Wiring PM 12x36 lathe, PM 9x32 mill

I don't think we're disagreeing... Here's what 12/3 Romex looks like so, you need to connect white and black as hot and the bare to the box neutral/ground bus. There are indeed 4 conductor 240V cables but I don't think this is what he has. I'm pretty sure the NEC/NFPA changed the rules this year and for electric dryers and stoves, you need to use 4 wire systems and carry a ground to the appliance.
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This picture of romex wire would be 12/2 wg (with ground)
as Hawkeyes description implies. 12/3 wg would have the red insulated conductor also.
 
Say I think we missed something. If there is one hot one neutral and one ground, isn't that 110v single phase? Re reading the op gives me the impression that there are not 2 lines and a ground, not two lines a neutral and a ground, but a line a neutral and a ground. That is on the mill. I would look over your motor plate and call the seller if you have a question as to if you are doing right. Good luck EDIT the website shows both machines as having 220v motors. Can we have a peek at that diagram?
 
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Another though I had was if they are the same voltage, you can put 2 outlets on the same circuit and only operate one machine at a time to avoid overloads and lots of plugging/unplugging.
 
Apples and Oranges, and there are no second chances with these voltages. There is no "neutral" on 240V, only 120V. So for "240V" technically there is no white or return. A white wire may be used in a 240V circuit to carry the other power leg (L1 and L2 both connected to the dual pole breaker) , but it needs to be labeled at both ends to indicate it carries power (this only applies to 12/2 wire or when a separate white wire is hot), usually with red electrical tape. See information below. In 4 wire cable (12/3), you would have a red and black to carry both hots, a neutral, and a ground. Neutral and ground may only be bonded together at the main power panel. Romex and armored BX cable would not be used as extension cords. BX cable might be used if hardwired directly to the machine, no plug. I am pretty sure NEC code does not allow an extension cord to be hardwired directly into the panel. The most appropriate is to hardwired a box with a socket(s) connected with conduit with individual wires pulled or BX cable to the panel (either 3 wire BX cable or puled 12G wire in conduit, no romex), then plug into the socket(s) as needed or use a dual socket and have both machines plugged into the sockets all the time (dual 20A 240V socket). The plug is specific to the load, voltage, phase and if a neutral is used. Just because you only have one 240V 20A breaker does not mean you can only have one machine plugged into it, the premise is that both sockets will not be used at the same time. Similar to sockets in a kitchen or rooms.

Neutral and ground are not the same, and the old BX cable without a separate ground wire is not permissible, it was used in years past when sockets had no ground plug. Issue has to do with the resistance back to the main ground. Lots of local electrical codes also. Romex has to be installed in drilled holes in joists or studs even above suspended ceilings, not in conduit or exposed areas. Extension cords or power cords connected to machines should be something like SOOW or SJOOW 12/2 (2 conductors and a ground) or 12/3 (3 conductors which include a neutral, and a ground).

The National Electrical Code requires a neutral-to-ground connection to be made at service equipment only and there shall not be any neutral-to-ground connection on the load side of service equipment [250-23(a), 250-24(a)(5)], except as permitted in Section 250-61 [250-142]. It is complicated, that's why there are electricians, and they don't always agree.
Grounding presentation: http://fyi.uwex.edu/mrec/files/2011/04/W4.-Biesterveld-NEC-grounding-MREC2010.pdf

In the grouping below from my sub-panel, 30A 240V twist-lock at the button, upper box is a dual 20A 240V socket and a 20A 120V dual GFI. Each is on a separate circuit breaker. In general 12G is used for 20A, 10G for 30A, but also dependent on distance and number of current carrying wires in the conduit.

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http://www.doityourself.com/stry/220-wiring-color-code-interpretation
Homes in North America are supplied with a 120/240V single-phase electrical service. The incoming 240V power is split onto two legs. Each leg can provide 120V hot-to-neutral, and the two legs together will supply 240V, which is used to supply heavy loads such as air conditioning compressors and cookstoves.

In every home, there are branch circuits that supply the lights, receptacles and built-in appliances with electricity. The wires, or conductors, in those circuits are classified based on wiring type, size and color, and it is the color of the wire’s insulation which designates the function of the wire. Understanding the information those colors convey helps you work with greater safety and ease when troubleshooting an electrical problem or making repairs or improvements to your electrical system. The connections should not be made haphazardly. In the United States, the color of the wire used must comply with the requirements of the National Electrical Code (NEC).

A Word of Caution - Always use a line voltage meter or circuit tester to determine if a wire is "hot" or "live." Never rely on a wire's color alone.

Wiring Types
Depending on where you live, the branch circuit wiring in your home will be made with individual conductors run through hollow metal conduit, or with one of three types of cable. A cable is a factory-made assembly of conductors in an outer jacket or sheath. Plastic sheathed, or Type NM (NonMetallic), cable, is widely used for home wiring circuits. Modern Type NM cables have different color sheathing which indicates the size of the conductors: White for 14AWG (American Wire Gauge) conductors, Yellow for 12 AWG conductors, and Orange for 10 AWG conductors. Type NM cable will also have markings on the cable sheath of the cable, indicating the size and type of the conductors in it, along with other information “14-2/G,” for example, shows that that cable has two insulated, current-carrying conductors and one grounding conductor, size 14 AWG.

The other two types of cable, which are often used to extend wiring in a system wired with metal conduit, are Type MC (Metal Clad) and Type AC (Armor Clad). Both Type MC and Type AC are sheathed in a flexible metal coil. Type AC cable, commonly called BX, does not have a grounding conductor. The metal sheath, plus a thin aluminum bonding wire, provide the required path to ground. Type MC cable does have a grounding conductor. In recent years, manufacturers have begun spraying color codes onto cables with metal sheathing. The colored marks correspond to the colors of the current-carrying conductors in that cable.

Black and Red Wires
According to NEC, a black or red wire must be used as an ungrounded conductor, or hot wire. In fact, any color wire except white, gray or green may be used in conduit to carry ungrounded power. No wire with any of those colors can be used for establishing a ground or neutral connection.

Because a red colored wire also serves as an ungrounded conductor, these wires are used to connect the second leg of the electrical system to loads which require 240 volts. A red wire is also often used as an interconnection, or communication, wire in a circuit that requires that, such as a smoke detector circuit.

Blue, Yellow and Other Colors
In systems where individual conductors, or wires, are run through hollow conduit, wires that are blue or yellow, or any color except white, gray or green are sometimes installed to designate a specific use. For example, if power needs to be run from a ceiling box down to a box with three switches and then brought back to the ceiling to power three different sets of lights, a black wire could be used to take the power down to the switches and three wires with other colors – say red, blue and yellow – could be used to bring the power up from each of the switches. That makes it easier to tell, at a glance, which switch is being used to control each set of lights.

White Wires
A white wire is typically used as the neutral wire, or grounded conductor. For conductors as small as those found in residential branch circuits, only a white or gray wire may be used for that purpose.
In the past, a white wire in a cable assembly was allowed to be used to carry ungrounded potential – to function as a hot wire – in a switch leg or when connecting a set of 3-way switches. This changed with the adoption of the 2011 cycle of the NEC, which requires the presence of a grounded conductor in every switch box, to facilitate the installation of lighted switches, motion detectors, timers and similar energy-saving controls. In new work, the white wire in a cable assembly cannot be used to carry ungrounded power. Because that requirement was only adopted in 2011, though, a homeowner may find that one has been used that way in an existing installation. In those cases, the white wire should be marked with red or black electrical tape or permanent marker – or any color other than gray or green – to show that it is being used as a hot wire and is carrying ungrounded potential. That wasn’t always done, so be careful of white wires in switch boxes. Since a neutral should never be switched, assume that any white wire that you find connected to a switch is a hot wire until you determine that it isn’t.

The White Wire in a 240V Circuit
There is one case in which a white may be used to carry ungrounded potential that is still in conformity with the most recent cycle of the NEC. That is when a cable is used to feed a straight 240V load. If an appliance does not need or use 120V power, but only needs and uses 240V power, a standard 2-conductor cable, which has a black, white and bare set of wires, may be used to connect that appliance. In that case, the black wire is connected to one pole of the two-pole 240V breaker in the panel. The white wire is redesignated as an ungrounded conductor by using black or red (or any color except gray or green) electrical tape or permanent marker, and connected to the other pole of the breaker, and the bare ground wire is connected to the ground bus. At the appliance end, the white wire is marked again and the two insulated wires are connected to the two input terminals for ungrounded power on the appliance, or on its disconnect switch, and the ground wire is connected to the frame of the appliance, or the box that the disconnect is in.

This wiring method – two hots and a ground - was in common usage for many years to supply most of the larger appliances in our homes, so it is often found in place, and in service, today. With the increased use of electrical and electronic controls in many appliances, though, a four wire service which includes a neutral conductor is being required for a new circuit. Most new cooking appliances – ranges, wall ovens and cooktops – are being built to use that wiring. So are the newer electric clothes dryers. They may, however, be capable of working with either type of wiring. If you are replacing an older cooking appliance or dryer, the instructions may tell you that you can, by replacing the cord on the appliance, connect it to an existing three-wire 240V circuit.

There are still 240V appliances that only need two hot wires and a ground. An electric water heaters and the outdoor condensing unit, or compressor, for central air conditioning, are two of those.
The important thing to keep in mind here is that a white wire in a 240V circuit may be carrying ungrounded power, and it may not have been marked to show that it is. Don’t assume that, because it’s white, it can’t shock you.

Green and Bare Wires
Wires with green colored insulation and non-insulated wires are equipment grounding conductors, or ground wires. The equipment grounding conductor, or EGC, is an important addition to residential wiring that became widely adopted in the 1970s. This separate set of conductors is connected directly to the earth. The EGC wiring carries no power at all when everything is working normally. But if there’s a fault, and ungrounded power is present where it could damage an appliance or shock someone, a properly connected EGC provides that power with a low-resistance path to earth. Since the power is trying to return to its source, it will take that path. This may trip a circuit breaker or blow a fuse, but appliance damage, a fire, or a shock to a human being will have been averted. For the EGC to function properly, green and bare wires need to be connected together, to devices such as switches and receptacles, and to any metal electrical box.
 
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