Analytical Description of Dc Motor with Determination of Rotor Damping Constant (Β) Of 12v Dc Motor

Transcription

1 The Interntionl Journl of Engineering nd Science (IJES) Volume 6 Iue 6 Pge PP ISSN (e): ISSN (p): nlyticl Decriion of Dc Motor with Determintion of Rotor Dmping Contnt (Β) Of v Dc Motor Onwol, Hn Jimoh, dewunmi, Olugbeng Titu, Ehigwin, Frederick Ojiemhende 3, Iromini, Nurudeen jibol 4,4 Deprtment of Computer Engineering Technology, Federl Polytechnic, Off, PMB 4, Off, wr Stte, Nigeri,3 Deprtment of Electricl/Electronic Engineering, Federl Polytechnic, Off, BSTRCT DC motor n electric mchine hve been pplied in numerou control ytem. However, criticl prmeter of interet tht mut be evluted in deigning DC motor bed ytem i the dmping contnt of the rotor. Thi pper nlyticlly exmine how to determine the dmping contnt of the rotor of V DC motor, with the determintion bed on the following prmeter: rmture reitnce (R ), inductnce (L), Cpcitnce, the Stll current nd the ngulr rte of excittion of the motor with vrying rmture excittion of the current. Thee prmeter help to certin the mximum nd the minimum operting limit of the motor o not to exceed the boundry-operting limit of the V motor. Experiment were performed in the lbortory nd t the end of the nlyi, the reult how tht the vlue of dmping contnt of V DC motor w N-m-ec. Thi prmeter cn be fctored in future control ytem deign. eyword: Motor, mchine, impednce, rmture, inductnce Dte of Submiion: 7 My 7 Dte of cceed: 7 June I. INTRODUCTION DC motor i the mot vertile nd widely ued rotting electricl mchine. It peed my be eily controlled or djuted in very fine increment rnging from initil vlue to rted peed for which the motor w deigned for; if the peed i not properly controlled, it my rech peed high enough to cue detruction to the motor. Menwhile, peed control of dc motor i chieved by vrying the flux () or the rmture reitnce R. However, if R i increed the field current I f i decreed. more inightful overview of DC motor opertion nd ppliction in control ytem re preented in [3, 5,7, 9,6] There re everl reported ppliction of DC motor which would be dicued in the reerch tudy. [5] developed phe vrible model of the bruhle DC motor. The model w ued to exmine the performnce of bruhle DC motor peed ervo drive ytem when fed by hyterei nd pule width modulted current controller. The imulted reult reveled tht the lrge- nd mll ignl repone re the me due to imilr overll peed repone. Furthermore, two method bed on either voltge model nd current model from peed nd poition enorle control of permnent mgnet bruhle DC motor with inuoidl flux ditribution w reported by [] In ddition, DC motor w pplied in two-wheeled vehicle becue of it configurtion with two coxil wheel with ech coupled to it by [6]. Menwhile, [8] developed electric power teering ytem control logic for reduction of teering torque exerted by driver. It improved the return-to-centre performnce nd reliztion of vriou teering feel. The uthor further oberved tht bruhle DC motor poe imilr chrcteritic DC motor when it come modelling. [8] propoe frctionl order, Proportionl Integrl Derivtive (PID) control of DC motor, which poee eltic hft, nd ued for poition ervomechnim control ytem. The reerch conidered the torionl flexibility of the motor hft nd ctutor turtion. The ytem h the poibility of better performnce in comprion with conventionl integer order PID controller. Furthermore, [] preented ppliction of DC motor for driving flpping wing t lrge wing troke nd high frequencie. However, in thi ce inted of the DC motor rotting, it reciprocte, thu voiding the ue of nonliner trnmiion. With thi improvement, the propoed ytem could be deployed in utonomou micro-eril vehicle. Other ppliction of DC motor include: electric vehicle [4], grnulr fertilizer pplictor [7], wter pump [9], xi olr trcking ytem [], knee prothetic, [] nd o on. lo nlyi nd decriion of DC motor w reported in [3, 4]. DOI:.979/ Pge 37

2 nlyticl Decriion of Dc Motor with Determintion of Rotor Dmping Contnt (Β) Of v Dc.. The repone to dmping cn be under, over nd criticl dmping. The under dmped ytem yield n exponentilly decreing inuoidl output in repone to tep input where over dmped ytem yield nonocilltory output in repone to tep input but h more dmping thn necery, in order to chieve the nonocilltory output. However criticl dmped ytem yield non-ocilltory output in repone to tep input. For V DC motor to operte efficiently there i need to know the following prmeter pecified by the mnufcturer. The minimum nd mximum operting limit cpcity of the motor, the dmping contnt () of the V dc nd to determine whether the motor i under dmping, over dmping or criticlly dmped bed on thee prmeter. Dmping i the energy diiion propertie of mteril or ytem under cyclic tre. The repone of control ytem conit two prt tht i the trnient repone nd tedy tte repone. Determintion of dmping contnt of motor require n ppliction tht i mthemticlly inclined, which del with the bic principle underlying the deign nd nlyi of the ytem involved. If trnient repone C nd the tedy-tte repone C, ytem repone i given by eqution (): SS TR C ( t ) C ( t ) C ( t ) () TR SS For time contnt, the firt order ytem i given eqution () t C ( t ) U ( t ) () t Eqution (3) i derived by pplying Lplce trnform to eqution () with implifiction. C ( ) ( ) C ( ) U ( t ) (b) C ( ) ( ) U ( ) C ( ) U ( ) C ( ) (3) U ( ) ( ) ( ) Menwhile, n unforced dmped hrmonic ocilltor h the form of eqution (4). C n C nc nc (4) Where: C nd U re function of t. Mthemticlly, in mot ce over dmping i conider pproprite to work with, becue the root re rel. II. METHODOLOGY The vlue of rmture Reitnce R, rmture inductnce L nd Cpcitnce C were determined in the lbortory uing n intrument clled impednce meter nd the reult obtined re follow: R=.3 3,L =.5 H, C =.7-8 F. DETERMINTION OF THE STLL CURRENT OF THE V DC MOTOR The Voltmeter w connected cro the vrible power upply; with the mmeter connected in erie with motor hown in fig.. The vrible D.C ource w et to 3V with the witch ON, the rotor trted to rotte, the rmture current on No- lod nd peed of the motor were meured when the hft of motor w tlled i.e. ( zero peed), the rmture current w found to hve increed nd the rmture current w red from the mmeter. The Experiment w crried out three more time for different voltge rting of 4.5V, 6V nd 9V ee tble E V Fig.: Circuit of peed of V motor on No-lod DETERMINTION OF THE NGULR RTE OF ROTTION OF THE 9V DC MOTOR WITH VRYING RMTURE EXCITTION CURRENT voltmeter w connected cro the vrible D.C ource, Rheott, mmeter in erie with the motor, with the counter ttched to the pindle of the motor by men of belt hown in fig.. The vrible D.C ource w et to 3V, the D.C ource w then ON for period of 5 econd, the rmture current nd the peed of the rotor poition were red from the counter. The ngulr rte of rottion were clculted. DOI:.979/ Pge 38

3 nlyticl Decriion of Dc Motor with Determintion of Rotor Dmping Contnt (Β) Of v Dc.. The experiment w crried out for nother four more time for different voltge vlue of 5V, 6V nd 9V.See tble. The ngulr rottion were lo clculted uing the expreion. T E V Fig. : Circuit of the peed rottionl of V DC motor III. DISCUSSION OF RESULTS Tble : Reult obtined for the peed of Motor on No-lod V (v) Stll Current I (m) No-lod current I (m) Tble : Reult obtined for the ngulr rottion of 9V DC Motor IV V I (m) T/(ec.) (rp) (rp) NLYSIS ND DISCUSSION OF RESULTS Fig..: Grph of V gint Fig..b: Grph of V gint Fig..: Grph of V gint Fig..b: Grph of V gint It i umed tht ll initil condition re zero. Tking the Lplce trnform of eqution (4) nd further implifiction, we obtined eqution (5) C ( ) C ( ) C ( ) C ( ) C ( ) U ( ) U ( ) U ( ) (5) DOI:.979/ Pge 39

4 nlyticl Decriion of Dc Motor with Determintion of Rotor Dmping Contnt (Β) Of v Dc.. But U ( ) i the unit tep, tht i, U ( ) Hence, eqution (5) become the expreion hown in eqution (6), C ( ) (6) ( ) The olution i of the form, with p nd p being the pole of the ytem C ( ) (7) ( p ) ( p ) (S-p ) nd (S-p ) re the root of qudrtic eqution of the form X b b 4 c From eqution 4 ( ) When the mgnitude i poitive, P, P By prtil frction reolution,,, By pplying invere Lplce trnform fter ubtitution, eqution (8) i relized. C ( t ) (8) I f R L J Fig. 3: chemtic of motor genertor ytem with inerti lod J, vicou dmping β t ngulr velocity nlyi of the Mthemticl Model of DC Motor Opertion If the torque of the DC motor i T Nm, moment of inerti i J Nm nd the dmping contnt i Nm ; then T J (9) Tking the Lplce trnform of eqution (9) give eqution (). T ( ) J ( ) ( ) () However, T EI RI () Where: E = EMF generted by the motor V I = rmture current R = reitnce of the motor It i to be noted tht eqution (9) cn be put in the form hown in eqution (). DOI:.979/ Pge 4

5 nlyticl Decriion of Dc Motor with Determintion of Rotor Dmping Contnt (Β) Of v Dc.. T J () Subtituting eqution () into (), we obtined: J EI RI (3) Let Thu, E I, C RI (Ohmic lo). Hence, J E C (4) Let J C (5) x E x J t the tedy tte E x Hence the lope of fig. 3 i equted to the eqution to give the vlue of β i. e M Where =Current on No-lod. Similrly =Stll current M M M M.337 M. 3 MI 3.37 Similrly t tll MI 7 N m ec N m From eqution 4 = Stedy Stte, ec =Trnient Stte, If ; Complex root under dmping, If ; Rel & unequl root Over dmping, If =; Rel & equl root criticlly dmping IV. CONCLUSION ND RECOMMENDTION From the Mthemticl Modelling nd nlyi of V DC Motor, the vlue of the Dmping Contnt (β) w found to be N-m-ec. Thi vlue i very ignificnt in the determintion of dmping contnt in the deigning procee, thi vlue hould be tken into conidertion when determining whether the dmping of rotor of motor i under, over or criticlly dmped nd hould be properly looked into in order to vert under-deigning nd if thi i tken into ccount, the life pn of the motor would be prolonged nd unwrrnted form of dmge nd brekdown of the component of the motor reult of voltge fluctution would be verted. However from the nlyi Dmping Contnt of N-m-ec thi men tht the vlue of i complex root mening tht the ytem i under dmping. REFERENCES []. wd, M. I., Dehghni-Snij, b,., Moer, D., & Zhedi, S. (6). Motor electricl dmping for bck-drivble prothetic knee. In Mechtronic (MECTRONICS)/7th Interntionl Conference on Reerch nd Eduction in Mechtronic (REM), 6 th Frnce-Jpn & 9th Europe-i Congre on. IEEE. []. Cmpolo, D., zhr, M., Lu, G.-., & Sitti, M. (). Cn DC motor directly drive flpping wing t high frequency nd lrge DOI:.979/ Pge 4

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