A conical reamer would be great, but this requires a metalworking lathe which I don't have.
Another ruse is to turn a conical former of the right size in wood and fit a cutting blade into a lengthwise slot. This works well enough for larger diameters, but not for the small diameter end of the bore (down to 6mm).
A third way is to cut a flat metal strip to the correct tapered outline, and form two cutting edges on the opposite sides. This is very doable, and this is what I did.
The upper one is in 2.5mm steel, and the lower one in 4.5mm steel. It's only mild steel but this is quite adequate for low speed cutting (scraping, really) of wood. Some careful work with an angle grinder and hand file had these ready to go quite quickly.
The thin reamer tapers down to 6mm, while the thicker one starts at about 14mm.
I used the narrow reamer to open out the bore sufficiently to start the wider reamer in the open end.
Once the wider reamer had cut the bulk of the bore as in the next picture, the narrow reamer went in again to finish off. In the end only fine dust was coming out which was encouraging.
I was pleasantly surprised at the quality of the finished surface in the bore. It could stand a little buffing but was essentially smooth and even.
The final opening was not altogether circular and not altogether central (see the image further down this page).
- fit a proper two-handed handle to each reamer, which will allow better lateral control and more even rotation.
- do the reaming in a vertical axis, which with the better handle will allow better lateral control.
Since the bore was not centred on the original driven centre locating hole, I made an adapter to provide a new centre. The dowel is turned down to be an interference fit in the 6mm bore in the end of the workpiece.
This wasn't a total success since it flexed slightly under the side load of the cutting chisels, so centrality suffered a bit.
Here is the workpiece approximately shaved down to size based on the actual bore axis.The middle section is being rounded down. I used a drawknife to round it down further while mounted in the lathe, after this photo was taken. This was a faster removal of material than turning it off.
With a powered lathe, this may not be the case.
Note the adapter blocks at each endof the workpiece, to line up with the actual bore axis. This was not wonderfully rigid; the process needs improving for next time.
Here is the shaped and smoothed top section of the shawm.
This is about 70% of the overall length. The pirouette and reed will be in the left hand end and the bell and foot section will slide on to the rebated tenon section on the right hand end.
Note the multi-lobal shape of the bore and being slightly off centre. The lobes could be reduced by better control of the reamer as discussed above. The centrality can be improved by better use of the adaptor block or some different technique.
Neither of these aspects is fatal, I think. Final finishing of the instrument will probably allow any effects to be compensated.