefact for practical reasons. Another struggle that has continued until todayis the preference of material length; whether to use an end standard (seesection 4.2 and Figure 2.2) with two flat faces that define a distance, or a linestandard where two lines engraved in a material define a length. In 1889 theplatinum metre was replaced by a platinum-iridium line standard, the socalled X-metre, that kept the same defined distance as well as possible.The X-metre was used until 1960 [6], when the metre was defined as:the metre is the length equal to 1 650 763.73 wavelengths in vacuumof the radiation corresponding to the transition between the levels2p10 and 5d5 of the krypton 86 atomFIGURE 2.2 Metal bar length standards (gauge blocks and length bars).LengthThis redefinition was possible because of the developments in interferometry and the sharp spectral line of the krypton atom that enabled interferometry up to 1 m – with gauge blocks.
Around 1910, such a re-definitionwas proposed, but at that time the metre could not be reproduced witha lower uncertainty than with the material artefact.In 1983, advances in the development of the laser, where many stabilization methods resulted in lasers that were more stable than the kryptonspectral line, led to the need for a new definition. In the meantime, it wasfound that the speed of light in a vacuum is constant within all experimentallimits, independent of frequency, intensity, source movement and time.
Alsoit became possible to link optical frequencies to the time standard. Thisenabled a redefinition of the metre as [7]:the length of the path travelled by light in a vacuum in a timeinterval of 1/c of a second, where c is the speed of light given by299 792 458 m$s1Together with this definition, a list of reference frequencies was given,with associated uncertainties [8].
These included spectral lamps, forexample. The krypton spectral line was unchanged but it received anattributed uncertainty. More convenient and precise, however, are stabilizedlaser systems. Such a current realization of the metre can have an uncertainty in frequency of one part in 1011. Figure 2.3 shows an iodine-stabilizedhelium-neon laser held at NPL. This new definition was only possiblebecause it could be realized with a chain of comparisons.As discussed, the speed of light in a vacuum is generally regarded asa universal constant of nature, therefore, making it ideal as the basis fora length standard.
The speed of an electromagnetic wave is given byc ¼ nl(2.1)where n is the frequency and l is the wavelength of the radiation. Therefore,length can be disseminated by measuring frequency or wavelength, usuallyusing either time of flight measurements or interferometry (see chapter 4).Note that length can be considered to be a base quantity that is realized ina manner that is based upon the principles of quantum mechanics.
Theemission of electromagnetic waves from an atom (as occurs in a laser – seesection 2.9) is a quantized phenomenon and not subject to change providedcertain conditions are kept constant. This is a highly desirable property ofa base unit definition and realization [9].Note that the modern definition of length has become dependent on thetime definition. This was proposed earlier; in the seventeenth centuryChristiaan Huygens proposed to define the metre as the length of a bar with910C H A P T ER 2 : Some basics of measurementFIGURE 2.3 An iodine-stabilised helium-neon laser based at NPL, UK.a time of oscillation of one second.
However, this failed because of thevariation of local acceleration due to gravity with geographic location. Most ofthe measurements that are described in this book are length measurements.Displacement is a change in length, surface profile is made up of height andlateral displacement, and coordinate measuring machines (CMMs, seechapter 10) measure the three-dimensional geometry of an object.2.4 MassIn 1790, Louis XVI of France commissioned scientists to recommenda consistent system for weights and measures.
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