The first thing I would like you to do is to find the data plate on the motor. It'll have all sorts of useful stuff, but find the "phase" information. It will either have a circle with a vertical line running through it (the Greek letter phi), with either a 1 or a 3 right in front of it, or it will just say "Phase" and either 1 or 3.
I'm concerned that you may have bought a tool with a three-phase industrial motor, and if you did you've got a problem: they don't bring three-phase off the pole in residential areas. I certainly wish they would--three-phase motors on central air handlers would save America a LOT of power--but you can understand the reason they don't, mainly people like me would put huge arc welders in our garages.
Anyway, if you've got a three-phase motor you need to do one of two things: install a "phase converter" to change single-phase to three-phase, or replace the motor.
Don't do this! The fuses, breakers and outlets on a household 240 Volt power circuit should be left as they are to supply standard 240 Volt domestic appliances such as clothes dryers, water heaters, kitchen ranges, etc. and nothing else.
If you want to use a 120 volt appliance in the same location and there is no wall outlet yet, it is only safe to install a new 120 volt circuit by fitting a new 20 Amp breaker and run new wiring, of the correct size for the length of run, all the way from the breaker panel to the new 120 Volt socket outlet.
Before you do this you must check the Wiring Code or Wiring Regulations for your locality (town/state) to be sure you know if the new circuit needs a protective device such as a GFCI or RCD.
In most places a GFCI or RCD will be mandatory if the new socket outlet is to be installed in a place that is likely to be subject to water spray, wet or damp floors, walls or ceilings. This includes kitchens, bathrooms or shower rooms, or anywhere outside the building such as pool areas.
Hire an electrician to wire you in the proper line to a new receptacle, with proper-size circuit breakers on the main supply panel and proper-sized wiring in the circuit.
If you try to wire this yourself you would be risking electrocution for yourself or other members of your household.
If you don't include the right size breakers in the circuit you risk starting a house fire.
Answer
A 40 to 55 ampere table saw? That's 13200 watts at 240 volts! What are you sawing?
There also might be another reason for the #6 wire:
- A number of table saws on the same 55 amp circuit, requiring #6 wires throughout the circuit
- Ampere rating might be to handle locked rotor current of the saw
- A long cable run from the breaker box to the saw
- A local law requiring heavier wiring
- A low motor voltage (used in an environment where high voltages are a hazard)
- A DC motor
- A requirement for flexible cord size in an area where frequent movement occurs
Note that 120 volt power tools should be on 20 amp breakers, not 15 amp.
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As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.
Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized
IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.