"J. Nielsen" wrote in message
...

The part was to be grounded on the cylindrical (white) part of the tail
roundness +- 0.0005" as it had to seal against the stripping plate.
The fillet at the base, and the tapered part should also have a "grind
quality" surface finish. Actual size was not too important.

There was a catch, though. The roundness of the tail was measured
perpendicular to the centerline of the helix, not the centerline of the
part.

Hmm - this might actually make the job /easier/.

The part came from the customer hardned and pre-milled to about 0.05
oversize. Since they only had 3axis VMC, the part was milled from four
sides
rotating the part 90 degrees each time. (I did suggest the part could be
milled to finished size, but they didn't think it was possible to achieve
the
necessary finish/roundness.)

The grinder I used was a Jungner US-450 CNC with four axis - think of an
ordinary lathe, and swap X with Z & Y with X. Tool up&down = third axis
[X]
Spindle = fourth axis [b] )

The Siemens 810 control only allow for three axis to move simultaneously.

I'm completely ignorant of the Jungner machine /and/ the Siemens control. My
only experience is with my own 3-axis router (for which I have a fourth axis
accessory that allows mounting a geared stepper-driven "headstock" and
"tailstock" wherever I choose on the 96"x48" table. With this lash-up I can
move the spindle around in (x,y,z) and rotate the part on the accessory axis
(r). I'm making the assumption that the tooling you've described can be
configured similarly.

How would you have done it?

[1] Mount the headstock and tailstock so that the accessory axis is aligned
with the machine's y-axis and perpendicular to the x- and z-axes.

[2] Mount the part on the accessory headstock so that the axis of the helix
coincided with the accessory axix.

[3] support the "tail" of the helix at the accessory tailstock to minimize
error due to flexing of the helix.

[4] Chuck up a cylindrical grinder. In my woodworking world, this would be a
mandrel with a sandpaper sleeve. I'm making the assumption that there are
similar tools in the world of metalworking - something like a HSS or
micrograin carbide rod with a bonded fine diamond abrasive. (Is there
actually such a tool?)

[5] I grind longitudinally. IOW, rotate the workpiece to the next angle,
position the tool in x- and z-axes and grind the full length of the helix
moving the spindle only in y and the part in r. Then move the tool back to
the starting point, rotate the workpiece slightly, and repeat.

Rationale: It's easy to calculate points on the helical curve and my tool
need only be moved parallel to the central axis of the helix. If my grinding
surface is a vertical cylinder, I can get away with needing to control only
two axes and can use constant feed rates for each of them.

It's an interesting problem -- and I'm looking foreward to learning how you
solved it!

--
Morris
(CNC woodworker)