Air-gap flux in induction motors

In determining the variation of the value of the flux in polyphase induction motors, and its progression around the air-gap, it is customary to assume that the current in each phase follows a sine law. In this way it has been shown that the flux rotates synchronously around the air-gap and that its magnitude varies between a maximum and a minimum; but it does not appear that the law of this variation in magnitude has been investigated. It is common practice in determining its mean value to consider the flux a maximum (in the case of three-phase motors) when the three currents are, respectively, I, − 1/2 I, − 1/2 I, where I is the maximum current per phase; and a minimum when the currents are √3/2 I, 0, and −√3/2 I; the mean of these two values being then considered as the average for the cycle.∗ This method is, of course, only approximate; but it will be shown in what follows that the actual average is not only greater than the value obtained as above, but it may even exceed the above assumed maximum.