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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 mathematical formulas and principles for armature wave windings.

Identifier  ExFiles\Box 68\4\  scan0167
Date  9th October 1918
  
EFC/L.9.10.18.

ARMATURE WINDINGS.

(1) Wave Windings.

Let number of conductors = n (virtual)
" " " poles = p

Then both n and p must be even.

In n ± 2 conductors there must be p steps.
(+ means progressive)
(- means retrogressive)

Hence pitch z = (n ± 2) / p

The pitch must be odd.
Hence (n ± 2) / p = 2k + 1 where k is an integer representing step of winding.

n ± 2 = (2K + 1)p
n = (2K + 1)p โˆ“ 2.

(-means progressive)
(+means retrogressive)

z = 2k + 1
No of coils = n/2 = (2K + 1) p/2 โˆ“ 1

(so must be odd for 4 pole machine.
If with 4 pole machine, winding is retrogressive
n/2 = 4(k+1) - 1

contd.
  
  


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