Lighting goes out when using plasma cutter
I have 6 fluorescent lighting fixtures in my garage each one has 2-40watt bulbs and they are all on a 20 amp breaker.My problem is when I go to use my plasma cutter my lights flicker like a strobe when I turn on the plasma cutter.Do I have too many lights on one circuit?I wouldn't think it would be.I checked all my grounds in the main circuit box and everything seems fine.Anyone have any ideas what it could be?Also I am using 12g wiring.and the plasma cutter is only drawing 27 amps when I cut steel with it.Thanks