Usnig Two Wires to Run a Three-Phase Motor

You can try it with the connection of two wires(two lines) instead of three in a three phase delta connection for motor but just for a short period of time. The motor will run either forward or reverse direction.

The only different is that the motor will operate in unbalance magnetic field and voltage due to the two phase supply to the motor in delta connection. The speed of the motor will reduce and gradually and the motor temperature will increase slowly.

Sometime, we do have this problem of 2 phase power supply to the roller table motor due to one of the phase cable under the roller table damage and the motor is running on 2 phase. Sometime it goes reverse direction and sometime it go forward direction.

You may connect the motor the same as a single phase motor, with capacitor and supply with 2 phase. The motor however will only produce about a ½ of the 3 phase power rating

That true. The motor torque will be less than the normal motor torque

The motor will stall, and either:

1. Its overload will operate, or,
2. The circuit protective device in one or both of the connected phases will operate, or
3. If neither of these happens, the motor will self-destruct. Have a CO₂ fire extinguisher handy.

Transfrom the two phase to three phase and then use.

As it is - no you can not, efficiently and without the high probability of burning it.

But the transformation is easy and easied if you have the neutral available and the supply corporation allows you to use such an unbalanced loading.

Nothing good as others have said. You need three phases, two wont do.

There is a semantics issue here with regards to what you are referring to as "2 phase". There is such thing as true 2 phase power, but it is extremely rare. It is a legacy polyphase system left over from the earliest days of electrification, but still exists in parts of Philadelphia and Niagara Falls as far as I know. True 2 phase power uses 4 wires and the phases are 180 degrees separated from each other, or really, 90 degrees from one pole to the next.

If you are referring to 2 phases of a 3 phase system, that is technically not 2 phase power, but it is often mistakenly referred to that way in IEC terminology. In the US, we call that single phase. But that is slightly different again from distributed 1 phase power in the US, where the Line-to-Line relationship is 180 degrees out.

In a situation where we are looking at 2 out of 3 phases; A 3 phase motor will RUN if one phase is disconnected after it was already spinning, but it will only put out 58% of it's available torque and as such, slip will increase under load and the motor will likely overload. If you attempt to Start it with only 2 of 3 phases, it may try to start, but as mentioned by others there is no way to predict the direction of rotation. The 2 connected phases are separated by 120 degrees on one side and 240 degrees the other way. if the contactor connects when there is a 120 deg. separation, it may try to turn one direction, but if it connects when there is a 240 deg. separation, it may try to go the other way. But again, torque is reduced to 58% so if it needed LRT to accelerate, it isn't likely to start at all.

In a situation where you try to feed a 3 phase motor from a US 1 phase supply, where the line-to-line voltage separation is 180 deg. out, the motor will not even try to rotate at all without mechanical assistance because there is no relative phase rotation.