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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
The magnetising flux density and stator currents of a variable frequency induction motor transformer.

Identifier  ExFiles\Box 32\4\  Scan063
Date  28th October 1929
  
X1581
28.10.29.

VARIABLE FREQUENCY INDUCTION MOTOR TRANSFORMER.
THREE PHASE STATOR TO SINGLE PHASE ROTOR.

Magnetising flux density
b = B sin(pt - qx)
a travelling wave, in which p is the electrical angular velocity of the wave and p/q the linear velocity. This travelling wave produces a single phase E.M.F. in the rotor winding. Rotor flux due to rotor current when rotor (loaded) is turning with electrical angular velocity r or linear velocity r/q
a = -2A sin(rt - qx+α) cos(p - r)t
= -A sin(pt - qx+α)-A sin{(2r - p)t - qx+α}
which consists of a forward travelling wave differing in phase by π - α with the stator flux wave plus a travelling wave of electrical angular velocity 2r - p.
Stator currents additional to those required to produce b, must flow to produce stator fluxes of
a1 = A sin(pt - qx+α)
and a2 = A sin{(2r - p)t - qx+α}
in order to annihilate the fluxes due to the rotor current.
a1 is supplied by a normal system of three phase currents, and a2 must be supplied by a three phase system of currents of frequency
(2r - p) / 2π
  
  


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