We don't have experience running a spindle directly from a rotary phase converter, unfortunately. The fear that I have is the control of the voltage and current to the spindle and how that relates to the coil winding for each phase. If your rotary phase converter can operate within these tolerances (which need to be known), then I don't see the problem, but the spindle will exhaust its warranty by doing this.
Regarding the CAM software, speed can be set for various machining operations, but the actual speed control will be controlled by the control program that interprets the g-code output by the CAM.
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I am looking at purchasing your 2.2 kw water cooled spindle. I'm assuming it comes with the VFD. I have a rotary phase converter in my shop. Are these spindles 3 phase? And if so, can I bypass use of the VFD and control the spindle speed by the CAM software instead? Or is the VFD an absolute necessity to use on the spindle?