Ticndig is correct about your find. It is definitely a part from a late-1800s-through-early-1900s umbrella. You can see it in the scan of the original US Patent Office diagram for that version of umbrella. The photograph shows the umbrella's "canopy spines" fit into the slots around your find's edge. Credit for the photo goes to T-Net's Ironman, who dug the nearly-complete umbrella you see in the photo.
Your part held the spines at the top of the umbrella's shaft, with a pin through it to lock it firmly in place on the shaft because unlike the lower spine-collar yours does not move.