The 3-phase machine will be more energy efficient when compared with a single-phase machine, and because of the way they are built, 3-phase motors are likely to be more robust than single-phase motors. A 3-phase machine could also potentially be less expensive than a single-phase machine.

This assumes that the location you are in has 3-phase 220V power installed.

If it does (and you have the space in your panel) - it always makes sense to go for the 3-phase machine. If you do not have 3-phase installed, it is almost always cheaper to go with a single-phase machine than to either a) get 3-phase installed, or b) get a rotary phase converter.

Getting 3-phase installed can cost tens of thousands of dollars and take months and months and is often (in my experience) up to the whim of the local electric company. While it might be nice to use a static phase converter, because of the changing reactive loads in the tempering machine (compressor, heaters, stop/start of motors), a static phase converter is not the best choice. Rotary phase converters can easily cost well over $1000 (depending on the loads in the tempering machine) which is lots of kilowatt hours of electricity. So - you have to weigh the lifetime savings cost against the CapEx of the phase converter.

Note that you do have to let your equipment supplier know in advance which you need - as the power cord used to connect to the supply will be different. The cord in a 3-phase machine will have four wires, whereas a single-phase machine will have just three wires, and you need to wire the plug, socket, and panel accordingly. Because code.

You can always connect a single-phase machine to a 3-phase panel, the reverse is not true.

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clay - http://www.thechocolatelife.com/clay/

Letting the equipment supplier know is exactly where I am.  I have the option and there are no additional costs to purchase one versus the other-which is a positive surprise.  

At the place I will be using the equipment access to phase 3 power is available.  I anticipate a move in 1-2 years because of location access to shipping options.  If I go with 3 phase I will have to make certain the next locale has it.

The details are all an education to me.  Is it a different motor that is installed choosing one type over the other or is it the wear and tear on the same  motor that distinguishes the choice?  If the motor is more robust in a 3 phase why is the single phase more (usually) expensive?

Here is a link to some information on the differences.

It is true that if you get 3-phase now you will either have to make sure that the place you move to has 3-phase installed or you get a phase converter installed ... you might be able to negotiate that into the lease (I would).

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clay - http://www.thechocolatelife.com/clay/

Clay, were one to run a single phase and three phase tempering machine side by side, would you expect to see any difference in operation? 

As you say 'robust' and 'energy efficient,' are we only discussing the cost of electricity and length of life in the motor? Or is the usage affected in some other way?