On Thursday I done some quick shopping. I bought a connecting socket for the spindle and some new HSS milling bit.
Yesterday morning I connected the new PSU in without any speed control.
Look the miracle, it was milling the hole without any hassle.
This means I don't need to buy a new spindle motor, because the old one is doing it's job, just the power supply inadequate. Only the rotation speed control's question need to be solved, and find out the maximum feed rate.
Now coming the milling of the front and back panels of the external PSU.