Stepping up 208V 3-phase to 240V 3-phase ?

I'm no expert here, but I think it is generally understood that "230 - 240" is pretty much the same. Come in Bruce.
Bob Swinney

Maybe. It depends on whether the motor is under-excited at 208 v all the time, or just at full load. Can you measure the line current draw? Does the motor seem to deliver full power? Do you expect to load the motor to full load? (Ie, if it is a 3 Hp mill with R-8 spindle, you may never need the full 3 Hp from it, and it will likely be fine running at a bit reduced voltage.) If you expect to need the full power from the motor in routine work, and the plate says 230 only, not 208/230, and especially if the motor draws a lot of current or runs hot, then I think you would do well to deliver 230 V to it.
Jon

Unless you are experiencing motor stalling and/or over-loading, causing motor overheating or trip-out on a regular basis, there is no reason to boost the voltage. Theoretically, you get (208²/230²) or 81% of normal starting and max running torque, and a little slower full load speed, but most people never more.
Randy

You can consider 240V to be the 'US Standard' nominal voltage, but if it sags to 230V under load and voltage drop it's still acceptable.
You really shouldn't run 230V or 240V marked equipment hard on a 208V feed unless the motors are double-rated 208/240V, or you check that it is not running overloaded - check the running full-load current against the nameplate amps.
If the load is highly variable (like on a lathe) just don't take as big a cut - they really should put panel ammeters on all machines (with a marked redline) so you can see at a glance if you have the feed rate set too high - BEFORE the motor has a "Magic Smoke Escape" moment...
That said, if you want to be sure not to have a motor-toasting incident get a set of 16/32V buck-boost transformers and hook them up. A small transformer can boost the voltage for quite a large load, but you need to read the instructions.
If you aren't going to use the connected equipment for a while, turn off the power at the transformer primary breakers - no sense wasting power exciting the transformers for weeks at a time.
Last time I messed with a buck-boost was for a friend who needed to service 208V wired automated stage lights, and only had 120/240V 1ph available at his shop. Rewiring them to 240v before servicing them and changing them back when done is out (terminal strips break), so he put in a bucker and a set of permanent 20A 208V receptacles - twist-lock, straight-blade and stage pin.
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So what about the opposite ???
I have several ventilation fans within a greenhouse rated @ 208 I am running on ~ 236V......Dayton 24in dia fans to be exact.
They start fine and dont heat up even if run all day long in hot weather--any cause for major concern in your opinion ???

You can consider 240V to be the 'US Standard' nominal voltage ... Only for single-phase machinery and data processing equipment.
Standard U.S. voltages include: 120, 120/240 (cooktops and the like), 240 (commercial only), 120Y208, 277Y480.
Motors and the like are usually specified as 208-240.

It depends on the motors. We used to run on 240V here in UK but other countries ran 220V. The cheap motors designed for 220V didn't last as long as our domestic ones designed for 240V even when fitted as OE to machines. Now we are slowly dropping our voltage to be in line with Europe and will eventually end up at 220V. All the above are single phase voltages. For 3 phase, multiply by 1.732
John

The engineers at Dayton are based in the USA and know they're liable to be run on 240V, I'm surprised they weren't marked as dual rated. Call them and ask, or if a newer one smokes they may not honor the warranty.
Other than that (and considering you already own them...) if they don't draw over nameplate current and don't run hot, I wouldn't worry. I'll bet they're running well under max current.
But as they die off through normal attrition, see if you can find dual-rated or 240V rated motors - and if you have a whole bunch (dozen to hundreds) already bought and installed you might give up and consider a buck-boost or two.
Some of the stuff in this business falls into big gray areas, and as long as it works and it's safe, who cares why - leave it alone. ;-)
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Basically my feelings too.
Thanks for the reply.