VFD will trip on over current or over voltage. If the spindle is getting hot with no load, that means the current is too high. For there to be too high a current the voltage the VFD is applying must be too high (ohms law), so check what the voltage is at rpm.

The vfd, when using vf control, should increase the voltage proportional to the frequency, so (generally) rated voltage at rated speed, half voltage at half speed etc.. What might be happening is the voltage/frequency curve is set wrong, so it's applying much too high a voltage, which in turn causes too much current to flow, so the VFD trips.