A while back I purchased a CNC XY table at auction It was used to position a riveting jig and was part of a odds and ends lot. The linear ballscrews are protected by round bellows that have been stitched together.
The disks are made from a vinyl or other coated fabric with the coating on the outside, there is a hole in the centre big enough to clear the ballscrew by about 5mm when the bellows is extended, the difference between the inner and outer diameters was about 15mm. There is approximately a 4 to 1 difference between the open and closed position.
The disks were sewn alternately at their inner and outer edges. to form the bellows. The start and end was clamped between metal washers made to fit the bellows.
They appear to have been glued at the edges as well as Ian S C mentioned. This would also make them easier to stitch.
For sewing a size 14 or 16 sewing needle with a 40 cotton/nylon blend thread should work fine with a domestic sewing machine. The stitch length set at about 2 – 2.5mm with just enough tension on the presser foot to feed. If the vinyl sticks on the presser foot and will not feed a little oil (or silicone spray if you have some) will help the vinyl feed without sticking to the foot.
It would be quite easy to stitch two disks together at their inner edges as they are laying flat with the fabric side out.. A little more difficult but doable to stitch the pairs of washers already stitched at their inner edges at their outer edges, pre gluing will greatly assist, avoid contact adhesive it will make the needle overheat a small amount of white glue will work better. I learnt this when I worked in manufacturing.
I have also seen the same method used on rectangular bellows, sometimes with metal or plastic sliders spaced every 100mm or so to assist and support the bellows as it slides along the bearing way.
Vinyl is available through upholstery suppliers, or maybe your local re upholsterer has an offcut; you want the harder faced fabric (non stretch) type not the soft spongy backed and faced stretchy type used to simulate leather.
Vinyl would be well worth trying for machines that do not produce red hot chips that would melt vinyl. so good for woodworking and grinding. It is fairly inexpensive by the metre normally 1370mm wide. a single metre would make a lot of bellows.
There are high temperature coated fabrics that would work better with hot chips made from silicone rubber and similar, as used by food manufactures conveying foods through baking ovens, these materials are more expensive. some specialist power transmission and material handling suppliers stock them.
Regards
John