How to generate an eccentric turning program using CAM?

Hi,

I need to create a CNC program capable of machining the bore detail on the component attached.

The bore of the component is essentially a cone with its centre line offset at 12.5 degrees to that of the components centre line.

This means that to achieve this I need to create a program that reciprocates quickly in the x-axis while the spindle rotates. I have seen this done but I'm unsure on how to program this.

I have access to a number of CNC lathes using Fanuc control that would be capable of machining the part and I currently use Fusion 360 or Inventor HSM to generate CNC programs. I'm unsure that these software's will have the capability to do this so I'm after some advice if it can be done or what software would make this possible.

I can easily generate a milling cycle for a 5th axis machine that could produce this detail but a Ra0.4 surface finish is required and so the component needs to be turned with finely tuned

Any advice would be much appreciated. I've attached a rough model of the part with the bore detail required for reference.

Thanks in advance.