Why are guys asking about external braking resistors. Unless you’re suspending a load as in a winch why would you need one.
I think
@TorontoBuilder nailed it. But given your followup question, I think it would help to provide a few more details.
The need for external braking is a mid-size lathe concern for lathes in the 10 to 14 inch swing size. It may also apply to some smaller and bigger lathes.
These lathes don't always include a foot brake. But they always have a huge gear, shaft, chuck, and rotating part mass that does not wind up very quickly and NEVER stops fast enough in an emergency.
This does not apply to mills or small lathes or big lathes or a hundred other machines. It might apply to a big shaper with a big flywheel though, and I'm sure there are others.
The bottom line is that a VFD cannot stop the inertia of a large rotating mass fast enough in an emergency situation. The need is for an external resistor to handle the large back current associated with a fast emergency stop.
This isn't about holding a load on a winch, it isn't even about stopping the lathe. It's about stopping it FAST in an EMERGENCY.
It takes about 10 seconds (WAG) to wind up my lathe at its highest speed with a heavy chuck and a big part. And maybe 4 times that to stop it. If something goes wrong, I don't want to wait 30 seconds or more while my lathe is winching in a critical body part or thrashing my ways to shreds with a part that bent in my jaws.
I want two stops for my system. A normal stop that applies normal stopping forces, and an emergency stop that almost breaks the gears to stop as fast as possible.
I think you would instantly understand if you stood in front of my lathe with a big part in my big chuck running at high speed.