A ROTATIONAL SPEED MEASURING AND CALIBRATION SYSTEM BASED ON LASER DOPPLER VELOCIMETRY

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1 XXI IMEKO World Cogress Measuremet i Research ad Idustry August 30 September 4, 2015, Prague, Czech Republic A ROTATIONAL SPEED MEASURING AND CALIBRATION SYSTEM BASED ON LASER DOPPLER VELOCIMETRY Cheg Liu 1, Ji-Gou Liu 1, Ralph Keel 2 1 CheYag Techologies GmbH & Co. KG, Markt Schwabeer Straße 8, Fisig, Germay cheg.liu@cheyag-ism.com, jigou.liu@cheyag-ism.com 2 Istitute for Electrical Drive Systems ad Power Electroics, Techische Uiversität Müche, Arcisstraße 21, Muich, Germay ralph.keel@tum.de Abstract A rotatioal speed measurig ad calibratio system based o the Laser Doppler Velocimetry is proposed i this paper. The rotatioal speed of a motor i the system ca be determied by measurig the tagetial liear velocity of a rotatig referece disc mouted o the motor shaft with a Laser Surface Velocimeter. Measurig deviatios caused by maufacturig ad moutig errors of the referece disc are aalyzed ad compesated. Therefore, a measurig accuracy of better tha 0.1% is realized. Keywords: Rotatioal Speed Measuremet, Laser Doppler Velocimetry, Laser Surface Velocimeter, Sigal Processig, Electrical Drive 1. INTRODUCTION Rotatioal speed measuremet is a importat operatio for applicatios i idustry ad automatio. Especially i electrical drive systems, rotatioal speed sesors are essetial for a proper fuctioality of the whole machie [1]. I the past, aalogue precisio tachometers or tachogeerators did a quite good job for drive systems. But with the digital era ad the associated techical developmet of digital cotrol i electrical drives, these sesors are replaced by high resolutio resolvers or ecoders. Nevertheless, the performaces of digital speed cotrol are t as good as those of the former aalogue speed cotrol [2]. For solvig the problems, a ovel sigal processig method is proposed for directly determiig the rotatioal speed uder usig samplig data from rotatioal speed sesors. High resolutio ad accuracy ca be realized by usig this method. This method ca be used i all rotatioal speed sesors ad ecoders [3]. I order to evaluate the sigal processig method, a rotatioal speed measurig system with high resolutio ad accuracy is eeded. Laser Doppler Velocimetry ca be used for measurig liear velocity with high resolutio ad accuracy [7]. Therefore it is the best choice for buildig the rotatioal speed measurig system, which provides both high resolutio ad accuracy i compariso to optical ecoders ad magetic resolvers [4]. However, such a precise measurig system does ot exist o the market. I this paper a rotatioal speed measurig ad calibratio system is itroduced by usig Laser Doppler Velocimetry. The tagetial liear velocity of a rotatig referece disc mouted o the shaft of a motor ca be measured with a Laser Surface Velocimeter (LSV) [7]. The rotatioal speed of the motor ca be determied by usig the measurig results of the liear velocity. The accuracy of the measurig system is cotrolled withi 0.1% after the system optimizatio ad error compesatio. 2. ROTATIONAL SPEED MEASURING SYSTEM Fig. 1 shows the rotatioal speed measurig ad calibratio system, which cosists of a velocimeter Polytec LSV-1000 (1) [7], a motor test stad (2), a oscilloscope (3) ad a PC system with a data acquisitio uit (4). Fig. 1. Rotatioal Speed Measurig ad Calibratio System O the motor test stad (see Fig. 2), a referece disc (6) ad a target wheel (7) are mouted o the shaft of the motor (5). The rotatioal speed of the motor ca be measured with the velocimeter LSV-1000 ad referece disc. A speed sesor uder test (8), for istace Hall-Effect Gear Tooth Sesor coupled with the target wheel, is used also to measure the rotatioal speed of the motor. This measurig system cosists of two chaels, as show i the block diagram (Fig. 3). The first chael is called Referece Chael, which cosists of the velocimeter LSV-1000 ad the referece disc. The referece disc is drive by the motor with a ukow rotatioal speed. The tagetial liear speed of the rotatig referece disc is measured by the velocimeter LSV The secod chael, which is kow as the Sesor Chael, cotais the target wheel, the speed sesor uder test ad a oscilloscope. The target wheel is also drive by the motor, the rotatioal speed of which is detected with the

2 rotatioal speed sesor at the same time. The sesor output sigal is sampled with the oscilloscope. based o the priciple of Laser Doppler Velocimetry, which is explaied i the followig. A Laser Doppler Velocimeter (LDV), which is also kow as a Laser Doppler Aemometer (LDA), is a iterferometric measurig system that detects the liear velocity of objects usig laser light [4]. The objects ca be particles i a fluid or solid surfaces. Laser Doppler Velocimetry is based o the priciple of Laser Doppler Effect which uses the frequecy of light istead of soud for measuremets [5]. As we kow from the Doppler Effect, the soud frequecy of a object chages at a statioary iertial poit if this object passes it. The same effect ca be see with the diffractig light o a object i motio Fig. 2. Motor Test Stad (motor (5), referece disc (6), target gear (7) ad Hall-Effect Gear Tooth Sesor (8)) The Referece ad Sesor Chaels are coected to the PC system, which samples the measurig data from both chaels, i.e. the LSV-1000 ad the oscilloscope. The referece rotatioal speed ω ref of the motor ca be determied by usig the measured data of the Referece Chael. The rotatioal speed ω of the motor ca be also calculated by sigal processig uder usig the measurig data of the Sesor Chael. The measurig deviatio ω of the sesor uder test ca be determied by: The Polytec LSV-1000 uses cocretely the Differece Doppler Process. I the Differece Doppler Process, two laser beams are aliged to the optical axis i a agle φ. Both laser beams are superimposed o the surface of the movig object. Thus a iterferece patter of dark ad bright friges is detectable (see Fig. 4). ω = ω ω ref ω ref (1) with ω ref as measurig deviatio of the Referece Chael. Fig. 4. Two laser beams with same wavelegth λ are superimposed o the surface of a movig object ad create a iterferece patter with dark ad bright friges of distace s [7]. Whe both laser beams are from the same light source, they have the same wavelegth λ. The friges have a distace Δs ad ca be calculated by the wavelegth λ ad the agle φ: Δs = λ 2 siφ (2) Fig. 3. Block Diagram of Rotatioal Speed Measurig System. 3. LASER DOPPLER VELOCIMETRY I order to use this system to test ad calibrate rotatioal speed sesors ad ecoders, the Referece Chael must have a high accuracy. The Polytec LSV-1000 is a liear velocity measurig system with a high accuracy of 0.05% ad a high resolutio of 5 mm/mi. The maximum detectable speed is 7200 m/mi. This measurig device is We ca assume a poit P i the iterfered regio, which moves with a velocity v P. Due to the Laser Doppler Effect, both laser beams affect a Doppler shifted frequecy at this poit P. The object surface is t ideally smooth. Thus this object emits a scattered light waves, which is also Doppler shifted by the velocity v P. With the frige patter ad superimposed diffracted light waves, the photo detector gets a modulated AC sigal with the Doppler frequecy f D. Because the optical axis is perpedicular to the object surface ad the movig directio, the fial equatio is

3 f D = 2v P siφ (3) λ For detectig velocity directios, the iterferometer works i the heterodye mode. I this mode, oe laser beam has a shifted offset frequecy of f B, so that the modulated Doppler frequecy should be writte as f D = 2v P λ siφ + f B (4) The offset frequecy f B should be chose i i the rage of Megahertz, e.g. 40 MHz i products of Polytec GmbH ([6], [7]). As you ca see, the Differece Doppler techology is suitable for measurig the liear velocity ad for velocity directio detectio. Therefore the Polytec LSV-1000 ad its workig priciple ca be used for rotatioal speed measuremets. 4. ERROR ANALYSIS AND ACCURACY IMPROVEMENT By measurig the tagetial liear velocity v of the referece disc with the LSV-1000, the rotatioal speed ω ref ca be determied by v ad the circumferece U = πd = 2πR (see Fig. 5): ω ref = v U = v πd = v 2πR (5) Fig. 6. Deviatio a betwee the rotatioal ceter ad the circle ceter of the referece disc The distace X betwee P ad M2 chages with the agle β. It ca be derived uder the coditio R a: X = R + a cosβ (6) For a further aalysis, a small circular segmet ds ca be cosidered, which is illustrated i Fig. 7. This segmet is detailed by the variable radius X ad the agle dγ: ds = X dγ (7) Because this segmet is very small, oe ca assume dβ = β 2 β 1. So the equatio (4) ca be writte as: ds = (R+a cos β) β 2 β 1 dγ dβ (8) For determiig the circumferece U, ds should be itegrated over all circular segmets of the disc. The circumferece ca be determied by: U = ds = α β 2 (R+a cos β) 0 β 1 β 2 β 1 dγdβ (9) Fig. 5. Rotatioal Speed Measuremet with Polytec LSV-1000 ad Referece Disc. Due to maufacturig ad moutig toleraces, two mai errors of the referece disc are existig: the ceter deviatio a ad the radius deviatio R. Both errors cause deviatios of the circumferece U ad therefore measurig deviatios i the Referece Chael. 4.1 Ceter Deviatio The ceter deviatio of a disc is visualized i Fig. 6. M1 is the ceter of the circle which has the radius R, while M2 is the ceter of rotatio. P is the poit where the laser beam from the Laser Doppler Velocimeter impiges o the referece disc. The distace betwee M1 ad M2 is a. Fig. 7. Circular Segmet ds with variable Radius X ad Agle dγ. By solvig this double itegratio, the circumferece is also depedet o the siusoid fuctio of the rotatioal agle α: U = 2πR + a siα (10) Therefore the maximum deviatio of the circumferece is U = ±a, whe siα = ±1. For compesatig this udesired deviatio, measurig values i oe or more full rotatios should be take ito accout for the calculatio of the referece rotatioal speed. That meas α = 2 π, εν, ad thus siα = 0. I this way, the deviatio U does t exist aymore, ad oe obtais U = 2πR.

4 Diameter (mm) 4.2 Radius Deviatio The maximum relative deviatio of the rotatioal speed measuremet is the sum of the relative deviatios of the liear velocity ad the disc radius accordig to (5): ω ref ω ref max = v v max + R R max (11) The measurig deviatio of the liear velocity is kow as 0.05%. Therefore the task here is to determie the maximum deviatio of the disc radius. I fact, the radius R ca be described as follows: R(α) = r + r(α) = R i (12) 40,24 40,23 40,22 40,21 40,2 40,19 40,18 40,17 40,16 40, Number of Measuremets The deviatio of the radius R at rotatio agle α ad the mea radius r is give by r(α) = r i. Because this error has a Gaussia distributio, the mea radius r ca be calculated by r = 1 R i=1 i = r s (13) By cosiderig a larger umber of measuremets <, the result is the estimated radius r s, which ca be assumed as the true value [9]. The diameter of the referece disc ca be measured with a precise legth measurig istrumet. Oe obtais measured values R i at measurig poits. After calculatig the mea radius r s accordig to (13), the referece rotatioal speed ω ref ca be determied by Fig. 8. Measured Diameters of the referece disc with a Caliper of measurig tolerace 0.01 mm From these measuremets, a mea diameter of mm ca be determied, which is used for further referece rotatioal speed calculatios. For istace, a rotatioal speed measuremet from the Referece Chael is show i Fig. 9. The measured values are disturbed with a white oise, which shows a Gaussia distributio. For gettig the real rotatioal speed value, the mea value over the umber of samples is cosidered as referece rotatioal speed. ω ref = v 2πr s (14) I this way the errors r i are compesated completely: i=1 r i = i=1 (R i r s ) = 0 (15) So oly the tolerace of the precise legth measurig istrumet plays a role. For example, if this istrumet has a measurig tolerace e G of mm, with a referece disc of mea radius 40 mm, the relative deviatio is R R max = e G r s % (16) This results i a relative deviatio ( ω ref/ω ref) of % for the whole measurig system accordig to equatio (11). 5. EXPERIMENTAL RESULTS AND APPLICATION EXAMPLE Fig. 8 shows the measured diameters of the real referece disc with a electroic caliper. The desiged diameter of this referece disc is 40 mm. This caliper has a measurig tolerace of ±0.01 mm. Therefore, a relative deviatio is ±0.025% for the diameter ad the radius. It meas a total accuracy of 0.075%. Thus the accuracy of the measurig system ca be cotrolled withi 0.1%. Fig. 9. Measuremet of Rotatioal Speed with Velocimeter LSV ad Referece Disc. With a system accuracy of 0.1%, this measurig system is able to use for testig ad calibratig rotatio speed sesors with a relative accuracy of 0.4% [10]. Therefore it ca be used for verifyig the ovel sigal processig method for rotatioal speed sesors ad ecoders, which is described i [3]. This ovel method is applied to the Hall-Effect Gear Tooth Sesor CYGTS101DC-S, where all teeth of the target gear are take ito accout for the rotatioal speed calculatio. Table 1 shows the compariso of the rotatioal speed results ω ref ad ω from the Referece Chael ad the Sesor Chael. The relative deviatio ω + ω ref ω ω ref tha 0.2%. is less

5 Relative Deviatio [%] Table 1. Compariso of Results from the Sigal Processig Method ad the Referece Measurig System. Referece Chael Rotatioal Speed (ωref) Sesor Chael Rotatioal Speed (ω) Relative Deviatio ( ω/ω+ ωref/ωref see (1) ) rpm rpm 0.04% rpm rpm 0.15% rpm rpm 0.03% rpm rpm 0.06% rpm rpm 0.04% rpm rpm 0.08% rpm rpm 0.14% Fig. 10 shows the results from 10 measuremets at the Referece Rotatioal Speed Measuremet System. For each measuremet, 16 differet speed poits are measured. The relative deviatio betwee both chaels is also less tha 0.2%. 0,20 0,15 0,10 0,05 0,00-0,05-0,10-0,15-0, Rotatioal Speed [rpm] Fig. 10. Results from 10 Measuremets with the Referece Rotatioal Speed Measurig System. Accordig to (1) the followig two poits are proved by the results: 1) The accuracy of the measurig system (Referece Chael) is higher tha 0.1%. 2) The accuracy of speed sesors uder usig ovel sigal processig method ca be cotrolled withi 0.2%. This ovel sigal processig method ca be applied to all kids of rotatioal speed sesors with aalogue output. This method will be itroduced i aother paper. 6. CONCLUSIONS I this paper, a rotatioal speed measurig ad calibratio system based o Laser Doppler Velocimetry has bee proposed. From the results oe ca draw the followig coclusios: The proposed rotatioal speed measurig system cosists of a motor, a Referece Chael, a Sesor Chael ad a PC System for data acquisitio. The referece rotatioal speed of a motor i the system ca be determied by measurig the tagetial liear velocity of a rotatig referece disc mouted o the motor shaft with a Laser Surface Velocimeter, for istace the Polytec LSV The Referece Chael, which is composed of the Polytec LSV-1000 ad a referece disc, should have a much higher accuracy ad resolutio tha the Sesor Chael, which cotais the sesor uder test ad a oscilloscope. The measurig accuracy of the Referece Chael ca be improved by compesatig the maufacturig ad moutig deviatios (maily ceter ad radius deviatios) uder usig the proposed sigal processig methods ad algorithms. The experimetal results show that the accuracy of measurig ad calibratio system is higher tha 0.1%. The developed rotatioal speed measurig system ca be used for testig ad calibratig rotatioal speed sesors ad ecoders with a accuracy of lower tha 0.2%. The ovel sigal processig method described i [3] is tested i this measurig system. Practical results of usig the method to Hall Effect gear tooth sesor CYGTS101DC-S idicate that the accuracy of speed sesors uder usig the ovel sigal processig method ca be cotrolled withi 0.2%. REFERENCES [1] D. Schröder, Elektrische Atriebe - Regelug vo Atriebssysteme, 2d Editio, Spriger-Verlag, Berli, Heidelberg, New York, [2] R. Keel, Why Do Icremetal Ecoders Do a Reasoably Good Job i Electrical Drives with Digital Cotrol?, 41th IEEE IAS 2006 Aual Meetig, Tampa, Florida, [3] J.-G. Liu, C. Liu, Verfahre ud Vorrichtug zur direkte Erfassug der Drehgeschwidigkeit mittels Drehzahlgeber, Deutsche Patetameldug, Aktezeiche, , 24. Oktober [4] P. Drabarek, R. Keel, Are Iterferometric Ecoders a Reasoable Alterative i Servo Drive Applicatios?, PEMD 2008, IET 4th Iteratioal Coferece o Power Electroics, Machies & Drives, York, Uited Kigdom, Apr [5] F. Durst, A. Mellig, J. H. Whitelaw, Priciples ad Practice of Laser-Doppler Aemometry, Academic Press, Lodo, [6] L. E. Drai, The Laser Doppler Techique, Joh Wiley & Sos, [7] Polytec GmbH, Steel Idustry. No-cotact Legth ad Speed Measuremets: Precise, Reliable, Repeatable. Competece Field, Waldbro, Germay. [8] Polytec GmbH, Basic Priciples of Velocimetry, Waldbro, Germay. [9] E. Schrüfer, Elektrische Messtechik Messug elektrischer ud ichtelektrischer Größe, 6th Editio, Carl Haser Verlag, Muich, Germay, [10] M. Cable, Calibratio: A Techicia's Guide, ISA - Istrumetatio, Systems, ad Automatio Society, 2005.