unless a VFD does not contain a step-up converter, like the Huanyang “B-T” Models or the Invertek Optidrive ODE-3-210058-104#, which are usually much more expensive, generally on VFDs, their voltage output class is the same than their voltage input class.
A VFD works this way: The incoming AC is rectified and stored in large capacitors, and then a microcontroller switches six IGBTs to form three quasi-sine waves out of this DC voltage, each wave shifted by 120° degrees, which results in three-phase current. The frequency of the three-phase current is what controls the speed of a three-phase induction motor. The 50 or 60 Hz frequency at the input of the VFD was rectified, which means it’s gone, and it’s now DC that is stored in the capacitors. The VFD’s microcontroller now takes care to output waves with the needed frequency. Many VFDs have the ability to produce three-phase electricity with frequencies of 0 – 600 Hz. To alter the frequency is necessary because the speed of induction motors is controlled by the frequency of the three-phase current. Note that when measuring and comparing AC voltages, you do never take the peak voltage of an AC wave, but the so-called RMS value.
What delimits the power of a spindle, besides the mechanical load capacity (e.g. bearings), is its heat dissipation because of the power loss. The power loss in induction motors depends on a few different factors, but one is whether the cross-section area of the the copper wires that make up the coils is dimensionated to have a certain (low) impedance to accomodate a certain current before getting too hot. The impedance of a coil, among other factors, depends on the cross-section area of the wires that make up the coil.
A VFD with 110 V AC input will vary the output voltage in a range of up to about 110 V to drive the motor and control the current this way. It will not be able to provide 220 V, regardless of how high currents it can deliver. The maximum current however that could flow depends on the motor coils impedance. The impedance of the spindle may allow you to deliver more current than is rated on its nameplate (which is 8 A for a 220 V 2.2 kW spindle).
In all VFDs, you have to limit the current that goes to the spindle. There are 2.2 kW spindles offered that are for both 230 and 400 V, and when using the first voltage you set 8 A as limit and with the second you set 6 A as the limit, to set them to the same power. But their copper wires that make up the coils are surely dimensionated to allow for the bigger of the two values, which would be 8 A current. I don’t want to guarantee that you will not harm your 2.2 kW 220 V spindle if you set more than 8 A in your 110 V VFD, because usually the spindle manufacturers make the motors for a certain operating conditions.
Anyway it is the frequency of the three-phase output current that controls the speed of the spindle, regardless of voltage or current.