All,
At the risk of starting a post that may go on for a considerable amount of time I would like to share the following with you.
I feel duty bound to explain a significant point in the safety of inverter installations, as has been previously described, the control inputs are normally low voltage, 12 or 24 volts, sometimes even 5. The start stop arrangements of inverter inputs are not as safe as you may assume. Consider the start input, 24 vdc or less is required from a momentary contact for a few milliseconds. With enough electrical noise on that input the drive could start while you are tightening the chuck or something else.
In industry we have to provide a more robust method of protection either disconnecting power from the inverter, disconnecting motor from inverter which has to be carefully controlled to a standstill before disconnection or the inverter can end up in smoke or there are new generations of inverters that have safety terminals to isolate the control electronics.
It is unlikely that an inverter would start up when your fan heater kicks in but there is a risk, I just have to make you aware of it. You can adopt a safe method of working of course, disengage your lathe clutch when making adjustments or isolation of power for other machines.
I am not trying to put anyone off, most of my machines are inverter controlled and better for it.
Reading what I have typed makes me sigh a little, I am an engineer not a safety officer, my post makes me sound like the latter, oh dear ……