XIII.  Commutation 

62.  The  most  important  problem  connected  with  commutating 
machines  is  that  of  commutation. 

Fig.  107  represents  diagrammatically  a  commutating  machine. 


FIG.  107. — Diagram  for  the  study  of  commutation. 

The  e.m.f.  generated  in  an  armature  coil  A  is  zero  with  this  coil 
at  or  near  the  position  of  the  commutator  brush  B\.  It  rises 
and  reaches  a  maximum  about  midway  between  two  adjacent 
sets  of  brushes,  BI  and  B2,  at  C,  and  then  decreases  again, 
reaching  zero  at  or  about  B2,  and  then  repeats  the  same  change 
in  opposite  direction.  The  current  in  armature  coil  A,  however, 
is  constant  during  the  motion  of  the  coil  from  BI  to  BI.  While 
the  coil  A  passes  the  brush  B2,  however,  the  current  in  the  coil 
A  reverses,  and  then  remains  constant  again  in  opposite  direc- 


200     ELEMENTS  OF  ELECTRICAL  ENGINEERING 

tion  during  the  motion  from  B2  to  B3.  Thus,  while  the  armature 
coils  of  a  commutating  machine  are  the  seat  of  a  system  of  poly- 
phase e.m.fs.  having  as  many  phases  as  coils,  the  current  in  these 
coils  is  constant,  reversing  successively. 

63.  The  reversal  of  current  in  coil  A  takes  place  while  the 
gap  G  between  the  two  adjacent  commutator  segments  between 
which  the  coil  A  is  connected  passes  the  brush  B2.     Thus,  if 
lw  =  width  of  brushes,  S  =  peripheral  speed  of  commutator  per 
second  in  the  same  measure  in  which  lw  is  given,  as  in  inches  per 

second  if  Z»  is  given  in  inches,  to  =  -£  is  the  time  during  which 

the  current  in  A  reverses.     Thus,  considering  the  reversal  as  a 

1  S 

single  alternation,  tQ  is  a  half  period,  and  thus  /0  =  ^-7-  =  ;ry-  is 

4  »o      z  iw 

the  frequency  of  commutation;  hence,  if  L  =  inductance  of  the 
armature  coil  A,  the  e.m.f.  generated  in  the  armature  coil  during 
commutation  is  eo  =  2irfoLiot  where  io  =  current  reversed,  and 
the  energy  which  has  to  be  dissipated  during  commutation  is  i<pL.~ 
The  frequency  of  commutation  is  very  much  higher  than  the 
frequency  of  synchronous  machines,  and  averages  from  300  to 
1000  cycles  per  second,  or  more. 

64.  In  reality,  however,  the  changes  of  current  during  com- 
mutation are  not  sinusoidal,  but  a  complex  exponential  func- 
tion, and  the  resistance  of  the  commutated  circuit   enters  the 
problem  as  an  important  factor.     In  the  moment  when  the  gap 
G  of  the  armature  coil  A  reaches  the  brush  Bz,  the  coil  A  is  short- 
circuited  by  the  brush,  and  the  current  iQ  in  the  coil  begins  to 
die  out,  or  rather  to  change  at  a  rate  depending  upon  the  internal 
resistance  and  the  inductance  of  the  coil  A  and  the  e.m.f.  gener- 
ated in  the  coil  by  the  magnetic  flux  of  armature  reaction  and  by 
the  field  magnetic  flux.     The  higher  the  internal  resistance  the 
faster  is  the  change  of  current,  and  the  higher  the  inductance 
the  slower  the  current  changes.     Thus  two  cases  have  to  be  dis- 
tinguished. 

1.  No  magnetic  flux  enters  the  armature  at  the  position  of 
the  brushes,  that  is,  no  e.m.f.  is  generated  in  the  armature  coil 
under  commutation,  except  that  of  its  own  self-inductance.     In 
this  case  the  commutation  is  entirely  determined  by  the  induc- 
tance and  resistance  of  the  armature  coil  A,  and  is  called  re- 
sistance commutation. 

2.  Commutation  takes  place  in  an  active  magnetic  field;  that