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EE331
Electromechanical Energy
      Conversion II

      Dr. Ali M. Eltamaly
          DC Motors




                            1
8.1 DC Motor
• The direct current (dc) machine can be used as
  a motor or as a generator.
• DC Machine is most often used for a motor.
• The major advantages of dc machines are the
  easy speed and torque regulation.
• However, their application is limited to mills,
  mines and trains. As examples, trolleys and
  underground subway cars may use dc motors.
• In the past, automobiles were equipped with dc
  dynamos to charge their batteries.

                                      2
8.1 DC Motor
• Even today the starter is a series dc motor
• However, the recent development of power
  electronics has reduced the use of dc motors
  and generators.
• The electronically controlled ac drives are
  gradually replacing the dc motor drives in
  factories.
• Nevertheless, a large number of dc motors are
  still used by industry and several thousand are
  sold annually.

                                      3
8.1 Construction



              4
DC Machine Construction




  Figure 8.1 General arrangement of a dc machine

                                            5
DC Machines
•   The stator of the dc motor has
    poles, which are excited by dc
    current to produce magnetic
    fields.
•   In the neutral zone, in the middle
    between the poles, commutating
    poles are placed to reduce
    sparking of the commutator.
    The commutating poles are
    supplied by dc current.
•   Compensating windings are
    mounted on the main poles.
    These short-circuited windings
    damp rotor oscillations. .




                                         6
DC Machines
•    The poles are mounted on an
    iron core that provides a
    closed magnetic circuit.
•   The motor housing supports
    the iron core, the brushes and
    the bearings.
•   The rotor has a ring-shaped
    laminated iron core with
    slots.
•     Coils with several turns are
    placed in the slots. The
    distance between the two legs
    of the coil is about 180
    electric degrees.

                                     7
DC Machines
•   The coils are connected in series
    through the commutator
    segments.
•    The ends of each coil are
    connected to a commutator
    segment.
•   The commutator consists of
    insulated copper segments
    mounted on an insulated tube.
•   Two brushes are pressed to the
    commutator to permit current
    flow.
•    The brushes are placed in the
    neutral zone, where the magnetic
    field is close to zero, to reduce
    arcing.


                                        8
DC Machines
•   The rotor has a ring-shaped
    laminated iron core with
    slots.
•   The commutator consists of
    insulated copper segments
    mounted on an insulated
    tube.
•   Two brushes are pressed to
    the commutator to permit
    current flow.
•    The brushes are placed in the
    neutral zone, where the
    magnetic field is close to zero,
    to reduce arcing.

                                       9
DC Machines
•   The commutator switches the
    current from one rotor coil to
    the adjacent coil,
•   The switching requires the
    interruption of the coil
    current.
•   The sudden interruption of
    an inductive current
    generates high voltages .
•   The high voltage produces
    flashover and arcing between
    the commutator segment and
    the brush.


                                     10
DC Machine Construction
                                  Rotation
                Ir_dc/2             Ir_dc           Ir_dc/2
                          Brush                                Pole
                                                              winding
                Shaft

                                     |
                                     1
                                            2
                              8


          N               7                     3
                                                                 S
                              6             4
                                     5




              Insulation                             Copper
                      Rotor         Ir_dc            segment
                    Winding


Figure 8.2 Commutator with the rotor coils connections.
                                           11
DC Machine Construction




  Figure 8.3 Details of the commutator of a dc motor.
                                             12
DC Machine Construction




Figure 8.4 DC motor stator with poles visible.
                                      13
DC Machine Construction




   Figure 8.5 Rotor of a dc motor.
                                     14
DC Machine Construction




   Figure 8.6 Cutaway view of a dc motor.
                                   15
8.2.1 DC Motor
    Operation


             16
DC Motor Operation
• In a dc motor, the stator
  poles are supplied by dc                            Rotation
                                                                        Ir_dc/2
                                    Ir_dc/2
  excitation current, which                   Brush
                                                        Ir_dc                      Pole

  produces a dc magnetic            Shaft
                                                                                  winding


  field.                                                 |


• The rotor is supplied by
                                                         1
                                                                2
                                                  8


  dc current through the      N               7                     3
                                                                                     S
  brushes, commutator
                                                  6             4
                                                         5


  and coils.
• The interaction of the          Insulation
                                          Rotor         Ir_dc
                                                                          Copper
                                                                         segment
  magnetic field and rotor              Winding

  current generates a force
  that drives the motor

                                                                17
8.2.1 DC Motor Operation
                                                                          v               B
• The magnetic field lines                                                    a

  enter into the rotor from the
                                         S                                                    N
  north pole (N) and exit                                                                               Vdc




                                                         1
                                                                  30

  toward the south pole (S).




                                                                      2
                                                     b
• The poles generate a                                   v
  magnetic field that is                                                                  Ir_dc
  perpendicular to the current      (a) Rotor current flow from segment 1 to 2 (slot a to b)
  carrying conductors.
• The interaction between the                    B

  field and the current                              a


  produces a Lorentz force,               S                                               N       Vdc




                                                                  2
                                                 v           30                   v
• The force is perpendicular to


                                                         1
  both the magnetic field and
                                                                          b



  conductor                                                                       Ir_dc

                                  (b) Rotor current flow from segment 2 to 1 (slot b to a)


                                                                       18
8.2.1 DC Motor Operation
                                                                               v           B
• The generated force turns the rotor                                              a

  until the coil reaches the neutral
                                               S                                               N
  point between the poles.                                                                               Vdc




                                                                 1
                                                                      30




                                                                          2
• At this point, the magnetic field                          b
  becomes practically zero together                              v
  with the force.                                                                          Ir_dc
• However, inertia drives the motor
                                          (a) Rotor current flow from segment 1 to 2 (slot a to b)
  beyond the neutral zone where the
  direction of the magnetic field                    B
  reverses.                                              a

• To avoid the reversal of the force
                                               S                                           N       Vdc
  direction, the commutator changes




                                                                      2
                                                     v           30                v




                                                             1
  the current direction, which                                             b

  maintains the counterclockwise
  rotation. .                                                                      Ir_dc

                                        (b) Rotor current flow from segment 2 to 1 (slot b to a)


                                                                           19
8.2.1 DC Motor Operation
•   Before reaching the neutral zone,                                                v
                                                                                         a
                                                                                                     B
    the current enters in segment 1 and
    exits from segment 2,                            S                                                   N         Vdc




                                                                       1
                                                                            30

•    Therefore, current enters the coil




                                                                                2
    end at slot a and exits from slot b                            b

    during this stage.                                                 v
                                                                                                     Ir_dc
•    After passing the neutral zone, the
    current enters segment 2 and exits          (a) Rotor current flow from segment 1 to 2 (slot a to b)

    from segment 1,                                        B
•   This reverses the current direction                        a

    through the rotor coil, when the coil           S                                            N
    passes the neutral zone.                                                                                 Vdc




                                                                            2
                                                           v           30                v




                                                                   1
•    The result of this current reversal is                                      b

    the maintenance of the rotation.                                                     Ir_dc


                                              (b) Rotor current flow from segment 2 to 1 (slot b to a)


                                                                                 20
8.2.2 DC Generator
      Operation


               21
8.2.2 DC Generator Operation
                                                                  v         B
• The N-S poles produce a                                             a

  dc magnetic field and the         S                                             N
  rotor coil turns in this                                                            Vdc




                                                     1
                                                         30




                                                              2
  field.                                         b

• A turbine or other                                 v
                                                                          Ir_dc
  machine drives the rotor.
                                 (a) Rotor current flow from segment 1 to 2 (slot a to b)
• The conductors in the
  slots cut the magnetic flux                                                B
  lines, which induce                            a


  voltage in the rotor coils.       S                                             N   Vdc




                                                              2
                                             v           30
                                                                            v
• The coil has two sides:


                                                     1
  one is placed in slot a, the
                                                                      b



  other in slot b.                                                        Ir_dc
                                 (b) Rotor current flow from segment 2 to 1 (slot b to a)

                                                              22
8.2.2 DC Generator Operation
• In Figure 8.11A, the                                           v
                                                                     a
                                                                           B

  conductors in slot a are
  cutting the field lines          S                                             N   Vdc




                                                    1
                                                        30

  entering into the rotor




                                                             2
  from the north pole,                          b

                                                    v
• The conductors in slot b                                               Ir_dc
  are cutting the field lines   (a) Rotor current flow from segment 1 to 2 (slot a to b)
  exiting from the rotor to
  the south pole.                                                           B
• The cutting of the field                      a


  lines generates voltage in       S                                             N   Vdc




                                                             2
                                            v
  the conductors.
                                                        30
                                                                           v




                                                    1
• The voltages generated in                                          b

  the two sides of the coil
                                                                         Ir_dc
  are added.
                                (b) Rotor current flow from segment 2 to 1 (slot b to a)

                                                             23
8.2.2 DC Generator Operation
• The induced voltage is                                           v
                                                                       a
                                                                             B

  connected to the generator
  terminals through the              S                                             N   Vdc




                                                      1
                                                          30

  commutator and brushes.




                                                               2
• In Figure 8.11A, the induced                    b

                                                      v
  voltage in b is positive, and                                            Ir_dc
  in a is negative.               (a) Rotor current flow from segment 1 to 2 (slot a to b)
• The positive terminal is
  connected to commutator                                                     B
  segment 2 and to the                            a


  conductors in slot b.              S                                             N   Vdc




                                                               2
                                              v           30
                                                                             v
• The negative terminal is



                                                      1
  connected to segment 1 and                                           b

  to the conductors in slot a.
                                                                           Ir_dc
                                  (b) Rotor current flow from segment 2 to 1 (slot b to a)

                                                               24
8.2.2 DC Generator Operation
• When the coil passes the                                            v
                                                                          a
                                                                                B

  neutral zone:
   – Conductors in slot a are           S                                             N   Vdc




                                                         1
                                                             30

     then moving toward the




                                                                  2
     south pole and cut flux lines                   b

     exiting from the rotor                              v
   – Conductors in slot b cut the                                             Ir_dc
     flux lines entering the in      (a) Rotor current flow from segment 1 to 2 (slot a to b)
     slot b.
• This changes the polarity                                                      B
  of the induced voltage in                          a


  the coil.                             S                                             N   Vdc




                                                                  2
                                                 v           30
                                                                                v
• The voltage induced in a



                                                         1
  is now positive, and in b is                                            b

  negative.
                                                                              Ir_dc
                                     (b) Rotor current flow from segment 2 to 1 (slot b to a)

                                                                  25
8.2.2 DC Generator Operation
                                                                     v         B
• The simultaneously the                                                 a

  commutator reverses its              S                                             N
  terminals, which assures                                                               Vdc




                                                        1
                                                            30




                                                                 2
  that the output voltage                           b

  (Vdc) polarity is                                     v
                                                                             Ir_dc
  unchanged.
                                    (a) Rotor current flow from segment 1 to 2 (slot a to b)
• In Figure 8.11B
   – the positive terminal is                                                   B
     connected to commutator                        a

     segment 1 and to the              S                                             N   Vdc




                                                                 2
     conductors in slot a.                      v           30
                                                                               v




                                                        1
   – The negative terminal is                                            b
     connected to segment 2 and
     to the conductors in slot b.                                            Ir_dc
                                    (b) Rotor current flow from segment 2 to 1 (slot b to a)

                                                                 26
8.2.3 DC Machine
Equivalent Circuit


               27
Generator



            28
8.2.3 DC Generator Equivalent
              circuit
• The magnetic field produced by the stator poles induces a
  voltage in the rotor (or armature) coils when the
  generator is rotated.
• This induced voltage is represented by a voltage source.
• The stator coil has resistance, which is connected in
  series.
• The pole flux is produced by the DC excitation/field
  current, which is magnetically coupled to the rotor
• The field circuit has resistance and a source
• The voltage drop on the brushes represented by a battery

                                            29
8.2.3 DC Generator Equivalent
              circuit
                           Vbrush
        Rf                           Ra                 Load
                Φmax
                                    Iag
     Vf If                   Eag                Vdc


              Mechanical                  Electrical
               power in                   power out

• Figure 8.12Equivalent circuit of a separately excited dc
  generator.

                                                       30
8.2.3 DC Generator Equivalent
             circuit
• The magnetic field produced by the stator poles
  induces a voltage in the rotor (or armature) coils
  when the generator is rotated.
• The dc field current of the poles generates a
  magnetic flux
• The flux is proportional with the field current if
  the iron core is not saturated:
            Φ ag = K 1 I f

                                       31
8.2.3 DC Generator Equivalent
             circuit
• The rotor conductors cut the field lines
  that generate voltage in the coils.
              E ag = 2 N r B  g v
• The motor speed and flux equations are :
         Dg
  v =ω                 Φ ag = B  g D g
         2

                                     32
8.2.3 DC Generator Equivalent
                    circuit
   • The combination of the three equation
     results the induced voltage equation:

                                      Dg 
E ag   = 2 N r B  g v = 2 N r B  g ω
                                          = N r ( B  g D g ) ω = N r Φ ag ω
                                       2 
                                          

   • The equation is simplified.
         E ag = N r Φ ag ω = N r K 1 I f ω = K m I f ω

                                                              33
8.2.3 DC Generator Equivalent
              circuit
• When the generator is loaded, the load current produces
  a voltage drop on the rotor winding resistance.
• In addition, there is a more or less constant 1–3 V voltage
  drop on the brushes.
• These two voltage drops reduce the terminal voltage of
  the generator. The terminal voltage is;


         E ag = Vdc + I ag Ra + Vbrush


                                             34
Motor



        35
8.2.3 DC Motor Equivalent circuit
                                 Vbrush         Electrical
             Rf                            Ra   power in
                     Φmax
                                                              DC Power
          V f If                          Iam   Vdc
                                   Eam                         supply


                    Mechanical
                    power out

•    Figure 8.13 Equivalent circuit of a separately excited dc motor
•    Equivalent circuit is similar to the generator only the current
     directions are different




                                                             36
8.2.3 DC Motor Equivalent circuit
• The operation equations are:
• Armature voltage equation

         Vdc = E am + I am Ra + Vbrush

   The induced voltage and motor speed vs angular
   frequency


   E am = K m I f ω          ω = 2 π nm

                                              37
8.2.3 DC Motor Equivalent circuit
• The operation equations are:
• The combination of the equations results in

    K m I f ω = E am = Vdc − I am Rm
   The current is calculated from this equation. The output
   power and torque are:

                                 Pout
  Pout = E am I am            T=      = K m I am I f
                                  ω

                                                38
8.2.4 DC Machine
Excitation Methods


              39
DC Motor Operation

•   There are four different methods for
    supplying the dc current to the motor
    or generator poles:
    –   Separate excitation;
    –   Shunt connection
    –   Series connection
    –   Compound


                                 40
8.2.3 DC Motor Equivalent circuit
                  Vbrush
                                  Ra

                                Iam         Im   DC Power
                                                  supply
       Eam          Φmax               Rf
                                                  Vdc

                           If
        Pout

• Figure 8.14   Equivalent circuit of a shunt dc motor



                                                         41
8.2.3 DC Motor Equivalent circuit
                Vbrush     Ra


                                                   Im        DC Power
                                          Rf                  supply
   Eam
                                                                Vdc
                         Φmax

     Pout

• Figure 8.15    Equivalent circuit of a series dc motor

                                                        42
8.2.3 DC Motor Equivalent circuit
             Vbrush
                        Ra

                                    Iam       Im     DC Power
                             Rfs                      supply
Eam
                      Φmax                                Vdc
                             Rfp     Ifp
    Pout


•    Figure 8.16   Equivalent circuit of a compound dc motor

                                                     43

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EE331 Electromechanical Energy Conversion II DC Motor Operation

  • 1. EE331 Electromechanical Energy Conversion II Dr. Ali M. Eltamaly DC Motors 1
  • 2. 8.1 DC Motor • The direct current (dc) machine can be used as a motor or as a generator. • DC Machine is most often used for a motor. • The major advantages of dc machines are the easy speed and torque regulation. • However, their application is limited to mills, mines and trains. As examples, trolleys and underground subway cars may use dc motors. • In the past, automobiles were equipped with dc dynamos to charge their batteries. 2
  • 3. 8.1 DC Motor • Even today the starter is a series dc motor • However, the recent development of power electronics has reduced the use of dc motors and generators. • The electronically controlled ac drives are gradually replacing the dc motor drives in factories. • Nevertheless, a large number of dc motors are still used by industry and several thousand are sold annually. 3
  • 5. DC Machine Construction Figure 8.1 General arrangement of a dc machine 5
  • 6. DC Machines • The stator of the dc motor has poles, which are excited by dc current to produce magnetic fields. • In the neutral zone, in the middle between the poles, commutating poles are placed to reduce sparking of the commutator. The commutating poles are supplied by dc current. • Compensating windings are mounted on the main poles. These short-circuited windings damp rotor oscillations. . 6
  • 7. DC Machines • The poles are mounted on an iron core that provides a closed magnetic circuit. • The motor housing supports the iron core, the brushes and the bearings. • The rotor has a ring-shaped laminated iron core with slots. • Coils with several turns are placed in the slots. The distance between the two legs of the coil is about 180 electric degrees. 7
  • 8. DC Machines • The coils are connected in series through the commutator segments. • The ends of each coil are connected to a commutator segment. • The commutator consists of insulated copper segments mounted on an insulated tube. • Two brushes are pressed to the commutator to permit current flow. • The brushes are placed in the neutral zone, where the magnetic field is close to zero, to reduce arcing. 8
  • 9. DC Machines • The rotor has a ring-shaped laminated iron core with slots. • The commutator consists of insulated copper segments mounted on an insulated tube. • Two brushes are pressed to the commutator to permit current flow. • The brushes are placed in the neutral zone, where the magnetic field is close to zero, to reduce arcing. 9
  • 10. DC Machines • The commutator switches the current from one rotor coil to the adjacent coil, • The switching requires the interruption of the coil current. • The sudden interruption of an inductive current generates high voltages . • The high voltage produces flashover and arcing between the commutator segment and the brush. 10
  • 11. DC Machine Construction Rotation Ir_dc/2 Ir_dc Ir_dc/2 Brush Pole winding Shaft | 1 2 8 N 7 3 S 6 4 5 Insulation Copper Rotor Ir_dc segment Winding Figure 8.2 Commutator with the rotor coils connections. 11
  • 12. DC Machine Construction Figure 8.3 Details of the commutator of a dc motor. 12
  • 13. DC Machine Construction Figure 8.4 DC motor stator with poles visible. 13
  • 14. DC Machine Construction Figure 8.5 Rotor of a dc motor. 14
  • 15. DC Machine Construction Figure 8.6 Cutaway view of a dc motor. 15
  • 16. 8.2.1 DC Motor Operation 16
  • 17. DC Motor Operation • In a dc motor, the stator poles are supplied by dc Rotation Ir_dc/2 Ir_dc/2 excitation current, which Brush Ir_dc Pole produces a dc magnetic Shaft winding field. | • The rotor is supplied by 1 2 8 dc current through the N 7 3 S brushes, commutator 6 4 5 and coils. • The interaction of the Insulation Rotor Ir_dc Copper segment magnetic field and rotor Winding current generates a force that drives the motor 17
  • 18. 8.2.1 DC Motor Operation v B • The magnetic field lines a enter into the rotor from the S N north pole (N) and exit Vdc 1 30 toward the south pole (S). 2 b • The poles generate a v magnetic field that is Ir_dc perpendicular to the current (a) Rotor current flow from segment 1 to 2 (slot a to b) carrying conductors. • The interaction between the B field and the current a produces a Lorentz force, S N Vdc 2 v 30 v • The force is perpendicular to 1 both the magnetic field and b conductor Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 18
  • 19. 8.2.1 DC Motor Operation v B • The generated force turns the rotor a until the coil reaches the neutral S N point between the poles. Vdc 1 30 2 • At this point, the magnetic field b becomes practically zero together v with the force. Ir_dc • However, inertia drives the motor (a) Rotor current flow from segment 1 to 2 (slot a to b) beyond the neutral zone where the direction of the magnetic field B reverses. a • To avoid the reversal of the force S N Vdc direction, the commutator changes 2 v 30 v 1 the current direction, which b maintains the counterclockwise rotation. . Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 19
  • 20. 8.2.1 DC Motor Operation • Before reaching the neutral zone, v a B the current enters in segment 1 and exits from segment 2, S N Vdc 1 30 • Therefore, current enters the coil 2 end at slot a and exits from slot b b during this stage. v Ir_dc • After passing the neutral zone, the current enters segment 2 and exits (a) Rotor current flow from segment 1 to 2 (slot a to b) from segment 1, B • This reverses the current direction a through the rotor coil, when the coil S N passes the neutral zone. Vdc 2 v 30 v 1 • The result of this current reversal is b the maintenance of the rotation. Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 20
  • 21. 8.2.2 DC Generator Operation 21
  • 22. 8.2.2 DC Generator Operation v B • The N-S poles produce a a dc magnetic field and the S N rotor coil turns in this Vdc 1 30 2 field. b • A turbine or other v Ir_dc machine drives the rotor. (a) Rotor current flow from segment 1 to 2 (slot a to b) • The conductors in the slots cut the magnetic flux B lines, which induce a voltage in the rotor coils. S N Vdc 2 v 30 v • The coil has two sides: 1 one is placed in slot a, the b other in slot b. Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 22
  • 23. 8.2.2 DC Generator Operation • In Figure 8.11A, the v a B conductors in slot a are cutting the field lines S N Vdc 1 30 entering into the rotor 2 from the north pole, b v • The conductors in slot b Ir_dc are cutting the field lines (a) Rotor current flow from segment 1 to 2 (slot a to b) exiting from the rotor to the south pole. B • The cutting of the field a lines generates voltage in S N Vdc 2 v the conductors. 30 v 1 • The voltages generated in b the two sides of the coil Ir_dc are added. (b) Rotor current flow from segment 2 to 1 (slot b to a) 23
  • 24. 8.2.2 DC Generator Operation • The induced voltage is v a B connected to the generator terminals through the S N Vdc 1 30 commutator and brushes. 2 • In Figure 8.11A, the induced b v voltage in b is positive, and Ir_dc in a is negative. (a) Rotor current flow from segment 1 to 2 (slot a to b) • The positive terminal is connected to commutator B segment 2 and to the a conductors in slot b. S N Vdc 2 v 30 v • The negative terminal is 1 connected to segment 1 and b to the conductors in slot a. Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 24
  • 25. 8.2.2 DC Generator Operation • When the coil passes the v a B neutral zone: – Conductors in slot a are S N Vdc 1 30 then moving toward the 2 south pole and cut flux lines b exiting from the rotor v – Conductors in slot b cut the Ir_dc flux lines entering the in (a) Rotor current flow from segment 1 to 2 (slot a to b) slot b. • This changes the polarity B of the induced voltage in a the coil. S N Vdc 2 v 30 v • The voltage induced in a 1 is now positive, and in b is b negative. Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 25
  • 26. 8.2.2 DC Generator Operation v B • The simultaneously the a commutator reverses its S N terminals, which assures Vdc 1 30 2 that the output voltage b (Vdc) polarity is v Ir_dc unchanged. (a) Rotor current flow from segment 1 to 2 (slot a to b) • In Figure 8.11B – the positive terminal is B connected to commutator a segment 1 and to the S N Vdc 2 conductors in slot a. v 30 v 1 – The negative terminal is b connected to segment 2 and to the conductors in slot b. Ir_dc (b) Rotor current flow from segment 2 to 1 (slot b to a) 26
  • 28. Generator 28
  • 29. 8.2.3 DC Generator Equivalent circuit • The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated. • This induced voltage is represented by a voltage source. • The stator coil has resistance, which is connected in series. • The pole flux is produced by the DC excitation/field current, which is magnetically coupled to the rotor • The field circuit has resistance and a source • The voltage drop on the brushes represented by a battery 29
  • 30. 8.2.3 DC Generator Equivalent circuit Vbrush Rf Ra Load Φmax Iag Vf If Eag Vdc Mechanical Electrical power in power out • Figure 8.12Equivalent circuit of a separately excited dc generator. 30
  • 31. 8.2.3 DC Generator Equivalent circuit • The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated. • The dc field current of the poles generates a magnetic flux • The flux is proportional with the field current if the iron core is not saturated: Φ ag = K 1 I f 31
  • 32. 8.2.3 DC Generator Equivalent circuit • The rotor conductors cut the field lines that generate voltage in the coils. E ag = 2 N r B  g v • The motor speed and flux equations are : Dg v =ω Φ ag = B  g D g 2 32
  • 33. 8.2.3 DC Generator Equivalent circuit • The combination of the three equation results the induced voltage equation:  Dg  E ag = 2 N r B  g v = 2 N r B  g ω   = N r ( B  g D g ) ω = N r Φ ag ω  2   • The equation is simplified. E ag = N r Φ ag ω = N r K 1 I f ω = K m I f ω 33
  • 34. 8.2.3 DC Generator Equivalent circuit • When the generator is loaded, the load current produces a voltage drop on the rotor winding resistance. • In addition, there is a more or less constant 1–3 V voltage drop on the brushes. • These two voltage drops reduce the terminal voltage of the generator. The terminal voltage is; E ag = Vdc + I ag Ra + Vbrush 34
  • 35. Motor 35
  • 36. 8.2.3 DC Motor Equivalent circuit Vbrush Electrical Rf Ra power in Φmax DC Power V f If Iam Vdc Eam supply Mechanical power out • Figure 8.13 Equivalent circuit of a separately excited dc motor • Equivalent circuit is similar to the generator only the current directions are different 36
  • 37. 8.2.3 DC Motor Equivalent circuit • The operation equations are: • Armature voltage equation Vdc = E am + I am Ra + Vbrush The induced voltage and motor speed vs angular frequency E am = K m I f ω ω = 2 π nm 37
  • 38. 8.2.3 DC Motor Equivalent circuit • The operation equations are: • The combination of the equations results in K m I f ω = E am = Vdc − I am Rm The current is calculated from this equation. The output power and torque are: Pout Pout = E am I am T= = K m I am I f ω 38
  • 40. DC Motor Operation • There are four different methods for supplying the dc current to the motor or generator poles: – Separate excitation; – Shunt connection – Series connection – Compound 40
  • 41. 8.2.3 DC Motor Equivalent circuit Vbrush Ra Iam Im DC Power supply Eam Φmax Rf Vdc If Pout • Figure 8.14 Equivalent circuit of a shunt dc motor 41
  • 42. 8.2.3 DC Motor Equivalent circuit Vbrush Ra Im DC Power Rf supply Eam Vdc Φmax Pout • Figure 8.15 Equivalent circuit of a series dc motor 42
  • 43. 8.2.3 DC Motor Equivalent circuit Vbrush Ra Iam Im DC Power Rfs supply Eam Φmax Vdc Rfp Ifp Pout • Figure 8.16 Equivalent circuit of a compound dc motor 43