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IEEE Instrumentation and MeasurementTechnology ConferenceOttawa, Canada, May 19-21, 1997A Mew Opti cal Sensor for Measurin g the Velocity of Webs

by Correlat ionTechniquesRud ger Zeit eInstitute of Measurement and ControlUniversity of Karlsruhe,76128 Karlsruhe, GermanyPhone (+49 721)608-3174 FAX (+49 721) 661874 E-Mail: zeitler@mrt.mach.uni-karlsruhe.de

Abstract - In this paper a newly developed measurementsystem is presented allowing to measure the velocity ofdifferent bdimensional objects. The measurement sys-tem has already been tested for paper- rubber- and tex-tile-webs sheet metal and road surfaces with a relativemeasurement error of typically less than 1% dependenton the dynamic response of the correlator.The measurement system consists of a sensor unittransforming the stochastic characteristics of the mov-ing object into two signals with a delay time T , and acorrelation unit extracting the delay time from the sig-nals and calculating the velocity of the surface.Different measurements at a test stand and at an indus-trial paper machine will be presented to demonstrate theaccuracy of the measurement system and its flexibilityand robustness. The measurements will include the ve-locity of the paper web in different sections of the ma-chine and velocity fluctuations of the web.

I INTRODUCTIONIn many applications laser Doppler anemometers,spatial frequency methods or simply wheel encodersare used for measuring the velocity of solid surfaces.But none of them are suitable as a measurementsystem for series production: laser Doppler anemome-ters and spatial frequency methods are too expensivewhile wheel encoders are invasive or measure thevelocity with a relative high systematic error due toslipping effects between the solid surface and theencoder wheel.In order to use the transit time correlation method anexisting correlator was simplified making it possible tointegrate the whole correlation system within one ASIC.Besides reducing difficult analog signal-pre-processingthe dynamic response of the system was improved andthe system was made self adaptive to various surfacesroughness. Most of the solbutions proposed in literatureusing correlation technique6 calculate the cross-corre-lation function of two sehsor signals requiring theimplementation of maximum seeking algorithms and

other time consuming calculations. In this paper adifferent method of transit time correlation is usedmaking a measurement range up to 1:400 possible.The digital correlator was developed with respect tosimplicity and low cost realisation. It consists only ofone full adder, three l-bit shift registers and a fewcounters.

II. PRINCIPLES OF TRANSIT TIME CORRELATIONThe mathematical description of a recently developeddigital correlator was discussed in [7]The method implemented in this correlator can beviewed as a closed loop system (Fig. 1). It interpretsthe process generating the sensor signals s l t ) ands 2 t ) = s 1 t - ~ : * ) + n t )s a linear system of the trans-port delay type with a delay time z . The correlatorimplements a model of the system and changes itsparameter - the model delay time z until the differencebetween the sensor signal s 2 t ) and the delayed signalq t - 1 ) is minimal in the mean square sense. In orderto reduce the hardware requirements the sensor signalsare clipped to one bit. The clipping operation producesslight amplitude distortion of the correlation function butdoes not displace the position of its maximum. Never-

s2(t)= sl(t *)+ n(t)

model 4 - t I W L

J IFig. 1. Principle of a closed loopcorrelator.

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theless not all of the information is used thus the RMSof the estimated delay time increases by a factor ofn/2.Compared to an open loop correlator which only calcu-lates the cross-correlation function of the two sensorsignals a t ) and s z t ) and estimates the position of itsmaximum, the closed loop algorithm is superior as faras statistical errors are concerned [3]. The trackingprinciple has the further advantage that any variationsof the system delay time z* and thus of the velocityare detected immediately providing a fast dynamicresponse of the system. Typical time constants of thesystern for measuring the velocity of rough surface areless than 4 ms, that means, velocity fluctuations ofmore than 250 Hz can be detected.

Ill. PRINCIPLE OF THE NEW SENSORThe cross-correlation unction of the two sensor signalsq t ) and9 t ) is given by [6]

where aii 6)xpresses the spatial auto-correlationfunction of the texture of the surface and KgIg2 denotesthe alperture correlation function of the sensor. As thenewly developed correlator does not estimate theposition of the maximum of the cross-correlation unc-tion but estimates the zero crossing of its first differencequotient with finite lag difference [7] the cross-correla-tion function has to be symmetrical to its maximum,othenlvise systematic errors occur. Equation (1) showsthat a necessary condition is given by a symmetricalaperture correlation function Kglg2.In preliminary experiments different sensor principleswere realised with a micro lens bank in order to find themost suitable one for measuring the velocity of 2-di-mensional rough surfaces. Beside a simple sensor with

objective telecentric detectorslens slit I

only two photo diodes and a sensor with orthogonalstructure [4] a differential sensor was tested, whichimages the surface of the web with one lens to threedifferent photo diodes (Fig. 2). The diodes are con-nected in difference, making the system independent ofcorrelated noise and removing the d.c. content of thesignal. But the sensor has to be calibrated in order tocompensate the different sensitivities of the 3 photodiodes and to receive a symmetrical aperture correla-tion function K g I g .Using a telecentric slit the system becomes nearlyindependent of distance variations between the weband the sensor.A small industrial prototype 0 60 mm, length 170 mm,weight 400 g) with an illumination source was devel-oped. The nominal measurement distance was set to170 mm. The signals of the diodes are amplified,filtered and clipped to one bit within the sensor allowingan easy connection of the correlator and the sensor unitwith a cable up to 20 m in length.First the sensor was examined at a test stand at theuniversity of Karlsruhe, Germany. In the following thesystematic and statistical errors of the system arediscussed.Fig. 3 shows the systematic errors dependent ondistance variations between the sensor and the paperweb.As it can be seen the telecentric slit works properly andthe systematic error is smaller than 2 % although thenominal distance changes by nearly 100 %. But there isstill a small dependence especially for distances greaterthan the nominal distance. This error is caused by anon-uniform illumination within the light spot, leading toan asymmetrical cross-correlation unction BI2 2).Next the velocity of the paper web was changed from0.5 m/s to 8 m/s (Fig. 4) whereas the sensor wascalibrated with a velocity of 0.5 m/s.

focal imageplane plane -150 -100 -50 0 50 100 150distance variation [mmlFig. 3 Systematic error dep endent on distance variations.Fig. 2 Set-up of the new op tical sensor.

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0.5

0.4

0.1

0 2 4 6 8velo ity test stand [ s]

Fig. 4. Systematic error depend ent on velocity variations.

The measurement system is slightly dependent on thechosen velocity v too, due to an asymmetrical cross-correlation function, but these errors can be neglected.Now we are interested in the statistical errors of thesystem. Theoretically it was shown in [2] that

where o / v denotes the variation coefficient of thevelocity v which is the relative statistical error, TcL isthe time constant of the correlator and a the band-width of the sensor signals. As the bandwidth is propor-tional to the velocity of the surface this yields

3)

with mn bandwidth of the texture in the spatial domain[4]. That means, as mn is fixed for a given rough sur-face, the higher the velocity the smaller are the statisti-cal errors of the system. Using the distance L = T,, .vmoving through the sensor within the time constant ofthe correlator, (3) yields(4)

Fig. 5 shows the dependence of the variation coefficientof the velocity on the mean velocity measured at thetest stand in Karlsruhe compared with 4), for fourdifferent time constants of the correlator.For a typical evaluated distance of L = 2 0 mm thevariation coefficient is smaller than 1 %.

O + 10 5 10 15

velocity [m/s]Fig. 5 Depend ence of the variation c oefficient of the velocity on themean velocity.

IV. EXPERIMENTAL SET-UPThe main principle of a paper machine is shown in Fig.6 The pulp suspension containing 99.5 Yo water isdispersed on a carrier textile in the wet section.The water is sucked out until the pulp suspensionchanges its state from liquid to solid and the formationof the paper web is nearly completed. In the presssection the paper web moves through two pairs ofcylinders in order to further reduce the water contentand to form the surface of the web. In the dry sectionthe paper web is dried with hot cylinders heated byoverheated steam.As the shrinking of the web requires different speeds inthe production line it is useful to monitor the velocity atdifferent positions. Moreover velocity fluctuations withhigh amplitudes especially in the formation sectionresult in an inhomogenous mass distribution per unitarea and in an increased risk of paper breaks.

presssect ion dry sectionwet section

Qsuction plant

V

99.5 75 55 watercontent 7Fig. 6 Principle set-up of a paper machine.

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V. MEASUREMENTSThe firial measurements were carried out at a papermachine for industrial purpose at the Ecole Frangaisede Papteterie et des Industries Graphiques in Grenoble,France, with a maximum velocity of 0.5 m/s.Two sensors were placed at position 1 in series in thewet section. This arrangement allows to eliminate thevelocity fluctuations of the paper web and only todetermine the statistical errors of the system. Thevelocity of the machine was set to 0.33 m/s and thetime constant of the correlator was set to 30 ms. Thisyields (an evaluated length of 10 mm and according toFig. 5a statistical error of 1 % is expected. The twocorrelators used were synchronised and the differencevelocity normalised by twice the mean velocity wascalculated in Fig. 7.The received values represent thestatistical errors due to the stochastic nature of thesignals and are not dependent on the velocity fluctua-tions of the web.The standard deviation of the statistical error of thesystem is 0.5 % showing the good accuracy at a realpaper machine. The error is clearly smaller than thevalue expected from Fig. 5because the paper used inthe paper machine has a finer structure than the paperat the test stand and the values in Fig. 5include somereal velocity fluctuations of the paper web at the teststand.Next we examined the velocity fluctuations of the webin the wet section at position 1 and in the presssection at position 2 each with one sensor. Thecorrelator and the paper machine were set to the sameconditilons as before. The discrete Fourier transform ofthe velocity variations was calculated, using a signallength of 60 s (Fig. 8 and Fig. 9).

4

3 1

.I1 lmean velocity: 0 33 m/s . IIRMS 0.50 %L-3

0 2 4 6 0 10time[s]

Fig. 7 . ] elative difference velocity of two sensors in the wet sectionnormalised by twice the m ean velocity.

0 01 0 1 1 10 100frequency [Hz]

Fig. 8. Spectrum of th e velocity of the p aper web in the wet section.

0 01 0 1 1 10 100frequency [Hz]

Fig 9 Spectrum of the velocity of the paper web in the press section.

In the wet section there exists a modulation of themean velocity with a frequency of approximately 0.2 Hzdue to longitudinal vibrations of the carrier textile. Asthese modulations are observed at the beginning of thewet section, too, the paper dispersion is disturbedwhich results in a periodical mass distribution per unitarea.In the press section a peak at 0.3 Hz occurs. Using themean velocity one obtains a characteristic length of0.91m which is the circumference of one cylinder in thedriving unit. Obviously the cylinders have an unbal-anced state which could damage the bearings.

VI. CONCLUSIONSThe measurements show the good accuracy androbustness of the new system for measuring the veloc-ity of paper webs. It is not only useful to measure thevelocity of a paper web with an error smaller than 1 %but it also can be used to increase the quality of thepaper web and to detect mechanical problems of themachine.

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The system has already been tested successfully forother surfaces so there exists an enormous potential inusing the new sensor for other applications e.g. meas-uring the velocity of sheet metal, of textile webs or roadsurfaces. In the next step there will be more measure-ments at a new paper machine with velocities up to 12m/s and a detailed analysis of velocity fluctuations up to250 Hz.

ACKNOWLEDGMENTThe author thanks Prof. J.C. Roux and Prof. G. Baudin,Ecole FranGaise de Papeterie et des IndustriesGraphiques, Grenoble, for their co-operation and C.Berger in carrying out the measurements at the papermachine in Grenoble.

REFERENCESl] G. Baudin, Print-thro ugh as a quality factor in printing, XI/

Technical Conference of Paper and Graphic Industry Budapest,1990.[2 ] H. Laqua, Beruhrungslose Geschwindigkeitsmessung vonStraOen- und Schienenfahrzeugen mit Mikrowellensensoren,Doctoral dissertation University of Karlsruhe,1996.

[3]F. Mesch, Speed and flow measurem ent by an intelligentcorrelation system , /SA 90 New Orleans, 1990.[4]F. Mesch, Systemtheoretische Beschreibung optisch-elektrischerSysteme, Technisches Messen atm pp 249-258 eft 718 977.[5] F. Rippinger, G. Schneider, Low cost self-adaptive correlationmeasurement system, IMEKO World CongressX Prague, 1985.[6]M. Weis, Beruhrungslose Geschwindigkeitsmessung an festenOberflachen mit Korrelationsverfahren, Doctoral dissertationUniversity of Karlsruhe, 1993.[7]R. Zeitler, Digital Correlato r for M easuring the Velocity of SolidSurfaces, Proceedings of the lEEE lnstrumentation and Measure-

ment Technology Conference Vol. 1, pp 490-495 russels, June[8]R. Zeitler, Optischer Sensor zur Lauflangenbestimmung vonFasergarnen, GMA Conference Sensors and Measurement Sys-

tems pp 77-82 Bad Nauheim, March 11-13 996.

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