The theory of armature windings

Abstract

In this paper an attempt is made to outline the theory of armature windings in heteropolar machines (i.e. machines with alternate north and south poles).Section 1.—Attention is drawn to the fundamental importance of the relation between the number of slots and the number of poles, and, by the aid of simple vector diagrams, the condition is established for obtaining a winding in which the sum of all the induced pressures is zero at any instant. If all the coils in such a winding are joined in series to form a closed winding, no internal current can circulate. Following this, the condition is found for obtaining a number of similar symmetrical polyphase systems in such a winding, this being essential when parallel circuits are needed, as in most commutator machines. A winding fulfilling these conditions is called symmetrical, and an extension of the argument reveals the relationship that must exist between the number of slots and the number of poles in a symmetrical 3-, 4-, or 6-phase winding. Table 1 shows the number of similar circuits it is possible to have with various numbers of poles.Section 2.—This deals solely with single-layer windings. The arrangement of the coils for various symmetrical and hemisymmetrical polyphase windings is discussed. The effect of the number of slots on the number of similar parts in each phase is shown, and the means indicated for suppressing tooth effects.Section 3.—The arrangement of open and closed double-layer windings is illustrated, and the methods of loading closed windings are compared. The connecting rules for lap and wave windings are deduced, and the restrictions examined for making these windings symmetrical. These results are given in Tables 2 and 3, along with the slottings possible for N-phase, lap and wave windings. These tables enable the designer to see at once the number of coil-sides per slot, the number of slots, and the number of phases possible in any symmetrical winding.Lastly, it is shown how to find the points where a winding must be tapped or opened to obtain phases, examples being given to illustrate the various cases.The sections of the paper are subdivided as follows :—1. Armature windings.(I) Condition for obtaining a closed winding.(II) Condition for obtaining a symmetrical winding.(III) Examples of symmetrical and unsymmetrical windings.(IV) Conditions for obtaining a symmetrical N-phase winding.(V) Phase-spread and coil-span.2. Single-layer windings.(I) Arrangement of single-layer windings.(II) Number of armature slots.(a) Whole number of slots per pole.(b) Fractional number of slots per pole.(i) Use of empty slots.(ii) Use of unequal coil groups.3. Double-layer windings.(I) Arrangement of double-layer windings.(a) Phase tappings off closed windings.(i) Polygon tappings.(ii) Diametral tappings.(b) Open double-layer windings.(II) Connecting rules for closed windings.(a) Closing rule for lap windings.(b) Closing rule for wave windings.(III) Conditions for obtaining symmetrical lap and wave windings.(a) Symmetrical lap windings.(b) Symmetrical wave windings.(IV) Conditions for obtaining symmetrical N-phase, lap and wave windings.(a) Symmetrical N-phase lap windings.(b) Symmetrical N-phase wave windings.(i) Number of poles.(ii) Number of slots.(V) Location of tappings and openings.(a) Tappings off symmetrical lap and wave windings.(b) Opened wave windings.(c) Illustrative examples.(VI) Wave windings with a whole number of slots per pole.