4. DC MOTORS Almost every mechnicl movement tht we see round us is ccomplished by n electric motor. Electric mchines re mens o converting energy. Motors tke electricl energy nd produce mechnicl energy. Electric motors re used to power hundreds o devices we use in everydy lie. Motors come in vrious sizes. Huge motors tht cn tke lods o 1000 s o Horsepower re typiclly used in the industry. Some exmples o lrge motor pplictions include elevtors, electric trins, hoists, nd hevy metl rolling mills. Exmples o smll motor pplictions include motors used in utomobiles, robots, hnd power tools nd ood blenders. Micro-mchines re electric mchines with prts the size o red blood cells, nd ind mny pplictions in medicine. Electric motors re brodly clssiied into two dierent ctegories: DC (Direct Current) nd AC (Alternting Current). Within these ctegories re numerous types, ech oering unique bilities tht suit them well or speciic pplictions. In most cses, regrdless o type, electric motors consist o sttor (sttionry ield) nd rotor (the rotting ield or rmture) nd operte through the interction o mgnetic lux nd electric current to produce rottionl speed nd torque. DC motors re distinguished by their bility to operte rom direct current. There re dierent kinds o D.C. motors, but they ll work on the sme principles. In this chpter, we will study their bsic principle o opertion nd their chrcteristics. It s importnt to understnd motor chrcteristics so we cn choose the right one or our ppliction requirement. The lerning objectives or this chpter re listed below. Lerning Objectives: Understnd the bsic principles o opertion o DC motor. Understnd the opertion nd bsic chrcteristics o simple DC motors. Compute electricl nd mechnicl quntities using the equivlent circuit. Use motor nmeplte dt. Study some pplictions o DC motors. Recommended text or this section o the course: (i) Alln R. Hmbley, Electricl Engineering Principles nd Applictions, Chpter 16. (ii) Giorgio Rizzoni, Principles nd Applictions o Electricl Engineering, Chpter 17 1
2 DC Motors 4.1 Electromechnicl Energy Conversion An electromechnicl energy conversion device is essentilly medium o trnser between n input side nd n output side. Three electricl mchines (DC, induction nd synchronous) re used extensively or electromechnicl energy conversion. Electromechnicl energy conversion occurs when there is chnge in mgnetic lux linking coil, ssocited with mechnicl motion. Electric Motor The input is electricl energy (rom the supply source), nd the output is mechnicl energy (to the lod). Electricl Electromechnicl Mechnicl energy energy conversion device energy Source Motor Lod Electric Genertor Figure. 1 The Input is mechnicl energy (rom the prime mover), nd the output is electricl energy. Mechnicl Electromechnicl Electricl energy energy conversion device energy Source Genertor Lod Figure. 2 4.2 Construction DC motors consist o one set o coils, clled rmture winding, inside nother set o coils or set o permnent mgnets, clled the sttor. Applying voltge to the coils produces torque in the rmture, resulting in motion. Sttor The sttor is the sttionry outside prt o motor. The sttor o permnent mgnet dc motor is composed o two or more permnent mgnet pole pieces. The mgnetic ield cn lterntively be creted by n electromgnet. In this cse, DC coil (ield winding) is wound round mgnetic mteril tht orms prt o the sttor. Rotor The rotor is the inner prt which rottes. The rotor is composed o windings (clled rmture windings) which re connected to the externl circuit through mechnicl commuttor. Both sttor nd rotor re mde o erromgnetic mterils. The two re seprted by ir-gp. Winding A winding is mde up o series or prllel connection o coils. Armture winding - The winding through which the voltge is pplied or induced. Field winding - The winding through which current is pssed to produce lux (or the electromgnet) Windings re usully mde o copper.
DC Motors 3 4.3. DC Motor Bsic Principles 4.3.1 Energy Conversion I electricl energy is supplied to conductor lying perpendiculr to mgnetic ield, the interction o current lowing in the conductor nd the mgnetic ield will produce mechnicl orce (nd thereore, mechnicl energy). 4.3.2 Vlue o Mechnicl Force There re two conditions which re necessry to produce orce on the conductor. The conductor must be crrying current, nd must be within mgnetic ield. When these two conditions exist, orce will be pplied to the conductor, which will ttempt to move the conductor in direction perpendiculr to the mgnetic ield. This is the bsic theory by which ll DC motors operte. The orce exerted upon the conductor cn be expressed s ollows. F = B i l Newton (1) where B is the density o the mgnetic ield, l is the length o conductor, nd i the vlue o current lowing in the conductor. The direction o motion cn be ound using Fleming s Let Hnd Rule. Figure 3: Fleming s Let Hnd Rule The irst inger points in the direction o the mgnetic ield (irst - ield), which goes rom the North pole to the South pole. The second inger points in the direction o the current in the wire (second - current). The thumb then points in the direction the wire is thrust or pushed while in the mgnetic ield (thumb - torque or thrust). How much orce will be creted on wire tht is prllel to the mgnetic ield?
4 DC Motors 4.3.3 Principle o opertion Consider coil in mgnetic ield o lux density B (igure 4). When the two ends o the coil re connected cross DC voltge source, current I lows through it. A orce is exerted on the coil s result o the interction o mgnetic ield nd electric current. The orce on the two sides o the coil is such tht the coil strts to move in the direction o orce. Figure 4: Torque production in DC motor In n ctul DC motor, severl such coils re wound on the rotor, ll o which experience orce, resulting in rottion. The greter the current in the wire, or the greter the mgnetic ield, the ster the wire moves becuse o the greter orce creted. At the sme time this torque is being produced, the conductors re moving in mgnetic ield. At dierent positions, the lux linked with it chnges, which cuses n em to be induced (e = d/dt) s shown in igure 5. This voltge is in opposition to the voltge tht cuses current low through the conductor nd is reerred to s counter-voltge or bck em. Induced em Flux Figure 5: Induced voltge in the rmture winding o DC motor The vlue o current lowing through the rmture is dependent upon the dierence between the pplied voltge nd this counter-voltge. The current due to this counter-voltge tends to oppose the very cuse or its production ccording to Lenz s lw. It results in the rotor slowing down. Eventully, the rotor slows just
DC Motors 5 enough so tht the orce creted by the mgnetic ield (F = Bil) equls the lod orce pplied on the sht. Then the system moves t constnt velocity. 4.3.4 Torque Developed The eqution or torque developed in DC motor cn be derived s ollows. The orce on one coil o wire F =i l x B Newton Note tht l nd B re vector quntities Since B = /A where A is the re o the coil, Thereore the torque or multi turn coil with n rmture current o I : T = K I (2) Where is the lux/pole in weber, K is constnt depending on coil geometry, nd I is the current lowing in the rmture winding. Note: Torque T is unction o orce nd the distnce, eqution (2) lumps ll the constnt prmeters (eg. length, re nd distnce) in constnt K. The mechnicl power generted is the product o the mchine torque nd the mechnicl speed o rottion, m Or, P m = m T = m K I (3) It is interesting to note tht the sme DC mchine cn be used either s motor or s genertor, by reversing the terminl connections. Electricl Power input T T Mechnicl output () Motor ction m T m T Mechnicl input (b) Genertor ction Electricl Power output Figure 6: Reversbility o DC mchine 4.3.5 Induced Counter-voltge (Bck em): Due to the rottion o this coil in the mgnetic ield, the lux linked with it chnges t dierent positions, which cuses n em to be induced (reer to igure 5). The induced em in single coil, e = d c /dt Since the lux linking the coil, c = Sin t Induced voltge : e = Cos t (4)
6 DC Motors Note tht eqution (4) gives the em induced in one coil. As there re severl coils wound ll round the rotor, ech with dierent em depending on the mount o lux chnge through it, the totl em cn be obtined by summing up the individul ems. The totl em induced in the motor by severl such coils wound on the rotor cn be obtined by integrting eqution (4), nd expressed s: E b = K m (5) where K is n rmture constnt, nd is relted to the geometry nd mgnetic properties o the motor, nd m is the speed o rottion. The electricl power generted by the mchine is given by: P dev = E b I = K m I (6) 4.3.6 DC Motor Equivlent circuit The schemtic digrm or DC motor is shown below. A DC motor hs two distinct circuits: Field circuit nd rmture circuit. The input is electricl power nd the output is mechnicl power. In this equivlent circuit, the ield winding is supplied rom seprte DC voltge source o voltge V. R nd L represent the resistnce nd inductnce o the ield winding. The current I produced in the winding estblishes the mgnetic ield necessry or motor opertion. In the rmture (rotor) circuit, is the voltge pplied cross the motor terminls, I is the current lowing in the rmture circuit, R is the resistnce o the rmture winding, nd E b is the totl voltge induced in the rmture. I V I L R Field circuit Figure 7: DC Motor representtion E b Armture (rotor) circuit R ω m, T 4.3.7 Voltge Eqution Applying KVL in the rmture circuit o Figure 7: = E b I R (7) where is voltge pplied to the rmture terminls o the motor nd R is the resistnce o the rmture winding. Note: The induced voltge is typiclly represented by symbol e (or E) nd the terminl voltge by v (or V). At stndstill, the motor speed is zero, thereore bck em is lso zero. The rmture current t strting is thus very lrge. Applying KVL in the ield circuit o Figure 7: V = R I (8)
DC Motors 7 Where V is voltge pplied to the ield winding (to produce the mgnetic ield), R is the resistnce o the ield winding, nd I is the current through the ield winding. How would the inductnce o the ield winding ect the motor opertion under stedy-stte? 4.3.8 Power Trnser Eqution We hve erlier obtined the ollowing reltionship or torque developed in the motor (rom eqution 2): T dev = K I The developed power is the power converted to mechnicl orm, nd is given by (rom eqution 3): P dev = m T dev This is the power delivered to the induced rmture voltge (counter-voltge) nd given by: E b I (electricl power) = m T dev (mechnicl power developed) (9) Note: The speed in revolutions per minute, N, is relted to the ngulr speed (in rdins per second) by = 2 N 60 N cn be written s r/min or rpm, both men the sme thing. Noting tht the lux in the mchine is proportionl to the current lowing in the ield winding (i.e. I ), we cn compre induced voltges t two dierent speeds. I the induced voltge t the irst operting speed N 1, nd ield winding current I 1 is given by: 2N 1 Eb 1 K ( K I 1) 60 nd the induced voltge t the irst operting speed N 2, nd ield winding current I 2 is given by: 2N 2 Eb2 K ( K I 2 ) 60 Then the induced voltges t these operting points cn be compred s: E I 1 1N b 1 E I N b2 2 2 This eqution is useul in determining the speed o the DC motor t dierent operting conditions.
8 DC Motors 4.4 DC Mchine Clssiiction DC Mchines cn be clssiied ccording to the electricl connections o the rmture winding nd the ield windings. The dierent wys in which these windings re connected led to mchines operting with dierent chrcteristics. The ield winding cn be either sel-excited or seprtely-excited, tht is, the terminls o the winding cn be connected cross the input voltge terminls or ed rom seprte voltge source (s in the previous section). Further, in sel-excited motors, the ield winding cn be connected either in series or in prllel with the rmture winding. These dierent types o connections give rise to very dierent types o mchines, s we will study in this section. 4.4.1 Seprtely excited mchines The rmture nd ield winding re electriclly seprte rom ech other. The ield winding is excited by seprte DC source. I V I L R E b R ω m, T Figure 8: Seprtely excited DC Motor The voltge nd power equtions or this mchine re sme s those derived in the previous section. Note tht the totl input power = V I I 4.4.2 Sel excited mchines In these mchines, insted o seprte voltge source, the ield winding is connected cross the min voltge terminls. Shunt mchine The rmture nd ield winding re connected in prllel. The rmture voltge nd ield voltge re the sme. I L I I R L ω m T dev E b R Notice tht in this type o motor, Figure 9: Shunt DC Motor
DC Motors 9 Totl current drwn rom the supply, I L = I I Totl input power = I L Voltge, current nd power equtions re given in equtions (7), (8) nd (9). Series DC mchine The ield winding nd rmture winding re connected in series. The ield winding crries the sme current s the rmture winding. A series wound motor is lso clled universl motor. It is universl in the sense tht it will run eqully well using either n c or dc voltge source. Reversing the polrity o both the sttor nd the rotor cncel out. Thus the motor will lwys rotte the sme direction irregrdless o the voltge polrity. I = I L R R ω m T dev E b Figure 10: Series DC Motor Compound DC mchine I both series nd shunt ield windings re used, the motor is sid to be compounded. In compound mchine, the series ield winding is connected in series with the rmture, nd the shunt ield winding is connected in prllel. Two types o rrngements re possible in compound motors: Cumultive compounding - I the mgnetic luxes produced by both series nd shunt ield windings re in the sme direction (i.e., dditive), the mchine is clled cumultive compound. Dierentil compounding - I the two luxes re in opposition, the mchine is dierentil compound. In both these types, the connection cn be either short shunt or long shunt. Note: Compound motors will not be discussed in this course. 4.5 Perormnce clcultions In most pplictions, DC motors re used or driving mechnicl lods. Some pplictions require tht the speed remin constnt s the lod on the motor chnges. In some pplictions the speed is required to be controlled over wide rnge. It is thereore importnt to study the reltionship between torque nd speed o the motor. 4.5.1 Speed Regultion
10 DC Motors The perormnce mesure o interest is the speed regultion, deined s the chnge in speed s ull lod is pplied to the motor. It cn be expressed s: N no lod N ull lod Speed regultion ( SR ) 100 % (10) N ull lod Where N no-lod is the speed t no lod, nd N ull-lod is the speed when ull lod is pplied. 4.5.2 Torque-Speed Chrcteristics: In order to eectively use D.C. motor or n ppliction, it is necessry to understnd its chrcteristic curves. For every motor, there is speciic Torque/Speed curve nd Power curve. The reltion between torque nd speed is importnt in choosing DC motor or prticulr ppliction. Seprtely excited DC motor A seprtely excited DC motor equivlent circuit is shown in Figure 8. From eqution (5) nd eqution (7)), we hve two expressions or the induced voltge. Compring the two: E b K V I R (11) m T The torque developed in the rotor (rmture) is given by: T dev = K I (12) From eqution (12), the current in the rmture winding cn be ound s: Tdev I (13) K Substituting or I in eqution (11) nd rerrnging the terms: Tdev VT Km R K (14) Thereore, the torque developed in the rotor cn be expressed s: K Tdev ( VT Km) (15) R This eqution shows the reltionship between the torque nd speed o seprtely excited DC motor. I the terminl voltge nd lux re kept constnt, the torque-speed reltionship is stright drooping line. T dev Stll torque Norml operting rnge No-lod speed = /k Figure 11: Torque-speed chrcteristics o seprtely excited DC motor ω m
DC Motors 11 The grph bove shows torque/speed curve o seprtely excited D.C. motor. Note tht torque is inversely proportionl to the speed o the output sht. In other words, there is trdeo between how much torque motor delivers, nd how st the output sht spins. Motor chrcteristics re requently given s two points on this grph: The stll torque, represents the point on the grph t which the torque is mximum, but the sht is not rotting. The no lod speed, is the mximum output speed o the motor (when no torque is pplied to the output sht). The motor lod determines the inl operting point on the torque curve. As illustrted in the igure below, when motor is connected to drive lod, the interction o torque demnded by the lod nd the torque produced by the motor determines the point o opertion. - - I Eb DC Motor - T dev T lod m Mechnicl Lod (Pump, Compressor) T dev Norml operting rnge Torque demnded by the lod Torque developed by the motor Finl operting point ω m Figure 12: Interction o the DC Motor nd Mechnicl Lod The bove grph shows the interction o DC motor nd mechnicl lod. The strting torque o the motor is higher thn the lod torque demnded by the lod. The dierence between these two torques orces the motor to rotte. As the motor strts to rotte nd picks up speed, the developed torque decreses (why?). The motor inlly comes to stble operting point when the two torques blnce ech other. DC Shunt Motor The DC shunt motor hs the sme equtions or torque s or the seprtely excited motor, nd hs the sme torque-speed chrcteristics s in Figure 11. DC Series Motor The DC series motor chrcteristics cn be nlyzed in much the sme wy s the shunt motor discussed erlier. In series motors, the series ield winding is connected in series with the rmture (reer to igure 10). The torque developed in the rotor is: T dev = K I Assuming tht the lux is directly proportionl to ield current (i.e. no mgnetic sturtion),
12 DC Motors I Since in series motor, I = I = K I (16) where K is constnt tht depends on the number o turns in the ield winding, the geometry o the mgnetic circuit nd the B-H chrcteristics o iron. Thereore, the torque developed in the rotor cn be expressed s: T dev (17) 2 ( K I )( K I ) K ' I I = I L R R ω m T dev E b Figure 10 (redrwn): DC Series motor equivlent circuit Applying KVL to the equivlent circuit (nd ignoring L under stedy stte conditions), = R I R I E b (18) But induced voltge cn be expressed s E b = K m = K (K I ) m = K I m Substituting this in eqution (18), we get VT I R R K' (19) m The torque developed: 2 K' VT T dev 2 ( R R K' m) (20) From this eqution, i the terminl voltge is kept constnt, the speed is lmost inversely proportionl to the squre root o the torque (igure 13). A high torque is obtined t low speed nd low torque is obtined t high speed. T dev Strting torque To Figure 13: Torque-speed chrcteristics o series motor ω m
DC Motors 13 Wht hppens when the lod rom series motor is suddenly tken o? Wht hppens i the direction o current t the terminls o series motor is reversed? 4.5.3 Eiciency As power lows rom DC motor input terminls to the output (sht), some losses tke plce. Figure 14 shows the low o power in seprtely excited DC Motor. Eiciency o the motor cn be clculted s the rtio o output power to the totl input power. Reerring to igure 8, totl electricl input power, P in = I V I (21) where I is the rmture current drwn rom the supply terminls. Power bsorbed by the ield winding is in turn converted to het nd is given by: P ield-loss = I 2 R (22) = V R 2 R V R 2 (23) Some power is lost in the resistnce o the rmture winding, nd cn be clculted s: P rm-loss = I 2 R (24) The totl power loss tking plce in the two windings (which re mde o copper) is the totl copper loss. Totl copper loss = Field loss Armture loss Power developed nd converted into mechnicl power, Power developed = Input power Totl copper loss Also, P dev = I E b = ω m T dev (25) The output power nd torque re less thn the developed vlues becuse o rottionl losses, which include riction, windge, eddy-current nd hysteresis losses. Rottionl power loss is pproximtely proportionl to motor speed. From igure 14, we cn ind the inl output power s: Power output = Power developed rottionl losses The eiciency o the DC motor cn be clculted s: Pout Eiciency 100% (26) Pin This eqution cn lso be expressed in terms o power losses in the motor: Pout Eiciency (27) P P P Rottionl loss out rmloss ield loss
14 DC Motors Power input I V I Field copper loss Power developed = E b I = m T dev Armture copper loss Figure 14: Power low in DC motor Rottionl loss Power output = m T out It is importnt to mention tht the totl input nd output power cn be clculted in mny dierent wys using the power low digrm, depending on the inormtion given. Also note tht the torque developed inside the rotor is dierent rom the inl (output) torque supplied to the lod due to rottionl losses. DC Shunt Motor Power Flow The losses nd eiciency in DC shunt motor cn be clculted in similr mnner to tht shown bove, except tht in this cse Power input = I L (where I L = I I ). DC Series Motor Power Flow The losses nd eiciency in DC series motor cn be clculted in similr mnner to tht or DC shunt motor using the equtions derived erlier, except tht in this cse I = I = I L 4.5.4 DC Motor Rting DC Motors re typiclly rted in terms o : Rted voltge: the operting voltge on the input side o the motor Rted power : Power (in horsepower hp or wtts) tht the motor is designed to deliver to the lod (i.e., output power) or continuous opertion. (Note tht 1 hp = 746 W) Rted speed Speed (in revolutions per minute, denoted by r/min or rpm) or which the motor is designed to operte or continuous opertion. Rted lod
DC Motors 15 The lod which the motor is designed to crry or (theoreticlly) ininite period o time. Full lod or rted lod operting condition reers to the opertion o motor when it is delivering rted power to the lod. Note: A motor my not lwys operte t its rted power nd/or speed. Opertion bove these vlues is not dvisble due to overloding. Exmple 1 A 230 V, 10 hp d.c. shunt motor delivers power to lod t 1200 r/min. The rmture current drwn by the motor is 200 A. The rmture circuit resistnce o the motor is 0.2 nd the ield resistnce is 115. I the rottionl losses re 500W, wht is the vlue o the lod torque? Solution The bck em induced in the rmture is: E b = - I R = 230-0.2 x 200 = 190 V Power developed (in the rotor), P dev = E b I = 190 x 200 = 38000 W Power delivered to the lod, P lod = P dev P rot = P out = 38000-500 = 37500 W Lod torque, T lod = P lod / m Since speed m = 2N/60 where N is the speed in revolutions per minute (r/min). The torque supplied to the lod cn be clculted s: 37500 T lod 298.4 N. m 2 1200 60 Further investigtion: Wht will be the eiciency o the motor in this exmple? Exmple 2 A series-connected DC motor hs n rmture resistnce o 0.5 nd ield winding resistnce o 1.5. In driving certin lod t 1200 rpm, the current drwn by the motor is 20A rom voltge source o VT = 220V. The rottionl loss is 150W. Find the output power nd eiciency. Solution Totl input power : P in I 220 20 4400 W Induced voltge, E V R R I 180 V b T Power developed in the rmture cn be clculted s: P dev E b I 180 20 3600 W Output power delivered to the lod:
16 DC Motors P out Pdev Prot 3600 150 3450 W Thereore, eiciency cn be clculted s: Pout 100% 78.41% P in 4.6 DC Motor Speed Control Mny pplictions require the speed o motor to be vried over wide rnge. One o the most ttrctive etures o DC motors in comprison with AC motors is the ese with which their speed cn be vried. We know tht the bck em or seprtely excited DC motor: E b = K ω m = - I R Rerrnging the terms, Speed ω m = ( - I R )/K (28) From this eqution, it is evident tht the speed cn be vried by using ny o the ollowing methods: Armture voltge control (By vrying ) Field Control (By Vrying ) Armture resistnce control (By vrying R ) 4.6.1 Armture voltge control This method is usully pplicble to seprtely excited DC motors. In this method o speed control, R nd re kept constnt. In norml opertion, the drop cross the rmture resistnce is smll compred to E b nd thereore: E b Since, E b = K m Angulr speed cn be expressed s: m (29) K From this eqution, I lux is kept constnt, the speed chnges linerly with. As the terminl voltge is incresed, the speed increses nd vice vers. The reltionship between speed nd pplied voltge is shown in igure 15. This method provides smooth vrition o speed control. m
DC Motors 17 Figure 15: Vrition o speed with pplied voltge 4.6.2 Field Control () In this method o speed control, R nd remin ixed. Thereore, rom eqution (28): m 1/ Assuming mgnetic linerity, I Or, m 1/ I (30) i.e., Speed cn be controlled by vrying ield current I. The ield current cn be chnged by vrying n djustble rheostt in the ield circuit (s shown in igure 16). By incresing the vlue o totl ield resistnce, ield current cn be reduced, nd thereore speed cn be incresed. V I L R R ext I E b R ω m, T Vrible resistnce or speed control Figure 16 The reltionship between the ield winding current nd ngulr speed is shown in igure 17. m I Figure 17: Vrition o speed with ield current
18 DC Motors 4.6.3 Armture Resistnce Control The voltge cross the rmture cn be vried by inserting vrible resistnce in series with the rmture circuit. Vrible resistnce or speed control Figure 18: Armture resistnce method or speed control From speed-torque chrcteristics (eqution 15), we know tht: K T ( ) dev VT Km R V I L R I For lod o constnt torque, i nd re kept constnt, s the rmture resistnce R is incresed, speed decreses. As the ctul resistnce o the rmture winding is ixed or given motor, the overll resistnce in the rmture circuit cn be incresed by inserting n dditionl vrible resistnce in series with the rmture. The vrition i speed with respect to chnge in this externl resistnce is shown in igure 19. This method provides smooth control o speed. E b R ω m, T ω m R ext Figure 19: Vrition o speed with externl rmture resistnce DC Shunt Motor speed control All three methods described bove cn be used or controlling the speed o DC Shunt Motors. Series Motor speed control The speed is usully controlled by chnging n externl resistnce in series with the rmture. The other two methods described bove re not pplicble to DC series motor speed control. 4.7 DC Motor Strting I connected directly cross the supply, the strting current is dngerously high. I = ( - E b )/R At stndstill, E b = 0, thereore the strting current I strt = /R
DC Motors 19 The strting current cn be reduced by: Reducing during strting - requires vrible voltge supply Incresing resistnce in the rmture circuit - n dditionl resistnce R ext cn be connected in the rmture circuit Wht hppens when DC motor is connected cross n AC supply?