McGraw-Hill CreateTM Review Copyfor lnstructor Nicolescu.Not fordistributionExperimental MethodsforEngineers,EighthEdition9092615.4OPTICAL METHODSOptically flatmirror, MLens, LAMonochromaticWork-piece, WsourceSplitterplate,S2Screen, S3Figure 5.6Schematicofinterferometer.Table 5.1MonochromaticlightsourcesHalf-wavelengthWavelength,Fringe Interval,SourceμumμmHelium0.5890.295Krypton 860.6060.3030.5460.273Mercury 1980.5980.299Sodiumcalibrationofgageblocksand otherapplicationswhereextremelypreciseabsolutedimensional measurements are required.For detailed information on experimentaltechniques used in interferometry the reader should consult Refs. [3] and [5]. The useoftheinterferometerforfluid-flowmeasurementswillbediscussed inChap.7.As shown inEq.(5.1),thewavelength of themonochromatic light sourcewillinfluence the fringe spacing.Table 5.1 lists the wavelengths of some common lightsources and thecorrespondinghalf-wavelengthfringeinterval.INTERFERENCEMEASUREMENT.A mercury light source employs a green filter suchExample5.2that the wavelength is 5460 A. This light is colliminated and directed onto two tilted surfaceslike those shown inFig.5.5.Atone endthe surfacesare in precise contact.Between the pointofcontactand a distance of3000 in five interferencefringes are observed.Calculate the separationdistance between the two surfaces and the tilt angle at this position.SolutionThefivefringe linescorrespond to入/2.3入/2..,9/2;that is,for the fifthfringeline9入2d=2
5.4 Optical Methods 261 Screen, S3 Lens, L Optically flat mirror, M Monochromatic source Splitter plate, S2 Workpiece, W Figure 5.6 Schematic of interferometer. Table 5.1 Monochromatic light sources Half-wavelength Wavelength, Fringe Interval, Source μm μm Helium 0.589 0.295 Krypton 86 0.606 0.303 Mercury 198 0.546 0.273 Sodium 0.598 0.299 calibration of gage blocks and other applications where extremely precise absolute dimensional measurements are required. For detailed information on experimental techniques used in interferometry the reader should consult Refs. [3] and [5]. The use of the interferometer for fluid-flow measurements will be discussed in Chap. 7. As shown in Eq. (5.1), the wavelength of the monochromatic light source will influence the fringe spacing. Table 5.1 lists the wavelengths of some common light sources and the corresponding half-wavelength fringe interval. INTERFERENCE MEASUREMENT. A mercury light source employs a green filter such Example 5.2 that the wavelength is 5460 A. This light is colliminated and directed onto two tilted surfaces ˚ like those shown in Fig. 5.5. At one end the surfaces are in precise contact. Between the point of contact and a distance of 3000 in five interference fringes are observed. Calculate the separation distance between the two surfaces and the tilt angle at this position. Solution The five fringe lines correspond to λ/2, 3λ/2,., 9λ/2; that is, for the fifth fringe line 2d = 9λ 2 hol29303_ch05_256-277.pdf 6 ol29303_ch05_256-277.pdf 6 8/12/2011 3:23:24 PM /12/2011 3:23:24 PM Experimental Methods for Engineers, Eighth Edition 909 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution
McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.Notfordistribution910Signal Processing and Engineering Measurements262CHAPTER SDISPLACEMENT AND AREA MEASUREMENTSWe have 入 = 5460 × 10-8 cm = 2.15 × 10-5 in so thatd = (2.15 × 10-5) = 48.4 μinThe tilt angle isΦ = tan-1 48.4 × 10-648.4 × 10-6= 16.1 × 10-6 rad3.0003.000Mechanical displacement may also be measured with the aid of the electric trans-ducers discussed in Chap.4.TheLVDT,for example,canbeused tosensedisplacements as small as1 μin.Use of LVDT devices for displacement measurements isdescribed in Ref. [17]. Resistance transducers are primarily of value for measure-mentoffairlylargedisplacementsbecauseoftheirpoorresolution.Capacitanceandpiezoelectric transducers,on the other hand,provide high resolution and are suitablefordynamicmeasurements.5.5PNEUMATICDISPLACEMENTGAGEConsider the system shown in Fig.5.7. Air is supplied at a constant pressure pi.Theflowthroughthe orifice and throughtheoutlet of diameterd2isgoverned bythe separation distancexbetween the outletand theworkpiece.Thechangein flowwith x will be indicated by a change in the pressure downstream from the orifice p2.Thus,ameasurementof thispressuremaybetakenasan indicationof theseparationdistancex.Forpurposesof analysisweassumeincompressibleflow.(SeeSec.7.3foradiscussion of thevalidityofthisassumption.)ThevolumetricflowthroughanorificemayberepresentedbyQ= CAVAp[5.2]Ambient pressure≤PoOrificeoFlowdidOFigure5.7Pneumaticdisplacementdevice
262 CHAPTER 5 • Displacement and Area Measurements We have λ = 5460 × 10−8 cm = 2.15 × 10−5 in so that d = 9 4 (2.15 × 10−5 ) = 48.4μin The tilt angle is φ = tan−1 48.4 × 10−6 3.000 = 48.4 × 10−6 3.000 = 16.1 × 10−6 rad Mechanical displacement may also be measured with the aid of the electric transducers discussed in Chap. 4. The LVDT, for example, can be used to sense displacements as small as 1 μin. Use of LVDT devices for displacement measurements is described in Ref. [17]. Resistance transducers are primarily of value for measurement of fairly large displacements because of their poor resolution. Capacitance and piezoelectric transducers, on the other hand, provide high resolution and are suitable for dynamic measurements. 5.5 Pneumatic Displacement Gage Consider the system shown in Fig. 5.7. Air is supplied at a constant pressure p1. The flow through the orifice and through the outlet of diameter d2 is governed by the separation distance x between the outlet and the workpiece. The change in flow with x will be indicated by a change in the pressure downstream from the orifice p2. Thus, a measurement of this pressure may be taken as an indication of the separation distance x. For purposes of analysis we assume incompressible flow. (See Sec. 7.3 for a discussion of the validity of this assumption.) The volumetric flow through an orifice may be represented by Q = CAp [5.2] Flow Orifice d1 d2 x Workpiece Ambient pressure pa 1 2 Figure 5.7 Pneumatic displacement device. hol29303_ch05_256-277.pdf 7 ol29303_ch05_256-277.pdf 7 8/12/2011 3:23:24 PM /12/2011 3:23:24 PM 910 Signal Processing and Engineering Measurements McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.