CHAP. V] EXCITING AMPERE-TURNS 87 



contribute to the useful torque of the machine, but actually reduce 

 it. In reality, there is of course but one flux, the resultant of the 

 three, but for the purposes of theory and computations the three 

 component fluxes can be considered as if they had a real separate 

 existence. In this and in the following chapter the main flux 

 only will be discussed for this type of machinery. Considera- 

 tion of the leakage flux will be reserved to Art. 66. 



The total magnetomotive force per magnetic circuit is equal 

 to the sum of the m.m.fs. necessary for establishing the required 

 flux in the separate parts of the circuit which are in series, viz., the 

 pole-pieces, the air-gap, the teeth, and the armature core. All the 

 necessary elements for the solution of this problem have been dis- 

 cussed in the first two chapters. It remains here to establish some 

 semi-empirical " short-cut " rules and formulae for the irregular 

 parts of the circuit, for which, although close approximations can 

 be made, the exact solution is either impossible or too complicated 

 for the purposes of this text. The following topics are considered 

 more in detail in the subsequent articles of this and of the follow- 

 ing chapter. 



(a) The ampere-turns necessary for the air-gap when it is 

 limited on one side or on both sides by teeth, so that the flux den- 

 sity in the air-gap is not uniform. 



(6) The ampere-turns necessary for the armature teeth when 

 they are so highly saturated that an appreciable part of the flux 

 passes through the slots between the teeth. 



(c) The ampere-turns necessary for the highly saturated cores 

 in which the lengths of the individual paths differ considerably 

 from one another, with a consequent lack of uniformity in the flux 

 density. 



(d) The leakage coefficient and the value of the leakage flux 

 which passes directly from pole to pole. This leakage flux 

 increases the flux density in the poles and in the field frame of the 

 machine, and consequently increases the required numl 

 ampere-tunis. 



All of the m.m.f. calculations that follow arc per pole of the 

 line, or what is the same, for one-half of a complete magnetic 

 circuit (rv//<r/ in Figs. 15,20, and 'JiD.the two halves being identical. 

 This fact must be borne in mind when comparing the fornmhc with 

 those given in other books, in which the required ampere-turns are 

 sometimes calculated for a complete magnetic n 



