So you're talking about the rings inserted as gaskets between Ring Type Joint (RTJ) Flanges ?
If so these are available as either "Oval" or "Octagonal". Either should be manufactured to the requirements of ASME B16.20.
If you are talking about a ring which can be used to connect two different sizes of flanges with the same pitch circle diameter but different ring groove diameters (see link below) then there is no industry standard that I am aware of that addresses these items. I've never seen a need for such an item and don't think I would use one. If I absolutely had to mate two different systems (ignoring the associated implications of different pressure ratings), I would build a short piping spool to get from one to the other (different flange on each end).
Actually, when you drill down to the details on the Wire Masters site you see the detailed description of the rings and they have both API and non-API rings. The transition rings are shown as "non-API". Take a look at this page ...
On my special application I have a transition ring one side R55/ and in the other side R51, which is really important is that both R55/R51 complies the ANSI # 2500, and the width of these rings fits into the groove flange.
Why this is not in accordance with API?
An R51 is for an 8" flange and an R55 is for a 10" flange. I suspect the issue is that flange joints are "designed" (look at Appendix 2 to ASME Section VIII Div 1) and the designers who came up with the standard configurations shown in the ASME and API standards probably didn't envision connecting two flanges of different sizes together and so these cases were not considered in designing and dimensioning the flange and bolting arrangements - and are thus not included in the standards.
Unfortunately, there is much more to the design of a flanged joint than ensuring that the gasket fits in the groove.
In theory, if you want to use a transition ring, you would need to do the flanged joint design yourself to ensure the stresses in the flanges / bolting where acceptable (using something like Appendix 2) and then you would need to have the gasket design confirmed to ensure it was acceptable (something like FEA). However, not sure that even with that the configuration would be acceptable to your design code or regulatory authority?
