Why are there no "even" harmonics in AC machines?
You know that a square wave with perfect symmetry has NO EVEN harmonics. (typo fixed)

You can imagine if a magnetic material had a "hard saturation" limit instead of a "Landau"? curve with hysteresis, you would get a square wave current for a sine wave voltage.  Thus all the current is fundamental &amp; odd harmonics. But with a symmetrical soft saturation curve the harmonics are attenuated. The harmonics increase as the current enters the soft saturation region, yet still remain ODD multiples as long as the non-linear soft saturation curve is symmetrical .



Thus the only time you would get even harmonics in a magnetic material is if there was remanence such as from DC bias.  Then the voltage swing produces more  asymmetrical current and no longer is  a symmetrical soft square wave but asymmetrical even harmonic producing fourier components of the distorted waveform. Then the apparent inductance drops quickly and is usually rated for -10% at rated DC or ac current. 

Normally large transformers experience remenance from abrupt disconnects and flux  leakage resistance balances the current after several seconds which is apparent by the hum of large MVA transformers during reconnect. This is why "smart reclosures" remember the phase of disconnect and reclose at exactly the same phase to minimize Remenance and saturation currents that produce many forces inside transformers and even harmonics.

To visualize fourier components with a hand-drawn waveform or std. waveform try this java app. then choose boxes for mag/phase and log view and change the frequency spikes with mouse and see the effects on time domain signal. Note the absence of even harmonics in both a square wave and a triangle wave but the phase is different in each harmonic.