A few years ago the VFD on my Jet 1640 lathe fried. A replacement was $800, but people on line steered me to a VFD on Amazon for $80. Only problem is that it was 240v and my lathe was 120v. Turns out it doesn't matter because the motor is 240v. The 120v VFD used a voltage doubler which made it less durable, and it couldn't supply all the power the motor was capable of handling, so I got 20% more power off the lathe with the 240 vfd.
BUT... the tach is 120v. I "fixed" it temporarily by simply running a 120v circuit to the lathe, but that is a nuisance to plug and unplug. I could put a switch on the cord, but that wouldn't be much better.
My original thought was to simply run the tach off of one leg of the 240v to ground. The obvious objection to that is that there would be voltage on the lathe, and a possibility of a shock if the neutral broke. I have never experienced a broken neutral and the worst case is 30ma that the tach uses (reduced significantly since I wouldn't be at all grounded...) but still. I considered running a wire from the lathe to a drill press next to it on a different circuit so even if the neutral broke it would still be grounded through the drill press, but of course you aren't supposed to ground in two places.
My next thought was to put a 4000ohm resistor in series with the tach so that the tach would see 120v, but someone told me that a resistor can fail in a short and that would fry the tach. I've never seen a resistor fail, but still.
My next thought was to use a 3.3w light bulb instead of a resistor, but wiring that in would be a pain.
Final thought was to run a multiwire circuit with the tach on one side and a resistor on the other. That would be like the second thought unless the resistor failed, and then it would be like the first thought. The resistor is unlikely to fail, especially in a short, but if it did, the tach would be protected by the neutral.
So, what do you think? Well, other than the obvious that I have spent way too much time planning this.