Its size is 2.2cm times 1.5cm. The width of axle is 0.92 cm (measured on the curved area, not probably the right way to measure) for axle in the hub Shimano Nexus SG 8R20 (12mm stop washer but cannot find its axle width from service manual). Its thread is unknown.
Please, see the picture. I want to learn how to measure the tread inside the thing and other conventions by which such things are named, such as the maximum torgue in Nm, so I can buy the thing in any unknown store. My local hardware store said that you cannot get it as bulk product because it has special thread. I am however interested whether there is any cheaper non-bicycle-store substitute to this thing. If not, I am still looking for ways to substitute this thing for inner hubs.
[Update, more images]
You can see that the left cap nut is in a very bad condition, it was new 6 months ago. The washer seems to be a bit damaged when looked from the side. The metal spaghetti shows that the internals of the cap nuts are broken.
The serrated washer eats into the paint, making very bad to the frame.
I am looking something better options to this inner hub thing, the expensive easily-broken cap nuts and damaging paint are not the way to go again.