Maintenance of Threaded Tenons
General maintenance
Always disassemble the joints of the flute after playing.
Grease the threads each time you assemble the flute
Always keep the tenons free of grit and fluff which may score the inside surface of the socket.
Never force the joints together if they are tight. To give you an idea of the tightness of the joint you should be able to assembly it whilst holding the two parts between thumbs and fingertips.
If the tenon is dry then grease it. If the tenon is still a bit tight then unwind a few turns and try the fit again. When the fit is just right trim off the excess.
If the tenon becomes a loose fit then add extra turns of thread as detailed below.
Replacing Lappings
I have tried a number of methods to secure lapping thread to the tenons in my Baroque flutes. The following method is the one I currently use, and is by far the most successful and simplest.
Thread
I have used a number of threads in the past but I currently usually use polyester sewing thread as it does not absorb moisture and swell, is hard wearing, is extremely cheap, and is available in bright colours! The best sewing thread to use is the cheapest, as the more expensive threads have a "silky" surface (Mercerised thread). The cheap threads, usually sold for hand sewing, have a slightly hairy surface, which is ideal as it holds onto the grease more successfully. My current batch of sewing threads were bought for 15 pence a roll from the Butter Market in Hereford!
Shellac Cement
The shellac cement is used to secure the lowest layer of the lapping to ensure that the whole lapping cannot slide off in one big lump. The cement can be bought from hardware stores as French Polish. French Polish is simply shellac resin dissolved in alcohol. If you want to make your own then simply dissolve shellac flakes (also bought from the hardware store in the same section as the bottles of French Polish!) in alcohol. Keep adding more flakes until they stop dissolving, then pour off the liquid into a bottle and keep the lid on tight.
The beauty of using shellac cement is that any residue can be cleaned off with alcohol when the lappings need to be replaced.
Thread Grease
There are many greases that can be used, petroleum jelly, lanolin, proprietary cork grease, but I use a grease I make myself from equal weights of beeswax and almond oil.
Lapping Method
Most tenons will have a series of narrow grooves which help to prevent the threads from slipping off:

Lay the end of the thread along the tenon and trap the free end under the first turn of thread around the end of the tenon:

Wind on the first layer covering the area of the tenon occupied by the grooves. Paint the surface of the threads with a thin layer of shellac cement allowing it to soak through.

Once the surface of the threads is no longer tacky cover the lappings with grease.

Try the tenon in the socket. It should be a rattly fit. Add another layer of threads and grease the surface again. Keep trying the tenon fit in the socket adding layers until the fit is just right.
Once you have the right fit cut off the thread and smooth it down onto the tenon. Trim off the projecting end of the trapped thread. The loose end of the thread is not tied off, tucked in, or secured in any way. It is held in place by the grease on the threads.
It is important to keep greasing the tenon over the next few days as the grease will soak into the threads and the surface will become dry.
Adding extra thread
If the tenon becomes loose and you feel it needs some extra thread to make the fit more secure you can wind a little thread over the top of an existing lapping. This is quicker than replacing the whole lapping, and if the change in fit is due to reduction in time spent playing you may find that the fit changes back when you resume your former pattern of practise.
First lay the loose end of the thread along the length of the tenon

Then lay the end of the thread from your spool alongside this and loop the thread around the back of the tenon trapping both loose ends of thread

Next take four or five quick turns around the tenon trapping the remainder of the loose ends. The idea is not to add very much to the thickness, but to trap the thread and prevent it from lifting. Four or five turns should be enough to trap the whole length of the loose ends.

Spread grease over the thread you have just wound onto the tenon. You can now proceed to add thread in the normal way over the top of these turns, alternately trying the fit, adding more thread and grease.
Checking for movement in joints
If you find that a joint is rocking when assembled you have probably wound the thread onto the tenon slightly unevenly. Alternatively the tenon and socket profile may not be ideally matched. In any case you will need to correct the fit by applying more thread to one end of the tenon or the other. For the most secure fit I aim for a dumbbell shape to the lappings, with the thread wound slightly thicker at either end of the lapping. This makes the lapping tight at two points as far apart as possible, making the joint firm without any movement. If you aim for a crowned lapping with more thread in the centre then movement in the joint is quite common.
If you look at the pictures below you can see how to check which end of the tenon is loose.
1. Assemble the joints.
2. Place your finger over the join so your finger can feel the body of the joint with the tenon, and the end of the socket at the same time.
3. Move the pieces of the flute relative to one another.
4. If you can feel the body moving relative to the socket (shown by the dotted line indicating the surface of the body moving relative to the end of the socket) then the shoulder end of the tenon is loose, allowing the shoulder to move against the end of the socket.
5. If the joints move and you cannot feel this relative movement (i.e. one part moving radially relative to the other, not just pivoting), then it is likely that the small end of the tenon is loose, and this radial movement is taking place within the cavity of the socket i.e. the small end of the tenon is flapping up and down inside the socket. In this case the small end of the tenon is loose and needs more thread.
