In reference to the patent: US 948,162 A
I'm wondering if this patent has expired, and the process to claim it? This is my great-grandfathers invention.
This patent has been expired since 1927, and since then it has been freely available for anyone to manufacture and sell.
If by "claim", you mean a patent model (miniature model of the invention), those were only required until 1880, so there is no actual physical device stored anywhere, just the paperwork (if the originals still exist). The scanned PDF on Google Patents is the closest you'll get to the original documentation, unless your grandfather retained a copy.