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Chapter 1

Alternating and rotating magnetic

fields

This chapter deals with the distribution along the airgap of the magnetic field due to the stator current.At first a single coil is considered, yielding an alternating magnetic field. Then a polyphase winding isstudied, so as a rotating magnetic field is achieved.

1. Magnetic potential due to a single coil

Consider the elementary twopole machine of Fig.1.1(a), including a single coil only, of nt turns. Thecoil may be considered as one phase of a polyphase winding with one slot per pole per phase, i.e. q=1,and ncs conductors in the slot.

Figure 1.1: One coil winding and reference axis

1.1. Current references

The dot and the cross of each coil side means the reference current direction. When the coil carries apositive current I, the coil current ncsI leaves the sheet towards the reader in the coil side marked bythe dot, while the coil current ncsI enters within the sheet in the coil side marked by the cross.

When the winding carries a positive current, the magnetic field lines (or lines of force) occur assketched in Fig. 1.2. Each line of force is linked with all ncs turns. The direction of the field lines isassociated to the direction of the current of the coil with the rule of the right hand.

Remark. Sometimes the coil is represented by means of the symbol shown in Fig.1.1(b). Thesymbol is posed along the axis of the phase. A positive current yields field lines in the direction ofthe arrow associated at the coil symbol. The positive direction of the current of the coil is associated

with the rule of the right hand.

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1. Magnetic potential due to a single coil

Figure 1.2: One coil winding and magnetic field lines

1.2. MMF and magnetic potentialThe line integral

Hdl is the same for all lines of force. Applying the Amperes theorem, it is the MMF

ncsI. Assuming a negligible magnetic drop along the iron paths, the stator surface in front the airgapassume a magnetic potential, as sketched in Fig. 1.3. The magnetic potential is

Us(s) = +U with

2p< s