A manufacturing method includes, cutting out a plurality of rings, polishing the rings, adjusting the plurality of rings so that they exhibit circumferential lengths respectively predetermined for them, nitriding the plurality of rings, and assembling in order to layer the plurality of rings into a multi-layered ring; wherein after the rings are cut out from the pipe, each of them is polished one by one so that their order is not changed; in nitriding, they are subjected to a nitriding process in a state where they are set in a jig in order to keep their order; and in assembling, the rings are assembled so that rings that were parts originally adjacent to each other in a state of the pipe become layers that are adjacent to each other in the multi-layered ring.