#2 to what Steviegtr says about satisfactory operation between 35 rpm and 65 rpm. Generally that pretty much seamlessly closes the gap between two belt steps on a lathe so you can leave it on middle speed most of the time.
Way, way back when VFD boxes started becoming available (but not affordable) I had discussions with the suppliers about what performance could usefully be got out of them and what effect the natural motor characteristics had. Bottom line was that ± 1/3 rd of nameplate speed would give generally acceptable performance in any application with engineeringly sensible power margin. Which translates to 33 to 67 Hz, near enough. Which is probably where the figures used by Steviegtr came in.
Back in those days the boxes were of much simpler design without the clever circuitry that can extend the performance of modern units so the overall performance was much more strongly defined by what the motor itself could do and what its torque / supply speed characteristics looked like. Up to a point modern control algorithms can extend the useful operating range but ultimately you are driving a device designed to self stabilise close to nominal speed when driven at 50 hz (or 60 in the USA). Ultimately you cant fool physics. Once you get significantly outside that range with a normal induction motor you will have to compromise and accept power reduction over and above the theoretical constant torque (at low rpm) and constant power (at high rpm) losses.
In my view the best way to exploit a VFD on our sort of machinery is to swop the common four pole 1,440 rpm motor for a 6 pole 950 rpm or even 8 pole 720 rpm. Or at least change the drive pulleys to give a similar effect. High machining speeds are for small components so we don't need monster power so the losses above + 1/3 nameplate speed don't much matter. Far better to pull the natural drive speed down so we have power at lower speed where we can really use it.
The servo substitute motor – VFD combinations which really can develop serious power down to very low speeds are rather different to the common induction motor. The way they work has much more in common with brushless DC motors. Connecting one directly to the power line without its controlling VFD would be a disaster.
Clive