National Conference on Advances in Mechanical Engineering Science (NCAMES-2016)

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1 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) Modelig Stepper Motor Cotrol System with Miro-Steppig Exittio Mode Nvy Thirumleshwr, Hegde 1 Dr. S. Meethi Sudrm 2,, Aldri Vz 3 1 Assistt Professor, Deprtmet of Mehil Egieerig, Sriivs Istitute of Tehology,Vlhil, Mgluru, Krtk Stte, Idi Assoite Professor, Deprtmet of Istrumettio & Cotrol Egieerig Mipl Istitute of Tehology, Mipl, Krtk, Idi Abstrt - This pper ims t providig detiled exposure to the bsi opertio of stepper motor, its drive d logi. The modelig d simultio of the eletromehil behvior of step motors re of high importe beuse they re ofte used i stellite d sub stellite systems. After hvig preseted the mthemtil modelig whih leds to the stepper motor ruig s solutio, usig the Ruge-Kutt umeril itegrtio method. This pper results i desigig driver iruits for full step, hlf step, miro steppig of bipolr permet mget stepper motor of give requiremets. The full-step d hlf-step motors ted to be slightly jerky i their mode of opertio s the motor moves from step to step. The mout of resolutio is iresig, i otrst we redue the resoe, vibrtio problems usig miro-steppig t low step rte. The miro-steppig with step motor is used i lrge umber of pplitios like poitig te towrds desired diretio i order to miimize de-poitig losses or movig the telesope to trk str/plet motio. Key Words - Stepper motor, full step, hlf step, miro-step. I. INTRODUCTION A stepper motor is mrvel i simpliity d relity. Motor hs o brushes or otts d it is syhroous motor with the mgeti field eletroilly swithed to rotte the rmture mget. The essetil futio of step motor is to trslte swithig exittio hges ito preisely defied iremets of rotor positio. A stepper motor is eletro mehil devie, whih overts eletril pulses ito disrete mehil movemets. The me stepper is used beuse this motor rottes through fixed gulr step i respose to eh iput urret pulse reeived by its otroller. A. Types of Step Motors First type is the vrible relute motors give. The seod type of step motor is the permet mget motor, whih utilizes permet mgets to perform eletromehil rottio. Filly, the hybrid step motors ombie mehil d eletromgeti properties of other two types to hieve higher torque. Eh oil roud sigle sttor tooth belogs to sigle phse i both motor types. This is lled the moofilr widig sheme. Sme voltge polrity pplied to moofilr widigs will rete mgeti flux lwys i the sme diretio. The sttor tooth roud whih the oil is woud will hve sigle mgeti polrity ditted by the widig oriettio. This kid of exittio is lled the uipolr drive of the widig. First of ll, the bsi method of wve drive exittio is give d it is followed by two-phse o exittio, whih is ltertive to produe full steps. The disussio otiues with hlf step exittio, whih doubles the effetive step umber d thus ireses the positiol ury. Filly, miro-steppig exittio, whih is the most importt of ll regrdig this pper, is explied. The detils of stepper motor modelig re give i setio 2. The stepper motor speifitios d simultio results re preseted i setio 4. II. STEPPER MOTOR MATHEMATICAL MODEL I order to ivestigte the dymis of mehisms drive by stepper motors model hd to be reted[2]. With miimum bkgroud of bsi lws of eletromgetism d motor physis, this setio provides brief derivtio of olier model of the 2-phse PM stepper motor show i Figure 1. As explied erlier, whe the widigs of phse re eergized, mgeti dipole is geerted o the sttor side. If for exmple phse 2 is tive (phse 1 is swithed off), widig 3 produes eletril orth pole d widig 4 South Pole. Altertively powerig the widigs of the sttor ommds the rotor flux to follow the sttor field. Figure 1.Blok digrm of stepper motor. V = voltge pplied to the widig A. i = widig urret. e = flux idued voltge i the widig. ISSN: Pge 136

2 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) V = voltge pplied to the widig C. i = widig urret. e = flux idued voltge i the widig. Sttor widig A, di V Ri L e Sttor widig C, di V Ri L e d Are the mgeti flux i the sttor widigs A d C, mos m = mximum sttor flux. e de tht re idued i the sttor The voltges widigs give by, d d e m m m si Kwsi d(4.6) d e m m m os Kwos m=umber of turs o the sttor widigs. Coservtio of eergy: Mehil power out = eletril power i wt i e wt i e T i K si T i K os Complete model usig equtios: 2 d d J D T T T 2 r r T i K si i K os di V Ri L wk si di V Ri L wk os Where, i, i = urrets i phses d. L, R = self-idute d resiste of eh phse widig e, e = urrets phses d. = umber of rotor teeth o eh of the two rotor poles. J r = rotor ierti. W = Rotor speed. θ= motor positio. D = Visous fritio ostt. K = motor torque ostt. Stte vrible form: d w dw T Dr K K w i si i os Jr Jr Jr Jr di 1 R K V i w si L L L di 1 R K V ib w os L L L III. STEPPER MOTOR MODEL SPECIFICATIONS Tble 1.Motor speifitios SSM motor vlues SAGEM vlues prmeter motor prmeter Rotor ierti 1e-07kgm 2 Rotor ierti 500e-07kgm 2 Power 11w Power 8w Resiste 48 ohms Resiste 42 ohms Time ost 2mse Time ost 2mse Voltge 28v Voltge 13v Idute 96mH Idute 105mH Lod ierti 1e-07kgm 2 Lod ierti 5kgm 2 Holdig 0.7Nm Holdig 0.7Nm torque torque Ger rtio 157 Ger rtio 200 Step size 1 degree Step size 15degree Torque 1.489Nm Torque 0.12Nm ostt Mximum rte urret ostt 0.47A Mximum rte urret 0.31A IV. METHODOLOGY Algorithms be implemeted with the help of MATLAB. The ommo methodology i implemetig lgorithms osists of the followig steps Defie the iitil d fil oditios. Defie the motor speifitios log with the iitil d fil time of the motor to ru. Defie Pulse wih i PPS depedig o the step size of motor hose. Fid the elertio/deelertio, speed d positio for differet exittio modes of the motor. Plot the results. V. STEP MOTOR EXCITATION MODES SIMULATION AND RESULTS Mthemtil modelig of the two phse stepper motor is derived d the equtio i the stte vrible form is solved usig Ruge-Kutt umeril itegrtio method. Solutios for ISSN: Pge 137

3 V i volts Ip i mps Ip i mps Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) I, Ib, w, Thet re lulted, simulted. Iitil time d fil time for opertio of motor d step size re defied. Totl ierti of the motor is lulted s J T =J m + (J l / N 2 ) whe the motor is oeted to the lod of ierti J l. The vlue of w d Thet is foud d the grph is plotted where lultio doe with lod oeted to the motor by ger rtio of 1:157 from the equtios of stepper modelig. A. Full Step Mode Exittio 1. Full step (sigle oil exittio) Motor operted with oly oe phse eergized t time. This mode used whe torque versus speed performe ot importt where motor opertes t fixed speed d lod oditios. This mode requires lest mout of power from the power supply of y of the exittio modes. Tble 2.Full step sequee. A C B D Whe iput voltge is pplied the oil AC gets eergies so BD de - eergizes. Coil A geertes positive pulse d sme wy whe the oil C eergies, the lso positive pulse re geerted s show i figure 3. I ext sequee whe iput voltge is pplied the oil BD gets eergies so AC de - eergizes. Where oil B geertes egtive pulse of tht of A d sme wy whe the oil D eergies, the egtive pulse of oil re geerted s show i fig 3. Pulse geerted by the ll widigs of the motor ABCD s show i below figure 2. Curret from the oil A, from the equtio s sme s the voltge i the widig A, where the first pulse strted from the zero s sme to otroller desig. Curret from the oil C, from the equtio s sme s the voltge i the widig C, where the first pulse is missig s sme to otroller desig s show i figure 4 d pulse geerted by oil ABCD Figure 3.Plot of pulse geerted by ABCD oils widig A urret time i mse Figure 4.Plot of Curret geerted by A oil widig C urret t mse Figure 2.Plot of pulse geerted by ABCD oils time i mse Figure 5.Plot of urret geerted by C oil. Two phse SSM stepper motor, whih is used i ASTROSAT SATELLITE hvig high resolutio d high ury where thet mesured to be of step gle of 1deg s show i the below figure 7. ISSN: Pge 138

Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) A C B D 1 1 1 0 0 2 0 1 1 0 3 0 0 1 1 4 1 0 0 1 Figure 6.Plot of motor speed motor rottio. Figure 9.Plot of pulse geerted by ABCD oil.

4 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) A C B D Figure 6.Plot of motor speed motor rottio. Figure 9.Plot of pulse geerted by ABCD oil. Pulse geerted by the ll widigs of the motor ABCD s show i bove figure 9. Curret geerted by the A d C oils i dul phse exittio is 2*I the urret s i se of sigle oil exittio i figure 10 d 11. Figure 7.Plot of motor speed motor rottio. Figure 10.Plot of urret geerted by A d C oil. Figure 8.Plot of torque geerted by motor. Torque geerted by SSM motor is s sow i figure 8 for sigle oil exittio. 2. Full step (dul phse oil exittio) Motor operted with two phses eergized t time. This mode provides good torque d speed performe with miimum of resoe problems. Dul exittio provides 30-40% more torque th sigle exittio. Motor requires twie power from driver power supply. Tble 3.Full step dul phse sequee Figure 11.Plot of urret geerted by A d C oil. Motor positio is hvig less resoe d vibrtio s ompred to sigle oil exittio s show i figure 12. This ISSN: Pge 139

Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) mode gives better speed d torque performe. Motor positio is hlf wy to tht of sigle oil exittio s show i below figure 13. resolutio.

A C B D 1 1 0 0 0 2 1 1 0 0 3 0 1 0 0 4 0 1 1 0 5 0 0 1 0 6 0 0 1 1 7 0 0 0 1 8 1 0 0 1 Figure12.Plot of motor speed.

5 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) mode gives better speed d torque performe. Motor positio is hlf wy to tht of sigle oil exittio s show i below figure 13. resolutio. Complete freedom from resoe problems. Motor operte t wide rge of speeds. This mode used to drive lmost y lod ommoly eoutered. This mode lso used i less torque pplitios. Tble 4.Hlf step sequee. A C B D Figure12.Plot of motor speed. Pulse geerted by the ll widigs of the motor ABCD s show i below figure 15: Figure13. Plot of motor rottio. Torque geerted by SSM motor is s sow i figure 14 for double oil exittio. Figure 15.Plot of pulse geerted by ABCD oils. Figure 14.Plot of torque geerted by motor. Figure 16.Plot of pulse geerted by ABCD oils. B. Hlf Step Mode Exittio It is lterte sigle d dul phse opertio results i hlf of orml step. This mode provides twie the full step ISSN: Pge 140

6 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) Figure 17.Plot of urret geerted by A oil. Curret geerted by the A d C oils i hlf step exittio is sme the urret s i se of full step exittio s show i figures 17 d 18. Figure 20.Plot of motor rottio. Figure 21.Plot of torque geerted by motor. Power geerted by the oils A d C is more s ompred to the full step s show i figures 22 d 23. Figure 18.Plot of urret geerted by oil. Motor speed d positio is s show below figures 19 d 20, where motor steps through gle hlf of the orml step. Figure 22.Plot of motor power geerted by A oil. Figure 19.Plot of motor speed. ISSN: Pge 141

7 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) Figure 23.Plot of motor power geerted by C oil. C. Miro Step Mode Exittio Miro-steppig mode tht otrols the urret i the motor widigs. Miro steppig is typilly used i pplitios tht require urte positioig d fie resolutio over wide rge of speeds. Smooth movemet t low speeds. Iresed step positioig resolutio s result of smller step gle. V V si 2 k v os 2 k v Where, = 0, 1, 2, (4K v -1) K v = umber of steps. Sie d osie of the iput voltge divided ito give umber of steps here K v = 8 d = 31 s show i the below figures 24 d 25. Figure 25. Plot of pulse geerted by C oil. I Miro steppig mode the urrets i the widig re otiuously vryig s show i figure 26 d 27. Plots of motor speed d motor rottio of step gle 1deg s show i the figures 28 d 29.Motor positio for mirosteppig is highly urte d lier, smooth. So mirosteppig is used i ll spe pplitio. Figure 26.Plot of urret geerted by A oil. Figure 24. Plot of pulse geerted by A oil. Figure 27.Plot of urret geerted by C oil. ISSN: Pge 142

8 Ntiol Coferee o Adves i Mehil Egieerig Siee (NCAMES-2016) Figure 28.Plot of motor speed. The mjor disdvtge of the miro step drive is the ost of implemettio due to the eed for prtil exittio of the motor widigs t differet urret levels. If stti fritio is i the system, the gulr preisio is limited. Cost of implemettio is high. I wve-drive d two-phse o exittio, step size is equl to the turl step size. I hlf-step exittio, step umber is doubled d step size is hlved. No-lier ftors of the system brig limittios o the umber of miro-steps hievble d itrodue diffiulties i hievig ostt urret d torque outputs. Miro-steppig method sigifitly improve system performe. motor llow for relisti simultio oditios, resemblig ommerilly vilble devies. All these highlight the pertiee d usefuless of the elborted mthemti model of the stepper motor. The model d the simultio progrm be used i the optimiztio proess of the desig d i elbortig effiiet otrol strtegy i order to improve the performes of the motor i study. Simultio is rried out d ompred to relisti motor lled SSM d SAGEM used i ASTRTOSAT stellite d its, speifitios. There re differet driver topologies for step motor otrol, eh hvig dvtges d disdvtges for erti eeds. Mirosteppig be ebled usig the H-bridge topology. Stepper motor is modeled usig differetil equtios d the umerilly solved by Ruge Kutt method. Stepper motor performes for differet step rtes re tested. Step motors provide fie otrol of rottio gle d speed through disrete exittio sigls. Miro-steppig ebles higher preisio through frtiol exittio of step motor widigs. REFERENCES [1] P.P.Arley, steppig motors: A Guide to Moder Theory d Prtise. Stevege, UK: P.Peregrius, Ltd., [2] M.Bodso d J.Chisso, Applitio of olier otrol methods to the positioig of permet mget stepper motor, i Pro.28 th IEEE Cof.DeisioCotr.,Tmp,FL [3] J. Chisso d M. Zribi, Positio otrol of PM stepper motor by ext lieriztio, IEEE Trs Automt Cotr., vol.36, o, 5, My [4] M.Aiello, R,Rekowski, M.Bodso, J.Chisso, d D.Shuerer, Experimetl results of usig ext lieriztio otroller o PM stepper motor, i Pro. IEEE It, Cof. Syst. Eg., Aug.1990, Pittsburg, PA. [5] M. Zribi, Mohmed, Cotrol of PM stepper motor usig moder olier otrol tehiques M.S.E.E.thesis, Purdue Uiversity Figure 29.Plot of motor rottio. Mximum torques t both low d high step rtes is s show i the figure 21. Figure 21.Plot of torque geerted by motor. VI. CONCLUSIONS The quttive results foud durig the simultios fit well with the expeted behviour of eletri stepper motor. I prtiulr, the proposed solutios to simultig rel stepper ISSN: Pge 143

SPH3UW Unit 7.5 Snell s Law Page 1 of Total Internal Reflection occurs when the incoming refraction angle is

$SPH3UW Unit 7.5 Snell s Law Page 1 of Total Internal Reflection occurs when the incoming refraction angle is$ SPH3UW Uit 7.5 Sell s Lw Pge 1 of 7 Notes Physis Tool ox Refrtio is the hge i diretio of wve due to hge i its speed. This is most ommoly see whe wve psses from oe medium to other. Idex of refrtio lso lled