Ingenious! A commutator AND a rotating rectifier - what else could a motor want? Also good because the mod can be reversed once the non-functional and suspiciously lightweight vacuum cleaner is discovered by the other half.
But a complex beastie to analyse I think, as there's a lot going on in there. During startup it develops torque ripple at the slip frequency (half that of a reluctance-synchronous induction start motor as it's polarised), while running as a slightly odd universal with a rotating short-circuit that periodically connects the brushes together leaving the supply across the field coils. Rather naughty, this bit. The diodes presumably also influence the other rotor coils and the stator quite heavily by transformer action, as well as due to being in the main current circuit.
At synchronism it's very much like a brushless generator with a distributed rotor winding in place of a salient-pole one, which approximates to an energised synchronous motor give or take the magnetising flux required. But in that critical final cycle of slip leading up to pull-in, you've got the distorted 50Hz waveforms in both rotor and stator, the transformer action, the influence of the diodes on the main circuit varying at slip speed...
Would be interesting to watch the diodes with a strobe, measure or observe the load angle (might be surprising) and see how it behaves at low slip. Also to find out about that oscillatory behaviour described with the strimmer motor. Can it synchronise any load that it can accelerate? A reluctance synchronous can't always do so, due to the need for the integral of the reluctance torque over one pole pitch to exceed the angular impulse required to accelerate the load from induction speed to synchronous. But the universal motor can run super-synchronous and its torque won't actually drop to zero at synchronism since the diodes don't have total control over all the armature coils. Maybe with the right moment of inertia attached it could even go through synchronism, and lock at double speed.
You'll have to post some videos and measurements Clive, I can't figure out the pull-in criterion at all. It's definitely sneaky and I like it.
E2A: Perhaps you could improve the efficiency by spanning fewer armature coils with the diodes, leading to less shunting out of induced voltage, e.g. just enough coil sides in the DC circuit to cover the field poles themselves.
Black was always meant to be a phase. The neutral phase.