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1 Sensors 006, 6, Special Issue Intelligent Sensors Eite by Wilmar Hernanez Full Research Paper sensors ISSN by MDPI Differential Laser Doppler base Non-Contact Sensor for Dimensional Inspection with Error Propagation Evaluation Samir Meki * an Ketsaya Vacharanukul The University of Manchester, School of Mechanical, Aerospace an Civil Engineering. PO Box 88, Manchester, UK * Author to whom corresponence shoul be aresse. S.Meki@manchester.ac.uk Receive: 5 April 006 / Accepte: 13 June 006 / Publishe: 15 June 006 Abstract: To achieve ynamic error compensation in CNC machine tools, a non-contact laser probe capable of imensional measurement of a workpiece while it is being machine has been evelope an presente in this paper. The measurements are automatically fe back to the machine controller for intelligent error compensations. Base on a well resolve laser Doppler technique an real time ata acquisition, the probe elivers a very promising imensional accuracy at few microns over a range of 100 mm. The evelope optical measuring apparatus employs a ifferential laser Doppler arrangement allowing acquisition of information from the workpiece surface. In aition, the measurements are traceable to stanars of frequency allowing higher precision. Keywors: In-process inspection, Differential Laser Doppler, Error propagation. 1 Introuction Zero efect parts coul only be obtaine via full automatic error compensation while they are being machine on the next generation of intelligent machining processes to ensure high quality proucts at low price an short time. Off-line axis error compensation is successfully achieve with NC machines incluing thermal growths while on-line compensation still has some ifficulties mainly with probes harware an controllers [1-]. Quality control of the manufacture parts is traitionally performe using manual inspection methos an statistical sampling proceures. It has the isavantages of releasing some efective parts an using an inspection area. To overcome these problems, in-process

2 Sensors 006, inspection with error correction in NC machines is propose as another alternative. In-process measurement techniques have been propose over the last two ecaes to control the quality of a workpiece with some ifficulties to be aresse. The tren principle in this type of inspection is to use a measuring probe with a measurement control system an to ajust machining parameters to reach the nominal imension with the require accuracy. A Full review of the evelope in-process methos since 1961 is iscusse in Shiraishi [3], Yanayan an Burekin [4], an, Vacharanukul an Meki [5]. Optical measurement techniques have the avantage to be fast an contact less. A variety of optical sensors are applie to measurement in metrology. The most common techniques inclue triangulation [6], shearing interference [7], coherence raar [8] an laser Doppler techniques [9]. Laser Doppler Velocimetry has proven to be very accurate an repeatable over years for flui applications such as anemometry [10]. Also Laser Doppler system fins applications in length measurement of sheet materials (e.g. paper, textiles an foils) [11]. Recently, an inirect measurement metho for the etermination of the surface velocity in vibrating structures base on laser Doppler vibrometry was investigate [1]. In mass prouction, the iameter is one of the significant parameters to be inspecte. Many measurement techniques have been evelope to measure the iameter of a workpiece [5]. In this paper, an in-process laser Doppler technique is presente to measure a iameter of the moving workpiece. The funamental metho of ifferential Doppler technique is employe for soli material with an emitting laser kept clean from back lights using polarizer an retarer as well as an optical amplification of the scattere light. The Doppler signal is acquire in real-time an processe for noise reuction an FFT autocorrelation to accurately etermine the Doppler frequency an hence the workpiece iameter. It is expecte to enhance the accuracy of measurement up to very few micrometers over a range of 100 mm with a very goo traceability of measurements as it uses Laser light as core component. Theory The principle of ifferential laser Doppler requires two beams to generate a measuring volume. The shape of the measuring volume is an ellipsoi as illustrate in Figure 1(a). The size of the measuring volume can be calculate by; e = (1) m cosθ l = e () m sinθ where is the waist iameter of the focuse laser beams after the focusing lens (Figure 1(c)), m e an l m are respectively the transversal size an the longituinal size of the measuring volume. can be approximately expresse as e 4Fλ (3) π where L is the iameter of the laser beam an F is the focal length of the focusing lens [6]. The Doppler signal occurs when particles or a moving surface pass through the ellipsoial measurement volume. L e

3 Sensors 006, (c) L (a) y e - θ m z l m x e - (b) Figure 1. Ellipsoi of fringes an measuring volume parameters. The light waves of two beams interfere with one another in the crossing region, creating an interference pattern which consists of parallel fringe planes (Figure (a)). The fringe spacing, f, is given by Eq.4, where θ is the angle between a beam an the optical axis an λ is the laser wavelength. f λ = sinθ (4) As the imension of the measuring volume an the fringe spacing are efine, the number of fringes in the measuring volume N f can be given by Eq.5. m N f = (5) f The number of fringes can also be expresse in terms of optic an wavelength parameters in Eq.6. N f 4Fλ λ = (6) π cosθ sinθ L Slightly ifferent expressions were propose in [13-14] to estimate the size of the measuring volume an the number of fringes epening on the crossing location of the beams for which the beam energy is calculate. The fringe counting has been checke with the current test-bench (Figure 1(b)) an it was foun that expression shown in Eq.6 is more accurate compare to those propose in [13-14]. Moreover, the occurrence of fringes epens on the properties of light source. One main property is calle the coherence length. If the optical path ifference between two beams is less than the coherence length, fringes will occur. Thus, the coherence length is one constraint for the optical arrangement base on the ifferential Doppler technique. The coherence length, L c, is etermine by Eq.7. c L c = (7) ν where c is the light spee in vacuum an ν the spectral linewith. In this arrangement, a common He- Ne laser is known to be stable an has a line with of approximately 1.5 GHz; as a result, the coherence length is approximately 0 cm accoring to Eq.7 an is greater than the current path ifference (i.e. 1-cm). However, the path ifference coul be cancelle by a simple optical arrangement. The frequency of the scattere light, f, inuce by a particle crossing the fringes is

4 Sensors 006, proportional to the component of the particle velocity,ν p, perpenicular to the fringe planes an inversely proportional to the fringe spacing as in Eq.8. v p v p sinθ f = = (8) f λ The scattere light is collecte by a photo etector which generates an electrical signal. The measurement of the object velocity is converte into frequency measurement of the electrical signal with a scale factor. As the frequency measurement can be easily performe in a wie span of frequencies up to 100 MHz, the flui velocity can therefore be measure from low to high velocities. A particle crossing through the interference region in Figure (a) will evelop a clean oscillation with a Gaussian envelope as the laser operates in the TEM 00 moe. This is the Transverse Electromagnetic Moes (TEM) of the laser beam, which is the wave pattern on the output aperture plane. This particular moe (TEM 00 ) has circular symmetry an a Gaussian profile as shown in Figure (b). The signal becomes weaker as the particles cross away from the center of the interference region. Laser Beam 1 w θ θ f m Laser Beam ν p l m TEM 00 moe (a) (b) Figure. (a) The interference pattern cause by crossing between two beams. (b) TEM 00 moe. 3 Laser probe escription A non-contact, in-process imensional probe has been evelope to measure workpiece iameter base on the ifferential laser Doppler technique. The basic principle of the arrangement is to generate fringes on the workpiece surface where the circumferential velocity is normal to the fringe pattern an to etect the Doppler signal obtaine from the scattere lights. The probe is shown in Figure 3. A laser beam is split into two beams whose parallelism is secure by a right angle prism. The beams go through the focusing lens an cross at the focal length. The scattere light from the workpiece surface is collecte by a lens an a photoetector. However, some reflecte lights an the scattere lights from the workpiece surface can return back to the laser hea causing a chaos in the emitting laser. Hence a polarizer an a retarer are place in front of the laser hea to block these lights before they reach the laser hea. If the laser light passes through a polarizer an a retarer, respectively, the output light will be a circular or elliptical. Lights reflecte an scattere from the workpiece surface have possibly

5 Sensors 006, other planes of polarization compare to the incient beam. As a result, the reflecte lights an the scattere lights shoul probably be stoppe or at least ecrease. Right angle Mirror Polariser/Retarer Fiber Optic Scattere light Workpiece Focusing lens Beam splitter Ampli-Filter circuit Photoioe Collecting lens Figure 3. Differential Doppler technique probe an its location on a Takisawa lathe machine. The laser light is scattere from the moving surface passing through the fringes. It oscillates with a specific frequency that is relate to the velocity of the workpiece. The workpiece iameter can be calculate using the relationship between the circumferential velocity, V, an the rotation spee, N, which equation is shown as follow: V = πnd (9) 60 where D is the iameter of the workpiece an N is the number of revolutions per minute. Accoring to Eq.7 an Eq.9, the Doppler frequency relates to the circumferential velocity of the workpiece epening on the angular velocity an the iameter of the workpiece. By revising the Doppler frequency equation, the iameter of a workpiece, D, is given by Eq λf D = (10) πn sinθ When a particle in flui or gas passes through the fringe volume, a burst of Doppler signal occurs. Scattering from a iffusing soli surface can be consiere equivalent to a multitue of particles istribute ranomly in the measuring volume for flow measurements. Figure 4 (b) shows a typical signal from a soli workpiece surface with the current probe. The signal inclues Doppler signal with noises. These low-frequency noises can be eliminate using a high-pass filter. The acquire signal was processe by fast Fourier transformations (FFT) technique. The spectrum is fitte with a Gaussian istribution to locate neatly the centre frequency (Figure 4(a)). The stanar eviation of the centre frequency ( σ ) is given by Eq.11. fc 1 σ f c = (11) πσ where σ t is the stanar eviation of the Gaussian or the acquisition time. Revising Eq.11, the relative accuracy ( σ /f ) of the Doppler measurement can be expresse by Eq.1. fc t

6 Sensors 006, σ f 1 c = (1) f π. n where n total is the number of fringes within the acquisition time. It appears from equations 11 an 1 that better accuracy can be achieve with the longer acquisition time. total (b) ) Figure 4. (a) Data Spectrum with Gaussian fit, (b) Bursts of Doppler signal from soli surface. 4 Parameters affecting the accuracy of iameter measurement an error propagation As this is not a irect measurement, the accuracy of the iameter measurement epens on the performance of its components. A unifie metho for the evaluation an expression of measurement uncertainties is publishe within the Guie to the expression of Uncertainty in Measurement (GUM) [15] which is accepte worlwie. The combine stanar uncertainty, u c, as the stanar uncertainty of the measurement of Y, by combining the iniviual stanar uncertainties an co-variance, epening on the case an using the law of propagation of uncertainty: u N f N c y = i= 1 ( ) u i i= 1 = + i j x j i i 1 (13) xi xj where f xi are the partial erivatives f X i evaluate at X i = xi an u ( x i, x j ) are the estimate covariance associate with x i an x j. Eq.13 is base on a first-orer Taylor series approximation of Y = f ( X X,..., ) (14) N 1 f f ( x ) + u( x, x ) Where Y is the measuran etermine from N input quantities X 1, X,,, X N through a functional relationship f. An estimate of the measuran Y, represente by y, is obtaine from Eq.13 using input estimates x 1, x,, x N for the values of the input quantities. The output estimate which is the results of measurement is then given by y = f ( x x,..., ) (15) The performance of each component for the in-process laser probe consiere in this paper as well as the propagation of uncertainty are iscusse hereafter. Other source of errors may be inuce by beams misalignment an ajustment. 1, 1, X N x N

7 Sensors 006, Accuracy of He-Ne Laser A He-Ne laser is recognise to have a narrow variation in wavelength, which generally falls within a range of 10-1 m. The wavelength stability epens on the linewith of the laser. The change in the wavelength ue to the linewith, λ, can be calculate by: λ ν λ = (16) c + ν λ Where λ is the wavelength of the laser, c is the light spee in vacuum an ν is the spectral linewith of the He-Ne laser (1.5GHz). By substituting λ = 63 nm into Eq.16, λ is approximately 0.00 nm. This variation causes an error in the iameter measurement base on the ifferential Doppler technique. The error owing to the wavelength variation at 0.00 nm for a 100 mm iameter workpiece at 1000 rpm an at θ = 7.15 is shown in table 1. Therefore the error in iameter will be approximately 0.3 µm. Thus, the effect of the laser wavelength on the require accuracy of iameter measurement of micrometer is consiere acceptable. Table 1. Variation of wavelength with Doppler frequency. λ [nm] f [Hz] Accuracy of the Doppler frequency As Gaussian fit is applie to etermine the Doppler frequency, the relative accuracy of the Doppler frequency measurement, σ f /f is etermine by equations 11 an 1 an is less than 0.01%. 4.3 Accuracy of the beam crossing angle The angle between a beam an the optical axis is given by Eq.17. = tan 1 θ (17) F where R os is the axial offset of the beams an F is the focal length of the transmitting lens. Thus, the angle error epens upon the accuracy of R os an F. The accuracy of is estimate to be 0.1%. R os 4.4 Accuracy of the number of revolutions per minute In general the number of revolutions per minute is measure using timers an counters within the motion controller car but usually the value is acquire from the NC machine controller. The accuracy of rotative spee is better than 0.01%.

8 Sensors 006, Error Propagation The error propagation has been calculate in this inirect measurement comprising the previous escribe four parameters with the associate estimate errors. The iameter which is calculate from Eq.10 can be expresse into a more general form as shown in Eq.18. D = f ( λ, f, N, θ ) (18) The overall expression of the error propagation of the first orer has been erive from Eq.13 as shown in Eq.19. D D D D D D δd = δλ + δf + δθ + δn + δf N λ f θ N f N (19) where D, f D, λ D D an θ N are the partial erivatives of D with respect to f, λ, θ an N while δλ, δ f, δθ an δ N are the change in λ, f, θ an N, respectively. Base on Eq.13 these changes are enote for example as δ f = u( f ). All the previous parameters are not correlate except the Doppler frequency; f an the rotation spee; N that are correlate parameters, hence the introuction of δ f N. The algebraic contribution of this part of the uncertainty is negative. 5 Experimental setup an calibration During the construction of the probe, a test bench has been built to host a laser source emitting a stable laser beam which is split into two beams. The two beams are aligne at long istance. The beams go then through an acromat lens an are focuse on the workpiece surface. The workpiece is rotate with stable, controlle angular spee at the relative accuracy of <0.5%. The scattere light is focuse onto the photoioe using a single biconvex lens. An electronic circuit has been evelope to amplify the signal an to filter it in high pass moe as the Doppler frequency is workpiece iameter an rotation spee epenant. The signal processing is evelope uner LabView environment with real time ata acquisition. The signal spectrum is calculate by FFT. A Gaussian fit to locate the centre of the spectrum which yiels the Doppler frequency. An auto focus system may be require to keep the measuring ellipsoi volume within the workpiece skin. If the workpiece has larger raial vibrations, measurement coul be interrupte as shown in Figure 5. Usually any raial vibration shoul be within the ellipsoi length. The probe has been calibrate over the range of measurement against four ifferent reference iameter parts (5, 50, 75 an 100mm.) inspecte accurately with a CMM machine. As a result, the factor, which represents the relationship between the Doppler frequency an spee, can be evaluate from the calibration process.

9 Sensors 006, Workpiece surface Ellipsoi of fringes Limit of reial vibration of the workpiece Figure 5. Raial vibration limit of the workpiece to achieve measurement. 6 Tests an results Extensive tests have been carrie out on various iameters up to 100 mm. A sample of measurements is presente in this paper. Two ientical imension workpieces with ifferent surface roughness values were rotate in a CNC machine. The workpiece iameters were measure using the current probe. The results of the measurements are shown in table. The measurements were taken at 550 rpm an the Doppler frequency for the iameter of 30 mm was 183 khz with an uncertainty of Hz which is less than 0.01%. The maximum systematic error for the measurements is within 10 µm over a range of 100 mm. Table. Diameters measurement. Workpiece 1 (Ra=0.080µm) δd D [mm] [µm] Workpiece (Ra=0.145µm) D [mm] δd [µm] The aim of testing the probe with two workpieces having ifferent surface roughness is to investigate whether the surface roughness affects to the probe. Figure 6 shows that the rougher workpiece generates more back-scattere light intensity than the smoother workpiece oes. This may occur as the rougher workpiece provies more scattere points.

10 Sensors 006, (a) (b) Figure 6. The Doppler signal from two ifferent surface roughness workpieces; (a) from the smoother workpiece an (b) from the rougher workpiece. 7 Conclusion An in-process an non-contact imensional measurement sensor has been presente in this paper. The performance of the ifferential laser Doppler technique applie to soli material has been emonstrate through various tests an iameter measurements. The overall accuracy epens on the accuracy performance of the probe components. The measurements have shown very goo accuracies but it is believe that these coul be improve accoring to the theory. The effects of thermal growth shoul be taken into account although the probe is usually to be use for preictive action near finishing passes to control the final accuracy. The ifferential laser Doppler technique seems to be well suite for non-contact imensional measurement. With the traceability of measurements, further evelopments are expecte to quantify the errors of form that a workpiece may have such as rounness an eccentricity. The work is also extene to profile etermination.

11 Sensors 006, References 1. Soons, J.A.; Theeuws, F.C.; Schellekens, P.H. Moelling the errors of multi-axis machines: a general methoology. Precision Engineering 199, 14(1), McKeown, P.A.; Weck, M.; Bonse, R. Reuction an compensation of thermal error in machine tools. Annals of the CIRP 1995, 44(), Shiraishi, M. Scope of in-process measurement, monitoring, control techniques in machining processes. Precision Engineering 1989, 11(1), Yanayan, T.; Burekin, M. In-process imensional measurement an control of workpiece accuracy, Int. J. Machine Tools an Manufacture 1997, 37, Vacharanukul, K.; Meki, S. In-process imensional inspection sensors. Measurements 005, 38, Dorsch, R.G.; Hausler, G.; Herrmann, J.M. Laser triangulation: funamentals uncertainty in istance measurement. Applie Optics 1994, 33(14). 7. Hausler, G.; Hermann, J.M. Range sensing by shearing interferometry: influence of speckle, Applie Optics 1988, 7(7) Dresel, T.; Hausler, G.; Venske, H. Three-imensional sensing of rough surfaces by coherence raar, Applie Optics 199, 31(5), Sriram, P.; Hanagun, S.; Craig, J.; Komerath, N.M. Scanning laser Doppler technique for velocity profile sensing on a moving surface. Applie Optics 1990, 9(17), Absil, L. H. J. Analysis of the laser Doppler measurement technique for application in turbulent flows, Deft University of Technology, Netherlans, Stork, W.; Wagner, A.; Kunze, C. Laser Doppler sensor for spee an length measurements at moving surfaces. Proceeings of SPIE 001, 4398, Martarelli, M.; Revel, G.M. Laser Doppler vibrometry an near-fiel acoustic holography: Different approaches for surface velocity istribution measurements. Mechanical Systems an Signal Processing 006, 0, Durrani, T. S.; Greate, C. A. Laser systems in flow measurement, Plenum Press, New York an Lonon, Donati, S. Electro-optical instrumentation: sensing an measuring with lasers, Prentice Hall PTR, Guie to the expression of uncertainty in measurement. International Organisation for Stanarization (ISO), Geneva, by MDPI ( Reprouction is permitte for noncommercial purposes.