Probably easier to use a phase imbalance detection relay e.g.
http://www.hobut.co.uk/protection-relays/phase-balance-protection-relayYour circuit will work, with reservations, there may be sufficient regeneration in an inductive load which may render the detection of a phase loss doubtful using voltage alone - It would be better to monitor the phase currents instead (as commercial units mostly do).
In your circuit, putting the outputs from the three Transformers in series like that should give a resultant of zero with 3 balanced phases. i.e. 3 phases @ 120 degrees apart. If a phase is lost, then there should be (if regeneration does not take place) a resultant voltage at the AC terminals of the bridge rectifier. The 220Uf cap will smooth the DC and give a very small delay. The diode is purely back-emf protection. For a longer delay in operation increase the capacitor to say 1000Uf
Taking into account the cost of the transformers, a relay would probably be a viable option. But, if it is for a lab project, and you have to build it yourself, then go ahead and try it!