Microsoft Word - B_21_Nagy_R.doc HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPRÉM Vol. 39(2) pp. 233-235 (2011) DETERMINATION OF THE INDUCTANCE OF STARTER RELAYS L. NAGY, J. LÉNÁRT, E. JAKAB University of Miskolc, Robert Bosch Department of Mechatronics, Miskolc-Egyetemváros, HUNGARY E-mail: nagy.lajos@uni-miskolc.hu E-mail: lenart.jozsef@uni-miksolc.hu E-mail: jakab.endre@uni-miksolc.hu This paper deals with the determination of the inductance of starter relays. The article proposes a method for the electro- mechanical determination of the self-inductance of the electromagnet and its derivative for various positions of the iron core. The results obtained at different current levels are given in tables and figures. Keywords: starter relay, electromechanical model, inductance measurement Introduction The actuator of the pinion-engaging mechanism of the starter motor consists of concentric iron core coils [1]. The coils are excited by relatively high currents. The electro-dynamic modelling of the mechanism requires inductance of the relay and its derivative depending on the position of the iron core. The electromagnet has self- inductance, electrical resistance and mechanical force acting on the iron core. The inductance of an electromagnet is generally determined by purely electrical measurements, e.g. by current-voltage methods or bridge methods, by the resonance method, etc. [2, 3]. Relatively few methods are available for DC excited inductance measurements [4]. The inductance of a coil without an iron core can be determined by measurement or also by calculation with sufficient accuracy. It is particularly difficult to determine the inductance of a coil in the case of movable iron cores. The iron core has in general nonlinear magnetic properties, i.e. B-H characteristic curves are nonlinear or hysteresis also may occur [5]. In this work, the inductance function is determined in an indirect way, by measuring the electromagnetic force in the case of direct current excitation. It is assumed that the inductance depends on the position of the iron core and on the current. The time dependency and hysteresis are neglected. The measurement provides the derivative of the inductance function directly. The induction function sought is produced by integration when the inductance of the air core coil and the derived function of the iron core coil are known. The measurement is repeated for three current values. The final objective of the measurement is to model electro-dynamically the pinion-engaging mechanism of the starter motor, which includes both the inductance function and its derivative. The electromechanical model Fig. 1 shows the cross-section of a typical starter relay [1]. The relay consists of a moving iron core – 1, a pull- in winding – 2 and a hold-in winding – 3, a fixed iron core – 4, a contact spring – 5, a switch contacts – 6, an electrical connection – 7, a switch contact – 8, an armature shaft – 9, and a return spring – 10. Figure 1: Cross-section of a starter relay An experiment is designed to measure the inductance electromechanically, without springs. The electromagnetic force is measured by a compact load cell in discrete positions of the iron core. Positioning is registered by a laser interferometer. The experiment is performed using a supply unit integrated into the measurement circuit. Apart from the phenomenon of switching on, the measurement is done with a constant current i. The electromechanical model of the measurement relies on the following coupled differential equation system: 234 ( ) ( ) 0,, UiRixixLdt di ixL =+′+ & , (1) ( ) ( )txFiixLxm , 2 , 2 =′−&& , (2) where L(x,i) is the equivalent self-inductance of the relay depending on position x and current i, L'(x,i) is the partial derivative of the self-inductance function by location, ẋ, ẋ̇ are the velocity and acceleration of the iron core, respectively, R is the equivalent resistance of the relay, U0 is the terminal voltage of the battery, m is the mass of the iron core and F(x,t) is the force acting on the compact load cell. Equations (1)-(2) are also suitable for describing the switch-on phenomenon. In a steady-state condition the time-derivative of the current as well as the velocity and acceleration of the iron core are zero. In this static state the following equations hold: 0UiR = , (3) ( ) ( )txFiixL , 2 , 2 =′− , (4) In the examination the current i and the force acting on the iron core are measured and equation (4) is used to determine the derivative inductance function: ( ) ( ) 2 2 ,, i txFixL −=′ , (5) The self-inductance factor of an air core coil can be calculated using the parameters of the coil: j jj j l AN L 2μ = , j=1, 2, ... (6) where μ is air permeability, N is the number of turns of the coil, A is the coil diameter and l is coil length. Mutual inductance is: 21 LLkM = , (7) where k is coupling factor. The self-inductance of the air core coil can also be determined using an inductance meter. In the present case the parallel connected two coils and the mutual inductance arising between the coils produce the equivalent inductance. The equivalent inductance is obtained by the following relation: ( )( ) M MLL MLML L + −+ −− = 221 21 0 , (8) The inductance function sought can be produced by integration when the inductance of the air core coil and the derivative function of the iron core coil are known: ( ) ( )∫ ′+= x dsisLLixL 0 0 ,, , (9) Measuring the inductance of the relay In order to design the measurements firstly the original relay with springs mechanism is tested during normal operation. The measured current of the operating relay versus time function is shown in Fig. 2. It can be seen that during the whole period (t=0–0.025 s) the current is varying between 0 to 35 Amperes. The measurements are planned to perform at three different current levels, i.e. i = 8 A, 26 A, 32 A. The set-up of the measurement is shown in Fig. 3. The instruments used for the measurements are given in Table 1. 0 0.005 0.01 0.015 0.02 0.025 0.03 0 5 10 15 20 25 30 35 Time [s] C ur re nt : i [ A ] Figure 2: The exciting current of an operating relay Figure 3: The measurement circuit used Table 1: Elements of the measurement circuit Nr. Title Type 1 AC power supply EA-STT 2000 B-4.5 A 0–260 V AC 2 Laser interferometer Renishaw XL-80 3 Data acquisition device Spider 8 4,8 kHz/DC 4a Relay VS440-22 220–230 V AC 4b Timer CRM-91H 5 DC power supply Matrix MPS-3005L-3 0–30 V 6 Battery 12V 544 402 440A (EN) 44 Ah 7 Laptop 8a Iron core actuator with compact load cell GEFRAN TU-K1C (0–100 kg) 8b The analyzed relay 31 4a, 4b2 5 6 7 8a, 8b 235 The measurements were done using a variety of supply units. In the first case a controlled unit supplies exciting current i < 10 A. In the second case the supply unit is a starter battery, supplying current typical of operating conditions. In the latter case a magnetic switch and timer were built in the measurement circle as protection against heating. Table 2 sums up the function values L'I(x,i), L'II(x,i) and L'III(x,i), obtained in the measurement series. Table 2: Measurement results xI [mm] L'I(x,i) xII [mm] L'II(x,i) xIII [mm] L'III(x,i) 0.00 0.0044 0.00 0.0596 0.00 0.07505 1.00 0.078 1.49 0.0894 1.68 0.0998 5.00 0.2343 4.39 0.1639 4.016 0.1628 7.1 0.2959 6.99 0.3309 5.95 0.2514 9.1 0.7078 8.5 0.4710 8.00 0.3913 9.95 1.1031 9.49 0.6255 10.00 0.5526 10.70 3.0653 10.44 0.7811 10.47 0.6039 10.95 5.025 11.01 0.9332 11.01 0.7583 The derivative functions are numerically integrated by the trapeze method. The inductance functions obtained at i = 8 A is approximated by an exponential function and the rest of them by five-degree polynomials. The coefficients of the functions are: x.x.I e.e.L 5151716430 10528159230 ⋅⋅+⋅= − , (10) 673800792100054050 003742000034660102 2 3455 .x.x. x.x.xLII +⋅+⋅− −⋅+⋅−⋅⋅= − , (11) 67420091940 00594200031920 00018260103387 23 455 .x. x.x. x.x.LIII +⋅+ +⋅−⋅+ +⋅−⋅⋅= − , (12) Figs 4 and 5 show the inductance functions and their derivatives obtained in the three measurement series. On the basis of the results of the measurement series it can be established that if the displacement of the iron core is more than 8 mm, i.e. the iron core is located deep in the coils, dependence on current appears to be significant. This non-linear characteristic can be explained by the saturation of the iron core. 0 10 20 30 40 0 5 10 15 0 2 4 6 8 10 i [A]s [mm] L( s, i) [m H ] Figure 4: Inductance functions 0 10 20 30 40 0 5 10 15 0 2 4 6 8 10 i [A]s [mm] dL (s ,i) Figure 5: Derivative inductance We note that the exciting current of the relay falls in the interval i = 25–35 A, where the inductance slightly depends on the variation of current. Conclusion The paper recommends an electro-mechanical method for determining the inductance function of starter relays. The inductance depends on the position of the iron core and on the current. The time dependency and hysteresis are neglected. The method is based on the direct measurement of the inductance derivative with respect to the iron core position. The inductance is obtained by numerical integration. It is assumed that the inductance of the air core coil is given. The current dependency is significant when the whole geometry of the iron core is situated in coils. ACKNOWLEDGEMENTS The described work was carried out as part of the TÁMOP-4.2.1.B-10/2/KONV-2010-0001 project in the framework of the New Hungarian Development Plan. The realization of this project is supported by the European Union, co-financed by the European Social Found. REFERENCES 1. R. MEYER, H. BRAUN, R. REHAGE, H. WEINMANN: Alternators and starter motors, Robert Bosch GmbH, 2003 2. S.-Y. MAK: The RCL circuit and the determination of inductance, Phys. Educ. 29, (1994), 94–97 3. S.-Y. MAK: Six ways to measure inductance, Phys. Educ. 37(5), (2002), 439–445 4. A. STANKOVIC, E. R. BENEDICT, V. JOHN, T. A. LIPO: A novel method for measuring induction machine magnetizing inductance, IEEE Transactions on Industry Applications, 39(5), 2003, 1257–1263 5. J. ELBAUM: Electromagnets (in Hungarian), Műszaki Könyvkiadó, Budapest, 1968 << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJDFFile false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description << /CHS /CHT /DAN /DEU /ESP /FRA /ITA /JPN /KOR /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR /PTB /SUO /SVE /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.) >> /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ << /AsReaderSpreads false /CropImagesToFrames true /ErrorControl /WarnAndContinue /FlattenerIgnoreSpreadOverrides false /IncludeGuidesGrids false /IncludeNonPrinting false /IncludeSlug false /Namespace [ (Adobe) (InDesign) (4.0) ] /OmitPlacedBitmaps false /OmitPlacedEPS false /OmitPlacedPDF false /SimulateOverprint /Legacy >> << /AddBleedMarks false /AddColorBars false /AddCropMarks false /AddPageInfo false /AddRegMarks false /ConvertColors /ConvertToCMYK /DestinationProfileName () /DestinationProfileSelector /DocumentCMYK /Downsample16BitImages true /FlattenerPreset << /PresetSelector /MediumResolution >> /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ] >> setdistillerparams << /HWResolution [2400 2400] /PageSize [612.000 792.000] >> setpagedevice