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over a frequency range fromabout 10 Hz to 1000 Hz in the form of sharp coherent resonances as well astransient excitations [33]. Sound pressure levels in a typical laboratoryenvironment are greater than 35 dB, usually due to air-conditioning systems.Consider an enclosure that is a simple bottomless rectangular box whosewalls are rigidly attached at each edge.
When a panel is acoustically excited bya diffuse sound field, forced bending waves govern its sound transmissioncharacteristics and the sound pressure attenuation is determined by thepanel mass per unit area [32]. The panel sound pressure attenuation (dB) isgiven by [34]" #prs f 2a ¼ 10 log10 1 þþ 5 dB(3.19)r0 cwhere rs is its mass per unit area, r0 is the density of air at standard pressureand f is the incident acoustic field frequency. Equation (3.19) suggests thatthe enclosure wall should be constructed from high-density materials toobtain the largest rs possible given the load-bearing capacity of any supporting structure. Note that the attenuation decreases for every 20 dB perdecade increase in either rs or frequency.5152C H A P T ER 3 : Precision measurement instrumentation – some design principles3.10 References[1] Hume K J 1980 A history of engineering metrology (Mechanical EngineeringPublications Ltd)[2] Flack D R, Hannaford J 2005 Fundamental good practice in dimensionalmetrology.
NPL good practice guide No. 80 (National Physical Laboratory)[3] Smith S T, Chetwynd D G 1992 Foundations of ultraprecision mechanismdesign (Gordan & Breach Science Publishers)[4] Slocum A H 1992 Precision machine design (Society of ManufacturingEngineers: Michigan)[5] Schellekens P, Roseille N, Vermeulen J, Vermeulen M, Wetzels S, Pril W 1998Design for high precision: current status and trends Ann. CIRP 2 557–586[6] Nagazawa H 1994 Principles of precision engineering (Oxford SciencePublications)[7] Schouten C H, Rosielle P C J N, Schellekens P H J 1997 Design of a kinematic coupling for precision applications Precision Engineering 20 46–52[8] Petersen K E 1982 Silicon as a mechanical material Proc.
IEEE 70 420–456[9] Monteiro A F, Smith S T, Chetwynd D G 1996 A super-precision linearslideway with angular correction in three axes Nanotechnology 7 27–36[10] Smith S T 2000 Flexures: elements of elastic mechanisms (Gordon & BreachScience Publishers)[11] Teo T J, Chen I-M, Yang G, Lin W 2008 A flexure-based electromagneticlinear actuator Nanotechnology 19 515501[12] Leach R K 2000 Traceable measurement of surface texture at the NationalPhysical Laboratory using NanoSurf IV Meas.
Sci. Technol. 11 1162–1172[13] Hicks T R, Atherton P D 1997 The nanopositioning book: moving andmeasuring to better than a nanometre (Queensgate Instruments)[14] Atherton P D 1998 Nanometre precision mechanisms Measurement þControl 31 37–42[15] Bryan J B 1979 The Abbé principle revisited: an updated interpretationPrecision Engineering 1 129–132[16] Vermeulen M M P A 1999 High precision 3D coordinate measuring machine,design and prototype development (PhD thesis: Eindhoven University ofTechnlogy)[17] van Seggelen J K, Roseille P C J N, Schellenkens P H J, Spaan H A M,Bergmans R H, Kotte G J W L 2005 An elastically guided machine axis withnanometer repeatability Ann. CIRP 54 487–490[18] Hearn E J 1997 Mechanics of materials volume 1: an introduction to themechanics of elastic and plastic deformation of solids and structural materials (Butterworth-Heinneman) 3rd edition[19] Young W C, Budynas R 2001 Roark’s formulas for stress and strain (McGrawHill Professional) 7th editionReferences[20] Hughes E B 1996 Measurement of the linear thermal expansion coefficient ofgauge blocks by interferometry Proc.
SPIE 2088 179–189[21] Edlén B 1966 The refractive index of air Metrologia 2 71–80[22] Birch K P, Downs M J 1994 Correction to the updated Edlén equation for therefractive index of air Metrologia 31 315–316[23] Cebon D, Ashby M F 1994 Materials selection for precision instrumentsMeas. Sci. Technol. 5 296–306[24] Chetwynd D G 1987 Selection of structural materials for precision devicesPrecision Engineering 9 3–7[25] Lindsey K 1992 Tetrafrom grinding Proc.
SPIE 1573 129–135[26] McKeown P A, Corbett J, Shore P, Morantz P 2008 Ultraprecision machinetools - design and development Nanotechnology Perceptions 4 5–14[27] Reilly S P, Leach R K 2006 Critical review of seismic vibration isolationtechniques NPL Report DEPC-EM 007[28] Goldman S 1999 Vibration spectrum analysis: a practical approach (Industrial Press: New York) 2nd edition[29] Newell D B, Richman S J, Nelson P G, Stebbins R T, Bender P L, Mason J1997 An ultra-low-noise, low-frequency, six degrees of freedom activevibration isolator Rev. Sci. Instrum. 68 3211–3219[30] Araya A 2002 Ground noise studies using the TAMA300 gravitational-wavedetector and related highly sensitive instruments Proc. 7th Int. Workshop onAccelerometer Alignment 367–378[31] Weaver W, Timoshenko S P, Young D H 1990 Vibration problems in engineering (Wiley-IEEE) 5th edition[32] Beranek L L, Vér I L 1993 Noise and vibration control engineering: principlesand applications (Wiley Interscience)[33] Filinski I, Gordon R A 1974 The minimization of ac phase noise in interferometric systems Rev.
Sci. Instrum. 65 576–58[34] Brenan C J H, Charette P G, Hunter I W 1992 Environmental isolation platform for microrobot system development Rev. Sci. Instrum. 63 3492–349853This page intentionally left blankCHAPTER 4Length traceability usinginterferometryDr.
Han HaitjemaMitutoyo Research Centre Europe4.1 Traceability in lengthA short historical overview of length measurement was given in chapter 2.This chapter will take one small branch of length measurement, that of staticlength standards, and discuss in detail how the most accurate lengthmeasurements are made on macro-scale length standards using the technique of interferometry. These macro-scale length standards and thespecialist equipment used for their measurement may not appear, at firstsight, to have much relevance to MNT.
However, macro-scale length standards are measured to nanometre uncertainties and many of the conceptsdiscussed in this chapter will have relevance in later chapters. For example,much of the information here that relates to static surface-based interferometry will be developed further or modified in chapter 5, which discussesthe development of displacement interferometry.It is also important to discuss traditional macro-scale length standards,both specification standards and artefact standards, because the subject ofthis book is engineering nanometrology.
In other words, this book is concerned with the tools, theory and practical application of nanometrology inan engineering context, rather than as an academic study. It is anticipatedthat the development of standards for engineering nanometrology will verymuch follow the route taken for macro-scale engineering in that problemsconcerning the interoperability of devices, interconnections, tolerancing andstandardization will lead to the requirement for testing and calibration, andthis in turn will lead to the writing of specification standards and the preparation of nanoscale artefact standards and the metrology tools with which tocalibrate them.
It may well be that a MNT version of the ISO GeometricalFundamental Principles of Engineering NanometrologyCopyright Ó 2010 by Elsevier Inc. All rights reserved.CONTENTSTraceability in lengthGauge blocks – both apractical andtraceable artefactIntroduction tointerferometryInterferometer designsGauge blockinterferometryReferences5556C H A P T ER 4 : Length traceability using interferometryProduct Specification (GPS) matrix [1] will evolve to serve the needs fordimensional metrology at these small scales. A discussion on this subject isas presented in [2].There is a large range of macro-scale length standards and lengthmeasuring instruments that are used throughout engineering, for examplesimple rulers, callipers, gauge blocks, setting rods, micrometers, step gauges,coordinate measuring machines, linescales, ring and plug gauges, verniers,stage micrometers, depth gauges, ball bars, laser trackers, ball plates, threadgauges, angle blocks, autocollimators, etc.; the list is quite extensive [3].
Forany of these standards or equipment to be of any practical application toengineers, end users or metrologists, the measurements have to be traceable.Chapter 2 explained the concept of traceability and described the comparisonchain for some quantities. In this chapter we will examine in detail thetraceable measurement of some of the length standards with the most basicconcepts known as gauge blocks and, in doing so, we will show many of thebasic principles of interferometry – perhaps the most directly traceablemeasurement technique for length metrology.4.2 Gauge blocks – both a practical and traceable artefactAs discussed in section 2.3, the end standard is one of the basic forms ofmaterial length artefact (a line standard being the alternative form of artefact).
It is not only the basic form of an end standard that makes them sopopular, but also the fact that Johannsson greatly enhanced the practicalusability of end standards by defining gauge block sizes so that they could beused in sets and be combined to give any length with micrometre accuracy[3,4]. For these reasons the end standard found its way from the NMIsthrough to the shop floor.In summary, the combination of direct traceability to the level of primarystandards, the flexibility of combining them to produce any length witha minimal loss of accuracy, their availability in a range of accuracy classes andmaterials and the standardization of sizes and accuracies make end standardswidespread, and their traceability well established and respected.The most commonly used gauge blocks have a standardized cross-section of9 mm by 35 mm for a nominal length ln > 10 mm and 9 mm by 30 mm fornominal length 0.5 mm < ln < 10 mm.
The flatness of the surfaces (less than0.1 mm) is such that gauge blocks can be wrung on top of each other withoutcausing a significant additional uncertainty in length.1 This is due to the1Wringing is the process of attaching two flat surfaces together by a sliding action [6]Gauge blocks – both a practical and traceable artefactdefinition of a gauge block, which states that the length is defined as the distancefrom the measurement (reference) point on the top surface to the plane ofa platen (a flat plate) adjacent to the wrung gauge block [5]. This platen should bemanufactured from the same material as the gauge block and have the samesurface properties (surface roughness and refractive index).
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