To produce consistent and tightly fitting parts when forging steel washers or field-frame rings you need some sort of template. The template described here is one option, and is well-suited for forging relatively thin and wide loops such as those used as washer cores. For washer rims and field-frame rings a different kind of template is more suitable.
The type of template described here is made from steel pipe with thick walls. The outer diameter of this template should be slightly (~1mm) smaller than the desired inner diameter of the part you're forging. If pipe of suitable outer diameter can't be found, forge a piece of steel around the pipe and weld it in place. Here we've used a washer core to expand the outer diameter of the steel pipe:
The template is probably easiest to use if it's not attached to the anvil. This is especially true if you got an assistant who can hold the template for you while forging.