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Chapter 1 DC Machines1.1 Introduction to dc machines1.2 Armature windings1.3 Magnetic fields of dc machines1.4 Induced voltage and electromagnetic torque1.5 Equivalent circuit of a dc machine1.6 Power flow and losses in dc machine1.7 Operation characteristics of dc generator1.8 Operation characteristics of dc motors1.9 Speed control of shunt dc motor1.10 Starting of dc motor1.11 Braking of dc motor1.12 CommutationBrief Content 1.1.1 The Construction of DC MachinesDC Machine(Armature core)(Armature winding)(Brushes)(Brushes)(Commutator)(Shaft)Field poleField winding The cross-section of a dc machine (interpole)(Fieldpole)(York)(Armature core)(Armature winding)(Frame)Field windingSheet of rotorStator and RotorAir gapwhich is separating stator and rotorStationary part:Frame,Field Pole and Brushes Rotating part:Armature core，Winding Shaft and Commutator DC MachinesThe armature winding is placed in the rotor slot and connected to rotating commutator which rectifies the induced voltageThe brushes which are connected to the armature winding,ride on commutator 1.1.2 Operation Principle of DC Machines(slip rings)（brushes）(commutator)（brushes）DC Motors:operation principlesSupply a DC voltage to the brushes X and Y.1.1.3 Excitation types of DC Machines Separately excited DC machine Shunt(excited)DC machine Series(excited)DC machine Compounded(excited)DC machineDC Motor 他励他励(Separately excited)+-并励并励(Shunt excited)+_串励串励(Series excited)复励复励 (Compound excited)他励他励(Separately excited)并励并励(Shunt excited)串励串励(Series excited)复励复励(Compound excited)DC Generator1、Rated power：W,kWMotor:the output mechanical power：Generator:the output electrical power：2、Rated current：A3、Rated voltage：V4、Rated speed：r/min5、Rated excitation current：A6、Rated excitation voltage：V8、Pole number：pole pair number1.1.4 Ratings of dc machinesExample 1-1 A dc generator,its rated power PN=10kW,rated voltage UN=230V,rated speed nN=2850r/min,rated efficiency N=0.85.Calculate its rated current and its rated input power?Solution:the rated current of the dc generator is IN=PN/UN=10*1000/230=43.48(A);The rated input power is P1=PN/N=10*1000/0.85=11 765(W).Example 1-2 A dc motor,its rated power PN=17kW,rated voltage UN=220V,rated speed nN=1500r/min,rated efficiency N=0.83.Calculate its rated current and its rated input power?Solution:the rated input power of the dc motor is P1=PN/N=17*1000/0.83=20 482(W);Its rated current is IN=P1/UN=20 482/220=93.1(A).1.2 Armature winding of DC Machines Different connection ways of loops to commutator segments(换向片换向片)affect the number of parallel current paths（并联支路数）（并联支路数）,the output voltage（输出电压输出电压），），the number and position of the brushes（电刷的数目和位置电刷的数目和位置）riding on the commutator segments.Lap winding（叠绕组，叠绕组，simplex lap-单叠，单叠，multiplex lap-复叠复叠）Wave winding（波绕组，波绕组，simplex wave-单波，单波，multiplex wave-复波复波）Lap winding Wave winding Elements of a lap winding and a wave winding with two turns are shown.Winding pitch of a lap and a wave winding Lap winding Wave winding铁芯齿铁芯齿槽楔槽楔xie绝缘绝缘导体导体端接端接有效边有效边Some terms are employed for better description of the construction of DC armature windings.They are winding pitch(y),pole number(2p),pole pitch(),slot number(Q),winding element number(S),commutator bar number(K),commutator pitch(yc),the first pitch(or coil pitch)(y1)and the second pitch(y2).The distance between the beginnings of two consecutive turns is called the winding pitch(y).The distance between the beginning of one turn to the end of the same turn is called the first pitch(or coil pitch)(y1).The length of the step necessary to follow through from the end of one turn to the beginning of the next following turn are called the second pitch(y2).The distance between the two commutator bars connecting to the two ends of an element winding is called the commutator pitch(yc).y=y1y2 (lap winding)y=y1+y2 (wave winding)y=yc (lap and wave winding)The first pitch(coil pitch,y1)of lap and wave windings must be equal or approximately equal to the pole pitch (=Q/2p in slot pitches).y1=(lap and wave winding)when the coil pitch y1 is equal to the pole pitch (=0),the winding is defined as full-pitch winding;if y1 is greater than (0),the winding is defined as a long-pitch winding;and if y1 is less than (0),the winding is defined as short-pitch winding,and is also called fractional-pitch winding.y=yc=1 (simplex lap winding)y=yc=(K1)/p (simplex wave winding)1.2.1 Simplex lap winding For a 4-pole machine with full-pitch progressive simplex lap winding having the same number of winding elements,slots and commutator bars,i.e.,Q=S=K=16,1.Pitches calculation:For the full-pitch progressive simplex lap winding,y=yc=1.According to Eq.1-6:y1=Q/2p=16/4=4,According to Eq.1-3:y2=y1 y=4-1=32.Winding elements connection:3.Developed winding diagram:Developed winding connection with 4-poles is shown in below.the upper and lower layers are shown side by side.The upper layer is represented by solid line and the lower layer is represented by dotted line.the upper layer of the element 1 is connected to commutator bar 1;the lower layer of element 1 is connected to the upper layer of element 2 and commutator bar 2,and so forth.The lower layer of the last element 16 is then connected with the upper layer of element 1 and commutator bar 1,and the winding is closed.4.Placing magnetic poles and brushes:The magnetic poles are placed evenly on the stator with N and S alternately,and the pole width is usually equal to 0.75.the axis between two adjacent N and S poles is called neutral axis or quadrature-axis.The brushes are positioned around the commutator in a way that they are connected with the conductors lying at the middle points of the two magnetic poles(N and S).the two conductors of coil 1,5,9,13 are lying at the middle points of N and S poles and coil 1,5,9,13 are shorted by brush A1,B1,A2 and B2 respectively.The emf induced in the conductors of coil 1,5,9,13 is so small that the circulating current flowing through the brushes is negligible.In general,lap windings have equal number of brushes and poles.5.Instantaneous circuit diagram:6.Parallel branches of windings 2a=2p (simplex lap winding)1.2.2 Simplex wave windings For a 4-pole machine with short-pitch retrogressive simplex wave winding,noted that the number of winding elements,slots and commutator bars is the same with each other,i.e.,Q=S=K=15.1、Pitches calculation:For the short-pitch retrogressive simplex wave winding,according to Eq.1-8,y=yc=(K1)/p=(151)/2=7.According to Eq.1-6,y1=Q/2p =15/4=3.According to Eq.1-4,y2=y y1=73=4.2、Winding elements connection:3.Developed winding diagram:the first wave is connected to commutator bar 1,8,15;the second wave is connected to commutator bar 15,7,14;the third wave is connected to commutator bar 14,6,13;the fourth,fifth and sixth wave are connected to commutator bars(13,5,12);(12,4,11);(11,3,10)respectively.The last wave is connected to commutator bar 10,2,9,and the last turn is connected to commutator bar 9 and 1,and the winding is closed.The brushes are attached on the commutator in a way that they are connected with the conductors lying between two magnetic poles(N and S).In general,wave windings have equal number of brushes and poles.4.Parallel branches of windings 2a=2 (simplex wave winding)1.3 Magnetic fields of DC machines No load operationLoaded operationArmature reaction1.3.1 Magnetic field in no-load conditionwe can see that the length of the air gap between the pole and the armature is not uniform.The air gap length is larger under the pole shoe than those under other parts of the pole.So the flux density in the air gap between pole shoe and the armature is smaller than that of the air gap between pole face and armature.the flux density curve of a DC machine at no-load is a flat-top shaped curve.a flat-topped curve 1.3.2 Magnetic field in loaded condition 1.MMF of armature windings To illustrate the armature winding MMF,it is assumed that only armature windings carry current.Field curves,i.e.,the flux density distribution Bax as a function of distance x,are determined by the mmf Fax curve and the length of the air-gap x(or the magnetic reluctance)for the different tubes of force,i.e.Bax=0Fax/x.Since the magnetic reluctance is very high in the interpolar space,the flux density in the q-axis is very small.The approximated shape of the field curve which corresponds to the mmf curve in Fig.b is shown in Fig.c.In accordance with Faradays law for induced emf,all conductors lying under north pole will induce emf in one direction and all those under south poles will induce emf in the opposite direction.If the brushes lie in the neutral axis,the same rule as that of the voltage also applies to current,thus,all conductors above(or below)the neutral axis will induce current flowing in the same direction.If the brushes shift away from the neutral axis,Faradays law for emf will no longer hold for current.This is due to the fact that brushes position determines the parallel circuits.Since the current direction is the same for all conductors within the parallel circuits,all conductors above(or below)the line determined the brushes must have the currents of the same direction.2.Both field windings and armature windings carry current and Armature reaction.(1)Quadrature-axis armature reaction Quadrature-axis armature mmf produces the non-uniform flux distribution within a pole,and as a result,the air-gap flux density under one half pole is greater than that of the other half pole.If there is low magnetic saturation in the armature teeth and in the pole shoe,the mmfs of the field and armature windings can be considered separately.The armature flux distribution is then a straight line under the pole and a saddle-shaped curve in the interpolar space.The flux distribution curve is flat-topped produced by the field mmf alone.Since the saturation of iron is low,the armature flux and the axis of abscissa are symmetrical.That means the magnitude of the air-gap flux,which is proportional to the area of the flux density curve,remains the same under load as that of no-load.If the armature teeth and pole shoes are saturated,the area lying above curve b0 between curve b and curve b0 will be smaller than that of lying below curve b0.As a result of armature reaction,the resultant air-gap flux under load will be less than that of no-load and the neutral axis will shift degree to the left/right.(2)Demagnetizing effect of armatures In general,flux can be weakened under two conditions:1)brushes of generators are placed in the direction of rotation.2)brushes of motors are displaced in the opposite direction of rotation.Contrarily,flux can be strengthened by 1)brushes of generators are displaced in the opposite direction of rotation and 2)brushes of motors are displaced in the direction of rotation.1.4 Induced voltage and Electromagnetic(Induced)TorqueVoltage generated from DC machines is the same as the DC voltage between two brushes,i.e.,the total voltage of a parallel circuit.1、the average voltage eav induced in conductorsBav is the average density per pole,T;eav is the average voltage of one conductor,V;l is the effective length of the conductor,m;v is the mechanical speed of the conductor cutting the field,m/s,and v=2p n/60,n is the rotation speed of the armature,r/min.2、The average voltage Ea between two brushes Ce is the voltage constant which depends upon the construction parameters of DC machines,N is the total number of turns in series between armature terminals;n is the rotation speed of the armature,r/min.In general,the voltage of all real DC machines depends on the same factors:(a)The per pole flux in the machine;(b)The speed(n)of the machines rotor;(c)The constant Ce with respect to the construction of DC machines.If the saturation of iron is low,the per pole flux can be expressed KfIf,where Kf is a constant and If is the excitation current.is the mechanical speed of rotor,rad/s,and 1.4.2 Electromagnetic torque when the armature rotates one-pole distance,the average force fav produced by conductors is Bav:the average density per pole,T;l:the effective length of the conductor,m;Ic:the current per conductor in ampere;fav:the average force in newton.The torque(in newton-meter)produced by a single conductor of smooth armature is Tav is the average torque of one conductor,N.m;Da is the armature diameter,m,and Da=2p/.the total torque can be obtained by adding up the torques of all N conductors around the armature.CT is the torque constant with respect to the construction parameters of the machine,In general,the electromagnetic torque of a machine depends on three factors:(a)The per pole flux in the machine;(b)The armature(or rotor)current Ia;(c)The constant CT with respect to the construction of the DC machine.If the saturation of iron is low,the per pole flux can be expressed as KfIf,where Kf is a constant and If is the excitation current.Example 1-3:A dc motor has the simplex lap winding,the pole pair p=3,the total conductor number N=398,the per pole flux =2.1 10-2Wb,Calculated the induced voltage when speed n1=1 500r/min and n2=500r/min?Solution:According to the simplex lap winding,the parallel current paths a equal to the pole pair p,namely,a=p=3;According to Eq.1-14,when speed n1=1 500r/min,the induced voltage is (V);When speed n2=500r/min,the induced voltage is (V).Example 1-4:A dc motor has the simplex lap winding,the pole pair p=3,the total conductor number N=398,the per pole flux =2.1 10-2Wb,Calculated the induced torque when armature current I1=10 A and I2=15 A?Solution:According to the simplex lap winding,the parallel current paths a equal to the pole pair p,namely,a=p=3;According to Eq.1-20,when armature current I1=10 A,the induced torque is (Nm);When armature current I2=15 A,the induced torque is (Nm).Example 1-5:A dc generator has the simplex lap winding,the pole pair p=3,the total conductor number N=780,the per pole flux=1.310-2Wb,its rated power PN=17kW,rated voltage UN=230V,rated speed nN=1 500r/min.Calculated the rated current and the induced voltage?Solution:The rated current is IN=PN/UN=171000/230=73.91(A);The armature winding is simplex lap winding,the parallel current paths a equal to the pole pair p,namely,a=p=3;when the speed nN=1 500r/min,the induced voltage is (V).1.5 Equivalent circuit of DC machine Separately excited DC machineShunt DC machineSeries DC machineCompounded DC machineDC generator1.Separately excited DC generator2.Shunt DC generator3.Series DC generator4.Cumulatively Compounded DC generator (a)long-shunt connection(b)short-shunt connectionDC Motor1.Separately excited DC generator2.Shunt DC Motor3.Series DC Motor4.Cumulatively Compounded DC Motor (a)long-shunt connection(b)short-shunt connection1.6 Power Flow and LossesThe LossesCopper lossesBrush lossesCore(iron)lossesMechanical lossesStray losses1.Copper Losses(I2R Loss)2.Brush LossesArmature winding:Field winding:VBD is usually assumed to be about a 2V constant over a large range of armature currents.3.Core LossesHysteresis and Eddy Current Loss4.Mechanical LossesFriction and windage loss5.Stray LossesLosses that cannot be placed in previous categories and usually be taken by convention to be 1%of full load.The Power-Flow Diagram for DC MachinesDC GeneratorEffciency：Stray lossesMechanical lossesCore lossesI2R loss转换功率转换功率(电磁功率电磁功率)DC MotorThe Power-Flow Diagram for DC MachinesEffciency：I2R lossesCore lossesMechanical lossesStray loss转换功率转换功率(电磁功率电磁功率)Torque equationDC generator:DC motor:1.7 Operation characteristics of DC GeneratorThe following characteristic curves of a DC generator will be considered.(1)No-load characteristic,or magnetization curve;n=constant(2)Regulation characteristic;U and n=constant(3)Terminal characteristic,or external curve;n=constantA simplified equivalent circuit1.7.1 The operation characteristics of a separately excited DC generator1.The magnetization curveThe magnetization curve of a ferromagnetic materialThe magnetization curve of a dc machine expressed as a plot of EA versus IF for a fixed speed w wo o.NOTE:Most machines are designed to operate near the saturation point on the magnetization curve(at the knee of the curve膝点膝点).This implies that a fairly large increase in field current is often necessary to get a small increase in EA when operation is near full load.2.The terminal characteristic of a separately excited DC generatorThe terminal characteristic of a separately excited generator is thus a plot of U versus Ia for a constant speed n.By Kirchhoffs voltage law,the terminal voltage is 3.The regulation characteristic of a separately excited DC generatorThe regulation characteristic of a separately excited generator is thus a plot of If versus Ia for a constant speed n and a constant terminal voltage U.4.Voltage control for a separately excited DC generator1)Change the speed of rotation.If n increase,then will increase,so will increase too.2)Change the field current If.If Rf is decreased,then the field current increases.Therefore,the flux in the machine increases.As the flux rises,must raise too,so increase.In many applications,the speed range of the prime mover is quite limited,so the terminal voltage is most commonly controlled changing by the field current.1.7.2 The operation characteristics of a shunt DC generator 1、The voltage buildup in a shunt dc generator Possible causes for the voltage to fail to build up during starting(How can the voltage buildup?)Residual magnetic fluxDirection rotation generate voltage produces a flux increase the residual flux.Field resistance should be less than the critical resistanceVoltage Buildup in a shunt generator Depends on the presence of a residual fluxin the poles res.When generator starts to turn,res causes a voltage EA=K resnEA.Causes a current to flow in the field coil IF,and this current produces a magnetomotive force in the poles which increase the flux.,EA,VT,IF,these happen circularly until the voltage buildup.n1n2n3n1 n2 n3R3 R2 R1 R02.The terminal characteristic of a shunt DC generator The terminal characteristic of a shunt dc generator is thus a plot of U versus Ia for a constant speed n.Same and different behavior to that of a separately excited DC GeneratorSame:IA,VT=EA-IARA,thus a decrease characteristicDifferent:VF=VT,IF,EA，a further decrease happens.3.The regulation characteristic of a shunt dc generatorThe regulation curve of a shunt dc generator is the same as that of the separately excited dc generator,because the voltage drop produced by the field current is very small and,in comparison with the voltage drop caused by the load current,can be neglected.4.Voltage control for a shunt dc generator As with the separately excited generator,there are two ways to control the voltage of a shunt dc generator.(1).Change the shaft speed n of the generator.(2).Change the field resistor of the generator,thus changing the field current.Example 1-6:A shunt dc generator,its rated power PN=9kW,rated voltage UN=115V,rated speed nN=1 450r/min,armature resistance Ra=0.15,when the generator turning at rated operation state,the total resistance of the field circuit RfN=33,the core loss is 410W,the mechanical loss is 101W,the stray loss is taken by 0.5 percent of rated power.Calculate the following:(1)the induced torque of the generator?(2)The efficiency of the generator turning at rated operation state?Solution:(1)the rated current of the machine is IN=PN/UN=9000/115=78.26(A)The rated field current is If=UN/RfN=115/33=3.48(A)The armature current is Ia=IN+If=78.26+3.48=81.74(A)The electromagnetic power is Pe=PN+pcuf+pcua=9000+1153.48+81.7420.15=10402.4(W)The induced torque is Te=Pe/=10402.460/(23.141450)=68.54(N.m)(2)the efficiency of the machine is N=PN/(Pe+pFe+p+pad)=9000/(10402.4+410+101+0.0059000)=82.13%解法解法2：(1)the rated current of the machine is IN=PN/UN=9000/115=78.26(A)The rated field current is If=UN/RfN=115/33=3.48(A)The armature current is Ia=IN+If=78.26+3.48=81.74(A)the induced voltage is Ea=U+IaRa=115+81.74 0.15=127.26(V)The ele
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