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They are precision machining equipment.
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Read Article 409, I believe it will apply to the control panel that houses whatever is in the overall machining center. I don't see why it makes a difference if it is plug-in or hard wired.
409.1 Scope. This article covers industrial control panels
intended for general use and operating at 600 volts or less.
FPN: UL 508A is a safety standard for industrial control
panels.
409.2 Definitions.
Industrial Control Panel. An assembly of a systematic
and standard arrangement of two or more components such
as motor controllers, overload relays, fused disconnect
switches, and circuit breakers and related control devices
such as pushbutton stations, selector switches, timers,
switches, control relays, and the like with associated wiring,
terminal blocks, pilot lights, and similar components.
The industrial control panel does not include the controlled
equipment.
While it's still true that 409 will not require an NRTL listing, it requires adherence to basic standards of construction, which if it WERE listed, would allow the AHJ to forgo further investigation for approval. But without it, he can insist on you either getting an NRTL listing, or he can open it up and start tearing it apart (figuratively), piece by piece. For example; "Show me the listed ampacity of the conductors used on this circuit? Not using listed wire and it is metric sized? Replace it with listed wire..." etc. etc. etc. You must either be REALLY really nice to him, or go get someone to list the machine for you (in my opinion). This is a common issue with people who import machines. Either the salespeople lead the customers astray by telling them that CE is acceptable, or someone shops for it and orders it directly from the mfr overseas, bypassing an importer who WOULD have known to get it listed first.
I used to take in machinery like this all the time and rebuild the control panels to UL list them. ovens for production bakeries were a very common problem with this, because there will be some specialty product they want to make that took some kind of whiz-bang special Italian oven lined with bricks made from some special mud collected by virgins on a full moon, so they had them imported directly and ended up not being able to install them legally. Most of the time when people find out too late about the UL listing issue like that, they would tell me it would have cost them less to just buy a similar domestically made product. Couldn't find any domestic virgins however...